Identification of nonlinear anelastic models
International Nuclear Information System (INIS)
Draganescu, G E; Bereteu, L; Ercuta, A
2008-01-01
A useful nonlinear identification technique applied to the anelastic and rheologic models is presented in this paper. First introduced by Feldman, the method is based on the Hilbert transform, and is currently used for identification of the nonlinear vibrations
Model Updating Nonlinear System Identification Toolbox, Phase II
National Aeronautics and Space Administration — ZONA Technology (ZONA) proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology that utilizes flight data with...
Model Updating Nonlinear System Identification Toolbox, Phase I
National Aeronautics and Space Administration — ZONA Technology proposes to develop an enhanced model updating nonlinear system identification (MUNSID) methodology by adopting the flight data with state-of-the-art...
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
Reduced Complexity Volterra Models for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Hacıoğlu Rıfat
2001-01-01
Full Text Available A broad class of nonlinear systems and filters can be modeled by the Volterra series representation. However, its practical use in nonlinear system identification is sometimes limited due to the large number of parameters associated with the Volterra filter′s structure. The parametric complexity also complicates design procedures based upon such a model. This limitation for system identification is addressed in this paper using a Fixed Pole Expansion Technique (FPET within the Volterra model structure. The FPET approach employs orthonormal basis functions derived from fixed (real or complex pole locations to expand the Volterra kernels and reduce the number of estimated parameters. That the performance of FPET can considerably reduce the number of estimated parameters is demonstrated by a digital satellite channel example in which we use the proposed method to identify the channel dynamics. Furthermore, a gradient-descent procedure that adaptively selects the pole locations in the FPET structure is developed in the paper.
Global Nonlinear Model Identification with Multivariate Splines
De Visser, C.C.
2011-01-01
At present, model based control systems play an essential role in many aspects of modern society. Application areas of model based control systems range from food processing to medical imaging, and from process control in oil refineries to the flight control systems of modern aircraft. Central to a
Parameter identification in a nonlinear nuclear reactor model using quasilinearization
International Nuclear Information System (INIS)
Barreto, J.M.; Martins Neto, A.F.; Tanomaru, N.
1980-09-01
Parameter identification in a nonlinear, lumped parameter, nuclear reactor model is carried out using discrete output power measurements during the transient caused by an external reactivity change. In order to minimize the difference between the model and the reactor power responses, the parameter promt neutron generation time and a parameter in fuel temperature reactivity coefficient equation are adjusted using quasilinearization. The influences of the external reactivity disturbance, the number and frequency of measurements and the measurement noise level on the method accuracy and rate of convergence are analysed through simulation. Procedures for the design of the identification experiments are suggested. The method proved to be very effective for low level noise measurements. (Author) [pt
Parameter Identification for Nonlinear Circuit Models of Power BAW Resonator
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CONSTANTINESCU, F.
2011-02-01
Full Text Available The large signal operation of the bulk acoustic wave (BAW resonators is characterized by the amplitude-frequency effect and the intermodulation effect. The measurement of these effects, together with that of the small signal frequency characteristic, are used in this paper for the parameter identification of the nonlinear circuit models developed previously by authors. As the resonator has been connected to the measurement bench by wire bonding, the parasitic elements of this connection have been taken into account, being estimated solving some electrical and magnetic field problems.
International Nuclear Information System (INIS)
Kara, Tolgay; Eker, Ilyas
2004-01-01
Modeling and identification of mechanical systems constitute an essential stage in practical control design and applications. Controllers commanding systems that operate at varying conditions or require high precision operation raise the need for a nonlinear approach in modeling and identification. Most mechanical systems used in industry are composed of masses moving under the action of position and velocity dependent forces. These forces exhibit nonlinear behavior in certain regions of operation. For a multi-mass rotational system, the nonlinearities, like Coulomb friction and dead zone, significantly influence the system operation when the rotation changes direction. The paper presents nonlinear modeling and identification of a DC motor rotating in two directions together with real time experiments. Linear and nonlinear models for the system are obtained for identification purposes, and the major nonlinearities in the system, such as Coulomb friction and dead zone, are investigated and integrated in the nonlinear model. The Hammerstein nonlinear system approach is used for identification of the nonlinear system model. Online identification of the linear and nonlinear system models is performed using the recursive least squares method. Results of the real time experiments are graphically and numerically presented, and the advantages of the nonlinear identification approach are revealed
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent....
Identification of stochastic interactions in nonlinear models of structural mechanics
Kala, Zdeněk
2017-07-01
In the paper, the polynomial approximation is presented by which the Sobol sensitivity analysis can be evaluated with all sensitivity indices. The nonlinear FEM model is approximated. The input area is mapped using simulations runs of Latin Hypercube Sampling method. The domain of the approximation polynomial is chosen so that it were possible to apply large number of simulation runs of Latin Hypercube Sampling method. The method presented also makes possible to evaluate higher-order sensitivity indices, which could not be identified in case of nonlinear FEM.
Pescara benchmarks: nonlinear identification
Gandino, E.; Garibaldi, L.; Marchesiello, S.
2011-07-01
Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.
Pescara benchmarks: nonlinear identification
International Nuclear Information System (INIS)
Gandino, E; Garibaldi, L; Marchesiello, S
2011-01-01
Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled M onitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing , financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.
Directory of Open Access Journals (Sweden)
Roger Skjetne
2004-01-01
Full Text Available Complete nonlinear dynamic manoeuvering models of ships, with numerical values, are hard to find in the literature. This paper presents a modeling, identification, and control design where the objective is to manoeuver a ship along desired paths at different velocities. Material from a variety of references have been used to describe the ship model, its difficulties, limitations, and possible simplifications for the purpose of automatic control design. The numerical values of the parameters in the model is identified in towing tests and adaptive manoeuvering experiments for a small ship in a marine control laboratory.
CVA identification of nonlinear systems with LPV state-space models of affine dependence
Larimore, W.E.; Cox, P.B.; Toth, R.
2015-01-01
This paper discusses an improvement on the extension of linear subspace methods (originally developed in the Linear Time-Invariant (LTI) context) to the identification of Linear Parameter-Varying (LPV) and state-affine nonlinear system models. This includes the fitting of a special polynomial
Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model
Directory of Open Access Journals (Sweden)
Yazid Edwar
2014-07-01
Full Text Available This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA. The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.
Nonlinear System Identification Using Quasi-ARX RBFN Models with a Parameter-Classified Scheme
Directory of Open Access Journals (Sweden)
Lan Wang
2017-01-01
Full Text Available Quasi-linear autoregressive with exogenous inputs (Quasi-ARX models have received considerable attention for their usefulness in nonlinear system identification and control. In this paper, identification methods of quasi-ARX type models are reviewed and categorized in three main groups, and a two-step learning approach is proposed as an extension of the parameter-classified methods to identify the quasi-ARX radial basis function network (RBFN model. Firstly, a clustering method is utilized to provide statistical properties of the dataset for determining the parameters nonlinear to the model, which are interpreted meaningfully in the sense of interpolation parameters of a local linear model. Secondly, support vector regression is used to estimate the parameters linear to the model; meanwhile, an explicit kernel mapping is given in terms of the nonlinear parameter identification procedure, in which the model is transformed from the nonlinear-in-nature to the linear-in-parameter. Numerical and real cases are carried out finally to demonstrate the effectiveness and generalization ability of the proposed method.
Data-Driven Photovoltaic System Modeling Based on Nonlinear System Identification
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Ayedh Alqahtani
2016-01-01
Full Text Available Solar photovoltaic (PV energy sources are rapidly gaining potential growth and popularity compared to conventional fossil fuel sources. As the merging of PV systems with existing power sources increases, reliable and accurate PV system identification is essential, to address the highly nonlinear change in PV system dynamic and operational characteristics. This paper deals with the identification of a PV system characteristic with a switch-mode power converter. Measured input-output data are collected from a real PV panel to be used for the identification. The data are divided into estimation and validation sets. The identification methodology is discussed. A Hammerstein-Wiener model is identified and selected due to its suitability to best capture the PV system dynamics, and results and discussion are provided to demonstrate the accuracy of the selected model structure.
Nonlinear Modeling and Identification of an Aluminum Honeycomb Panel with Multiple Bolts
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Yongpeng Chu
2016-01-01
Full Text Available This paper focuses on the nonlinear dynamics modeling and parameter identification of an Aluminum Honeycomb Panel (AHP with multiple bolted joints. Finite element method using eight-node solid elements is exploited to model the panel and the bolted connection interface as a homogeneous, isotropic plate and as a thin layer of nonlinear elastic-plastic material, respectively. The material properties of a thin layer are defined by a bilinear elastic plastic model, which can describe the energy dissipation and softening phenomena in the bolted joints under nonlinear states. Experimental tests at low and high excitation levels are performed to reveal the dynamic characteristics of the bolted structure. In particular, the linear material parameters of the panel are identified via experimental tests at low excitation levels, whereas the nonlinear material parameters of the thin layer are updated by using the genetic algorithm to minimize the residual error between the measured and the simulation data at a high excitation level. It is demonstrated by comparing the frequency responses of the updated FEM and the experimental system that the thin layer of bilinear elastic-plastic material is very effective for modeling the nonlinear joint interface of the assembled structure with multiple bolts.
International Nuclear Information System (INIS)
Ma Huanfei; Lin Wei
2009-01-01
The existing adaptive synchronization technique based on the stability theory and invariance principle of dynamical systems, though theoretically proved to be valid for parameters identification in specific models, is always showing slow convergence rate and even failed in practice when the number of parameters becomes large. Here, for parameters update, a novel nonlinear adaptive rule is proposed to accelerate the rate. Its feasibility is validated by analytical arguments as well as by specific parameters identification in the Lotka-Volterra model with multiple species. Two adjustable factors in this rule influence the identification accuracy, which means that a proper choice of these factors leads to an optimal performance of this rule. In addition, a feasible method for avoiding the occurrence of the approximate linear dependence among terms with parameters on the synchronized manifold is also proposed.
Kazemi, Mahdi; Arefi, Mohammad Mehdi
2017-03-01
In this paper, an online identification algorithm is presented for nonlinear systems in the presence of output colored noise. The proposed method is based on extended recursive least squares (ERLS) algorithm, where the identified system is in polynomial Wiener form. To this end, an unknown intermediate signal is estimated by using an inner iterative algorithm. The iterative recursive algorithm adaptively modifies the vector of parameters of the presented Wiener model when the system parameters vary. In addition, to increase the robustness of the proposed method against variations, a robust RLS algorithm is applied to the model. Simulation results are provided to show the effectiveness of the proposed approach. Results confirm that the proposed method has fast convergence rate with robust characteristics, which increases the efficiency of the proposed model and identification approach. For instance, the FIT criterion will be achieved 92% in CSTR process where about 400 data is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.
2017-09-01
The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.
Carroll, Raymond J.
2010-05-01
This paper considers identification and estimation of a general nonlinear Errors-in-Variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values; and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest - the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates - is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterized, we propose sieve Quasi Maximum Likelihood Estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.
Nonlinear system identification based on Takagi-Sugeno fuzzy modeling and unscented Kalman filter.
Vafamand, Navid; Arefi, Mohammad Mehdi; Khayatian, Alireza
2018-03-01
This paper proposes two novel Kalman-based learning algorithms for an online Takagi-Sugeno (TS) fuzzy model identification. The proposed approaches are designed based on the unscented Kalman filter (UKF) and the concept of dual estimation. Contrary to the extended Kalman filter (EKF) which utilizes derivatives of nonlinear functions, the UKF employs the unscented transformation. Consequently, non-differentiable membership functions can be considered in the structure of the TS models. This makes the proposed algorithms to be applicable for the online parameter calculation of wider classes of TS models compared to the recently published papers concerning the same issue. Furthermore, because of the great capability of the UKF in handling severe nonlinear dynamics, the proposed approaches can effectively approximate the nonlinear systems. Finally, numerical and practical examples are provided to show the advantages of the proposed approaches. Simulation results reveal the effectiveness of the proposed methods and performance improvement based on the root mean square (RMS) of the estimation error compared to the existing results. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan
2018-05-01
Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.
Identification of a Class of Non-linear State Space Models using RPE Techniques
DEFF Research Database (Denmark)
Zhou, Wei-Wu; Blanke, Mogens
1989-01-01
The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...
Directory of Open Access Journals (Sweden)
Jeng-Wen Lin
2009-01-01
Full Text Available This paper proposes a statistical confidence interval based nonlinear model parameter refinement approach for the health monitoring of structural systems subjected to seismic excitations. The developed model refinement approach uses the 95% confidence interval of the estimated structural parameters to determine their statistical significance in a least-squares regression setting. When the parameters' confidence interval covers the zero value, it is statistically sustainable to truncate such parameters. The remaining parameters will repetitively undergo such parameter sifting process for model refinement until all the parameters' statistical significance cannot be further improved. This newly developed model refinement approach is implemented for the series models of multivariable polynomial expansions: the linear, the Taylor series, and the power series model, leading to a more accurate identification as well as a more controllable design for system vibration control. Because the statistical regression based model refinement approach is intrinsically used to process a “batch” of data and obtain an ensemble average estimation such as the structural stiffness, the Kalman filter and one of its extended versions is introduced to the refined power series model for structural health monitoring.
Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities
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Y. N. Pavlov
2015-01-01
Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic
Pourrezaei Khaligh, Sepehr
Model-based control design of small-scale helicopters involves considerable challenges due to their nonlinear and underactuated dynamics with strong couplings between the different degrees-of-freedom (DOFs). Most nonlinear model-based multi-input multi-output (MIMO) control approaches require the dynamic model of the system to be affine-in-control and fully actuated. Since the existing formulations for helicopter nonlinear dynamic model do not meet these requirements, these MIMO approaches cannot be applied for control of helicopters and control designs in the literature mostly use the linearized model of the helicopter dynamics around different trim conditions instead of directly using the nonlinear model. The purpose of this thesis is to derive the 6-DOF nonlinear model of the helicopter in an affine-in-control, non-iterative and square input-output formulation to enable many nonlinear control approaches, that require a control-affine and square model such as the sliding mode control (SMC), to be used for control design of small-scale helicopters. A combination of the first-principles approach and system identification is used to derive this model. To complete the nonlinear model of the helicopter required for the control design, the inverse kinematics of the actuating mechanisms of the main and tail rotors are also derived using an approach suitable for the real-time control applications. The parameters of the new control-oriented formulation are identified using a time-domain system identification strategy and the model is validated using flight test data. A robust sliding mode control (SMC) is then designed using the new formulation of the helicopter dynamics and its robustness to parameter uncertainties and wind disturbances is tested in simulations. Next, a hardware-in-the-loop (HIL) testbed is designed to allow for the control implementation and gain tuning as well as testing the robustness of the controller to external disturbances in a controlled
Astroza, Rodrigo; Ebrahimian, Hamed; Li, Yong; Conte, Joel P.
2017-09-01
A methodology is proposed to update mechanics-based nonlinear finite element (FE) models of civil structures subjected to unknown input excitation. The approach allows to jointly estimate unknown time-invariant model parameters of a nonlinear FE model of the structure and the unknown time histories of input excitations using spatially-sparse output response measurements recorded during an earthquake event. The unscented Kalman filter, which circumvents the computation of FE response sensitivities with respect to the unknown model parameters and unknown input excitations by using a deterministic sampling approach, is employed as the estimation tool. The use of measurement data obtained from arrays of heterogeneous sensors, including accelerometers, displacement sensors, and strain gauges is investigated. Based on the estimated FE model parameters and input excitations, the updated nonlinear FE model can be interrogated to detect, localize, classify, and assess damage in the structure. Numerically simulated response data of a three-dimensional 4-story 2-by-1 bay steel frame structure with six unknown model parameters subjected to unknown bi-directional horizontal seismic excitation, and a three-dimensional 5-story 2-by-1 bay reinforced concrete frame structure with nine unknown model parameters subjected to unknown bi-directional horizontal seismic excitation are used to illustrate and validate the proposed methodology. The results of the validation studies show the excellent performance and robustness of the proposed algorithm to jointly estimate unknown FE model parameters and unknown input excitations.
Directory of Open Access Journals (Sweden)
Mosbeh R. Kaloop
2016-10-01
Full Text Available The present study investigates the prediction efficiency of nonlinear system-identification models, in assessing the behavior of a coupled structure-passive vibration controller. Two system-identification models, including Nonlinear AutoRegresive with eXogenous inputs (NARX and adaptive neuro-fuzzy inference system (ANFIS, are used to model the behavior of an experimentally scaled three-story building incorporated with a tuned mass damper (TMD subjected to seismic loads. The experimental study is performed to generate the input and output data sets for training and testing the designed models. The parameters of root-mean-squared error, mean absolute error and determination coefficient statistics are used to compare the performance of the aforementioned models. A TMD controller system works efficiently to mitigate the structural vibration. The results revealed that the NARX and ANFIS models could be used to identify the response of a controlled structure. The parameters of both two time-delays of the structure response and the seismic load were proven to be effective tools in identifying the performance of the models. A comparison based on the parametric evaluation of the two methods showed that the NARX model outperforms the ANFIS model in identifying structures response.
Tuan, Nguyen Huy; Van Au, Vo; Khoa, Vo Anh; Lesnic, Daniel
2017-05-01
The identification of the population density of a logistic equation backwards in time associated with nonlocal diffusion and nonlinear reaction, motivated by biology and ecology fields, is investigated. The diffusion depends on an integral average of the population density whilst the reaction term is a global or local Lipschitz function of the population density. After discussing the ill-posedness of the problem, we apply the quasi-reversibility method to construct stable approximation problems. It is shown that the regularized solutions stemming from such method not only depend continuously on the final data, but also strongly converge to the exact solution in L 2-norm. New error estimates together with stability results are obtained. Furthermore, numerical examples are provided to illustrate the theoretical results.
International Nuclear Information System (INIS)
Truong, Bui Ngoc Minh; Nam, Doan Ngoc Chi; Ahn, Kyoung Kwan
2013-01-01
Dielectric electro-active polymer (DEAP) materials are attractive since they are low cost, lightweight and have a large deformation capability. They have no operating noise, very low electric power consumption and higher performance and efficiency than competing technologies. However, DEAP materials generally have strong hysteresis as well as uncertain and nonlinear characteristics. These disadvantages can limit the efficiency in the use of DEAP materials. To address these limitations, this research will present the combination of the Preisach model and the dynamic nonlinear autoregressive exogenous (NARX) fuzzy model-based adaptive particle swarm optimization (APSO) identification algorithm for modeling and identification of the nonlinear behavior of one typical type of DEAP actuator. Firstly, open loop input signals are applied to obtain nonlinear features and to investigate the responses of the DEAP actuator system. Then, a Preisach model can be combined with a dynamic NARX fuzzy structure to estimate the tip displacement of a DEAP actuator. To optimize all unknown parameters of the designed combination, an identification scheme based on a least squares method and an APSO algorithm is carried out. Finally, experimental validation research is carefully completed, and the effectiveness of the proposed model is evaluated by employing various input signals. (paper)
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-01-01
With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth...
Yang, Kangjian; Yang, Ping; Wang, Shuai; Dong, Lizhi; Xu, Bing
2018-05-01
We propose a method to identify tip-tilt disturbance model for Linear Quadratic Gaussian control. This identification method based on Levenberg-Marquardt method conducts with a little prior information and no auxiliary system and it is convenient to identify the tip-tilt disturbance model on-line for real-time control. This identification method makes it easy that Linear Quadratic Gaussian control runs efficiently in different adaptive optics systems for vibration mitigation. The validity of the Linear Quadratic Gaussian control associated with this tip-tilt disturbance model identification method is verified by experimental data, which is conducted in replay mode by simulation.
On identification of nonlinear systems
Mous, S.L.J.
1994-01-01
The development of accurate models is very important for analyzing problems concerning simulation, prediction, control, etc. Therefore it is not astonishing that many studies in applied science are about the modeling of these processes. In this thesis we will focus on the building of models
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Upport vector machines for nonlinear kernel ARMA system identification.
Martínez-Ramón, Manel; Rojo-Alvarez, José Luis; Camps-Valls, Gustavo; Muñioz-Marí, Jordi; Navia-Vázquez, Angel; Soria-Olivas, Emilio; Figueiras-Vidal, Aníbal R
2006-11-01
Nonlinear system identification based on support vector machines (SVM) has been usually addressed by means of the standard SVM regression (SVR), which can be seen as an implicit nonlinear autoregressive and moving average (ARMA) model in some reproducing kernel Hilbert space (RKHS). The proposal of this letter is twofold. First, the explicit consideration of an ARMA model in an RKHS (SVM-ARMA2K) is proposed. We show that stating the ARMA equations in an RKHS leads to solving the regularized normal equations in that RKHS, in terms of the autocorrelation and cross correlation of the (nonlinearly) transformed input and output discrete time processes. Second, a general class of SVM-based system identification nonlinear models is presented, based on the use of composite Mercer's kernels. This general class can improve model flexibility by emphasizing the input-output cross information (SVM-ARMA4K), which leads to straightforward and natural combinations of implicit and explicit ARMA models (SVR-ARMA2K and SVR-ARMA4K). Capabilities of these different SVM-based system identification schemes are illustrated with two benchmark problems.
Directory of Open Access Journals (Sweden)
Zongyan Li
2016-01-01
Full Text Available This paper describes an improved global harmony search (IGHS algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes.
Identification of an Equivalent Linear Model for a Non-Linear Time-Variant RC-Structure
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Andersen, P.; Brincker, Rune
are investigated and compared with ARMAX models used on a running window. The techniques are evaluated using simulated data generated by the non-linear finite element program SARCOF modeling a 10-storey 3-bay concrete structure subjected to amplitude modulated Gaussian white noise filtered through a Kanai......This paper considers estimation of the maximum softening for a RC-structure subjected to earthquake excitation. The so-called Maximum Softening damage indicator relates the global damage state of the RC-structure to the relative decrease of the fundamental eigenfrequency in an equivalent linear...
Parametric Identification of Nonlinear Dynamical Systems
Feeny, Brian
2002-01-01
In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Identification of Non-Linear Structures using Recurrent Neural Networks
DEFF Research Database (Denmark)
Kirkegaard, Poul Henning; Nielsen, Søren R. K.; Hansen, H. I.
1995-01-01
Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure.......Two different partially recurrent neural networks structured as Multi Layer Perceptrons (MLP) are investigated for time domain identification of a non-linear structure....
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.
Grey-box state-space identification of nonlinear mechanical vibrations
Noël, J. P.; Schoukens, J.
2018-05-01
The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.
LDRD report nonlinear model reduction
Energy Technology Data Exchange (ETDEWEB)
Segalman, D.; Heinstein, M.
1997-09-01
The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.
Nonlinear system identification NARMAX methods in the time, frequency, and spatio-temporal domains
Billings, Stephen A
2013-01-01
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice. Includes coverage of: The NARMAX (nonlinear autoregressive moving average with exogenous inputs) modelThe orthogonal least squares algorithm that allows models to be built term by
Modeling nonlinearities in MEMS oscillators.
Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A
2013-08-01
We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.
Modelling nonlinear viscoelastic behaviours of loudspeaker suspensions-like structures
Maillou, Balbine; Lotton, Pierrick; Novak, Antonin; Simon, Laurent
2018-03-01
Mechanical properties of an electrodynamic loudspeaker are mainly determined by its suspensions (surround and spider) that behave nonlinearly and typically exhibit frequency dependent viscoelastic properties such as creep effect. The paper aims at characterizing the mechanical behaviour of electrodynamic loudspeaker suspensions at low frequencies using nonlinear identification techniques developed in recent years. A Generalized Hammerstein based model can take into account both frequency dependency and nonlinear properties. As shown in the paper, the model generalizes existing nonlinear or viscoelastic models commonly used for loudspeaker modelling. It is further experimentally shown that a possible input-dependent law may play a key role in suspension characterization.
Point source identification in nonlinear advection–diffusion–reaction systems
International Nuclear Information System (INIS)
Mamonov, A V; Tsai, Y-H R
2013-01-01
We consider a problem of identification of point sources in time-dependent advection–diffusion systems with a nonlinear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of nonlinear algebraic equations via the use of adjoint equations. We extend this approach by constructing an algorithm that solves the problem iteratively to account for the nonlinearity of the reaction term. We study the question of improving the quality of source identification by adding more measurements adaptively using the solution obtained previously with a smaller number of measurements. (paper)
Nonlinear Modeling by Assembling Piecewise Linear Models
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
Nonlinear Control of Heartbeat Models
Directory of Open Access Journals (Sweden)
Witt Thanom
2011-02-01
Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.
Nonlinear identification of process dynamics using neural networks
International Nuclear Information System (INIS)
Parlos, A.G.; Atiya, A.F.; Chong, K.T.
1992-01-01
In this paper the nonlinear identification of process dynamics encountered in nuclear power plant components is addressed, in an input-output sense, using artificial neural systems. A hybrid feedforward/feedback neural network, namely, a recurrent multilayer perceptron, is used as the model structure to be identified. The feedforward portion of the network architecture provides its well-known interpolation property, while through recurrency and cross-talk, the local information feedback enables representation of temporal variations in the system nonlinearities. The standard backpropagation learning algorithm is modified, and it is used for the supervised training of the proposed hybrid network. The performance of recurrent multilayer perceptron networks in identifying process dynamics is investigated via the case study of a U-tube steam generator. The response of representative steam generator is predicted using a neural network, and it is compared to the response obtained from a sophisticated computer model based on first principles. The transient responses compare well, although further research is warranted to determine the predictive capabilities of these networks during more severe operational transients and accident scenarios
Nonlinear System Identification and Its Applications in Fault Detection and Diagnosis
DEFF Research Database (Denmark)
Sun, Zhen
equation, the ISDE model generally consists of not only a structured deterministic part called drift term, but also a structured random part called diffusion term. The model can describe the system in which the random features are correlated with system states (inputs, outputs) and this relationship can......Interest in nonlinear system identification has grown significantly in recent years. It is much more difficult to develop general results than the concern for linear models since the nonlinear model structures are often much more complicated. As a consequence, the thesis only considers two...... different kinds of models, one is a type of state space model which is described by Itô Stochastic Differential Equations (ISDE), the other one is a nonlinear First Order Plus Dead Time (FOPDT) model. This thesis aims to investigate these two different kinds of nonlinear models and to propose...
PWL approximation of nonlinear dynamical systems, part II: identification issues
International Nuclear Information System (INIS)
De Feo, O; Storace, M
2005-01-01
This paper and its companion address the problem of the approximation/identification of nonlinear dynamical systems depending on parameters, with a view to their circuit implementation. The proposed method is based on a piecewise-linear approximation technique. In particular, this paper describes a black-box identification method based on state space reconstruction and PWL approximation, and applies it to some particularly significant dynamical systems (two topological normal forms and the Colpitts oscillator)
Crack identification for rotating machines based on a nonlinear approach
Cavalini, A. A., Jr.; Sanches, L.; Bachschmid, N.; Steffen, V., Jr.
2016-10-01
In a previous contribution, a crack identification methodology based on a nonlinear approach was proposed. The technique uses external applied diagnostic forces at certain frequencies attaining combinational resonances, together with a pseudo-random optimization code, known as Differential Evolution, in order to characterize the signatures of the crack in the spectral responses of the flexible rotor. The conditions under which combinational resonances appear were determined by using the method of multiple scales. In real conditions, the breathing phenomenon arises from the stress and strain distribution on the cross-sectional area of the crack. This mechanism behavior follows the static and dynamic loads acting on the rotor. Therefore, the breathing crack can be simulated according to the Mayes' model, in which the crack transition from fully opened to fully closed is described by a cosine function. However, many contributions try to represent the crack behavior by machining a small notch on the shaft instead of the fatigue process. In this paper, the open and breathing crack models are compared regarding their dynamic behavior and the efficiency of the proposed identification technique. The additional flexibility introduced by the crack is calculated by using the linear fracture mechanics theory (LFM). The open crack model is based on LFM and the breathing crack model corresponds to the Mayes' model, which combines LFM with a given breathing mechanism. For illustration purposes, a rotor composed by a horizontal flexible shaft, two rigid discs, and two self-aligning ball bearings is used to compose a finite element model of the system. Then, numerical simulation is performed to determine the dynamic behavior of the rotor. Finally, the results of the inverse problem conveyed show that the methodology is a reliable tool that is able to estimate satisfactorily the location and depth of the crack.
Smoothing identification of systems with small non-linearities
Czech Academy of Sciences Publication Activity Database
Kozánek, Jan; Piranda, J.
2003-01-01
Roč. 38, č. 1 (2003), s. 71-84 ISSN 0025-6455 R&D Projects: GA ČR GA101/00/1471 Institutional research plan: CEZ:AV0Z2076919 Keywords : identification * small non-linearities * smoothing methods Subject RIV: BI - Acoustics Impact factor: 0.237, year: 2003
Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed
2014-01-01
In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown
A study on identification of nonlinear structure by experimental modal analysis
International Nuclear Information System (INIS)
Sone, Akira; Suzuki, Kohei; Nakamura, Hajime.
1990-01-01
In this paper, identification techniques based on the experimental modal analysis for the equivalent modal parameters of nonlinear structures are examined from a practical viewpoint. First, using a simple cantilever model with gap or friction at the supported end, the gain characteristics of transfer function are evaluated through the sinusoidal sweep test and random wave test. Second, the equivalent modal parameters such as natural frequency and damping ratio are estimated by two types of identification techniques: ARMA (autoregressive/moving average) model fitting and curve fitting with iterative calculations. From the comparison of the response of the model obtained by the random excitation test and numerical calculation using the equivalent modal parameters, it has been clarified that the ARMA model fitting can be applied to linearized modal parameter identification for nonlinear structures. (author)
Modelling Loudspeaker Non-Linearities
DEFF Research Database (Denmark)
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Nonlinear dynamical system identification using unscented Kalman filter
Rehman, M. Javvad ur; Dass, Sarat Chandra; Asirvadam, Vijanth Sagayan
2016-11-01
Kalman Filter is the most suitable choice for linear state space and Gaussian error distribution from decades. In general practical systems are not linear and Gaussian so these assumptions give inconsistent results. System Identification for nonlinear dynamical systems is a difficult task to perform. Usually, Extended Kalman Filter (EKF) is used to deal with non-linearity in which Jacobian method is used for linearizing the system dynamics, But it has been observed that in highly non-linear environment performance of EKF is poor. Unscented Kalman Filter (UKF) is proposed here as a better option because instead of analytical linearization of state space, UKF performs statistical linearization by using sigma point calculated from deterministic samples. Formation of the posterior distribution is based on the propagation of mean and covariance through sigma points.
Adaptive regression for modeling nonlinear relationships
Knafl, George J
2016-01-01
This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...
Coupled oscillators in identification of nonlinear damping of a real parametric pendulum
Olejnik, Paweł; Awrejcewicz, Jan
2018-01-01
A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.
Identification of physical models
DEFF Research Database (Denmark)
Melgaard, Henrik
1994-01-01
of the model with the available prior knowledge. The methods for identification of physical models have been applied in two different case studies. One case is the identification of thermal dynamics of building components. The work is related to a CEC research project called PASSYS (Passive Solar Components......The problem of identification of physical models is considered within the frame of stochastic differential equations. Methods for estimation of parameters of these continuous time models based on descrete time measurements are discussed. The important algorithms of a computer program for ML or MAP...... design of experiments, which is for instance the design of an input signal that are optimal according to a criterion based on the information provided by the experiment. Also model validation is discussed. An important verification of a physical model is to compare the physical characteristics...
Nonlinear models for autoregressive conditional heteroskedasticity
DEFF Research Database (Denmark)
Teräsvirta, Timo
This paper contains a brief survey of nonlinear models of autore- gressive conditional heteroskedasticity. The models in question are parametric nonlinear extensions of the original model by Engle (1982). After presenting the individual models, linearity testing and parameter estimation are discu...
Relation between nonlinear models and gauge ambiguities
International Nuclear Information System (INIS)
Balachandran, A.P.; Ramachandran, R.; Rupertsberger, H.; Skagerstam, B.S.
1980-01-01
We show that the solutions of a class of nonlinear models also generate gauge ambiguities in the vacuum sector of Yang-Mills theories. Our results extend known connections between gauge ambiguities and certain nonlinear sigma-models, and clarify the underlying group theory. For many nonlinear models, we also give a simple, intrinsic parametrization of physical fields (which have values in a homogeneous space of a group). (orig.)
Superspace formulation of new nonlinear sigma models
International Nuclear Information System (INIS)
Gates, S.J. Jr.
1983-07-01
The superspace formulation of two classes of supersymmetric nonlinear σ-models are presented. Two alternative N=1 superspace formulations are given for the d=2 supersymmetric nonlinear σ-models with Killing vector potentials: (a) formulation uses an active central charge and, (b) formulation uses a spurion superfield without inducing a classical breakdown of supersymmetry. The N=2 vector multiplet is used to construct a new class of d=4 nonlinear σ-models which when reduced to d=2 possess N=4 supersymmetry. Implications of these two classes of nonlinear σ-models for N>=4 superfield supergravity are discussed. (author)
A deep belief network with PLSR for nonlinear system modeling.
Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli
2017-10-31
Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
On the orthogonalised reverse path method for nonlinear system identification
Muhamad, P.; Sims, N. D.; Worden, K.
2012-09-01
The problem of obtaining the underlying linear dynamic compliance matrix in the presence of nonlinearities in a general multi-degree-of-freedom (MDOF) system can be solved using the conditioned reverse path (CRP) method introduced by Richards and Singh (1998 Journal of Sound and Vibration, 213(4): pp. 673-708). The CRP method also provides a means of identifying the coefficients of any nonlinear terms which can be specified a priori in the candidate equations of motion. Although the CRP has proved extremely useful in the context of nonlinear system identification, it has a number of small issues associated with it. One of these issues is the fact that the nonlinear coefficients are actually returned in the form of spectra which need to be averaged over frequency in order to generate parameter estimates. The parameter spectra are typically polluted by artefacts from the identification of the underlying linear system which manifest themselves at the resonance and anti-resonance frequencies. A further problem is associated with the fact that the parameter estimates are extracted in a recursive fashion which leads to an accumulation of errors. The first minor objective of this paper is to suggest ways to alleviate these problems without major modification to the algorithm. The results are demonstrated on numerically-simulated responses from MDOF systems. In the second part of the paper, a more radical suggestion is made, to replace the conditioned spectral analysis (which is the basis of the CRP method) with an alternative time domain decorrelation method. The suggested approach - the orthogonalised reverse path (ORP) method - is illustrated here using data from simulated single-degree-of-freedom (SDOF) and MDOF systems.
Modeling and identification in structural dynamics
Jayakumar, Paramsothy
1987-01-01
Analytical modeling of structures subjected to ground motions is an important aspect of fully dynamic earthquake-resistant design. In general, linear models are only sufficient to represent structural responses resulting from earthquake motions of small amplitudes. However, the response of structures during strong ground motions is highly nonlinear and hysteretic. System identification is an effective tool for developing analytical models from experimental data. Testing of full-scale prot...
Non-linear characterisation of the physical model of an ancient masonry bridge
International Nuclear Information System (INIS)
Fragonara, L Zanotti; Ceravolo, R; Matta, E; Quattrone, A; De Stefano, A; Pecorelli, M
2012-01-01
This paper presents the non-linear investigations carried out on a scaled model of a two-span masonry arch bridge. The model has been built in order to study the effect of the central pile settlement due to riverbank erosion. Progressive damage was induced in several steps by applying increasing settlements at the central pier. For each settlement step, harmonic shaker tests were conducted under different excitation levels, this allowing for the non-linear identification of the progressively damaged system. The shaker tests have been performed at resonance with the modal frequency of the structure, which were determined from a previous linear identification. Estimated non-linearity parameters, which result from the systematic application of restoring force based identification algorithms, can corroborate models to be used in the reassessment of existing structures. The method used for non-linear identification allows monitoring the evolution of non-linear parameters or indicators which can be used in damage and safety assessment.
Nonlinear identification and control a neural network approach
Liu, G P
2001-01-01
The series Advances in Industrial Control aims to report and encourage technology transfer in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. New theory, new controllers, actuators, sensors, new industrial processes, computer methods, new applications, new philosophies . . . , new challenges. Much of this development work resides in industrial reports, feasibility study papers and the reports of advanced collaborative projects. The series otTers an opportunity for researchers to present an extended exposition of such new work in all aspects of industrial control for wider and rapid dissemination. The time for nonlinear control to enter routine application seems to be approaching. Nonlinear control has had a long gestation period but much ofthe past has been concerned with methods that involve formal nonlinear functional model representations. It seems more likely that the breakthough will come through the use of other more flexible and ame...
Modeling of nonlinear responses for reciprocal transducers involving polarization switching
DEFF Research Database (Denmark)
Willatzen, Morten; Wang, Linxiang
2007-01-01
Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...
A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems
Liu, Zuolin; Xu, Jian
2018-04-01
In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.
Nonlinear system identification of smart structures under high impact loads
International Nuclear Information System (INIS)
Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon
2013-01-01
The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure–MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure–MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes. (paper)
Nonlinear system identification of smart structures under high impact loads
Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon
2013-05-01
The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...
NONPARAMETRIC IDENTIFICATION FOR NONLINEAR AUTOREGRESSIVE TIMESERIES MODELS： CONVERGENCE RATES
Institute of Scientific and Technical Information of China (English)
LUZUDI; CHENGPING
1999-01-01
In this paper the optimal convergence rates of estimators ba~ed on kernel approach fornonlinear AR model are investigated in the sense of Stone[17'1a]. By combining the mixingproperty of the stationary solution with the characteristics of the model itself, the restrictiveconditions in the literature which are not easy to be satisfied by the nonlinear AR model axeremoved, and the mild conditions are obtained to guarantee the optimal ratea of the estimatorof autoregTession function. In addition: the strongly coasistent estimator of the ~riance ofwhite noise is also constructed.
Comparing coefficients of nested nonlinear probability models
DEFF Research Database (Denmark)
Kohler, Ulrich; Karlson, Kristian Bernt; Holm, Anders
2011-01-01
In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general decomposi......In a series of recent articles, Karlson, Holm and Breen have developed a method for comparing the estimated coeffcients of two nested nonlinear probability models. This article describes this method and the user-written program khb that implements the method. The KHB-method is a general...... decomposition method that is unaffected by the rescaling or attenuation bias that arise in cross-model comparisons in nonlinear models. It recovers the degree to which a control variable, Z, mediates or explains the relationship between X and a latent outcome variable, Y*, underlying the nonlinear probability...
International Nuclear Information System (INIS)
Zhao, Yibo; Jiang, Yi; Feng, Jiuchao; Wu, Lifu
2016-01-01
Highlights: • A novel nonlinear Wiener adaptive filters based on the backslash operator are proposed. • The identification approach to the memristor-based chaotic systems using the proposed adaptive filters. • The weight update algorithm and convergence characteristics for the proposed adaptive filters are derived. - Abstract: Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.
Non-linear Loudspeaker Unit Modelling
DEFF Research Database (Denmark)
Pedersen, Bo Rohde; Agerkvist, Finn T.
2008-01-01
Simulations of a 6½-inch loudspeaker unit are performed and compared with a displacement measurement. The non-linear loudspeaker model is based on the major nonlinear functions and expanded with time-varying suspension behaviour and flux modulation. The results are presented with FFT plots of thr...... frequencies and different displacement levels. The model errors are discussed and analysed including a test with loudspeaker unit where the diaphragm is removed....
Parameter Estimation of Nonlinear Models in Forestry.
Fekedulegn, Desta; Mac Siúrtáin, Máirtín Pádraig; Colbert, Jim J.
1999-01-01
Partial derivatives of the negative exponential, monomolecular, Mitcherlich, Gompertz, logistic, Chapman-Richards, von Bertalanffy, Weibull and the Richard’s nonlinear growth models are presented. The application of these partial derivatives in estimating the model parameters is illustrated. The parameters are estimated using the Marquardt iterative method of nonlinear regression relating top height to age of Norway spruce (Picea abies L.) from the Bowmont Norway Spruce Thinnin...
Forecasting with nonlinear time series models
DEFF Research Database (Denmark)
Kock, Anders Bredahl; Teräsvirta, Timo
In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...
Neural network modeling of nonlinear systems based on Volterra series extension of a linear model
Soloway, Donald I.; Bialasiewicz, Jan T.
1992-01-01
A Volterra series approach was applied to the identification of nonlinear systems which are described by a neural network model. A procedure is outlined by which a mathematical model can be developed from experimental data obtained from the network structure. Applications of the results to the control of robotic systems are discussed.
Nonlinear model predictive control theory and algorithms
Grüne, Lars
2017-01-01
This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...
Topological approximation of the nonlinear Anderson model
Milovanov, Alexander V.; Iomin, Alexander
2014-06-01
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.
2009-06-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Nonlinear control of the Salnikov model reaction
DEFF Research Database (Denmark)
Recke, Bodil; Jørgensen, Sten Bay
1999-01-01
This paper explores different nonlinear control schemes, applied to a simple model reaction. The model is the Salnikov model, consisting of two ordinary differential equations. The control strategies investigated are I/O-linearisation, Exact linearisation, exact linearisation combined with LQR...
On the nonlinear modeling of ring oscillators
Elwakil, Ahmed S.; Salama, Khaled N.
2009-01-01
We develop higher-order nonlinear models of three-stage and five-stage ring oscillators based on a novel inverter model. The oscillation condition and oscillation frequency are derived and compared to classical linear model analysis. Two important special cases for five-stage ring oscillators are also studied. Numerical simulations are shown. © 2009 World Scientific Publishing Company.
Correlations and Non-Linear Probability Models
DEFF Research Database (Denmark)
Breen, Richard; Holm, Anders; Karlson, Kristian Bernt
2014-01-01
the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of non-linear probability models, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under......Although the parameters of logit and probit and other non-linear probability models are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between...... certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of non-linear probability models....
Lu, Zhao; Sun, Jing; Butts, Kenneth
2016-02-03
A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.
Rizvi, S.Z.; Mohammadpour, J.; Toth, R.; Meskin, N.
2015-01-01
This paper first describes the development of a nonparametric identification method for linear parameter-varying (LPV) state-space models and then applies it to a nonlinear process system. The proposed method uses kernel-based least-squares support vector machines (LS-SVM). While parametric
Nonparametric identification of nonlinear dynamic systems using a synchronisation-based method
Kenderi, Gábor; Fidlin, Alexander
2014-12-01
The present study proposes an identification method for highly nonlinear mechanical systems that does not require a priori knowledge of the underlying nonlinearities to reconstruct arbitrary restoring force surfaces between degrees of freedom. This approach is based on the master-slave synchronisation between a dynamic model of the system as the slave and the real system as the master using measurements of the latter. As the model synchronises to the measurements, it becomes an observer of the real system. The optimal observer algorithm in a least-squares sense is given by the Kalman filter. Using the well-known state augmentation technique, the Kalman filter can be turned into a dual state and parameter estimator to identify parameters of a priori characterised nonlinearities. The paper proposes an extension of this technique towards nonparametric identification. A general system model is introduced by describing the restoring forces as bilateral spring-dampers with time-variant coefficients, which are estimated as augmented states. The estimation procedure is followed by an a posteriori statistical analysis to reconstruct noise-free restoring force characteristics using the estimated states and their estimated variances. Observability is provided using only one measured mechanical quantity per degree of freedom, which makes this approach less demanding in the number of necessary measurement signals compared with truly nonparametric solutions, which typically require displacement, velocity and acceleration signals. Additionally, due to the statistical rigour of the procedure, it successfully addresses signals corrupted by significant measurement noise. In the present paper, the method is described in detail, which is followed by numerical examples of one degree of freedom (1DoF) and 2DoF mechanical systems with strong nonlinearities of vibro-impact type to demonstrate the effectiveness of the proposed technique.
Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint
Bullock, S. J.; Peterson, L. D.
1994-01-01
The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.
Differential Neural Networks for Identification and Filtering in Nonlinear Dynamic Games
Directory of Open Access Journals (Sweden)
Emmanuel García
2014-01-01
Full Text Available This paper deals with the problem of identifying and filtering a class of continuous-time nonlinear dynamic games (nonlinear differential games subject to additive and undesired deterministic perturbations. Moreover, the mathematical model of this class is completely unknown with the exception of the control actions of each player, and even though the deterministic noises are known, their power (or their effect is not. Therefore, two differential neural networks are designed in order to obtain a feedback (perfect state information pattern for the mentioned class of games. In this way, the stability conditions for two state identification errors and for a filtering error are established, the upper bounds of these errors are obtained, and two new learning laws for each neural network are suggested. Finally, an illustrating example shows the applicability of this approach.
Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.
Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo
2007-10-01
Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.
Nonlinear Model Reduction for RTCVD
National Research Council Canada - National Science Library
Newman, Andrew J; Krishnaprasad, P. S
1998-01-01
...) for semiconductor manufacturing. They focus on model reduction for the ordinary differential equation model describing heat transfer to, from, and within a semiconductor wafer in the RTCVD chamber...
Nonlinear finite element modeling of corrugated board
A. C. Gilchrist; J. C. Suhling; T. J. Urbanik
1999-01-01
In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low frequency loudspeakers a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann
1997-01-01
In the Danish LoDist project on distortion from dynamic low-frequency loudspeakers, a detailed nonlinear model of loudspeakers has been developed. The model has been implemented in a PC program so that it can be used to create signals for listening tests and analysis. Also, different methods...
Modeling vector nonlinear time series using POLYMARS
de Gooijer, J.G.; Ray, B.K.
2003-01-01
A modified multivariate adaptive regression splines method for modeling vector nonlinear time series is investigated. The method results in models that can capture certain types of vector self-exciting threshold autoregressive behavior, as well as provide good predictions for more general vector
Nonlinear friction model for servo press simulation
Ma, Ninshu; Sugitomo, Nobuhiko; Kyuno, Takunori; Tamura, Shintaro; Naka, Tetsuo
2013-12-01
The friction coefficient was measured under an idealized condition for a pulse servo motion. The measured friction coefficient and its changing with both sliding distance and a pulse motion showed that the friction resistance can be reduced due to the re-lubrication during unloading process of the pulse servo motion. Based on the measured friction coefficient and its changes with sliding distance and re-lubrication of oil, a nonlinear friction model was developed. Using the newly developed the nonlinear friction model, a deep draw simulation was performed and the formability was evaluated. The results were compared with experimental ones and the effectiveness was verified.
Finite element model for nonlinear shells of revolution
International Nuclear Information System (INIS)
Cook, W.A.
1979-01-01
Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials
Lu, Zhao; Sun, Jing; Butts, Kenneth
2014-05-01
Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.
Modeling of Volatility with Non-linear Time Series Model
Kim Song Yon; Kim Mun Chol
2013-01-01
In this paper, non-linear time series models are used to describe volatility in financial time series data. To describe volatility, two of the non-linear time series are combined into form TAR (Threshold Auto-Regressive Model) with AARCH (Asymmetric Auto-Regressive Conditional Heteroskedasticity) error term and its parameter estimation is studied.
On nonlinear reduced order modeling
International Nuclear Information System (INIS)
Abdel-Khalik, Hany S.
2011-01-01
When applied to a model that receives n input parameters and predicts m output responses, a reduced order model estimates the variations in the m outputs of the original model resulting from variations in its n inputs. While direct execution of the forward model could provide these variations, reduced order modeling plays an indispensable role for most real-world complex models. This follows because the solutions of complex models are expensive in terms of required computational overhead, thus rendering their repeated execution computationally infeasible. To overcome this problem, reduced order modeling determines a relationship (often referred to as a surrogate model) between the input and output variations that is much cheaper to evaluate than the original model. While it is desirable to seek highly accurate surrogates, the computational overhead becomes quickly intractable especially for high dimensional model, n ≫ 10. In this manuscript, we demonstrate a novel reduced order modeling method for building a surrogate model that employs only 'local first-order' derivatives and a new tensor-free expansion to efficiently identify all the important features of the original model to reach a predetermined level of accuracy. This is achieved via a hybrid approach in which local first-order derivatives (i.e., gradient) of a pseudo response (a pseudo response represents a random linear combination of original model’s responses) are randomly sampled utilizing a tensor-free expansion around some reference point, with the resulting gradient information aggregated in a subspace (denoted by the active subspace) of dimension much less than the dimension of the input parameters space. The active subspace is then sampled employing the state-of-the-art techniques for global sampling methods. The proposed method hybridizes the use of global sampling methods for uncertainty quantification and local variational methods for sensitivity analysis. In a similar manner to
Perturbation analysis of nonlinear matrix population models
Directory of Open Access Journals (Sweden)
Hal Caswell
2008-03-01
Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.
Nonlinear distortion in wireless systems modeling and simulation with Matlab
Gharaibeh, Khaled M
2011-01-01
This book covers the principles of modeling and simulation of nonlinear distortion in wireless communication systems with MATLAB simulations and techniques In this book, the author describes the principles of modeling and simulation of nonlinear distortion in single and multichannel wireless communication systems using both deterministic and stochastic signals. Models and simulation methods of nonlinear amplifiers explain in detail how to analyze and evaluate the performance of data communication links under nonlinear amplification. The book addresses the analysis of nonlinear systems
Nonlinear optical model for strip plasmonic waveguides
DEFF Research Database (Denmark)
Lysenko, Oleg; Bache, Morten; Lavrinenko, Andrei
2016-01-01
This paper presents a theoretical model of nonlinear optical properties for strip plasmonic waveguides. The particular waveguides geometry that we investigate contains a gold core, adhesion layers, and silicon dioxide cladding. It is shown that the third-order susceptibility of the gold core...... significantly depends on the layer thickness and has the dominant contribution to the effective third-order susceptibility of the long-range plasmon polariton mode. This results in two nonlinear optical effects in plasmonic waveguides, which we experimentally observed and reported in [Opt. Lett. 41, 317 (2016...... approaches. (C) 2016 Optical Society of America...
Nonlinear GARCH model and 1 / f noise
Kononovicius, A.; Ruseckas, J.
2015-06-01
Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the 1 /fβ form, including 1 / f noise.
Xia, Youshen; Kamel, Mohamed S
2007-06-01
Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.
Nonlinear Dynamic Models in Advanced Life Support
Jones, Harry
2002-01-01
To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.
Analysis of nonlinear systems using ARMA [autoregressive moving average] models
International Nuclear Information System (INIS)
Hunter, N.F. Jr.
1990-01-01
While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs
Identification of cascade water tanks using a PWARX model
Mattsson, Per; Zachariah, Dave; Stoica, Petre
2018-06-01
In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.
A nonlinear model for AC induced corrosion
Directory of Open Access Journals (Sweden)
N. Ida
2012-09-01
Full Text Available The modeling of corrosion poses particular difficulties. The understanding of corrosion as an electrochemical process has led to simple capacitive-resistive models that take into account the resistance of the electrolytic cell and the capacitive effect of the surface potential at the interface between conductors and the electrolyte. In some models nonlinear conduction effects have been added to account for more complex observed behavior. While these models are sufficient to describe the behavior in systems with cathodic protection, the behavior in the presence of induced AC currents from power lines and from RF sources cannot be accounted for and are insufficient to describe the effects observed in the field. Field observations have shown that a rectifying effect exists that affects the cathodic protection potential and this effect is responsible for corrosion in the presence of AC currents. The rectifying effects of the metal-corrosion interface are totally missing from current models. This work proposes a nonlinear model based on finite element analysis that takes into account the nonlinear behavior of the metal-oxide interface and promises to improve modeling by including the rectification effects at the interface.
Research on nonlinear stochastic dynamical price model
International Nuclear Information System (INIS)
Li Jiaorui; Xu Wei; Xie Wenxian; Ren Zhengzheng
2008-01-01
In consideration of many uncertain factors existing in economic system, nonlinear stochastic dynamical price model which is subjected to Gaussian white noise excitation is proposed based on deterministic model. One-dimensional averaged Ito stochastic differential equation for the model is derived by using the stochastic averaging method, and applied to investigate the stability of the trivial solution and the first-passage failure of the stochastic price model. The stochastic price model and the methods presented in this paper are verified by numerical studies
Simplified Model of Nonlinear Landau Damping
International Nuclear Information System (INIS)
Yampolsky, N.A.; Fisch, N.J.
2009-01-01
The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.
Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.
2018-04-01
The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.
Directory of Open Access Journals (Sweden)
Chouiyakh H.
2016-01-01
Full Text Available The aim of this work is to investigate the nonlinear forced vibration of beams containing an arbitrary number of cracks and to perform a multi-crack identification procedure based on the obtained signals. Cracks are assumed to be open and modelled trough rotational springs linking two adjacent sub-beams. Forced vibration analysis is performed by a developed time differential quadrature method. The obtained nonlinear vibration responses are analyzed by Huang Hilbert Transform. The instantaneous frequency is used as damage index tool for cracks detection.
International Nuclear Information System (INIS)
Delaune, X.; Piteau, Ph.; Borsoi, L.; Antunes, J.; Debut, V.
2010-01-01
Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, experimental results are still very important, for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information that is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this area using wave-propagation techniques (De Araujo, Antunes, and Piteau, 1998, 'Remote Identification of Impact Forces on Loosely Supported Tubes: Part 1-Basic Theory and Experiments', J. Sound Vib., 215, pp. 1015-1041; Antunes, Paulino, and Piteau, 1998, 'Remote Identification of Impact Forces on Loosely Supported Tubes: Part 2-Complex Vibro-Impact Motions', J. Sound Vib., 215, pp. 1043-1064; Paulino, Antunes, and Izquierdo, 1999, 'Remote Identification of Impact Forces on Loosely Supported Tubes: Analysis of Multi-Supported Systems', ASME J. Pressure Vessel Technol., 121, pp. 61-70), we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results may prove quite sensitive to noise and modeling errors. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of non-measured noise perturbations. In particular, a method is proposed to improve the
Thermoviscous Model Equations in Nonlinear Acoustics
DEFF Research Database (Denmark)
Rasmussen, Anders Rønne
Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....
Energy Technology Data Exchange (ETDEWEB)
Barus, R. P. P., E-mail: rismawan.ppb@gmail.com [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung and Centre for Material and Technical Product, Jalan Sangkuriang No. 14 Bandung (Indonesia); Tjokronegoro, H. A.; Leksono, E. [Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia); Ismunandar [Chemistry Study, Faculty of Mathematics and Science, Institut Teknologi Bandung, Jalan Ganesa 10 Bandung (Indonesia)
2014-09-25
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range.
International Nuclear Information System (INIS)
Barus, R. P. P.; Tjokronegoro, H. A.; Leksono, E.; Ismunandar
2014-01-01
Fuel cells are promising new energy conversion devices that are friendly to the environment. A set of control systems are required in order to operate a fuel cell based power plant system optimally. For the purpose of control system design, an accurate fuel cell stack model in describing the dynamics of the real system is needed. Currently, linear model are widely used for fuel cell stack control purposes, but it has limitations in narrow operation range. While nonlinear models lead to nonlinear control implemnetation whos more complex and hard computing. In this research, nonlinear cancellation technique will be used to transform a nonlinear model into a linear form while maintaining the nonlinear characteristics. The transformation is done by replacing the input of the original model by a certain virtual input that has nonlinear relationship with the original input. Then the equality of the two models is tested by running a series of simulation. Input variation of H2, O2 and H2O as well as disturbance input I (current load) are studied by simulation. The error of comparison between the proposed model and the original nonlinear model are less than 1 %. Thus we can conclude that nonlinear cancellation technique can be used to represent fuel cell nonlinear model in a simple linear form while maintaining the nonlinear characteristics and therefore retain the wide operation range
Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform
Ta, Minh-Nghi; Lardiès, Joseph
2006-05-01
We consider the free response of a nonlinear vibrating system. Using the ridges and skeletons of the continuous wavelet transform, we identify weak nonlinearities on damping and stiffness and estimate their physical parameters. The crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform. The method is applied to simulated single-degree-of-freedom systems and multi-degree-of-freedom systems with nonlinearities on damping and stiffness. Experimental validation of the nonlinear identification and parameter estimation method is presented. The experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor.
Model reduction of systems with localized nonlinearities.
Energy Technology Data Exchange (ETDEWEB)
Segalman, Daniel Joseph
2006-03-01
An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.
Nonlinear Inertia Classification Model and Application
Directory of Open Access Journals (Sweden)
Mei Wang
2014-01-01
Full Text Available Classification model of support vector machine (SVM overcomes the problem of a big number of samples. But the kernel parameter and the punishment factor have great influence on the quality of SVM model. Particle swarm optimization (PSO is an evolutionary search algorithm based on the swarm intelligence, which is suitable for parameter optimization. Accordingly, a nonlinear inertia convergence classification model (NICCM is proposed after the nonlinear inertia convergence (NICPSO is developed in this paper. The velocity of NICPSO is firstly defined as the weighted velocity of the inertia PSO, and the inertia factor is selected to be a nonlinear function. NICPSO is used to optimize the kernel parameter and a punishment factor of SVM. Then, NICCM classifier is trained by using the optical punishment factor and the optical kernel parameter that comes from the optimal particle. Finally, NICCM is applied to the classification of the normal state and fault states of online power cable. It is experimentally proved that the iteration number for the proposed NICPSO to reach the optimal position decreases from 15 to 5 compared with PSO; the training duration is decreased by 0.0052 s and the recognition precision is increased by 4.12% compared with SVM.
NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES
Directory of Open Access Journals (Sweden)
SILVA R. G.
1999-01-01
Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.
Nonlinear chaotic model for predicting storm surges
Directory of Open Access Journals (Sweden)
M. Siek
2010-09-01
Full Text Available This paper addresses the use of the methods of nonlinear dynamics and chaos theory for building a predictive chaotic model from time series. The chaotic model predictions are made by the adaptive local models based on the dynamical neighbors found in the reconstructed phase space of the observables. We implemented the univariate and multivariate chaotic models with direct and multi-steps prediction techniques and optimized these models using an exhaustive search method. The built models were tested for predicting storm surge dynamics for different stormy conditions in the North Sea, and are compared to neural network models. The results show that the chaotic models can generally provide reliable and accurate short-term storm surge predictions.
Spatiotemporal drought forecasting using nonlinear models
Vasiliades, Lampros; Loukas, Athanasios
2010-05-01
Spatiotemporal data mining is the extraction of unknown and implicit knowledge, structures, spatiotemporal relationships, or patterns not explicitly stored in spatiotemporal databases. As one of data mining techniques, forecasting is widely used to predict the unknown future based upon the patterns hidden in the current and past data. In order to achieve spatiotemporal forecasting, some mature analysis tools, e.g., time series and spatial statistics are extended to the spatial dimension and the temporal dimension, respectively. Drought forecasting plays an important role in the planning and management of natural resources and water resource systems in a river basin. Early and timelines forecasting of a drought event can help to take proactive measures and set out drought mitigation strategies to alleviate the impacts of drought. Despite the widespread application of nonlinear mathematical models, comparative studies on spatiotemporal drought forecasting using different models are still a huge task for modellers. This study uses a promising approach, the Gamma Test (GT), to select the input variables and the training data length, so that the trial and error workload could be greatly reduced. The GT enables to quickly evaluate and estimate the best mean squared error that can be achieved by a smooth model on any unseen data for a given selection of inputs, prior to model construction. The GT is applied to forecast droughts using monthly Standardized Precipitation Index (SPI) timeseries at multiple timescales in several precipitation stations at Pinios river basin in Thessaly region, Greece. Several nonlinear models have been developed efficiently, with the aid of the GT, for 1-month up to 12-month ahead forecasting. Several temporal and spatial statistical indices were considered for the performance evaluation of the models. The predicted results show reasonably good agreement with the actual data for short lead times, whereas the forecasting accuracy decreases with
Efficient Parameterization for Grey-box Model Identification of Complex Physical Systems
DEFF Research Database (Denmark)
Blanke, Mogens; Knudsen, Morten Haack
2006-01-01
Grey box model identification preserves known physical structures in a model but with limits to the possible excitation, all parameters are rarely identifiable, and different parametrizations give significantly different model quality. Convenient methods to show which parameterizations are the be...... that need be constrained to achieve satisfactory convergence. Identification of nonlinear models for a ship illustrate the concept....
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian
2012-01-01
This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
Monte Carlo filters for identification of nonlinear structural dynamical ...
Indian Academy of Sciences (India)
The theory of Kalman filtering provides one of ...... expansion (appendix B contains a reasonably self-contained account of how such expansions ...... Shinozuka M, Ghanem R 1995 Structural system identification II: experimental verification.
Unger, Johannes; Hametner, Christoph; Jakubek, Stefan; Quasthoff, Marcus
2014-12-01
An accurate state of charge (SoC) estimation of a traction battery in hybrid electric non-road vehicles, which possess higher dynamics and power densities than on-road vehicles, requires a precise battery cell terminal voltage model. This paper presents a novel methodology for non-linear system identification of battery cells to obtain precise battery models. The methodology comprises the architecture of local model networks (LMN) and optimal model based design of experiments (DoE). Three main novelties are proposed: 1) Optimal model based DoE, which aims to high dynamically excite the battery cells at load ranges frequently used in operation. 2) The integration of corresponding inputs in the LMN to regard the non-linearities SoC, relaxation, hysteresis as well as temperature effects. 3) Enhancements to the local linear model tree (LOLIMOT) construction algorithm, to achieve a physical appropriate interpretation of the LMN. The framework is applicable for different battery cell chemistries and different temperatures, and is real time capable, which is shown on an industrial PC. The accuracy of the obtained non-linear battery model is demonstrated on cells with different chemistries and temperatures. The results show significant improvement due to optimal experiment design and integration of the battery non-linearities within the LMN structure.
Model of anisotropic nonlinearity in self-defocusing photorefractive media.
Barsi, C; Fleischer, J W
2015-09-21
We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.
Ndoye, Ibrahima
2014-12-01
In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.
Nonlinear interaction model of subsonic jet noise.
Sandham, Neil D; Salgado, Adriana M
2008-08-13
Noise generation in a subsonic round jet is studied by a simplified model, in which nonlinear interactions of spatially evolving instability modes lead to the radiation of sound. The spatial mode evolution is computed using linear parabolized stability equations. Nonlinear interactions are found on a mode-by-mode basis and the sound radiation characteristics are determined by solution of the Lilley-Goldstein equation. Since mode interactions are computed explicitly, it is possible to find their relative importance for sound radiation. The method is applied to a single stream jet for which experimental data are available. The model gives Strouhal numbers of 0.45 for the most amplified waves in the jet and 0.19 for the dominant sound radiation. While in near field axisymmetric and the first azimuthal modes are both important, far-field sound is predominantly axisymmetric. These results are in close correspondence with experiment, suggesting that the simplified model is capturing at least some of the important mechanisms of subsonic jet noise.
Nonlinear price impact from linear models
Patzelt, Felix; Bouchaud, Jean-Philippe
2017-12-01
The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators, and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales (Patzelt and Bouchaud 2017 arXiv:1706.04163). Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear ‘propagator’ models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.
Identification of Nonlinear Oscillatory Activity Embedded in Broadband Neural Signals
Czech Academy of Sciences Publication Activity Database
Vejmelka, Martin; Paluš, Milan; Šušmáková, K.
2010-01-01
Roč. 20, č. 2 (2010), s. 117-128 ISSN 0129-0657 R&D Projects: GA MŠk 7E08027 EU Projects: European Commission(XE) 200728 - BRAINSYNC Institutional research plan: CEZ:AV0Z10300504 Keywords : nonlinear dynamical systems * oscillations * random processes * time series analysis * EEG Subject RIV: FH - Neurology Impact factor: 4.237, year: 2010
From spiking neuron models to linear-nonlinear models.
Ostojic, Srdjan; Brunel, Nicolas
2011-01-20
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates.
Fuzzy Wavelet Neural Network Using a Correntropy Criterion for Nonlinear System Identification
Directory of Open Access Journals (Sweden)
Leandro L. S. Linhares
2015-01-01
Full Text Available Recent researches have demonstrated that the Fuzzy Wavelet Neural Networks (FWNNs are an efficient tool to identify nonlinear systems. In these structures, features related to fuzzy logic, wavelet functions, and neural networks are combined in an architecture similar to the Adaptive Neurofuzzy Inference Systems (ANFIS. In practical applications, the experimental data set used in the identification task often contains unknown noise and outliers, which decrease the FWNN model reliability. In order to reduce the negative effects of these erroneous measurements, this work proposes the direct use of a similarity measure based on information theory in the FWNN learning procedure. The Mean Squared Error (MSE cost function is replaced by the Maximum Correntropy Criterion (MCC in the traditional error backpropagation (BP algorithm. The input-output maps of a real nonlinear system studied in this work are identified from an experimental data set corrupted by different outliers rates and additive white Gaussian noise. The results demonstrate the advantages of the proposed cost function using the MCC as compared to the MSE. This work also investigates the influence of the kernel size on the performance of the MCC in the BP algorithm, since it is the only free parameter of correntropy.
Control Valve Stiction Identification, Modelling, Quantification and Control - A Review
Directory of Open Access Journals (Sweden)
Srinivasan Arumugam
2011-09-01
Full Text Available Most of the processes found in process industries exhibit undesirable nonlinearity due to backlash, saturation, hysteresis, stiction (friction, dead-zone and stuck-fault existing in control valves. The control valve is the actuator for most process control loops and, as the only moving part in the loop, its function is to implement the control action. If the control valve malfunctions, the performance of the control loop is likely to deteriorate, no matter how good the controller is. Commonly encountered control valve problems include nonlinear responses to the demand signal caused by effects such as stiction, dead-band or saturation. Because of these problems, the control loop may be oscillatory, which in turn may cause oscillations in many process variables causing a range of operational problems including increased valve wear. Understanding nonlinear behaviour of control valves in order to maintain the quality of the end products in the industry, this review article surveys the identification, modelling, estimation and design of dynamic models of stiction nonlinearity and providing appropriate controller to obtain optimum responses of the process. The primary objective of this work is to present state-of-art-review of common nonlinear problems associated with mechanical and chemical processes for encouraging researchers, practicing engineers working in this field, so that readers can invent their goals for future research work on nonlinear systems identification and control.
Tao, Dongwang; Li, Hui; Ma, Qiang
2016-04-01
Complete structure identification of complicate nonlinear system using extend Kalman filter (EKF) or unscented Kalman filter (UKF) may have the problems of divergence, huge computation and low estimation precision due to the large dimension of the extended state space for the system. In this article, a decentralized identification method of hysteretic system based on the joint EKF and UKF is proposed. The complete structure is divided into linear substructures and nonlinear substructures. The substructures are identified from the top to the bottom. For the linear substructure, EKF is used to identify the extended space including the displacements, velocities, stiffness and damping coefficients of the substructures, using the limited absolute accelerations and the identified interface force above the substructure. Similarly, for the nonlinear substructure, UKF is used to identify the extended space including the displacements, velocities, stiffness, damping coefficients and control parameters for the hysteretic Bouc-Wen model and the force at the interface of substructures. Finally a 10-story shear-type structure with multiple inter-story hysteresis is used for numerical simulation and is identified using the decentralized approach, and the identified results are compared with those using only EKF or UKF for the complete structure identification. The results show that the decentralized approach has the advantage of more stability, relative less computation and higher estimation precision.
PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems
Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai
2017-09-01
In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.
Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system
Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.
2017-05-01
We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.
Nonlinear Aerodynamic Modeling From Flight Data Using Advanced Piloted Maneuvers and Fuzzy Logic
Brandon, Jay M.; Morelli, Eugene A.
2012-01-01
Results of the Aeronautics Research Mission Directorate Seedling Project Phase I research project entitled "Nonlinear Aerodynamics Modeling using Fuzzy Logic" are presented. Efficient and rapid flight test capabilities were developed for estimating highly nonlinear models of airplane aerodynamics over a large flight envelope. Results showed that the flight maneuvers developed, used in conjunction with the fuzzy-logic system identification algorithms, produced very good model fits of the data, with no model structure inputs required, for flight conditions ranging from cruise to departure and spin conditions.
Banks, H. T.; Kunisch, K.
1982-01-01
Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.
Nonlinear System Identification Using Neural Networks Trained with Natural Gradient Descent
Directory of Open Access Journals (Sweden)
Ibnkahla Mohamed
2003-01-01
Full Text Available We use natural gradient (NG learning neural networks (NNs for modeling and identifying nonlinear systems with memory. The nonlinear system is comprised of a discrete-time linear filter followed by a zero-memory nonlinearity . The NN model is composed of a linear adaptive filter followed by a two-layer memoryless nonlinear NN. A Kalman filter-based technique and a search-and-converge method have been employed for the NG algorithm. It is shown that the NG descent learning significantly outperforms the ordinary gradient descent and the Levenberg-Marquardt (LM procedure in terms of convergence speed and mean squared error (MSE performance.
Pal, Partha S; Kar, R; Mandal, D; Ghoshal, S P
2015-11-01
This paper presents an efficient approach to identify different stable and practically useful Hammerstein models as well as unstable nonlinear process along with its stable closed loop counterpart with the help of an evolutionary algorithm as Colliding Bodies Optimization (CBO) optimization algorithm. The performance measures of the CBO based optimization approach such as precision, accuracy are justified with the minimum output mean square value (MSE) which signifies that the amount of bias and variance in the output domain are also the least. It is also observed that the optimization of output MSE in the presence of outliers has resulted in a very close estimation of the output parameters consistently, which also justifies the effective general applicability of the CBO algorithm towards the system identification problem and also establishes the practical usefulness of the applied approach. Optimum values of the MSEs, computational times and statistical information of the MSEs are all found to be the superior as compared with those of the other existing similar types of stochastic algorithms based approaches reported in different recent literature, which establish the robustness and efficiency of the applied CBO based identification scheme. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Nonlinear Model of Tape Wound Core Transformers
Directory of Open Access Journals (Sweden)
A. Vahedi
2015-03-01
Full Text Available Recently, tape wound cores due to their excellent magnetic properties, are widely used in different types of transformers. Performance prediction of these transformers needs an accurate model with ability to determine flux distribution within the core and magnetic loss. Spiral structure of tape wound cores affects the flux distribution and always cause complication of analysis. In this paper, a model based on reluctance networks method is presented for analysis of magnetic flux in wound cores. Using this model, distribution of longitudinal and transverse fluxes within the core can be determined. To consider the nonlinearity of the core, a dynamic hysteresis model is included in the presented model. Having flux density in different points of the core, magnetic losses can be calculated. To evaluate the validity of the model, results are compared with 2-D FEM simulations. In addition, a transformer designed for series-resonant converter and simulation results are compared with experimental measurements. Comparisons show accuracy of the model besides simplicity and fast convergence
NONLINEAR PLANT PIECEWISE-CONTINUOUS MODEL MATRIX PARAMETERS ESTIMATION
Directory of Open Access Journals (Sweden)
Roman L. Leibov
2017-09-01
Full Text Available This paper presents a nonlinear plant piecewise-continuous model matrix parameters estimation technique using nonlinear model time responses and random search method. One of piecewise-continuous model application areas is defined. The results of proposed approach application for aircraft turbofan engine piecewisecontinuous model formation are presented
Nonlinear Analysis and Modeling of Tires
Noor, Ahmed K.
1996-01-01
The objective of the study was to develop efficient modeling techniques and computational strategies for: (1) predicting the nonlinear response of tires subjected to inflation pressure, mechanical and thermal loads; (2) determining the footprint region, and analyzing the tire pavement contact problem, including the effect of friction; and (3) determining the sensitivity of the tire response (displacements, stresses, strain energy, contact pressures and contact area) to variations in the different material and geometric parameters. Two computational strategies were developed. In the first strategy the tire was modeled by using either a two-dimensional shear flexible mixed shell finite elements or a quasi-three-dimensional solid model. The contact conditions were incorporated into the formulation by using a perturbed Lagrangian approach. A number of model reduction techniques were applied to substantially reduce the number of degrees of freedom used in describing the response outside the contact region. The second strategy exploited the axial symmetry of the undeformed tire, and uses cylindrical coordinates in the development of three-dimensional elements for modeling each of the different parts of the tire cross section. Model reduction techniques are also used with this strategy.
Nonlinear integral equations for the sausage model
Ahn, Changrim; Balog, Janos; Ravanini, Francesco
2017-08-01
The sausage model, first proposed by Fateev, Onofri, and Zamolodchikov, is a deformation of the O(3) sigma model preserving integrability. The target space is deformed from the sphere to ‘sausage’ shape by a deformation parameter ν. This model is defined by a factorizable S-matrix which is obtained by deforming that of the O(3) sigma model by a parameter λ. Clues for the deformed sigma model are provided by various UV and IR information through the thermodynamic Bethe ansatz (TBA) analysis based on the S-matrix. Application of TBA to the sausage model is, however, limited to the case of 1/λ integer where the coupled integral equations can be truncated to a finite number. In this paper, we propose a finite set of nonlinear integral equations (NLIEs), which are applicable to generic value of λ. Our derivation is based on T-Q relations extracted from the truncated TBA equations. For a consistency check, we compute next-leading order corrections of the vacuum energy and extract the S-matrix information in the IR limit. We also solved the NLIE both analytically and numerically in the UV limit to get the effective central charge and compared with that of the zero-mode dynamics to obtain exact relation between ν and λ. Dedicated to the memory of Petr Petrovich Kulish.
Nonlinear Convective Models of RR Lyrae Stars
Feuchtinger, M.; Dorfi, E. A.
The nonlinear behavior of RR Lyrae pulsations is investigated using a state-of-the-art numerical technique solving the full time-dependent system of radiation hydrodynamics. Grey radiative transfer is included by a variable Eddington-factor method and we use the time-dependent turbulent convection model according to Kuhfuss (1986, A&A 160, 116) in the version of Wuchterl (1995, Comp. Phys. Comm. 89, 19). OPAL opacities extended by the Alexander molecule opacities at temperatures below 6000 K and an equation of state according to Wuchterl (1990, A&A 238, 83) close the system. The resulting nonlinear system is discretized on an adaptive mesh developed by Dorfi & Drury (1987, J. Comp. Phys. 69, 175), which is important to provide the necessary spatial resolution in critical regions like ionization zones and shock waves. Additionally, we employ a second order advection scheme, a time centered temporal discretizaton and an artificial tensor viscosity in order to treat discontinuities. We compute fundamental as well first overtone models of RR Lyrae stars for a grid of stellar parameters both with and without convective energy transport in order to give a detailed picture of the pulsation-convection interaction. In order to investigate the influence of the different features of the convection model calculations with and without overshooting, turbulent pressure and turbulent viscosity are performed and compared with each other. A standard Fourier decomposition is used to confront the resulting light and radial velocity variations with recent observations and we show that the well known RR Lyrae phase discrepancy problem (Simon 1985, ApJ 299, 723) can be resolved with these stellar pulsation computations.
Computational Models for Nonlinear Aeroelastic Systems, Phase II
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate new and efficient computational methods of modeling nonlinear aeroelastic systems. The...
International Nuclear Information System (INIS)
Jang, T. S.; Kwon, S. H.; Han, S. L.
2009-01-01
A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the 'first' kind: the solution lacks stability because the integral equation is the 'first' kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber's regularization in this study. The capability of the proposed procedure is investigated through numerical examples
DEFF Research Database (Denmark)
Chon, K H; Cohen, R J; Holstein-Rathlou, N H
1997-01-01
A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving...... average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre...
Nonlinear structural mechanics theory, dynamical phenomena and modeling
Lacarbonara, Walter
2013-01-01
Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...
Nonlinear Rheology in a Model Biological Tissue
Matoz-Fernandez, D. A.; Agoritsas, Elisabeth; Barrat, Jean-Louis; Bertin, Eric; Martens, Kirsten
2017-04-01
The rheological response of dense active matter is a topic of fundamental importance for many processes in nature such as the mechanics of biological tissues. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with an increasing shear rate. To rationalize this nonlinear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are, respectively, generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.
Coherent nonlinear quantum model for composite fermions
Energy Technology Data Exchange (ETDEWEB)
Reinisch, Gilbert [Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik (Iceland); Gudmundsson, Vidar, E-mail: vidar@hi.is [Science Institute, University of Iceland, Dunhaga 3, IS-107 Reykjavik (Iceland); Manolescu, Andrei [School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101 Reykjavik (Iceland)
2014-04-01
Originally proposed by Read [1] and Jain [2], the so-called “composite-fermion” is a phenomenological quasi-particle resulting from the attachment of two local flux quanta, seen as nonlocal vortices, to electrons situated on a two-dimensional (2D) surface embedded in a strong orthogonal magnetic field. In this Letter this phenomenon is described as a highly-nonlinear and coherent mean-field quantum process of the soliton type by use of a 2D stationary Schrödinger–Poisson differential model with only two Coulomb-interacting electrons. At filling factor ν=1/3 of the lowest Landau level the solution agrees with both the exact two-electron antisymmetric Schrödinger wavefunction and with Laughlin's Jastrow-type guess for the fractional quantum Hall effect, hence providing this latter with a tentative physical justification deduced from the experimental results and based on first principles.
Energy Technology Data Exchange (ETDEWEB)
Lyshevski, S.E. [Purdue University at Indianapolis (United States). Dept. of Electrical and Computer Engineering
2002-11-01
Microelectromechanical systems (MEMS), which integrate motion microstructures, radiating energy microdevices, controlling and signal processing integrated circuits (ICs), are widely used. Rotational and translational electromagnetic based micromachines are used in MEMS as actuators and sensors. Brushless high performance micromachines are the preferable choice in different MEMS applications, and therefore, synchronous and induction micromachines are the best candidates. Affordability, good performance characteristics (efficiency, controllability, robustness, reliability, power and torque densities etc.) and expanded operating envelopes result in a strong interest in the application of induction micromachines. In addition, induction micromachines can be easily fabricated using surface micromachining and high aspect ratio fabrication technologies. Thus, it is anticipated that induction micromachines, controlled using different control algorithms implemented using ICs, will be widely used in MEMS. Controllers can be implemented using specifically designed ICs to attain superior performance, maximize efficiency and controllability, minimize losses and electromagnetic interference, reduce noise and vibration, etc. In order to design controllers, the induction micromachine must be modeled, and its mathematical model parameters must be identified. Using microelectromechanics, nonlinear mathematical models are derived. This paper illustrates the application of nonlinear identification methods as applied to identify the unknown parameters of three phase induction micromachines. Two identification methods are studied. In particular, nonlinear error mapping technique and least squares identification are researched. Analytical and numerical results, as well as practical capabilities and effectiveness, are illustrated, identifying the unknown parameters of a three phase brushless induction micromotor. Experimental results fully support the identification methods. (author)
Nonlinear Kalman Filtering in Affine Term Structure Models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris
When the relationship between security prices and state variables in dynamic term structure models is nonlinear, existing studies usually linearize this relationship because nonlinear fi…ltering is computationally demanding. We conduct an extensive investigation of this linearization and analyze...... the potential of the unscented Kalman …filter to properly capture nonlinearities. To illustrate the advantages of the unscented Kalman …filter, we analyze the cross section of swap rates, which are relatively simple non-linear instruments, and cap prices, which are highly nonlinear in the states. An extensive...
A simple numerical model of a geometrically nonlinear Timoshenko beam
Keijdener, C.; Metrikine, A.
2015-01-01
In the original problem for which this model was developed, onedimensional flexible objects interact through a non-linear contact model. Due to the non-linear nature of the contact model, a numerical time-domain approach was adopted. One of the goals was to see if the coupling between axial and
Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes
DEFF Research Database (Denmark)
Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan
2013-01-01
The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...
Santos, Serge Dos; Farova, Zuzana; Kus, Vaclav; Prevorovsky, Zdenek
2012-05-01
This paper examines possibilities of using Nonlinear Elastic Wave Spectroscopy (NEWS) methods in dental investigations. Themain task consisted in imaging cracks or other degradation signatures located in dentin close to the Enamel-Dentine Junction (EDJ). NEWS approach was investigated experimentally with a new bi-modal acousto-optic set-up based on the chirp-coded nonlinear ultrasonic time reversal (TR) concepts. Complex internal structure of the tooth is analyzed by the TR-NEWS procedure adapted to tomography-like imaging of the tooth damages. Ultrasonic instrumentation with 10 MHz bandwidth has been set together including laser vibrometer used to detect responses of the tooth on its excitation carried out by a contact piezoelectric transducer. Bi-modal TR-NEWS images of the tooth were created before and after focusing, which resulted from the time compression. The polar B-scan of the tooth realized with TR-NEWS procedure is suggested to be applied as a new echodentography imaging.
Cazzulani, Gabriele; Resta, Ferruccio; Ripamonti, Francesco
2012-04-01
During the last years, more and more mechanical applications saw the introduction of active control strategies. In particular, the need of improving the performances and/or the system health is very often associated to vibration suppression. This goal can be achieved considering both passive and active solutions. In this sense, many active control strategies have been developed, such as the Independent Modal Space Control (IMSC) or the resonant controllers (PPF, IRC, . . .). In all these cases, in order to tune and optimize the control strategy, the knowledge of the system dynamic behaviour is very important and it can be achieved both considering a numerical model of the system or through an experimental identification process. Anyway, dealing with non-linear or time-varying systems, a tool able to online identify the system parameters becomes a key-point for the control logic synthesis. The aim of the present work is the definition of a real-time technique, based on ARMAX models, that estimates the system parameters starting from the measurements of piezoelectric sensors. These parameters are returned to the control logic, that automatically adapts itself to the system dynamics. The problem is numerically investigated considering a carbon-fiber plate model forced through a piezoelectric patch.
COMBINING LONG MEMORY AND NONLINEAR MODEL OUTPUTS FOR INFLATION FORECAST
Heri Kuswanto; Irhamah Alimuhajin; Laylia Afidah
2014-01-01
Long memory and nonlinearity have been proven as two models that are easily to be mistaken. In other words, nonlinearity is a strong candidate of spurious long memory by introducing a certain degree of fractional integration that lies in the region of long memory. Indeed, nonlinear process belongs to short memory with zero integration order. The idea of the forecast is to obtain the future condition with minimum error. Some researches argued that no matter what the model is, the important thi...
Explicit Nonlinear Model Predictive Control Theory and Applications
Grancharova, Alexandra
2012-01-01
Nonlinear Model Predictive Control (NMPC) has become the accepted methodology to solve complex control problems related to process industries. The main motivation behind explicit NMPC is that an explicit state feedback law avoids the need for executing a numerical optimization algorithm in real time. The benefits of an explicit solution, in addition to the efficient on-line computations, include also verifiability of the implementation and the possibility to design embedded control systems with low software and hardware complexity. This book considers the multi-parametric Nonlinear Programming (mp-NLP) approaches to explicit approximate NMPC of constrained nonlinear systems, developed by the authors, as well as their applications to various NMPC problem formulations and several case studies. The following types of nonlinear systems are considered, resulting in different NMPC problem formulations: Ø Nonlinear systems described by first-principles models and nonlinear systems described by black-box models; �...
Gubin, V.; Firsov, A.
2018-03-01
As the title implies the article describes the nonlinear system identification of the reduction smelting process of nickel oxide in electric arc furnaces. It is suggested that for operational control ratio of components of the charge must be solved the problem of determining the qualitative composition of the melt in real time. The use of 0th harmonic of phase voltage AC furnace as an indirect measure of the melt composition is proposed. Brief description of the mechanism of occurrence and nature of the non-zero 0th harmonic of the AC voltage of the arc is given. It is shown that value of 0th harmonic of the arc voltage is not function of electrical parameters but depends of the material composition of the melt. Processed industrial data are given. Hammerstein-Wiener model is used for description of the dependence of 0th harmonic of the furnace voltage from the technical parameters of melting furnace: the melt composition and current. Recommendations are given about the practical use of the model.
Nonlinear Growth Models in M"plus" and SAS
Grimm, Kevin J.; Ram, Nilam
2009-01-01
Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the M"plus" structural modeling program and the nonlinear…
Modeling Non-Linear Material Properties in Composite Materials
2016-06-28
Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions
Identification of time-varying nonlinear systems using differential evolution algorithm
DEFF Research Database (Denmark)
Perisic, Nevena; Green, Peter L; Worden, Keith
2013-01-01
(DE) algorithm for the identification of time-varying systems. DE is an evolutionary optimisation method developed to perform direct search in a continuous space without requiring any derivative estimation. DE is modified so that the objective function changes with time to account for the continuing......, thus identification of time-varying systems with nonlinearities can be a very challenging task. In order to avoid conventional least squares and gradient identification methods which require uni-modal and double differentiable objective functions, this work proposes a modified differential evolution...... inclusion of new data within an error metric. This paper presents results of identification of a time-varying SDOF system with Coulomb friction using simulated noise-free and noisy data for the case of time-varying friction coefficient, stiffness and damping. The obtained results are promising and the focus...
Parameter estimation in nonlinear models for pesticide degradation
International Nuclear Information System (INIS)
Richter, O.; Pestemer, W.; Bunte, D.; Diekkrueger, B.
1991-01-01
A wide class of environmental transfer models is formulated as ordinary or partial differential equations. With the availability of fast computers, the numerical solution of large systems became feasible. The main difficulty in performing a realistic and convincing simulation of the fate of a substance in the biosphere is not the implementation of numerical techniques but rather the incomplete data basis for parameter estimation. Parameter estimation is a synonym for statistical and numerical procedures to derive reasonable numerical values for model parameters from data. The classical method is the familiar linear regression technique which dates back to the 18th century. Because it is easy to handle, linear regression has long been established as a convenient tool for analysing relationships. However, the wide use of linear regression has led to an overemphasis of linear relationships. In nature, most relationships are nonlinear and linearization often gives a poor approximation of reality. Furthermore, pure regression models are not capable to map the dynamics of a process. Therefore, realistic models involve the evolution in time (and space). This leads in a natural way to the formulation of differential equations. To establish the link between data and dynamical models, numerical advanced parameter identification methods have been developed in recent years. This paper demonstrates the application of these techniques to estimation problems in the field of pesticide dynamics. (7 refs., 5 figs., 2 tabs.)
Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials
International Nuclear Information System (INIS)
Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan
2007-01-01
A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models
International Nuclear Information System (INIS)
Poterasu, V.F.
1984-01-01
It is presented a method and the phase resonance for damping characteristic identification of non-linear soil-structural interaction. The algorithm can be applied in case of any, not necessarily, damping characteristic of the system examined. For the identification, the system is harmonically excited and are considered the super-harmonic amplitudes for odd and even powers of the x. The response of shear beam system for different levels of base excitation and for different locations of the load is considered. (Author) [pt
Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory
DEFF Research Database (Denmark)
Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav
model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...
Identification and determination of solitary wave structures in nonlinear wave propagation
International Nuclear Information System (INIS)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of ''solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs
Nonlinear flow model for well production in an underground formation
Directory of Open Access Journals (Sweden)
J. C. Guo
2013-05-01
Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.
Nonlinear Parameter Identification of a Resonant Electrostatic MEMS Actuator
Al-Ghamdi, Majed S.; Alneamy, Ayman M.; Park, Sangtak; Li, Beichen; Khater, Mahmoud E.; Abdel-Rahman, Eihab M.; Heppler, Glenn R.; Yavuz, Mustafa
2017-01-01
We experimentally investigate the primary superharmonic of order two and subharmonic of order one-half resonances of an electrostatic MEMS actuator under direct excitation. We identify the parameters of a one degree of freedom (1-DOF) generalized Duffing oscillator model representing it. The experiments were conducted in soft vacuum to reduce squeeze-film damping, and the actuator response was measured optically using a laser vibrometer. The predictions of the identified model were found to be in close agreement with the experimental results. We also identified the noise spectral density of process (actuation voltage) and measurement noise. PMID:28505097
Model reduction of nonlinear systems subject to input disturbances
Ndoye, Ibrahima
2017-07-10
The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order nonlinear system with similar disturbance-output properties to the original plant. The proposed model reduction strategy preserves the nonlinearity and the input disturbance nature of the model. It guarantees a sufficiently small error between the outputs of the original and the reduced-order systems, and also maintains the properties of input-to-state stability. The matrices of the reduced order system are given in terms of a set of linear matrix inequalities (LMIs). The paper concludes with a demonstration of the proposed approach on model reduction of a nonlinear electronic circuit with additive disturbances.
Modeling of Nonlinear Beat Signals of TAE's
Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin
2012-03-01
Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core
Model reduction tools for nonlinear structural dynamics
Slaats, P.M.A.; Jongh, de J.; Sauren, A.A.H.J.
1995-01-01
Three mode types are proposed for reducing nonlinear dynamical system equations, resulting from finite element discretizations: tangent modes, modal derivatives, and newly added static modes. Tangent modes are obtained from an eigenvalue problem with a momentary tangent stiffness matrix. Their
Applications of Nonlinear Dynamics Model and Design of Complex Systems
In, Visarath; Palacios, Antonio
2009-01-01
This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.
Nonlinear Modeling of the PEMFC Based On NNARX Approach
Shan-Jen Cheng; Te-Jen Chang; Kuang-Hsiung Tan; Shou-Ling Kuo
2015-01-01
Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accurac...
International Nuclear Information System (INIS)
Brunet, M.; Morestin, F.; Godereaux, S.
2000-01-01
An inverse identification technique is proposed based on bending-unbending experiments on anisotropic sheet-metal strips. The initial anisotropy theory of plasticity is extended to include the concept of combined isotropic and non-linear kinematic hardening. This theory is adopted to characterise the anisotropic hardening due to loading-unloading which occurs in sheet-metal forming processes. To this end, a specific bending-unbending apparatus has been built to provide experimental moment-curvature curves. The constant bending moment applied over the length of the specimen to determine numerically the strain-stress behaviour but without Finite Element Analysis. Four constitutive parameters have to be identified by an inverse approach. Our identification results show that bending-unbending tests are suitable to model quite accurately the constitutive behaviour of sheet metals under complex loading paths. (author)
Directory of Open Access Journals (Sweden)
Li Zhao
2016-01-01
Full Text Available An improved smooth adaptive internal model control based on U model control method is presented to simplify modeling structure and parameter identification for a class of uncertain dynamic systems with unknown model parameters and bounded external disturbances. Differing from traditional adaptive methods, the proposed controller can simplify the identification of time-varying parameters in presence of bounded external disturbances. Combining the small gain theorem and the virtual equivalent system theory, learning rate of smooth adaptive internal model controller has been analyzed and the closed-loop virtual equivalent system based on discrete U model has been constructed as well. The convergence of this virtual equivalent system is proved, which further shows the convergence of the complex closed-loop discrete U model system. Finally, simulation and experimental results on a typical nonlinear dynamic system verified the feasibility of the proposed algorithm. The proposed method is shown to have lighter identification burden and higher control accuracy than the traditional adaptive controller.
Physics constrained nonlinear regression models for time series
International Nuclear Information System (INIS)
Majda, Andrew J; Harlim, John
2013-01-01
A central issue in contemporary science is the development of data driven statistical nonlinear dynamical models for time series of partial observations of nature or a complex physical model. It has been established recently that ad hoc quadratic multi-level regression (MLR) models can have finite-time blow up of statistical solutions and/or pathological behaviour of their invariant measure. Here a new class of physics constrained multi-level quadratic regression models are introduced, analysed and applied to build reduced stochastic models from data of nonlinear systems. These models have the advantages of incorporating memory effects in time as well as the nonlinear noise from energy conserving nonlinear interactions. The mathematical guidelines for the performance and behaviour of these physics constrained MLR models as well as filtering algorithms for their implementation are developed here. Data driven applications of these new multi-level nonlinear regression models are developed for test models involving a nonlinear oscillator with memory effects and the difficult test case of the truncated Burgers–Hopf model. These new physics constrained quadratic MLR models are proposed here as process models for Bayesian estimation through Markov chain Monte Carlo algorithms of low frequency behaviour in complex physical data. (paper)
Importance measures in global sensitivity analysis of nonlinear models
International Nuclear Information System (INIS)
Homma, Toshimitsu; Saltelli, Andrea
1996-01-01
The present paper deals with a new method of global sensitivity analysis of nonlinear models. This is based on a measure of importance to calculate the fractional contribution of the input parameters to the variance of the model prediction. Measures of importance in sensitivity analysis have been suggested by several authors, whose work is reviewed in this article. More emphasis is given to the developments of sensitivity indices by the Russian mathematician I.M. Sobol'. Given that Sobol' treatment of the measure of importance is the most general, his formalism is employed throughout this paper where conceptual and computational improvements of the method are presented. The computational novelty of this study is the introduction of the 'total effect' parameter index. This index provides a measure of the total effect of a given parameter, including all the possible synergetic terms between that parameter and all the others. Rank transformation of the data is also introduced in order to increase the reproducibility of the method. These methods are tested on a few analytical and computer models. The main conclusion of this work is the identification of a sensitivity analysis methodology which is both flexible, accurate and informative, and which can be achieved at reasonable computational cost
Variational Boussinesq model for strongly nonlinear dispersive waves
Lawrence, C.; Adytia, D.; van Groesen, E.
2018-01-01
For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be
Model reduction of nonlinear systems subject to input disturbances
Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem
2017-01-01
The method of convex optimization is used as a tool for model reduction of a class of nonlinear systems in the presence of disturbances. It is shown that under some conditions the nonlinear disturbed system can be approximated by a reduced order
Phenomenological modeling of nonlinear holograms based on metallic geometric metasurfaces.
Ye, Weimin; Li, Xin; Liu, Juan; Zhang, Shuang
2016-10-31
Benefiting from efficient local phase and amplitude control at the subwavelength scale, metasurfaces offer a new platform for computer generated holography with high spatial resolution. Three-dimensional and high efficient holograms have been realized by metasurfaces constituted by subwavelength meta-atoms with spatially varying geometries or orientations. Metasurfaces have been recently extended to the nonlinear optical regime to generate holographic images in harmonic generation waves. Thus far, there has been no vector field simulation of nonlinear metasurface holograms because of the tremendous computational challenge in numerically calculating the collective nonlinear responses of the large number of different subwavelength meta-atoms in a hologram. Here, we propose a general phenomenological method to model nonlinear metasurface holograms based on the assumption that every meta-atom could be described by a localized nonlinear polarizability tensor. Applied to geometric nonlinear metasurfaces, we numerically model the holographic images formed by the second-harmonic waves of different spins. We show that, in contrast to the metasurface holograms operating in the linear optical regime, the wavelength of incident fundamental light should be slightly detuned from the fundamental resonant wavelength to optimize the efficiency and quality of nonlinear holographic images. The proposed modeling provides a general method to simulate nonlinear optical devices based on metallic metasurfaces.
Nonlinear adaptive inverse control via the unified model neural network
Jeng, Jin-Tsong; Lee, Tsu-Tian
1999-03-01
In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.
Nonlinear Model Predictive Control with Constraint Satisfactions for a Quadcopter
Wang, Ye; Ramirez-Jaime, Andres; Xu, Feng; Puig, Vicenç
2017-01-01
This paper presents a nonlinear model predictive control (NMPC) strategy combined with constraint satisfactions for a quadcopter. The full dynamics of the quadcopter describing the attitude and position are nonlinear, which are quite sensitive to changes of inputs and disturbances. By means of constraint satisfactions, partial nonlinearities and modeling errors of the control-oriented model of full dynamics can be transformed into the inequality constraints. Subsequently, the quadcopter can be controlled by an NMPC controller with the updated constraints generated by constraint satisfactions. Finally, the simulation results applied to a quadcopter simulator are provided to show the effectiveness of the proposed strategy.
Heterotic sigma models and non-linear strings
International Nuclear Information System (INIS)
Hull, C.M.
1986-01-01
The two-dimensional supersymmetric non-linear sigma models are examined with respect to the heterotic string. The paper was presented at the workshop on :Supersymmetry and its applications', Cambridge, United Kingdom, 1985. The non-linear sigma model with Wess-Zumino-type term, the coupling of the fermionic superfields to the sigma model, super-conformal invariance, and the supersymmetric string, are all discussed. (U.K.)
Hidden physics models: Machine learning of nonlinear partial differential equations
Raissi, Maziar; Karniadakis, George Em
2018-03-01
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.
A Survey of Modelling and Identification of Quadrotor Robot
Directory of Open Access Journals (Sweden)
Xiaodong Zhang
2014-01-01
Full Text Available A quadrotor is a rotorcraft capable of hover, forward flight, and VTOL and is emerging as a fundamental research and application platform at present with flexibility, adaptability, and ease of construction. Since a quadrotor is basically considered an unstable system with the characteristics of dynamics such as being intensively nonlinear, multivariable, strongly coupled, and underactuated, a precise and practical model is critical to control the vehicle which seems to be simple to operate. As a rotorcraft, the dynamics of a quadrotor is mainly dominated by the complicated aerodynamic effects of the rotors. This paper gives a tutorial of the platform configuration, methodology of modeling, comprehensive nonlinear model, the aerodynamic effects, and model identification for a quadrotor.
Grimm, Kevin; Zhang, Zhiyong; Hamagami, Fumiaki; Mazzocco, Michele
2013-01-01
We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of "rates of change" and "acceleration" in latent growth curves--information available indirectly through traditional growth…
Sphaleron in a non-linear sigma model
International Nuclear Information System (INIS)
Sogo, Kiyoshi; Fujimoto, Yasushi.
1989-08-01
We present an exact classical saddle point solution in a non-linear sigma model. It has a topological charge 1/2 and mediates the vacuum transition. The quantum fluctuations and the transition rate are also examined. (author)
Computational Models for Nonlinear Aeroelastic Systems, Phase I
National Aeronautics and Space Administration — Clear Science Corp. and Duke University propose to develop and demonstrate a new and efficient computational method of modeling nonlinear aeroelastic systems. The...
forecasting with nonlinear time series model: a monte-carlo
African Journals Online (AJOL)
PUBLICATIONS1
Carlo method of forecasting using a special nonlinear time series model, called logistic smooth transition ... We illustrate this new method using some simulation ..... in MATLAB 7.5.0. ... process (DGP) using the logistic smooth transi-.
Discretization model for nonlinear dynamic analysis of three dimensional structures
International Nuclear Information System (INIS)
Hayashi, Y.
1982-12-01
A discretization model for nonlinear dynamic analysis of three dimensional structures is presented. The discretization is achieved through a three dimensional spring-mass system and the dynamic response obtained by direct integration of the equations of motion using central diferences. First the viability of the model is verified through the analysis of homogeneous linear structures and then its performance in the analysis of structures subjected to impulsive or impact loads, taking into account both geometrical and physical nonlinearities is evaluated. (Author) [pt
Nonlinear signal processing using neural networks: Prediction and system modelling
Energy Technology Data Exchange (ETDEWEB)
Lapedes, A.; Farber, R.
1987-06-01
The backpropagation learning algorithm for neural networks is developed into a formalism for nonlinear signal processing. We illustrate the method by selecting two common topics in signal processing, prediction and system modelling, and show that nonlinear applications can be handled extremely well by using neural networks. The formalism is a natural, nonlinear extension of the linear Least Mean Squares algorithm commonly used in adaptive signal processing. Simulations are presented that document the additional performance achieved by using nonlinear neural networks. First, we demonstrate that the formalism may be used to predict points in a highly chaotic time series with orders of magnitude increase in accuracy over conventional methods including the Linear Predictive Method and the Gabor-Volterra-Weiner Polynomial Method. Deterministic chaos is thought to be involved in many physical situations including the onset of turbulence in fluids, chemical reactions and plasma physics. Secondly, we demonstrate the use of the formalism in nonlinear system modelling by providing a graphic example in which it is clear that the neural network has accurately modelled the nonlinear transfer function. It is interesting to note that the formalism provides explicit, analytic, global, approximations to the nonlinear maps underlying the various time series. Furthermore, the neural net seems to be extremely parsimonious in its requirements for data points from the time series. We show that the neural net is able to perform well because it globally approximates the relevant maps by performing a kind of generalized mode decomposition of the maps. 24 refs., 13 figs.
Data based identification and prediction of nonlinear and complex dynamical systems
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-07-01
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The "inverse" problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear dynamical
Data based identification and prediction of nonlinear and complex dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Wang, Wen-Xu [School of Systems Science, Beijing Normal University, Beijing, 100875 (China); Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China); Lai, Ying-Cheng, E-mail: Ying-Cheng.Lai@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287 (United States); Department of Physics, Arizona State University, Tempe, AZ 85287 (United States); Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom); Grebogi, Celso [Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Aberdeen AB24 3UE (United Kingdom)
2016-07-12
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear
Data based identification and prediction of nonlinear and complex dynamical systems
International Nuclear Information System (INIS)
Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso
2016-01-01
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and economics. The classic approach to phase-space reconstruction through the methodology of delay-coordinate embedding has been practiced for more than three decades, but the paradigm is effective mostly for low-dimensional dynamical systems. Often, the methodology yields only a topological correspondence of the original system. There are situations in various fields of science and engineering where the systems of interest are complex and high dimensional with many interacting components. A complex system typically exhibits a rich variety of collective dynamics, and it is of great interest to be able to detect, classify, understand, predict, and control the dynamics using data that are becoming increasingly accessible due to the advances of modern information technology. To accomplish these goals, especially prediction and control, an accurate reconstruction of the original system is required. Nonlinear and complex systems identification aims at inferring, from data, the mathematical equations that govern the dynamical evolution and the complex interaction patterns, or topology, among the various components of the system. With successful reconstruction of the system equations and the connecting topology, it may be possible to address challenging and significant problems such as identification of causal relations among the interacting components and detection of hidden nodes. The “inverse” problem thus presents a grand challenge, requiring new paradigms beyond the traditional delay-coordinate embedding methodology. The past fifteen years have witnessed rapid development of contemporary complex graph theory with broad applications in interdisciplinary science and engineering. The combination of graph, information, and nonlinear
Nonlinear dynamics new directions models and applications
Ugalde, Edgardo
2015-01-01
This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynam...
Special class of nonlinear damping models in flexible space structures
Hu, Anren; Singh, Ramendra P.; Taylor, Lawrence W.
1991-01-01
A special class of nonlinear damping models is investigated in which the damping force is proportional to the product of positive integer or the fractional power of the absolute values of displacement and velocity. For a one-degree-of-freedom system, the classical Krylov-Bogoliubov 'averaging' method is used, whereas for a distributed system, both an ad hoc perturbation technique and the finite difference method are employed to study the effects of nonlinear damping. The results are compared with linear viscous damping models. The amplitude decrement of free vibration for a single mode system with nonlinear models depends not only on the damping ratio but also on the initial amplitude, the time to measure the response, the frequency of the system, and the powers of displacement and velocity. For the distributed system, the action of nonlinear damping is found to reduce the energy of the system and to pass energy to lower modes.
A finite element model for nonlinear shells of revolution
International Nuclear Information System (INIS)
Cook, W.A.
1979-01-01
A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)
Nonlinear mirror mode dynamics: Simulations and modeling
Czech Academy of Sciences Publication Activity Database
Califano, F.; Hellinger, Petr; Kuznetsov, E.; Passot, T.; Sulem, P. L.; Trávníček, Pavel
2008-01-01
Roč. 113, - (2008), A08219/1-A08219/20 ISSN 0148-0227 R&D Projects: GA AV ČR IAA300420702; GA AV ČR IAA300420602 Grant - others:PECS(CZ) 98024 Institutional research plan: CEZ:AV0Z30420517 Keywords : mirror instability * nonlinear evolution * numerical simulations * magnetic holes * mirror structures * kinetic plasma instabilities Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 3.147, year: 2008
Förner, K.; Polifke, W.
2017-10-01
The nonlinear acoustic behavior of Helmholtz resonators is characterized by a data-based reduced-order model, which is obtained by a combination of high-resolution CFD simulation and system identification. It is shown that even in the nonlinear regime, a linear model is capable of describing the reflection behavior at a particular amplitude with quantitative accuracy. This observation motivates to choose a local-linear model structure for this study, which consists of a network of parallel linear submodels. A so-called fuzzy-neuron layer distributes the input signal over the linear submodels, depending on the root mean square of the particle velocity at the resonator surface. The resulting model structure is referred to as an local-linear neuro-fuzzy network. System identification techniques are used to estimate the free parameters of this model from training data. The training data are generated by CFD simulations of the resonator, with persistent acoustic excitation over a wide range of frequencies and sound pressure levels. The estimated nonlinear, reduced-order models show good agreement with CFD and experimental data over a wide range of amplitudes for several test cases.
An integer optimization algorithm for robust identification of non-linear gene regulatory networks
Directory of Open Access Journals (Sweden)
Chemmangattuvalappil Nishanth
2012-09-01
Full Text Available Abstract Background Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. Results We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters
Non-parametric system identification from non-linear stochastic response
DEFF Research Database (Denmark)
Rüdinger, Finn; Krenk, Steen
2001-01-01
An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable...... of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method...
Practical Soil-Shallow Foundation Model for Nonlinear Structural Analysis
Directory of Open Access Journals (Sweden)
Moussa Leblouba
2016-01-01
Full Text Available Soil-shallow foundation interaction models that are incorporated into most structural analysis programs generally lack accuracy and efficiency or neglect some aspects of foundation behavior. For instance, soil-shallow foundation systems have been observed to show both small and large loops under increasing amplitude load reversals. This paper presents a practical macroelement model for soil-shallow foundation system and its stability under simultaneous horizontal and vertical loads. The model comprises three spring elements: nonlinear horizontal, nonlinear rotational, and linear vertical springs. The proposed macroelement model was verified using experimental test results from large-scale model foundations subjected to small and large cyclic loading cases.
A REMARK ON FORMAL MODELS FOR NONLINEARLY ELASTIC MEMBRANE SHELLS
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical” linear limiting membrane model, whose juetification has already been established by a convergence theorem.
Convex models and probabilistic approach of nonlinear fatigue failure
International Nuclear Information System (INIS)
Qiu Zhiping; Lin Qiang; Wang Xiaojun
2008-01-01
This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach
2010-09-30
Hyperfast Modeling of Nonlinear Ocean Waves A. R. Osborne Dipartimento di Fisica Generale, Università di Torino Via Pietro Giuria 1, 10125...PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Universit?i Torino,Dipartimento di Fisica Generale,Via Pietro Giuria 1,10125 Torino, Italy, 8. PERFORMING
A nonlinear complementarity approach for the national energy modeling system
International Nuclear Information System (INIS)
Gabriel, S.A.; Kydes, A.S.
1995-01-01
The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector. At present, to generate these equilibrium values, NEMS sequentially solves a collection of linear programs and nonlinear equations. The NEMS solution procedure then incorporates the solutions of these linear programs and nonlinear equations in a nonlinear Gauss-Seidel approach. The authors describe how the current version of NEMS can be formulated as a particular nonlinear complementarity problem (NCP), thereby possibly avoiding current convergence problems. In addition, they show that the NCP format is equally valid for a more general form of NEMS. They also describe several promising approaches for solving the NCP form of NEMS based on recent Newton type methods for general NCPs. These approaches share the feature of needing to solve their direction-finding subproblems only approximately. Hence, they can effectively exploit the sparsity inherent in the NEMS NCP
Nandola, Naresh N.; Rivera, Daniel E.
2011-01-01
This paper presents a data-centric modeling and predictive control approach for nonlinear hybrid systems. System identification of hybrid systems represents a challenging problem because model parameters depend on the mode or operating point of the system. The proposed algorithm applies Model-on-Demand (MoD) estimation to generate a local linear approximation of the nonlinear hybrid system at each time step, using a small subset of data selected by an adaptive bandwidth selector. The appeal of the MoD approach lies in the fact that model parameters are estimated based on a current operating point; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local MoD model is then converted into a mixed logical dynamical (MLD) system representation which can be used directly in a model predictive control (MPC) law for hybrid systems using multiple-degree-of-freedom tuning. The effectiveness of the proposed MoD predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results demonstrate that the proposed algorithm can be useful for adaptive intervention problems exhibiting both nonlinear and hybrid character. PMID:21874087
Recursive Subspace Identification of AUV Dynamic Model under General Noise Assumption
Directory of Open Access Journals (Sweden)
Zheping Yan
2014-01-01
Full Text Available A recursive subspace identification algorithm for autonomous underwater vehicles (AUVs is proposed in this paper. Due to the advantages at handling nonlinearities and couplings, the AUV model investigated here is for the first time constructed as a Hammerstein model with nonlinear feedback in the linear part. To better take the environment and sensor noises into consideration, the identification problem is concerned as an errors-in-variables (EIV one which means that the identification procedure is under general noise assumption. In order to make the algorithm recursively, propagator method (PM based subspace approach is extended into EIV framework to form the recursive identification method called PM-EIV algorithm. With several identification experiments carried out by the AUV simulation platform, the proposed algorithm demonstrates its effectiveness and feasibility.
Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction
Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.
2005-03-01
We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.
Recent Advances in Explicit Multiparametric Nonlinear Model Predictive Control
Domínguez, Luis F.
2011-01-19
In this paper we present recent advances in multiparametric nonlinear programming (mp-NLP) algorithms for explicit nonlinear model predictive control (mp-NMPC). Three mp-NLP algorithms for NMPC are discussed, based on which novel mp-NMPC controllers are derived. The performance of the explicit controllers are then tested and compared in a simulation example involving the operation of a continuous stirred-tank reactor (CSTR). © 2010 American Chemical Society.
Modeling of nonlinear biological phenomena modeled by S-systems.
Mansouri, Majdi M; Nounou, Hazem N; Nounou, Mohamed N; Datta, Aniruddha A
2014-03-01
A central challenge in computational modeling of biological systems is the determination of the model parameters. In such cases, estimating these variables or parameters from other easily obtained measurements can be extremely useful. For example, time-series dynamic genomic data can be used to develop models representing dynamic genetic regulatory networks, which can be used to design intervention strategies to cure major diseases and to better understand the behavior of biological systems. Unfortunately, biological measurements are usually highly infected by errors that hide the important characteristics in the data. Therefore, these noisy measurements need to be filtered to enhance their usefulness in practice. This paper addresses the problem of state and parameter estimation of biological phenomena modeled by S-systems using Bayesian approaches, where the nonlinear observed system is assumed to progress according to a probabilistic state space model. The performances of various conventional and state-of-the-art state estimation techniques are compared. These techniques include the extended Kalman filter (EKF), unscented Kalman filter (UKF), particle filter (PF), and the developed variational Bayesian filter (VBF). Specifically, two comparative studies are performed. In the first comparative study, the state variables (the enzyme CadA, the model cadBA, the cadaverine Cadav and the lysine Lys for a model of the Cad System in Escherichia coli (CSEC)) are estimated from noisy measurements of these variables, and the various estimation techniques are compared by computing the estimation root mean square error (RMSE) with respect to the noise-free data. In the second comparative study, the state variables as well as the model parameters are simultaneously estimated. In this case, in addition to comparing the performances of the various state estimation techniques, the effect of the number of estimated model parameters on the accuracy and convergence of these
Fuzzy model-based servo and model following control for nonlinear systems.
Ohtake, Hiroshi; Tanaka, Kazuo; Wang, Hua O
2009-12-01
This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.
Directory of Open Access Journals (Sweden)
Fengxia Xu
2014-01-01
Full Text Available U-model can approximate a large class of smooth nonlinear time-varying delay system to any accuracy by using time-varying delay parameters polynomial. This paper proposes a new approach, namely, U-model approach, to solving the problems of analysis and synthesis for nonlinear systems. Based on the idea of discrete-time U-model with time-varying delay, the identification algorithm of adaptive neural network is given for the nonlinear model. Then, the controller is designed by using the Newton-Raphson formula and the stability analysis is given for the closed-loop nonlinear systems. Finally, illustrative examples are given to show the validity and applicability of the obtained results.
Yu, Bing; Shu, Wenjun; Cao, Can
2018-05-01
A novel modeling method for aircraft engine using nonlinear autoregressive exogenous (NARX) models based on wavelet neural networks is proposed. The identification principle and process based on wavelet neural networks are studied, and the modeling scheme based on NARX is proposed. Then, the time series data sets from three types of aircraft engines are utilized to build the corresponding NARX models, and these NARX models are validated by the simulation. The results show that all the best NARX models can capture the original aircraft engine's dynamic characteristic well with the high accuracy. For every type of engine, the relative identification errors of its best NARX model and the component level model are no more than 3.5 % and most of them are within 1 %.
Symmetries and discretizations of the O(3) nonlinear sigma model
Energy Technology Data Exchange (ETDEWEB)
Flore, Raphael [TPI, Universitaet Jena (Germany)
2011-07-01
Nonlinear sigma models possess many interesting properties like asymptotic freedom, confinement or dynamical mass generation, and hence serve as toy models for QCD and other theories. We derive a formulation of the N=2 supersymmetric extension of the O(3) nonlinear sigma model in terms of constrained field variables. Starting from this formulation, it is discussed how the model can be discretized in a way that maintains as many symmetries of the theory as possible. Finally, recent numerical results related to these discretizations are presented.
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2014-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen’s compact notation for marine vehicles, we first describe a nonlinear four-degree-of-freedom (DOF) dynamic model for a sailing yacht, including roll. Our model also...
Modeling and nonlinear heading control for sailing yachts
DEFF Research Database (Denmark)
Xiao, Lin; Jouffroy, Jerome
2011-01-01
This paper presents a study on the development and testing of a model-based heading controller for a sailing yacht. Using Fossen's compact notation for marine vehicles, we first describe a nonlinear 4-DOF dynamic model for a sailing yacht, including roll. Starting from this model, we then design...
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
We introduce a new stabilized high-order and unstructured numerical model for modeling fully nonlinear and dispersive water waves. The model is based on a nodal spectral element method of arbitrary order in space and a -transformed formulation due to Cai, Langtangen, Nielsen and Tveito (1998). In...
A Versatile Nonlinear Method for Predictive Modeling
Liou, Meng-Sing; Yao, Weigang
2015-01-01
As computational fluid dynamics techniques and tools become widely accepted for realworld practice today, it is intriguing to ask: what areas can it be utilized to its potential in the future. Some promising areas include design optimization and exploration of fluid dynamics phenomena (the concept of numerical wind tunnel), in which both have the common feature where some parameters are varied repeatedly and the computation can be costly. We are especially interested in the need for an accurate and efficient approach for handling these applications: (1) capturing complex nonlinear dynamics inherent in a system under consideration and (2) versatility (robustness) to encompass a range of parametric variations. In our previous paper, we proposed to use first-order Taylor expansion collected at numerous sampling points along a trajectory and assembled together via nonlinear weighting functions. The validity and performance of this approach was demonstrated for a number of problems with a vastly different input functions. In this study, we are especially interested in enhancing the method's accuracy; we extend it to include the second-orer Taylor expansion, which however requires a complicated evaluation of Hessian matrices for a system of equations, like in fluid dynamics. We propose a method to avoid these Hessian matrices, while maintaining the accuracy. Results based on the method are presented to confirm its validity.
Non-linear Growth Models in Mplus and SAS
Grimm, Kevin J.; Ram, Nilam
2013-01-01
Non-linear growth curves or growth curves that follow a specified non-linear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this paper we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the non-linear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data collected as part of a study examining the effects of preschool instruction on academic gain we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included. PMID:23882134
An Improved Nonlinear Five-Point Model for Photovoltaic Modules
Directory of Open Access Journals (Sweden)
Sakaros Bogning Dongue
2013-01-01
Full Text Available This paper presents an improved nonlinear five-point model capable of analytically describing the electrical behaviors of a photovoltaic module for each generic operating condition of temperature and solar irradiance. The models used to replicate the electrical behaviors of operating PV modules are usually based on some simplified assumptions which provide convenient mathematical model which can be used in conventional simulation tools. Unfortunately, these assumptions cause some inaccuracies, and hence unrealistic economic returns are predicted. As an alternative, we used the advantages of a nonlinear analytical five-point model to take into account the nonideal diode effects and nonlinear effects generally ignored, which PV modules operation depends on. To verify the capability of our method to fit PV panel characteristics, the procedure was tested on three different panels. Results were compared with the data issued by manufacturers and with the results obtained using the five-parameter model proposed by other authors.
Study of the nonlinear imperfect software debugging model
International Nuclear Information System (INIS)
Wang, Jinyong; Wu, Zhibo
2016-01-01
In recent years there has been a dramatic proliferation of research on imperfect software debugging phenomena. Software debugging is a complex process and is affected by a variety of factors, including the environment, resources, personnel skills, and personnel psychologies. Therefore, the simple assumption that debugging is perfect is inconsistent with the actual software debugging process, wherein a new fault can be introduced when removing a fault. Furthermore, the fault introduction process is nonlinear, and the cumulative number of nonlinearly introduced faults increases over time. Thus, this paper proposes a nonlinear, NHPP imperfect software debugging model in consideration of the fact that fault introduction is a nonlinear process. The fitting and predictive power of the NHPP-based proposed model are validated through related experiments. Experimental results show that this model displays better fitting and predicting performance than the traditional NHPP-based perfect and imperfect software debugging models. S-confidence bounds are set to analyze the performance of the proposed model. This study also examines and discusses optimal software release-time policy comprehensively. In addition, this research on the nonlinear process of fault introduction is significant given the recent surge of studies on software-intensive products, such as cloud computing and big data. - Highlights: • Fault introduction is a nonlinear changing process during the debugging phase. • The assumption that the process of fault introduction is nonlinear is credible. • Our proposed model can better fit and accurately predict software failure behavior. • Research on fault introduction case is significant to software-intensive products.
Enzymatic Synthesis of Ampicillin: Nonlinear Modeling, Kinetics Estimation, and Adaptive Control
Directory of Open Access Journals (Sweden)
Monica Roman
2012-01-01
Full Text Available Nowadays, the use of advanced control strategies in biotechnology is quite low. A main reason is the lack of quality of the data, and the fact that more sophisticated control strategies must be based on a model of the dynamics of bioprocesses. The nonlinearity of the bioprocesses and the absence of cheap and reliable instrumentation require an enhanced modeling effort and identification strategies for the kinetics. The present work approaches modeling and control strategies for the enzymatic synthesis of ampicillin that is carried out inside a fed-batch bioreactor. First, a nonlinear dynamical model of this bioprocess is obtained by using a novel modeling procedure for biotechnology: the bond graph methodology. Second, a high gain observer is designed for the estimation of the imprecisely known kinetics of the synthesis process. Third, by combining an exact linearizing control law with the on-line estimation kinetics algorithm, a nonlinear adaptive control law is designed. The case study discussed shows that a nonlinear feedback control strategy applied to the ampicillin synthesis bioprocess can cope with disturbances, noisy measurements, and parametric uncertainties. Numerical simulations performed with MATLAB environment are included in order to test the behavior and the performances of the proposed estimation and control strategies.
Subspace identification of Hammer stein models using support vector machines
International Nuclear Information System (INIS)
Al-Dhaifallah, Mujahed
2011-01-01
System identification is the art of finding mathematical tools and algorithms that build an appropriate mathematical model of a system from measured input and output data. Hammerstein model, consisting of a memoryless nonlinearity followed by a dynamic linear element, is often a good trade-off as it can represent some dynamic nonlinear systems very accurately, but is nonetheless quite simple. Moreover, the extensive knowledge about LTI system representations can be applied to the dynamic linear block. On the other hand, finding an effective representation for the nonlinearity is an active area of research. Recently, support vector machines (SVMs) and least squares support vector machines (LS-SVMs) have demonstrated powerful abilities in approximating linear and nonlinear functions. In contrast with other approximation methods, SVMs do not require a-priori structural information. Furthermore, there are well established methods with guaranteed convergence (ordinary least squares, quadratic programming) for fitting LS-SVMs and SVMs. The general objective of this research is to develop new subspace algorithms for Hammerstein systems based on SVM regression.
Modelling and control of a nonlinear magnetostrictive actuator system
Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.
2018-04-01
This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.
A Simple Model for Nonlinear Confocal Ultrasonic Beams
Zhang, Dong; Zhou, Lin; Si, Li-Sheng; Gong, Xiu-Fen
2007-01-01
A confocally and coaxially arranged pair of focused transmitter and receiver represents one of the best geometries for medical ultrasonic imaging and non-invasive detection. We develop a simple theoretical model for describing the nonlinear propagation of a confocal ultrasonic beam in biological tissues. On the basis of the parabolic approximation and quasi-linear approximation, the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation is solved by using the angular spectrum approach. Gaussian superposition technique is applied to simplify the solution, and an analytical solution for the second harmonics in the confocal ultrasonic beam is presented. Measurements are performed to examine the validity of the theoretical model. This model provides a preliminary model for acoustic nonlinear microscopy.
Modeling TAE Response To Nonlinear Drives
Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin
2012-10-01
Experiment has detected the Toroidal Alfven Eigenmodes (TAE) with signals at twice the eigenfrequency.These harmonic modes arise from the second order perturbation in amplitude of the MHD equation for the linear modes that are driven the energetic particle free energy. The structure of TAE in realistic geometry can be calculated by generalizing the linear numerical solver (AEGIS package). We have have inserted all the nonlinear MHD source terms, where are quadratic in the linear amplitudes, into AEGIS code. We then invert the linear MHD equation at the second harmonic frequency. The ratio of amplitudes of the first and second harmonic terms are used to determine the internal field amplitude. The spatial structure of energy and density distribution are investigated. The results can be directly employed to compare with experiments and determine the Alfven wave amplitude in the plasma region.
Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity
Directory of Open Access Journals (Sweden)
Isao Ishida
2015-01-01
Full Text Available We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500 and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.
Dissipative quantum dynamics and nonlinear sigma-model
International Nuclear Information System (INIS)
Tarasov, V.E.
1992-01-01
Sedov variational principle which is the generalization of the least action principle for the dissipative and irreversible processes and the classical dissipative mechanics in the phase space is considered. Quantum dynamics for the dissipative and irreversible processes is constructed. As an example of the dissipative quantum theory the nonlinear two-dimensional sigma-model is considered. The conformal anomaly of the energy momentum tensor trace for closed bosonic string on the affine-metric manifold is investigated. The two-loop metric beta-function for nonlinear dissipative sigma-model was calculated. The results are compared with the ultraviolet two-loop conterterms for affine-metric sigma model. 71 refs
Model Identification using Continuous Glucose Monitoring Data for Type 1 Diabetes
DEFF Research Database (Denmark)
Boiroux, Dimitri; Hagdrup, Morten; Mahmoudi, Zeinab
2016-01-01
This paper addresses model identification of continuous-discrete nonlinear models for people with type 1 diabetes using sampled data from a continuous glucose monitor (CGM). We compare five identification techniques: least squares, weighted least squares, Huber regression, maximum likelihood...... with extended Kalman filter and maximum likelihood with unscented Kalman filter. We perform the identification on a 24-hour simulation of a stochastic differential equation (SDE) version of the Medtronic Virtual Patient (MVP) model including process and output noise. We compare the fits with the actual CGM......, such as parameter tracking, population modeling and handling of outliers....
International Nuclear Information System (INIS)
Debut, V.; Antunes, J.; Delaune, X.
2010-01-01
For achieving realistic numerical simulations of bowed string instruments, based on physical modeling, a good understanding of the actual friction interaction phenomena is of great importance. Most work published in the field including our own has assumed that bow/string frictional forces behave according to the classical Coulomb stick-slip model, with an empirical velocity-dependent sliding friction coefficient. Indeed, the basic self-excited string motions (such as the Helmholtz regime) are well captured using such friction model. However, recent work has shown that the tribological behavior of the bow/string rosin interface is rather complex, therefore the basic velocity-dependent Coulomb model may be an over-simplistic representation of the friction force. More specifically, it was suggested that a more accurate model of the interaction force can be achieved by coupling the system dynamical equations with a thermal model which encapsulates the complex interface phenomena. In spite of the interesting work performed by Askenfelt, a direct measurement of the actual dynamical friction forces without disturbing the string motion is quite difficult. Therefore, in this work we develop a modal-based identification technique making use of inverse methods and optimization techniques, which enables the identification of the interface force, as well as the string self-excited motion, from the dynamical reactions measured at the string end supports. The method gives convincing results using simulated data originated from nonlinear computations of a bowed string. Furthermore, in cases where the force identifications are very sensitive to errors in the transfer function modal parameters, we suggest a method to improve the modal frequencies used for the identifications. Preliminary experimental results obtained using a basic bowing device, by which the string is excited with the stick of the bow, are then presented. Our identifications, from the two dynamical string reactions
A Comparative Study Of Stock Price Forecasting Using Nonlinear Models
Directory of Open Access Journals (Sweden)
Diteboho Xaba
2017-03-01
Full Text Available This study compared the in-sample forecasting accuracy of three forecasting nonlinear models namely: the Smooth Transition Regression (STR model, the Threshold Autoregressive (TAR model and the Markov-switching Autoregressive (MS-AR model. Nonlinearity tests were used to confirm the validity of the assumptions of the study. The study used model selection criteria, SBC to select the optimal lag order and for the selection of appropriate models. The Mean Square Error (MSE, Mean Absolute Error (MAE and Root Mean Square Error (RMSE served as the error measures in evaluating the forecasting ability of the models. The MS-AR models proved to perform well with lower error measures as compared to LSTR and TAR models in most cases.
forecasting with nonlinear time series model: a monte-carlo
African Journals Online (AJOL)
PUBLICATIONS1
erated recursively up to any step greater than one. For nonlinear time series model, point forecast for step one can be done easily like in the linear case but forecast for a step greater than or equal to ..... London. Franses, P. H. (1998). Time series models for business and Economic forecasting, Cam- bridge University press.
Nonlinear Dynamics of a Helicopter Model in Ground Resonance
Tang, D. M.; Dowell, E. H.
1985-01-01
An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis.
Linear and Nonlinear Career Models: Metaphors, Paradigms, and Ideologies.
Buzzanell, Patrice M.; Goldzwig, Steven R.
1991-01-01
Examines the linear or bureaucratic career models (dominant in career research, metaphors, paradigms, and ideologies) which maintain career myths of flexibility and individualized routes to success in organizations incapable of offering such versatility. Describes nonlinear career models which offer suggestive metaphors for re-visioning careers…
Line impedance estimation using model based identification technique
DEFF Research Database (Denmark)
Ciobotaru, Mihai; Agelidis, Vassilios; Teodorescu, Remus
2011-01-01
The estimation of the line impedance can be used by the control of numerous grid-connected systems, such as active filters, islanding detection techniques, non-linear current controllers, detection of the on/off grid operation mode. Therefore, estimating the line impedance can add extra functions...... into the operation of the grid-connected power converters. This paper describes a quasi passive method for estimating the line impedance of the distribution electricity network. The method uses the model based identification technique to obtain the resistive and inductive parts of the line impedance. The quasi...
An analog model for quantum lightcone fluctuations in nonlinear optics
International Nuclear Information System (INIS)
Ford, L.H.; De Lorenci, V.A.; Menezes, G.; Svaiter, N.F.
2013-01-01
We propose an analog model for quantum gravity effects using nonlinear dielectrics. Fluctuations of the spacetime lightcone are expected in quantum gravity, leading to variations in the flight times of pulses. This effect can also arise in a nonlinear material. We propose a model in which fluctuations of a background electric field, such as that produced by a squeezed photon state, can cause fluctuations in the effective lightcone for probe pulses. This leads to a variation in flight times analogous to that in quantum gravity. We make some numerical estimates which suggest that the effect might be large enough to be observable. - Highlights: ► Lightcone fluctuations, quantum fluctuations of the effective speed of light, are a feature of quantum gravity. ► Nonlinear dielectrics have a variable speed of light, analogous to the effects of gravity. ► Fluctuating electric fields create the effect of lightcone fluctuations in a nonlinear material. ► We propose to use squeezed light in a nonlinear material as an analog model of lightcone fluctuations. ► Variation in the speed of propagation of pulses is the observational signature of lightcone fluctuations.
Nonlinear Dynamic Modeling of Langevin-Type Piezoelectric Transducers
Directory of Open Access Journals (Sweden)
Nicolás Peréz Alvarez
2015-11-01
Full Text Available Langevin transducers are employed in several applications, such as power ultrasound systems, naval hydrophones, and high-displacement actuators. Nonlinear effects can influence their performance, especially at high vibration amplitude levels. These nonlinear effects produce variations in the resonant frequency, harmonics of the excitation frequency, in addition to loss of symmetry in the frequency response and “frequency domain hysteresis”. In this context, this paper presents a simplified nonlinear dynamic model of power ultrasound transducers requiring only two parameters for simulating the most relevant nonlinear effects. One parameter reproduces the changes in the resonance frequency and the other introduces the dependence of the frequency response on the history of the system. The piezoelectric constitutive equations are extended by a linear dependence of the elastic constant on the mechanical displacement amplitude. For introducing the frequency hysteresis, the elastic constant is computed by combining the current value of the mechanical amplitude with the previous state amplitude. The model developed in this work is applied for predicting the dynamic responses of a 26 kHz ultrasonic transducer. The comparison of theoretical and experimental responses, obtained at several input voltages around the tuned frequency, shows a good agreement, indicating that the model can accurately describe the transducer nonlinear behavior.
LPV system identification using series expansion models
Toth, R.; Heuberger, P.S.C.; Hof, Van den P.M.J.; Santos, dos P.L.; Perdicoúlis, T.P.A.; Novara, C.; Ramos, J.A.; Rivera, D.E.
2011-01-01
This review volume reports the state-of-the-art in Linear Parameter Varying (LPV) system identification. Written by world renowned researchers, the book contains twelve chapters, focusing on the most recent LPV identification methods for both discrete-time and continuous-time models, using different
Note on off-shell relations in nonlinear sigma model
International Nuclear Information System (INIS)
Chen, Gang; Du, Yi-Jian; Li, Shuyi; Liu, Hanqing
2015-01-01
In this note, we investigate relations between tree-level off-shell currents in nonlinear sigma model. Under Cayley parametrization, all odd-point currents vanish. We propose and prove a generalized U(1) identity for even-point currents. The off-shell U(1) identity given in http://dx.doi.org/10.1007/JHEP01(2014)061 is a special case of the generalized identity studied in this note. The on-shell limit of this identity is equivalent with the on-shell KK relation. Thus this relation provides the full off-shell correspondence of tree-level KK relation in nonlinear sigma model.
Likelihood-Based Inference in Nonlinear Error-Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
We consider a class of vector nonlinear error correction models where the transfer function (or loadings) of the stationary relation- ships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties...... and a linear trend in general. Gaussian likelihood-based estimators are considered for the long- run cointegration parameters, and the short-run parameters. Asymp- totic theory is provided for these and it is discussed to what extend asymptotic normality and mixed normaity can be found. A simulation study...
Modeling and identification for robot motion control
Kostic, D.; Jager, de A.G.; Steinbuch, M.; Kurfess, T.R.
2004-01-01
This chapter deals with the problems of robot modelling and identification for high-performance model-based motion control. A derivation of robot kinematic and dynamic models was explained. Modelling of friction effects was also discussed. Use of a writing task to establish correctness of the models
Nonlinear thermal reduced model for Microwave Circuit Analysis
Chang, Christophe; Sommet, Raphael; Quéré, Raymond; Dueme, Ph.
2004-01-01
With the constant increase of transistor power density, electro thermal modeling is becoming a necessity for accurate prediction of device electrical performances. For this reason, this paper deals with a methodology to obtain a precise nonlinear thermal model based on Model Order Reduction of a three dimensional thermal Finite Element (FE) description. This reduced thermal model is based on the Ritz vector approach which ensure the steady state solution in every case. An equi...
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbæk, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...... symmetric non-linear error correction considered. A simulation study shows that the fi…nite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....
Testing and Inference in Nonlinear Cointegrating Vector Error Correction Models
DEFF Research Database (Denmark)
Kristensen, Dennis; Rahbek, Anders
In this paper, we consider a general class of vector error correction models which allow for asymmetric and non-linear error correction. We provide asymptotic results for (quasi-)maximum likelihood (QML) based estimators and tests. General hypothesis testing is considered, where testing...... of non-stationary non-linear time series models. Thus the paper provides a full asymptotic theory for estimators as well as standard and non-standard test statistics. The derived asymptotic results prove to be new compared to results found elsewhere in the literature due to the impact of the estimated...... symmetric non-linear error correction are considered. A simulation study shows that the finite sample properties of the bootstrapped tests are satisfactory with good size and power properties for reasonable sample sizes....
Mathematical models for suspension bridges nonlinear structural instability
Gazzola, Filippo
2015-01-01
This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.
Modeling and non-linear responses of MEMS capacitive accelerometer
Directory of Open Access Journals (Sweden)
Sri Harsha C.
2014-01-01
Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.
Modelling of a bridge-shaped nonlinear piezoelectric energy harvester
International Nuclear Information System (INIS)
Gafforelli, G; Corigliano, A; Xu, R; Kim, S G
2013-01-01
Piezoelectric MicroElectroMechanical Systems (MEMS) energy harvesting is an attractive technology for harvesting small magnitudes of energy from ambient vibrations. Increasing the operating frequency bandwidth of such devices is one of the major issues for real world applications. A MEMS-scale doubly clamped nonlinear beam resonator is designed and developed to demonstrate very wide bandwidth and high power density. In this paper a first complete theoretical discussion of nonlinear resonating piezoelectric energy harvesting is provided. The sectional behaviour of the beam is studied through the Classical Lamination Theory (CLT) specifically modified to introduce the piezoelectric coupling and nonlinear Green-Lagrange strain tensor. A lumped parameter model is built through Rayleigh-Ritz Method and the resulting nonlinear coupled equations are solved in the frequency domain through the Harmonic Balance Method (HBM). Finally, the influence of external load resistance on the dynamic behaviour is studied. The theoretical model shows that nonlinear resonant harvesters have much wider power bandwidth than that of linear resonators but their maximum power is still bounded by the mechanical damping as is the case for linear resonating harvesters
Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses
DEFF Research Database (Denmark)
Fasil, Muhammed; Mijatovic, Nenad; Jensen, Bogi Bech
2017-01-01
The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless DC (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modelling fractional-slot machines. The inaccuracy of phase variable mod...... on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model....... of fractional-slot machines can be attributed to considerable armature flux harmonics, which causes an increased core loss. This study proposes a nonlinear phase variable model of PMBLDC motor that considers the core losses induced in the stator and the rotor. The core loss model is developed based...
Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.
2017-10-01
A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.
Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.
2017-03-01
Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.
Current algebra of classical non-linear sigma models
International Nuclear Information System (INIS)
Forger, M.; Laartz, J.; Schaeper, U.
1992-01-01
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)
Dynamics of breathers in discrete nonlinear Schrodinger models
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Johansson, Magnus; Aubry, Serge
1998-01-01
We review some recent results concerning the existence and stability of spatially localized and temporally quasiperiodic (non-stationary) excitations in discrete nonlinear Schrodinger (DNLS) models. In two dimensions, we show the existence of linearly stable, stationary and non-stationary localized...
Control mechanisms for a nonlinear model of international relations
Energy Technology Data Exchange (ETDEWEB)
Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.
1997-07-15
Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.
S-AMP for non-linear observation models
DEFF Research Database (Denmark)
Cakmak, Burak; Winther, Ole; Fleury, Bernard H.
2015-01-01
Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement...
Two-dimensional effects in nonlinear Kronig-Penney models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Christiansen, Peter Leth; Rasmussen, Kim
1997-01-01
An analysis of two-dimensional (2D) effects in the nonlinear Kronig-Penney model is presented. We establish an effective one-dimensional description of the 2D effects, resulting in a set of pseudodifferential equations. The stationary states of the 2D system and their stability is studied...
Modelling the nonlinearity of piezoelectric actuators in active ...
African Journals Online (AJOL)
Piezoelectric actuators have great capabilities as elements of intelligent structures for active vibration cancellation. One problem with this type of actuator is its nonlinear behaviour. In active vibration control systems, it is important to have an accurate model of the control branch. This paper demonstrates the ability of neural ...
Hybrid time/frequency domain modeling of nonlinear components
DEFF Research Database (Denmark)
Wiechowski, Wojciech Tomasz; Lykkegaard, Jan; Bak, Claus Leth
2007-01-01
This paper presents a novel, three-phase hybrid time/frequency methodology for modelling of nonlinear components. The algorithm has been implemented in the DIgSILENT PowerFactory software using the DIgSILENT Programming Language (DPL), as a part of the work described in [1]. Modified HVDC benchmark...
A non-linear dissipative model of magnetism
Czech Academy of Sciences Publication Activity Database
Durand, P.; Paidarová, Ivana
2010-01-01
Roč. 89, č. 6 (2010), s. 67004 ISSN 1286-4854 R&D Projects: GA AV ČR IAA100400501 Institutional research plan: CEZ:AV0Z40400503 Keywords : non-linear dissipative model of magnetism * thermodynamics * physical chemistry Subject RIV: CF - Physical ; Theoretical Chemistry http://epljournal.edpsciences.org/
Modeling and verifying non-linearities in heterodyne displacement interferometry
Cosijns, S.J.A.G.; Haitjema, H.; Schellekens, P.H.J.
2002-01-01
The non-linearities in a heterodyne laser interferometer system occurring from the phase measurement system of the interferometer andfrom non-ideal polarization effects of the optics are modeled into one analytical expression which includes the initial polarization state ofthe laser source, the
Multidimensional splines for modeling FET nonlinearities
Energy Technology Data Exchange (ETDEWEB)
Barby, J A
1986-01-01
Circuit simulators like SPICE and timing simulators like MOTIS are used extensively for critical path verification of integrated circuits. MOSFET model evaluation dominates the run time of these simulators. Changes in technology results in costly updates, since modifications require reprogramming of the functions and their derivatives. The computational cost of MOSFET models can be reduced by using multidimensional polynomial splines. Since simulators based on the Newton Raphson algorithm require the function and first derivative, quadratic splines are sufficient for this purpose. The cost of updating the MOSFET model due to technology changes is greatly reduced since splines are derived from a set of points. Crucial for convergence speed of simulators is the fact that MOSFET characteristic equations are monotonic. This must be maintained by any simulation model. The splines the author designed do maintain monotonicity.
Measurement Model Nonlinearity in Estimation of Dynamical Systems
Majji, Manoranjan; Junkins, J. L.; Turner, J. D.
2012-06-01
The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.
Model Reduction of Nonlinear Aeroelastic Systems Experiencing Hopf Bifurcation
Abdelkefi, Abdessattar
2013-06-18
In this paper, we employ the normal form to derive a reduced - order model that reproduces nonlinear dynamical behavior of aeroelastic systems that undergo Hopf bifurcation. As an example, we consider a rigid two - dimensional airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We apply the center manifold theorem on the governing equations to derive its normal form that constitutes a simplified representation of the aeroelastic sys tem near flutter onset (manifestation of Hopf bifurcation). Then, we use the normal form to identify a self - excited oscillator governed by a time - delay ordinary differential equation that approximates the dynamical behavior while reducing the dimension of the original system. Results obtained from this oscillator show a great capability to predict properly limit cycle oscillations that take place beyond and above flutter as compared with the original aeroelastic system.
Modelization of highly nonlinear waves in coastal regions
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2015-04-01
The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.
Advances in Modelling, System Identification and Parameter ...
Indian Academy of Sciences (India)
Authors show, using numerical simulation for two system functions, the improvement in percentage normalized ... of nonlinear systems. The approach is to use multiple linearizing models fitted along the operating trajectories. ... over emphasized in the light of present day high level of research activity in the field of aerospace ...
Nonlinear dynamic phenomena in the beer model
DEFF Research Database (Denmark)
Mosekilde, Erik; Laugesen, Jakob Lund
2007-01-01
The production-distribution system or "beer game" is one of the most well-known system dynamics models. Notorious for the complex dynamics it produces, the beer game has been used for nearly five decades to illustrate how structure generates behavior and to explore human decision making. Here we...
Nonlinear Modelling of Low Frequency Loudspeakers
DEFF Research Database (Denmark)
Olsen, Erling Sandermann; Christensen, Knud Bank
1996-01-01
A central part of the Danish LoDist project has been the derivation of an extended equivalent circuit and a corresponding set of differential equations suitable for the simulation of high-fidelity woofers under large and very large (clipping) signal conditions. A model including suspension creep ...
Directory of Open Access Journals (Sweden)
Christopher Heine
2014-08-01
Full Text Available A detailed description of the rubber parts’ properties is gaining in importance in the current simulation models of multi-body simulation. One application example is a multi-body simulation of the washing machine movement. Inside the washing machine, there are different force transmission elements, which consist completely or partly of rubber. Rubber parts or, generally, elastomers usually have amplitude-dependant and frequency-dependent force transmission properties. Rheological models are used to describe these properties. A method for characterization of the amplitude and frequency dependence of such a rheological model is presented within this paper. Within this method, the used rheological model can be reduced or expanded in order to illustrate various non-linear effects. An original result is given with the automated parameter identification. It is fully implemented in Matlab. Such identified rheological models are intended for subsequent implementation in a multi-body model. This allows a significant enhancement of the overall model quality.
Identification and MPC control of a circulation fluidized bed boiler using an LPV model
Huang, J.; Ji, G.; Zhu, Y.; Lin, W.; Kothare, M.; Tade, M.; Vande Wouwer, A.; Smets, I.
2010-01-01
This work studies the identification and control of circulation fluidized bed (CFB) boilers. The CFB boiler under investigation shows strong nonlinearity due to big changes of steam load. A linear parameter varying (LPV) model is used to represent the process dynamics and used in control. The steam
Nonclassical measurements errors in nonlinear models
DEFF Research Database (Denmark)
Madsen, Edith; Mulalic, Ismir
Discrete choice models and in particular logit type models play an important role in understanding and quantifying individual or household behavior in relation to transport demand. An example is the choice of travel mode for a given trip under the budget and time restrictions that the individuals...... estimates of the income effect it is of interest to investigate the magnitude of the estimation bias and if possible use estimation techniques that take the measurement error problem into account. We use data from the Danish National Travel Survey (NTS) and merge it with administrative register data...... that contains very detailed information about incomes. This gives a unique opportunity to learn about the magnitude and nature of the measurement error in income reported by the respondents in the Danish NTS compared to income from the administrative register (correct measure). We find that the classical...
Quark fragmentation function and the nonlinear chiral quark model
International Nuclear Information System (INIS)
Zhu, Z.K.
1993-01-01
The scaling law of the fragmentation function has been proved in this paper. With that, we show that low-P T quark fragmentation function can be studied as a low energy physocs in the light-cone coordinate frame. We therefore use the nonlinear chiral quark model which is able to study the low energy physics under scale Λ CSB to study such a function. Meanwhile the formalism for studying the quark fragmentation function has been established. The nonlinear chiral quark model is quantized on the light-front. We then use old-fashioned perturbation theory to study the quark fragmentation function. Our first order result for such a function shows in agreement with the phenomenological model study of e + e - jet. The probability for u,d pair formation in the e + e - jet from our calculation is also in agreement with the phenomenological model results
DEFF Research Database (Denmark)
Friis, Tobias; Orfanos, Antonios; Katsanos, Evangelos
The identification of the modal characteristics of engineering systems under operational conditions is commonly conducted with the use of the Operational Modal Analysis (OMA), being a class of useful tools employed within various fields of structural, mechanical as well as marine and naval...... engineering. The current OMA methods have been advanced on the basis of two fundamental, though, restrictive assumptions: (i) linearity and (ii) stationarity. Nevertheless, there are several applications that are inherently related to various nonlinear mechanisms, which, in turn, violate the two cornerstones...... of OMA and hence, question its robustness and efficiency. Along these lines, the current study addresses the effect of friction-induced nonlinearity on OMA-identified dynamic characteristics of an experimental set up consisting of a pair of reduced scale offshore platform models that are connected...
Nonlinear model of high-dose implantation
International Nuclear Information System (INIS)
Danilyuk, A.
2001-01-01
The models of high-dose implantation, using the distribution functions, are relatively simple. However, they must take into account the variation of the function of distribution of the implanted ions with increasing dose [1-4]. This variation takes place owing to the fact that the increase of the concentration of the implanted ions results in a change of the properties of the target. High-dose implantation is accompanied by sputtering, volume growth, diffusion, generation of defects, formation of new phases, etc. The variation of the distribution function is determined by many factors and is not known in advance. The variation within the framework of these models [1-4] is taken into account in advance by the introduction of intuitive assumptions on the basis of implicit considerations. Therefore, these attempts should be regarded as incorrect. The model prepared here makes it possible to take into account the sputtering of the target, volume growth and additional declaration on the implanted ions. Without any assumptions in relation to the variation of the distribution function with increasing dose. In our model it is assumed that the type of distribution function for small doses in a pure target substance is the same as in substances with implanted ions. A second assumption relates to the type of the distribution function valid for small doses in the given substances. These functions are determined as a result of a large number of theoretical and experimental investigations and are well-known at the present time. They include the symmetric and nonsymmetric Gauss distribution, the Pearson distribution, and others. We examine implantation with small doses of up to 10 14 - 10 15 cm -2 when the accurately known distribution is valid
Huang, Honglan; Mao, Hanying; Mao, Hanling; Zheng, Weixue; Huang, Zhenfeng; Li, Xinxin; Wang, Xianghong
2017-12-01
Cumulative fatigue damage detection for used parts plays a key role in the process of remanufacturing engineering and is related to the service safety of the remanufactured parts. In light of the nonlinear properties of used parts caused by cumulative fatigue damage, the based nonlinear output frequency response functions detection approach offers a breakthrough to solve this key problem. First, a modified PSO-adaptive lasso algorithm is introduced to improve the accuracy of the NARMAX model under impulse hammer excitation, and then, an effective new algorithm is derived to estimate the nonlinear output frequency response functions under rectangular pulse excitation, and a based nonlinear output frequency response functions index is introduced to detect the cumulative fatigue damage in used parts. Then, a novel damage detection approach that integrates the NARMAX model and the rectangular pulse is proposed for nonlinear output frequency response functions identification and cumulative fatigue damage detection of used parts. Finally, experimental studies of fatigued plate specimens and used connecting rod parts are conducted to verify the validity of the novel approach. The obtained results reveal that the new approach can detect cumulative fatigue damages of used parts effectively and efficiently and that the various values of the based nonlinear output frequency response functions index can be used to detect the different fatigue damages or working time. Since the proposed new approach can extract nonlinear properties of systems by only a single excitation of the inspected system, it shows great promise for use in remanufacturing engineering applications.
Soliton excitations in a class of nonlinear field theory models
International Nuclear Information System (INIS)
Makhan'kov, V.G.; Fedyanin, V.K.
1985-01-01
Investigation results of nonlinear models of the field theory with a lagrangian are described. The theory includes models both with zero stable vacuum epsilon=1 and with condensate epsilon=-1 (of disturbed symmetry). Conditions of existence of particle-like solutions (PLS), stability of these solutions are investigated. Soliton dynamics is studied. PLS formfactors are calculated. Statistical mechanics of solitons is built and their dynamic structure factors are calculated
The quantum nonlinear Schroedinger model with point-like defect
International Nuclear Information System (INIS)
Caudrelier, V; Mintchev, M; Ragoucy, E
2004-01-01
We establish a family of point-like impurities which preserve the quantum integrability of the nonlinear Schroedinger model in 1+1 spacetime dimensions. We briefly describe the construction of the exact second quantized solution of this model in terms of an appropriate reflection-transmission algebra. The basic physical properties of the solution, including the spacetime symmetry of the bulk scattering matrix, are also discussed. (letter to the editor)
Eddy current modeling in linear and nonlinear multifilamentary composite materials
Menana, Hocine; Farhat, Mohamad; Hinaje, Melika; Berger, Kevin; Douine, Bruno; Lévêque, Jean
2018-04-01
In this work, a numerical model is developed for a rapid computation of eddy currents in composite materials, adaptable for both carbon fiber reinforced polymers (CFRPs) for NDT applications and multifilamentary high temperature superconductive (HTS) tapes for AC loss evaluation. The proposed model is based on an integro-differential formulation in terms of the electric vector potential in the frequency domain. The high anisotropy and the nonlinearity of the considered materials are easily handled in the frequency domain.
Classical solutions for the 4-dimensional σ-nonlinear model
International Nuclear Information System (INIS)
Tataru-Mihai, P.
1979-01-01
By interpreting the σ-nonlinear model as describing the Gauss map associated to a certain immersion, several classes of classical solutions for the 4-dimensional model are derived. As by-products one points out i) an intimate connection between the energy-momentum tensor of the solution and the second differential form of the immersion associated to it and ii) a connection between self- (antiself-)duality of the solution and the minimality of the associated immersion. (author)
CEAI: CCM based Email Authorship Identification Model
DEFF Research Database (Denmark)
Nizamani, Sarwat; Memon, Nasrullah
2013-01-01
In this paper we present a model for email authorship identification (EAI) by employing a Cluster-based Classification (CCM) technique. Traditionally, stylometric features have been successfully employed in various authorship analysis tasks; we extend the traditional feature-set to include some...... more interesting and effective features for email authorship identification (e.g. the last punctuation mark used in an email, the tendency of an author to use capitalization at the start of an email, or the punctuation after a greeting or farewell). We also included Info Gain feature selection based...... reveal that the proposed CCM-based email authorship identification model, along with the proposed feature set, outperforms the state-of-the-art support vector machine (SVM)-based models, as well as the models proposed by Iqbal et al. [1, 2]. The proposed model attains an accuracy rate of 94% for 10...
Linear and nonlinear ARMA model parameter estimation using an artificial neural network
Chon, K. H.; Cohen, R. J.
1997-01-01
This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.
Nguyen, Nhan; Ting, Eric
2018-01-01
This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..
Observing and modeling nonlinear dynamics in an internal combustion engine
International Nuclear Information System (INIS)
Daw, C.S.; Kennel, M.B.; Finney, C.E.; Connolly, F.T.
1998-01-01
We propose a low-dimensional, physically motivated, nonlinear map as a model for cyclic combustion variation in spark-ignited internal combustion engines. A key feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Residual cylinder gas from each cycle alters the in-cylinder fuel-air ratio and thus the combustion efficiency in succeeding cycles. The model close-quote s simplicity allows rapid simulation of thousands of engine cycles, permitting statistical studies of cyclic-variation patterns and providing physical insight into this technologically important phenomenon. Using symbol statistics to characterize the noisy dynamics, we find good quantitative matches between our model and experimental time-series measurements. copyright 1998 The American Physical Society
Nonlinear dynamics of avian influenza epidemic models.
Liu, Sanhong; Ruan, Shigui; Zhang, Xinan
2017-01-01
Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior. We obtain a threshold value for the prevalence of avian influenza and investigate the local or global asymptotical stability of each equilibrium of these systems by using linear analysis technique or combining Liapunov function method and LaSalle's invariance principle, respectively. Moreover, we give necessary and sufficient conditions for the occurrence of periodic solutions in the avian influenza system with Allee effect of the avian population. Numerical simulations are also presented to illustrate the theoretical results. Copyright © 2016 Elsevier Inc. All rights reserved.
Multi-atom Jaynes-Cummings model with nonlinear effects
International Nuclear Information System (INIS)
Aleixo, Armando Nazareno Faria; Balantekin, Akif Baha; Ribeiro, Marco Antonio Candido
2001-01-01
The standard Jaynes-Cummings (JC) model and its extensions, normally used in quantum optics, idealizes the interaction of matter with electromagnetic radiation by a simple Hamiltonian of a two-level atom coupled to a single bosonic mode. This Hamiltonian has a fundamental importance to the field of quantum optics and it is a central ingredient in the quantized description of any optical system involving the interaction between light and atoms. The JC Hamiltonian defines a molecule, a composite system formed from the coupling of a two-state system and a quantized harmonic oscillator. For this Hamiltonian, mostly the single-particle situation has been studied. This model can also be extended for the situation where one has N two-level systems, which interact only with the electromagnetic radiation. In this case the effects of the spatial distribution of the particles it is not taken into account and the spin angular momentum S-circumflex i of each particle contributes to form a total angular momentum J-circumflex of the system. When one considers the effects due to the spatial variation in the field intensity in a nonlinear medium it is necessary to further add a Kerr term to the standard JC Hamiltonian. This kind of nonlinear JC Hamiltonian is used in the study of micro masers. Another nonlinear variant of the JC model takes the coupling between matter and the radiation to depend on the intensity of the electromagnetic field. This model is interesting since this kind of interaction means that effectively the coupling is proportional to the amplitude of the field representing a very simple case of a nonlinear interaction corresponding to a more realistic physical situation. In this work we solve exactly the problem of the interaction of a N two-level atoms with an electromagnetic radiation when nonlinear effects due to the spatial variation in the field intensity in a nonlinear Kerr medium and the dependence on the intensity of the electromagnetic field on the matter
A data driven nonlinear stochastic model for blood glucose dynamics.
Zhang, Yan; Holt, Tim A; Khovanova, Natalia
2016-03-01
The development of adequate mathematical models for blood glucose dynamics may improve early diagnosis and control of diabetes mellitus (DM). We have developed a stochastic nonlinear second order differential equation to describe the response of blood glucose concentration to food intake using continuous glucose monitoring (CGM) data. A variational Bayesian learning scheme was applied to define the number and values of the system's parameters by iterative optimisation of free energy. The model has the minimal order and number of parameters to successfully describe blood glucose dynamics in people with and without DM. The model accounts for the nonlinearity and stochasticity of the underlying glucose-insulin dynamic process. Being data-driven, it takes full advantage of available CGM data and, at the same time, reflects the intrinsic characteristics of the glucose-insulin system without detailed knowledge of the physiological mechanisms. We have shown that the dynamics of some postprandial blood glucose excursions can be described by a reduced (linear) model, previously seen in the literature. A comprehensive analysis demonstrates that deterministic system parameters belong to different ranges for diabetes and controls. Implications for clinical practice are discussed. This is the first study introducing a continuous data-driven nonlinear stochastic model capable of describing both DM and non-DM profiles. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.
Modal model for the nonlinear multimode Rayleigh endash Taylor instability
International Nuclear Information System (INIS)
Ofer, D.; Alon, U.; Shvarts, D.; McCrory, R.L.; Verdon, C.P.
1996-01-01
A modal model for the Rayleigh endash Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A<1) are also included in the model and the difference between various measures of the mixing zone penetration depth for A<1 is discussed. copyright 1996 American Institute of Physics
Nonlinear modeling of magnetorheological energy absorbers under impact conditions
Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M.; Browne, Alan L.; Ulicny, John; Johnson, Nancy
2013-11-01
Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s-1. Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R&D Center for nominal drop speeds of up to 6 m s-1.
Nonlinear modeling of magnetorheological energy absorbers under impact conditions
International Nuclear Information System (INIS)
Mao, Min; Hu, Wei; Choi, Young-Tai; Wereley, Norman M; Browne, Alan L; Ulicny, John; Johnson, Nancy
2013-01-01
Magnetorheological energy absorbers (MREAs) provide adaptive vibration and shock mitigation capabilities to accommodate varying payloads, vibration spectra, and shock pulses, as well as other environmental factors. A key performance metric is the dynamic range, which is defined as the ratio of the force at maximum field to the force in the absence of field. The off-state force is typically assumed to increase linearly with speed, but at the higher shaft speeds occurring in impact events, the off-state damping exhibits nonlinear velocity squared damping effects. To improve understanding of MREA behavior under high-speed impact conditions, this study focuses on nonlinear MREA models that can more accurately predict MREA dynamic behavior for nominal impact speeds of up to 6 m s −1 . Three models were examined in this study. First, a nonlinear Bingham-plastic (BP) model incorporating Darcy friction and fluid inertia (Unsteady-BP) was formulated where the force is proportional to the velocity. Second, a Bingham-plastic model incorporating minor loss factors and fluid inertia (Unsteady-BPM) to better account for high-speed behavior was formulated. Third, a hydromechanical (HM) analysis was developed to account for fluid compressibility and inertia as well as minor loss factors. These models were validated using drop test data obtained using the drop tower facility at GM R and D Center for nominal drop speeds of up to 6 m s −1 . (paper)
Nonlinear unitary quantum collapse model with self-generated noise
Geszti, Tamás
2018-04-01
Collapse models including some external noise of unknown origin are routinely used to describe phenomena on the quantum-classical border; in particular, quantum measurement. Although containing nonlinear dynamics and thereby exposed to the possibility of superluminal signaling in individual events, such models are widely accepted on the basis of fully reproducing the non-signaling statistical predictions of quantum mechanics. Here we present a deterministic nonlinear model without any external noise, in which randomness—instead of being universally present—emerges in the measurement process, from deterministic irregular dynamics of the detectors. The treatment is based on a minimally nonlinear von Neumann equation for a Stern–Gerlach or Bell-type measuring setup, containing coordinate and momentum operators in a self-adjoint skew-symmetric, split scalar product structure over the configuration space. The microscopic states of the detectors act as a nonlocal set of hidden parameters, controlling individual outcomes. The model is shown to display pumping of weights between setup-defined basis states, with a single winner randomly selected and the rest collapsing to zero. Environmental decoherence has no role in the scenario. Through stochastic modelling, based on Pearle’s ‘gambler’s ruin’ scheme, outcome probabilities are shown to obey Born’s rule under a no-drift or ‘fair-game’ condition. This fully reproduces quantum statistical predictions, implying that the proposed non-linear deterministic model satisfies the non-signaling requirement. Our treatment is still vulnerable to hidden signaling in individual events, which remains to be handled by future research.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan
2016-04-12
Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.
Non-linear sigma model on the fuzzy supersphere
International Nuclear Information System (INIS)
Kurkcuoglu, Seckin
2004-01-01
In this note we develop fuzzy versions of the supersymmetric non-linear sigma model on the supersphere S (2,2) . In hep-th/0212133 Bott projectors have been used to obtain the fuzzy C P 1 model. Our approach utilizes the use of supersymmetric extensions of these projectors. Here we obtain these (super)-projectors and quantize them in a fashion similar to the one given in hep-th/0212133. We discuss the interpretation of the resulting model as a finite dimensional matrix model. (author)
Cardiovascular oscillations: in search of a nonlinear parametric model
Bandrivskyy, Andriy; Luchinsky, Dmitry; McClintock, Peter V.; Smelyanskiy, Vadim; Stefanovska, Aneta; Timucin, Dogan
2003-05-01
We suggest a fresh approach to the modeling of the human cardiovascular system. Taking advantage of a new Bayesian inference technique, able to deal with stochastic nonlinear systems, we show that one can estimate parameters for models of the cardiovascular system directly from measured time series. We present preliminary results of inference of parameters of a model of coupled oscillators from measured cardiovascular data addressing cardiorespiratory interaction. We argue that the inference technique offers a very promising tool for the modeling, able to contribute significantly towards the solution of a long standing challenge -- development of new diagnostic techniques based on noninvasive measurements.
Spatio-temporal modeling of nonlinear distributed parameter systems
Li, Han-Xiong
2011-01-01
The purpose of this volume is to provide a brief review of the previous work on model reduction and identifi cation of distributed parameter systems (DPS), and develop new spatio-temporal models and their relevant identifi cation approaches. In this book, a systematic overview and classifi cation on the modeling of DPS is presented fi rst, which includes model reduction, parameter estimation and system identifi cation. Next, a class of block-oriented nonlinear systems in traditional lumped parameter systems (LPS) is extended to DPS, which results in the spatio-temporal Wiener and Hammerstein s
International Nuclear Information System (INIS)
Unsihuay-Vila, C.; Zambroni de Souza, A.C.; Marangon-Lima, J.W.; Balestrassi, P.P.
2010-01-01
This paper proposes a new hybrid approach based on nonlinear chaotic dynamics and evolutionary strategy to forecast electricity loads and prices. The main idea is to develop a new training or identification stage in a nonlinear chaotic dynamic based predictor. In the training stage five optimal parameters for a chaotic based predictor are searched through an optimization model based on evolutionary strategy. The objective function of the optimization model is the mismatch minimization between the multi-step-ahead forecasting of predictor and observed data such as it is done in identification problems. The first contribution of this paper is that the proposed approach is capable of capturing the complex dynamic of demand and price time series considered resulting in a more accuracy forecasting. The second contribution is that the proposed approach run on-line manner, i.e. the optimal set of parameters and prediction is executed automatically which can be used to prediction in real-time, it is an advantage in comparison with other models, where the choice of their input parameters are carried out off-line, following qualitative/experience-based recipes. A case study of load and price forecasting is presented using data from New England, Alberta, and Spain. A comparison with other methods such as autoregressive integrated moving average (ARIMA) and artificial neural network (ANN) is shown. The results show that the proposed approach provides a more accurate and effective forecasting than ARIMA and ANN methods. (author)
Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach
DEFF Research Database (Denmark)
Knudsen, Morten; Jensen, J.G.
1995-01-01
A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....
Linear theory for filtering nonlinear multiscale systems with model error.
Berry, Tyrus; Harlim, John
2014-07-08
In this paper, we study filtering of multiscale dynamical systems with model error arising from limitations in resolving the smaller scale processes. In particular, the analysis assumes the availability of continuous-time noisy observations of all components of the slow variables. Mathematically, this paper presents new results on higher order asymptotic expansion of the first two moments of a conditional measure. In particular, we are interested in the application of filtering multiscale problems in which the conditional distribution is defined over the slow variables, given noisy observation of the slow variables alone. From the mathematical analysis, we learn that for a continuous time linear model with Gaussian noise, there exists a unique choice of parameters in a linear reduced model for the slow variables which gives the optimal filtering when only the slow variables are observed. Moreover, these parameters simultaneously give the optimal equilibrium statistical estimates of the underlying system, and as a consequence they can be estimated offline from the equilibrium statistics of the true signal. By examining a nonlinear test model, we show that the linear theory extends in this non-Gaussian, nonlinear configuration as long as we know the optimal stochastic parametrization and the correct observation model. However, when the stochastic parametrization model is inappropriate, parameters chosen for good filter performance may give poor equilibrium statistical estimates and vice versa; this finding is based on analytical and numerical results on our nonlinear test model and the two-layer Lorenz-96 model. Finally, even when the correct stochastic ansatz is given, it is imperative to estimate the parameters simultaneously and to account for the nonlinear feedback of the stochastic parameters into the reduced filter estimates. In numerical experiments on the two-layer Lorenz-96 model, we find that the parameters estimated online , as part of a filtering
Chaotic System Identification Based on a Fuzzy Wiener Model with Particle Swarm Optimization
International Nuclear Information System (INIS)
Yong, Li; Ying-Gan, Tang
2010-01-01
A fuzzy Wiener model is proposed to identify chaotic systems. The proposed fuzzy Wiener model consists of two parts, one is a linear dynamic subsystem and the other is a static nonlinear part, which is represented by the Takagi–Sugeno fuzzy model. Identification of chaotic systems is converted to find optimal parameters of the fuzzy Wiener model by minimizing the state error between the original chaotic system and the fuzzy Wiener model. Particle swarm optimization algorithm, a global optimizer, is used to search the optimal parameter of the fuzzy Wiener model. The proposed method can identify the parameters of the linear part and nonlinear part simultaneously. Numerical simulations for Henón and Lozi chaotic system identification show the effectiveness of the proposed method
A non-linear model of economic production processes
Ponzi, A.; Yasutomi, A.; Kaneko, K.
2003-06-01
We present a new two phase model of economic production processes which is a non-linear dynamical version of von Neumann's neoclassical model of production, including a market price-setting phase as well as a production phase. The rate of an economic production process is observed, for the first time, to depend on the minimum of its input supplies. This creates highly non-linear supply and demand dynamics. By numerical simulation, production networks are shown to become unstable when the ratio of different products to total processes increases. This provides some insight into observed stability of competitive capitalist economies in comparison to monopolistic economies. Capitalist economies are also shown to have low unemployment.
Nonlinear Economic Model Predictive Control Strategy for Active Smart Buildings
DEFF Research Database (Denmark)
Santos, Rui Mirra; Zong, Yi; Sousa, Joao M. C.
2016-01-01
Nowadays, the development of advanced and innovative intelligent control techniques for energy management in buildings is a key issue within the smart grid topic. A nonlinear economic model predictive control (EMPC) scheme, based on the branch-and-bound tree search used as optimization algorithm ...... controller is shown very reliable keeping the comfort levels in the two considered seasons and shifting the load away from peak hours in order to achieve the desired flexible electricity consumption.......Nowadays, the development of advanced and innovative intelligent control techniques for energy management in buildings is a key issue within the smart grid topic. A nonlinear economic model predictive control (EMPC) scheme, based on the branch-and-bound tree search used as optimization algorithm...
Non-linear calibration models for near infrared spectroscopy
DEFF Research Database (Denmark)
Ni, Wangdong; Nørgaard, Lars; Mørup, Morten
2014-01-01
by ridge regression (RR). The performance of the different methods is demonstrated by their practical applications using three real-life near infrared (NIR) data sets. Different aspects of the various approaches including computational time, model interpretability, potential over-fitting using the non-linear...... models on linear problems, robustness to small or medium sample sets, and robustness to pre-processing, are discussed. The results suggest that GPR and BANN are powerful and promising methods for handling linear as well as nonlinear systems, even when the data sets are moderately small. The LS......-SVM), relevance vector machines (RVM), Gaussian process regression (GPR), artificial neural network (ANN), and Bayesian ANN (BANN). In this comparison, partial least squares (PLS) regression is used as a linear benchmark, while the relationship of the methods is considered in terms of traditional calibration...
Comparing Numerical Spall Simulations with a Nonlinear Spall Formation Model
Ong, L.; Melosh, H. J.
2012-12-01
Spallation accelerates lightly shocked ejecta fragments to speeds that can exceed the escape velocity of the parent body. We present high-resolution simulations of nonlinear shock interactions in the near surface. Initial results show the acceleration of near-surface material to velocities up to 1.8 times greater than the peak particle velocity in the detached shock, while experiencing little to no shock pressure. These simulations suggest a possible nonlinear spallation mechanism to produce the high-velocity, low show pressure meteorites from other planets. Here we pre-sent the numerical simulations that test the production of spall through nonlinear shock interactions in the near sur-face, and compare the results with a model proposed by Kamegai (1986 Lawrence Livermore National Laboratory Report). We simulate near-surface shock interactions using the SALES_2 hydrocode and the Murnaghan equation of state. We model the shock interactions in two geometries: rectangular and spherical. In the rectangular case, we model a planar shock approaching the surface at a constant angle phi. In the spherical case, the shock originates at a point below the surface of the domain and radiates spherically from that point. The angle of the shock front with the surface is dependent on the radial distance of the surface point from the shock origin. We model the target as a solid with a nonlinear Murnaghan equation of state. This idealized equation of state supports nonlinear shocks but is tem-perature independent. We track the maximum pressure and maximum velocity attained in every cell in our simula-tions and compare them to the Hugoniot equations that describe the material conditions in front of and behind the shock. Our simulations demonstrate that nonlinear shock interactions in the near surface produce lightly shocked high-velocity material for both planar and cylindrical shocks. The spall is the result of the free surface boundary condi-tion, which forces a pressure gradient
Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models
Low, Ian; Yin, Zhewei
2018-02-01
We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for S -matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
Directory of Open Access Journals (Sweden)
Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis
International Nuclear Information System (INIS)
Farshidianfar, A.; Saghafi, A.
2014-01-01
In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems. - Highlights: • This study deals with the prediction and control of chaos in a nonlinear gear system. • Melnikov analysis is extended to present a practical gear system to control the chaos. • The proposed system is effective to eliminate the homoclinic bifurcation and chaos. • This controller is proposed as a way of implementing the chaos control in gear system
Nonlinear dynamics mathematical models for rigid bodies with a liquid
Lukovsky, Ivan A
2015-01-01
This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.
Nonlinear Stochastic Models for Water Level Dynamics in Closed Lakes
Mishchenko, A.S.; Zelikin, M.I.; Zelikina, L.F.
1995-01-01
This paper presents the results of investigation of nonlinear mathematical models of the behavior of closed lakes using the example of the Caspian Sea. Forecasting the level of the Caspian Sea is crucial both for the economy of the region and for the region's environment. The Caspian Sea is a closed reservoir; it is well known that its level changes considerably due to a variety of factors including global climate change. A series of forecasts exists based on different methods and taking...
NON-LINEAR MODELING OF THE RHIC INTERACTION REGIONS
International Nuclear Information System (INIS)
TOMAS, R.; FISCHER, W.; JAIN, A.; LUO, Y.; PILAT, F.
2004-01-01
For RHIC's collision lattices the dominant sources of transverse non-linearities are located in the interaction regions. The field quality is available for most of the magnets in the interaction regions from the magnetic measurements, or from extrapolations of these measurements. We discuss the implementation of these measurements in the MADX models of the Blue and the Yellow rings and their impact on beam stability
Nonlinear evolution inclusions arising from phase change models
Czech Academy of Sciences Publication Activity Database
Colli, P.; Krejčí, Pavel; Rocca, E.; Sprekels, J.
2007-01-01
Roč. 57, č. 4 (2007), s. 1067-1098 ISSN 0011-4642 R&D Projects: GA ČR GA201/02/1058 Institutional research plan: CEZ:AV0Z10190503 Keywords : nonlinear and nonlocal evolution equations * Cahn-Hilliard type dynamics * phase transitions models Subject RIV: BA - General Mathematics Impact factor: 0.155, year: 2007 http://www.dml.cz/bitstream/handle/10338.dmlcz/128228/CzechMathJ_57-2007-4_2.pdf
Nonlinear Model Predictive Control for Cooperative Control and Estimation
Ru, Pengkai
Recent advances in computational power have made it possible to do expensive online computations for control systems. It is becoming more realistic to perform computationally intensive optimization schemes online on systems that are not intrinsically stable and/or have very small time constants. Being one of the most important optimization based control approaches, model predictive control (MPC) has attracted a lot of interest from the research community due to its natural ability to incorporate constraints into its control formulation. Linear MPC has been well researched and its stability can be guaranteed in the majority of its application scenarios. However, one issue that still remains with linear MPC is that it completely ignores the system's inherent nonlinearities thus giving a sub-optimal solution. On the other hand, if achievable, nonlinear MPC, would naturally yield a globally optimal solution and take into account all the innate nonlinear characteristics. While an exact solution to a nonlinear MPC problem remains extremely computationally intensive, if not impossible, one might wonder if there is a middle ground between the two. We tried to strike a balance in this dissertation by employing a state representation technique, namely, the state dependent coefficient (SDC) representation. This new technique would render an improved performance in terms of optimality compared to linear MPC while still keeping the problem tractable. In fact, the computational power required is bounded only by a constant factor of the completely linearized MPC. The purpose of this research is to provide a theoretical framework for the design of a specific kind of nonlinear MPC controller and its extension into a general cooperative scheme. The controller is designed and implemented on quadcopter systems.
Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach
Doeswijk, T.G.; Keesman, K.J.
2005-01-01
Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such
Shah, A A; Xing, W W; Triantafyllidis, V
2017-04-01
In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.
Use of nonlinear dose-effect models to predict consequences
International Nuclear Information System (INIS)
Seiler, F.A.; Alvarez, J.L.
1996-01-01
The linear dose-effect relationship was introduced as a model for the induction of cancer from exposure to nuclear radiation. Subsequently, it has been used by analogy to assess the risk of chemical carcinogens also. Recently, however, the model for radiation carcinogenesis has come increasingly under attack because its calculations contradict the epidemiological data, such as cancer in atomic bomb survivors. Even so, its proponents vigorously defend it, often using arguments that are not so much scientific as a mix of scientific, societal, and often political arguments. At least in part, the resilience of the linear model is due to two convenient properties that are exclusive to linearity: First, the risk of an event is determined solely by the event dose; second, the total risk of a population group depends only on the total population dose. In reality, the linear model has been conclusively falsified; i.e., it has been shown to make wrong predictions, and once this fact is generally realized, the scientific method calls for a new paradigm model. As all alternative models are by necessity nonlinear, all the convenient properties of the linear model are invalid, and calculational procedures have to be used that are appropriate for nonlinear models
El-Nagar, Ahmad M
2018-01-01
In this study, a novel structure of a recurrent interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy neural network (FNN) is introduced for nonlinear dynamic and time-varying systems identification. It combines the type-2 fuzzy sets (T2FSs) and a recurrent FNN to avoid the data uncertainties. The fuzzy firing strengths in the proposed structure are returned to the network input as internal variables. The interval type-2 fuzzy sets (IT2FSs) is used to describe the antecedent part for each rule while the consequent part is a TSK-type, which is a linear function of the internal variables and the external inputs with interval weights. All the type-2 fuzzy rules for the proposed RIT2TSKFNN are learned on-line based on structure and parameter learning, which are performed using the type-2 fuzzy clustering. The antecedent and consequent parameters of the proposed RIT2TSKFNN are updated based on the Lyapunov function to achieve network stability. The obtained results indicate that our proposed network has a small root mean square error (RMSE) and a small integral of square error (ISE) with a small number of rules and a small computation time compared with other type-2 FNNs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
On the Reliability of Nonlinear Modeling using Enhanced Genetic Programming Techniques
Winkler, S. M.; Affenzeller, M.; Wagner, S.
The use of genetic programming (GP) in nonlinear system identification enables the automated search for mathematical models that are evolved by an evolutionary process using the principles of selection, crossover and mutation. Due to the stochastic element that is intrinsic to any evolutionary process, GP cannot guarantee the generation of similar or even equal models in each GP process execution; still, if there is a physical model underlying to the data that are analyzed, then GP is expected to find these structures and produce somehow similar results. In this paper we define a function for measuring the syntactic similarity of mathematical models represented as structure trees; using this similarity function we compare the results produced by GP techniques for a data set representing measurement data of a BMW Diesel engine.
Structural system identification: Structural dynamics model validation
Energy Technology Data Exchange (ETDEWEB)
Red-Horse, J.R.
1997-04-01
Structural system identification is concerned with the development of systematic procedures and tools for developing predictive analytical models based on a physical structure`s dynamic response characteristics. It is a multidisciplinary process that involves the ability (1) to define high fidelity physics-based analysis models, (2) to acquire accurate test-derived information for physical specimens using diagnostic experiments, (3) to validate the numerical simulation model by reconciling differences that inevitably exist between the analysis model and the experimental data, and (4) to quantify uncertainties in the final system models and subsequent numerical simulations. The goal of this project was to develop structural system identification techniques and software suitable for both research and production applications in code and model validation.
Directory of Open Access Journals (Sweden)
Gang Chen
2012-01-01
Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.
Landau fluid model for weakly nonlinear dispersive magnetohydrodynamics
International Nuclear Information System (INIS)
Passot, T.; Sulem, P. L.
2005-01-01
In may astrophysical plasmas such as the solar wind, the terrestrial magnetosphere, or in the interstellar medium at small enough scales, collisions are negligible. When interested in the large-scale dynamics, a hydrodynamic approach is advantageous not only because its numerical simulations is easier than of the full Vlasov-Maxwell equations, but also because it provides a deep understanding of cross-scale nonlinear couplings. It is thus of great interest to construct fluid models that extended the classical magnetohydrodynamic (MHD) equations to collisionless situations. Two ingredients need to be included in such a model to capture the main kinetic effects: finite Larmor radius (FLR) corrections and Landau damping, the only fluid-particle resonance that can affect large scales and can be modeled in a relatively simple way. The Modelization of Landau damping in a fluid formalism is hardly possible in the framework of a systematic asymptotic expansion and was addressed mainly by means of parameter fitting in a linearized setting. We introduced a similar Landau fluid model but, that has the advantage of taking dispersive effects into account. This model properly describes dispersive MHD waves in quasi-parallel propagation. Since, by construction, the system correctly reproduces their linear dynamics, appropriate tests should address the nonlinear regime. In a first case, we show analytically that the weakly nonlinear modulational dynamics of quasi-parallel propagating Alfven waves is well captured. As a second test we consider the parametric decay instability of parallel Alfven waves and show that numerical simulations of the dispersive Landau fluid model lead to results that closely match the outcome of hybrid simulations. (Author)
The inherent complexity in nonlinear business cycle model in resonance
International Nuclear Information System (INIS)
Ma Junhai; Sun Tao; Liu Lixia
2008-01-01
Based on Abraham C.-L. Chian's research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements' amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future
Testing and inference in nonlinear cointegrating vector error correction models
DEFF Research Database (Denmark)
Kristensen, D.; Rahbek, A.
2013-01-01
We analyze estimators and tests for a general class of vector error correction models that allows for asymmetric and nonlinear error correction. For a given number of cointegration relationships, general hypothesis testing is considered, where testing for linearity is of particular interest. Under...... the null of linearity, parameters of nonlinear components vanish, leading to a nonstandard testing problem. We apply so-called sup-tests to resolve this issue, which requires development of new(uniform) functional central limit theory and results for convergence of stochastic integrals. We provide a full...... asymptotic theory for estimators and test statistics. The derived asymptotic results prove to be nonstandard compared to results found elsewhere in the literature due to the impact of the estimated cointegration relations. This complicates implementation of tests motivating the introduction of bootstrap...
Application of nonlinear forecasting techniques for meteorological modeling
Directory of Open Access Journals (Sweden)
V. Pérez-Muñuzuri
2000-10-01
Full Text Available A nonlinear forecasting method was used to predict the behavior of a cloud coverage time series several hours in advance. The method is based on the reconstruction of a chaotic strange attractor using four years of cloud absorption data obtained from half-hourly Meteosat infrared images from Northwestern Spain. An exhaustive nonlinear analysis of the time series was carried out to reconstruct the phase space of the underlying chaotic attractor. The forecast values are used by a non-hydrostatic meteorological model ARPS for daily weather prediction and their results compared with surface temperature measurements from a meteorological station and a vertical sounding. The effect of noise in the time series is analyzed in terms of the prediction results.Key words: Meterology and atmospheric dynamics (mesoscale meteorology; general – General (new fields
Application of nonlinear forecasting techniques for meteorological modeling
Directory of Open Access Journals (Sweden)
V. Pérez-Muñuzuri
Full Text Available A nonlinear forecasting method was used to predict the behavior of a cloud coverage time series several hours in advance. The method is based on the reconstruction of a chaotic strange attractor using four years of cloud absorption data obtained from half-hourly Meteosat infrared images from Northwestern Spain. An exhaustive nonlinear analysis of the time series was carried out to reconstruct the phase space of the underlying chaotic attractor. The forecast values are used by a non-hydrostatic meteorological model ARPS for daily weather prediction and their results compared with surface temperature measurements from a meteorological station and a vertical sounding. The effect of noise in the time series is analyzed in terms of the prediction results.
Key words: Meterology and atmospheric dynamics (mesoscale meteorology; general – General (new fields
Level-set techniques for facies identification in reservoir modeling
Iglesias, Marco A.; McLaughlin, Dennis
2011-03-01
In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil-water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301-29 2004 Inverse Problems 20 259-82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg-Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush-Kuhn-Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies.
Level-set techniques for facies identification in reservoir modeling
International Nuclear Information System (INIS)
Iglesias, Marco A; McLaughlin, Dennis
2011-01-01
In this paper we investigate the application of level-set techniques for facies identification in reservoir models. The identification of facies is a geometrical inverse ill-posed problem that we formulate in terms of shape optimization. The goal is to find a region (a geologic facies) that minimizes the misfit between predicted and measured data from an oil–water reservoir. In order to address the shape optimization problem, we present a novel application of the level-set iterative framework developed by Burger in (2002 Interfaces Free Bound. 5 301–29; 2004 Inverse Problems 20 259–82) for inverse obstacle problems. The optimization is constrained by (the reservoir model) a nonlinear large-scale system of PDEs that describes the reservoir dynamics. We reformulate this reservoir model in a weak (integral) form whose shape derivative can be formally computed from standard results of shape calculus. At each iteration of the scheme, the current estimate of the shape derivative is utilized to define a velocity in the level-set equation. The proper selection of this velocity ensures that the new shape decreases the cost functional. We present results of facies identification where the velocity is computed with the gradient-based (GB) approach of Burger (2002) and the Levenberg–Marquardt (LM) technique of Burger (2004). While an adjoint formulation allows the straightforward application of the GB approach, the LM technique requires the computation of the large-scale Karush–Kuhn–Tucker system that arises at each iteration of the scheme. We efficiently solve this system by means of the representer method. We present some synthetic experiments to show and compare the capabilities and limitations of the proposed implementations of level-set techniques for the identification of geologic facies
Validity testing of third-order nonlinear models for synchronous generators
Energy Technology Data Exchange (ETDEWEB)
Arjona, M.A. [Division de Estudios de Posgrado e Investigacion, Instituto Tecnologico de La Laguna Torreon, Coah. (Mexico); Escarela-Perez, R. [Universidad Autonoma Metropolitana - Azcapotzalco, Departamento de Energia, Av. San Pablo 180, Col. Reynosa, C.P. 02200 (Mexico); Espinosa-Perez, G. [Division de Estudios Posgrado de la Facultad de Ingenieria Universidad Nacional Autonoma de Mexico (Mexico); Alvarez-Ramirez, J. [Universidad Autonoma Metropolitana -Iztapalapa, Division de Ciencias Basicas e Ingenieria (Mexico)
2009-06-15
Third-order nonlinear models are commonly used in control theory for the analysis of the stability of both open-loop and closed-loop synchronous machines. However, the ability of these models to describe the electrical machine dynamics has not been tested experimentally. This work focuses on this issue by addressing the parameters identification problem for third-order models for synchronous generators. For a third-order model describing the dynamics of power angle {delta}, rotor speed {omega} and quadrature axis transient EMF E{sub q}{sup '}, it is shown that the parameters cannot be identified because of the effects of the unknown initial condition of E{sub q}{sup '}. To avoid this situation, a model that incorporates the measured electrical power dynamics is considered, showing that state measurements guarantee the identification of the model parameters. Data obtained from a 7 kVA lab-scale synchronous generator and from a 150 MVA finite-element simulation were used to show that, at least for the worked examples, the estimated parameters display only moderate variations over the operating region. This suggests that third-order models can suffice to describe the main dynamical features of synchronous generators, and that third-order models can be used to design and tune power system stabilizers and voltage regulators. (author)
Nonlinear dynamical modeling and prediction of the terrestrial magnetospheric activity
International Nuclear Information System (INIS)
Vassiliadis, D.
1992-01-01
The irregular activity of the magnetosphere results from its complex internal dynamics as well as the external influence of the solar wind. The dominating self-organization of the magnetospheric plasma gives rise to repetitive, large-scale coherent behavior manifested in phenomena such as the magnetic substorm. Based on the nonlinearity of the global dynamics this dissertation examines the magnetosphere as a nonlinear dynamical system using time series analysis techniques. Initially the magnetospheric activity is modeled in terms of an autonomous system. A dimension study shows that its observed time series is self-similar, but the correlation dimension is high. The implication of a large number of degrees of freedom is confirmed by other state space techniques such as Poincare sections and search for unstable periodic orbits. At the same time a stability study of the time series in terms of Lyapunov exponents suggests that the series is not chaotic. The absence of deterministic chaos is supported by the low predictive capability of the autonomous model. Rather than chaos, it is an external input which is largely responsible for the irregularity of the magnetospheric activity. In fact, the external driving is so strong that the above state space techniques give results for magnetospheric and solar wind time series that are at least qualitatively similar. Therefore the solar wind input has to be included in a low-dimensional nonautonomous model. Indeed it is shown that such a model can reproduce the observed magnetospheric behavior up to 80-90 percent. The characteristic coefficients of the model show little variation depending on the external disturbance. The impulse response is consistent with earlier results of linear prediction filters. The model can be easily extended to contain nonlinear features of the magnetospheric activity and in particular the loading-unloading behavior of substorms
Comparison of a nonlinear dynamic model of a piping system to test data
International Nuclear Information System (INIS)
Blakely, K.D.; Howard, G.E.; Walton, W.B.; Johnson, B.A.; Chitty, D.E.
1983-01-01
Response of a nonlinear finite element model of the Heissdampfreaktor recirculation piping loop (URL) was compared to measured data, representing the physical benchmarking of a nonlinear model. Analysis-test comparisons of piping response are presented for snapback tests that induced extreme nonlinear behavior of the URL system. Nonlinearities in the system are due to twelve swaybraces (pipe supports) that possessed nonlinear force-deflection characteristics. These nonlinearities distorted system damping estimates made by using the half-power bandwidth method on Fourier transforms of measured accelerations, with the severity of distortion increasing with increasing degree of nonlinearity. Time domain methods, which are not so severely affected by the presence of nonlinearities, were used to compute system damping ratios. Nonlinear dynamic analyses were accurately and efficiently performed using the pseudo-force technique and the finite element program MSC/NASTRAN. Measured damping was incorporated into the model for snapback simulations. Acceleration time histories, acceleration Fourier transforms, and swaybrace force time histories of the nonlinear model, plus several linear models, were compared to test measurements. The nonlinear model predicted three-fourths of the measured peak accelerations to within 50%, half of the accelerations to within 25%, and one-fifth of the accelerations to within 10%. This nonlinear model predicted accelerations (in the time and frequency domains) and swaybrace forces much better than did any of the linear models, demonstrating the increased accuracy resulting from properly simulating nonlinear support behavior. In addition, earthquake response comparisons were made between the experimentally validated nonlinear model and a linear model. Significantly lower element stresses were predicted for the nonlinear model, indicating the potential usefulness of nonlinear simulations in piping design assessments. (orig.)
Nonlinear Model Predictive Control for Solid Oxide Fuel Cell System Based On Wiener Model
T. H. Lee; J. H. Park; S. M. Lee; S. C. Lee
2010-01-01
In this paper, we consider Wiener nonlinear model for solid oxide fuel cell (SOFC). The Wiener model of the SOFC consists of a linear dynamic block and a static output non-linearity followed by the block, in which linear part is approximated by state-space model and the nonlinear part is identified by a polynomial form. To control the SOFC system, we have to consider various view points such as operating conditions, another constraint conditions, change of load current and so on. A change of ...
An SIRS model with a nonlinear incidence rate
International Nuclear Information System (INIS)
Jin Yu; Wang, Wendi; Xiao Shiwu
2007-01-01
The global dynamics of an SIRS model with a nonlinear incidence rate is investigated. We establish a threshold for a disease to be extinct or endemic, analyze the existence and asymptotic stability of equilibria, and verify the existence of bistable states, i.e., a stable disease free equilibrium and a stable endemic equilibrium or a stable limit cycle. In particular, we find that the model admits stability switches as a parameter changes. We also investigate the backward bifurcation, the Hopf bifurcation and Bogdanov-Takens bifurcation and obtain the Hopf bifurcation criteria and Bogdanov-Takens bifurcation curves, which are important for making strategies for controlling a disease
Stability Analysis of Some Nonlinear Anaerobic Digestion Models
Directory of Open Access Journals (Sweden)
Ivan Simeonov
2010-04-01
Full Text Available Abstract: The paper deals with local asymptotic stability analysis of some mass balance dynamic models (based on one and on two-stage reaction schemes of the anaerobic digestion (AD in CSTR. The equilibrium states for models based on one (with Monod, Contois and Haldane shapes for the specific growth rate and on two-stage (only with Monod shapes for both the specific growth rate of acidogenic and methanogenic bacterial populations reaction schemes have been determined solving sets of nonlinear algebraic equations using Maples. Their stability has been analyzed systematically, which provides insight and guidance for AD bioreactors design, operation and control.
The Precession Index and a Nonlinear Energy Balance Climate Model
Rubincam, David
2004-01-01
A simple nonlinear energy balance climate model yields a precession index-like term in the temperature. Despite its importance in the geologic record, the precession index e sin (Omega)S, where e is the Earth's orbital eccentricity and (Omega)S is the Sun's perigee in the geocentric frame, is not present in the insolation at the top of the atmosphere. Hence there is no one-for-one mapping of 23,000 and 19,000 year periodicities from the insolation to the paleoclimate record; a nonlinear climate model is needed to produce these long periods. A nonlinear energy balance climate model with radiative terms of form T n, where T is surface temperature and n less than 1, does produce e sin (omega)S terms in temperature; the e sin (omega)S terms are called Seversmith psychroterms. Without feedback mechanisms, the model achieves extreme values of 0.64 K at the maximum orbital eccentricity of 0.06, cooling one hemisphere while simultaneously warming the other; the hemisphere over which perihelion occurs is the cooler. In other words, the nonlinear energy balance model produces long-term cooling in the northern hemisphere when the Sun's perihelion is near northern summer solstice and long-term warming in the northern hemisphere when the aphelion is near northern summer solstice. (This behavior is similar to the inertialess gray body which radiates like T 4, but the amplitude is much lower for the energy balance model because of its thermal inertia.) This seemingly paradoxical behavior works against the standard Milankovitch model, which requires cool northern summers (Sun far from Earth in northern summer) to build up northern ice sheets, so that if the standard model is correct it must be more efficient than previously thought. Alternatively, the new mechanism could possibly be dominant and indicate southern hemisphere control of the northern ice sheets, wherein the southern oceans undergo a long-term cooling when the Sun is far from the Earth during northern summer. The cold
A nonlinear model for ionic polymer metal composites as actuators
Bonomo, C.; Fortuna, L.; Giannone, P.; Graziani, S.; Strazzeri, S.
2007-02-01
This paper introduces a comprehensive nonlinear dynamic model of motion actuators based on ionic polymer metal composites (IPMCs) working in air. Significant quantities ruling the acting properties of IPMC-based actuators are taken into account. The model is organized as follows. As a first step, the dependence of the IPMC absorbed current on the voltage applied across its thickness is taken into account; a nonlinear circuit model is proposed to describe this relationship. In a second step the transduction of the absorbed current into the IPMC mechanical reaction is modelled. The model resulting from the cascade of both the electrical and the electromechanical stages represents a novel contribution in the field of IPMCs, capable of describing the electromechanical behaviour of these materials and predicting relevant quantities in a large range of applied signals. The effect of actuator scaling is also investigated, giving interesting support to the activities involved in the design of actuating devices based on these novel materials. Evidence of the excellent agreement between the estimations obtained by using the proposed model and experimental signals is given.
Estimation methods for nonlinear state-space models in ecology
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Berg, Casper Willestofte; Thygesen, Uffe Høgsbro
2011-01-01
The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta...... logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden...... Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance...
Augmented twin-nonlinear two-box behavioral models for multicarrier LTE power amplifiers.
Hammi, Oualid
2014-01-01
A novel class of behavioral models is proposed for LTE-driven Doherty power amplifiers with strong memory effects. The proposed models, labeled augmented twin-nonlinear two-box models, are built by cascading a highly nonlinear memoryless function with a mildly nonlinear memory polynomial with cross terms. Experimental validation on gallium nitride based Doherty power amplifiers illustrates the accuracy enhancement and complexity reduction achieved by the proposed models. When strong memory effects are observed, the augmented twin-nonlinear two-box models can improve the normalized mean square error by up to 3 dB for the same number of coefficients when compared to state-of-the-art twin-nonlinear two-box models. Furthermore, the augmented twin-nonlinear two-box models lead to the same performance as previously reported twin-nonlinear two-box models while requiring up to 80% less coefficients.
Model Identification of Integrated ARMA Processes
Stadnytska, Tetiana; Braun, Simone; Werner, Joachim
2008-01-01
This article evaluates the Smallest Canonical Correlation Method (SCAN) and the Extended Sample Autocorrelation Function (ESACF), automated methods for the Autoregressive Integrated Moving-Average (ARIMA) model selection commonly available in current versions of SAS for Windows, as identification tools for integrated processes. SCAN and ESACF can…
Parameter identification in the logistic STAR model
DEFF Research Database (Denmark)
Ekner, Line Elvstrøm; Nejstgaard, Emil
We propose a new and simple parametrization of the so-called speed of transition parameter of the logistic smooth transition autoregressive (LSTAR) model. The new parametrization highlights that a consequence of the well-known identification problem of the speed of transition parameter is that th...
A non-linear state space approach to model groundwater fluctuations
Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.
2006-01-01
A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual
Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties
Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon
2012-01-01
Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong
2015-08-19
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.
A penalized framework for distributed lag non-linear models.
Gasparrini, Antonio; Scheipl, Fabian; Armstrong, Ben; Kenward, Michael G
2017-09-01
Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis. © 2017 The Authors Biometrics published by Wiley Periodicals, Inc. on behalf of International Biometric Society.
Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations
International Nuclear Information System (INIS)
Kushner, Harold J.
2012-01-01
This two-part paper deals with “foundational” issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.
A non-linear model of information seeking behaviour
Directory of Open Access Journals (Sweden)
Allen E. Foster
2005-01-01
Full Text Available The results of a qualitative, naturalistic, study of information seeking behaviour are reported in this paper. The study applied the methods recommended by Lincoln and Guba for maximising credibility, transferability, dependability, and confirmability in data collection and analysis. Sampling combined purposive and snowball methods, and led to a final sample of 45 inter-disciplinary researchers from the University of Sheffield. In-depth semi-structured interviews were used to elicit detailed examples of information seeking. Coding of interview transcripts took place in multiple iterations over time and used Atlas-ti software to support the process. The results of the study are represented in a non-linear Model of Information Seeking Behaviour. The model describes three core processes (Opening, Orientation, and Consolidation and three levels of contextual interaction (Internal Context, External Context, and Cognitive Approach, each composed of several individual activities and attributes. The interactivity and shifts described by the model show information seeking to be non-linear, dynamic, holistic, and flowing. The paper concludes by describing the whole model of behaviours as analogous to an artist's palette, in which activities remain available throughout information seeking. A summary of key implications of the model and directions for further research are included.
Nonlinear spectral mixing theory to model multispectral signatures
Energy Technology Data Exchange (ETDEWEB)
Borel, C.C. [Los Alamos National Lab., NM (United States). Astrophysics and Radiation Measurements Group
1996-02-01
Nonlinear spectral mixing occurs due to multiple reflections and transmissions between discrete surfaces, e.g. leaves or facets of a rough surface. The radiosity method is an energy conserving computational method used in thermal engineering and it models nonlinear spectral mixing realistically and accurately. In contrast to the radiative transfer method the radiosity method takes into account the discreteness of the scattering surfaces (e.g. exact location, orientation and shape) such as leaves and includes mutual shading between them. An analytic radiosity-based scattering model for vegetation was developed and used to compute vegetation indices for various configurations. The leaf reflectance and transmittance was modeled using the PROSPECT model for various amounts of water, chlorophyll and variable leaf structure. The soil background was modeled using SOILSPEC with a linear mixture of reflectances of sand, clay and peat. A neural network and a geometry based retrieval scheme were used to retrieve leaf area index and chlorophyll concentration for dense canopies. Only simulated canopy reflectances in the 6 visible through short wave IR Landsat TM channels were used. The authors used an empirical function to compute the signal-to-noise ratio of a retrieved quantity.
Nonlinear ECRH and ECCD modeling in toroidal devices
International Nuclear Information System (INIS)
Kamendje, R.; Kernbichler, W.; Heyn, M.F.; Kasilov, S.V.; Poli, E.
2003-01-01
A Monte Carlo method of evaluation of the electron distribution function which takes into account realistic orbits of electrons during their nonlinear cyclotron interaction with the wave beam has been proposed. The focus there was on a proper description of particle interaction with a wave beam while the geometry of the main magnetic field outside the beam was the simplest possible (slab model). In the actual work, a more realistic tokamak geometry has been implemented in the model. In addition, an expression for the parallel current density through Green's function has been used. This allows to reduce statistical errors which result from the fact that the current generated by particles with positive v parallel >0 is almost compensated by the current resulting from particles with v parallel <0 if the complete distribution function is taken into account in the expression for the current. The code ECNL which is a Monte Carlo kinetic equation solver based on this model, has been coupled with the beam tracing code TORBEAM. The results of nonlinear modeling of ECCD in a tokamak with ASDEX Upgrade parameters with help of this combination of codes are compared below to the results of linear modeling performed with TORBEAM alone. In addition, implications for stellarators are discussed. (orig.)
Directory of Open Access Journals (Sweden)
Bizhong Xia
2017-12-01
Full Text Available State of charge (SOC estimation is the core of any battery management system. Most closed-loop SOC estimation algorithms are based on the equivalent circuit model with fixed parameters. However, the parameters of the equivalent circuit model will change as temperature or SOC changes, resulting in reduced SOC estimation accuracy. In this paper, two SOC estimation algorithms with online parameter identification are proposed to solve this problem based on forgetting factor recursive least squares (FFRLS and nonlinear Kalman filter. The parameters of a Thevenin model are constantly updated by FFRLS. The nonlinear Kalman filter is used to perform the recursive operation to estimate SOC. Experiments in variable temperature environments verify the effectiveness of the proposed algorithms. A combination of four driving cycles is loaded on lithium-ion batteries to test the adaptability of the approaches to different working conditions. Under certain conditions, the average error of the SOC estimation dropped from 5.6% to 1.1% after adding the online parameters identification, showing that the estimation accuracy of proposed algorithms is greatly improved. Besides, simulated measurement noise is added to the test data to prove the robustness of the algorithms.
Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation
Semper, Sean R.; Crassidis, John L.; George, Jemin; Mukherjee, Siddharth; Singla, Puneet
2015-01-01
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating
Neutron stars in non-linear coupling models
International Nuclear Information System (INIS)
Taurines, Andre R.; Vasconcellos, Cesar A.Z.; Malheiro, Manuel; Chiapparini, Marcelo
2001-01-01
We present a class of relativistic models for nuclear matter and neutron stars which exhibits a parameterization, through mathematical constants, of the non-linear meson-baryon couplings. For appropriate choices of the parameters, it recovers current QHD models found in the literature: Walecka, ZM and ZM3 models. We have found that the ZM3 model predicts a very small maximum neutron star mass, ∼ 0.72M s un. A strong similarity between the results of ZM-like models and those with exponential couplings is noted. Finally, we discuss the very intense scalar condensates found in the interior of neutron stars which may lead to negative effective masses. (author)
Neutron stars in non-linear coupling models
Energy Technology Data Exchange (ETDEWEB)
Taurines, Andre R.; Vasconcellos, Cesar A.Z. [Rio Grande do Sul Univ., Porto Alegre, RS (Brazil); Malheiro, Manuel [Universidade Federal Fluminense, Niteroi, RJ (Brazil); Chiapparini, Marcelo [Universidade do Estado, Rio de Janeiro, RJ (Brazil)
2001-07-01
We present a class of relativistic models for nuclear matter and neutron stars which exhibits a parameterization, through mathematical constants, of the non-linear meson-baryon couplings. For appropriate choices of the parameters, it recovers current QHD models found in the literature: Walecka, ZM and ZM3 models. We have found that the ZM3 model predicts a very small maximum neutron star mass, {approx} 0.72M{sub s}un. A strong similarity between the results of ZM-like models and those with exponential couplings is noted. Finally, we discuss the very intense scalar condensates found in the interior of neutron stars which may lead to negative effective masses. (author)
Abhinav, S.; Manohar, C. S.
2018-03-01
The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blackwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam-moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion.
A nonlinear model of gold production in Malaysia
Ramli, Norashikin; Muda, Nora; Umor, Mohd Rozi
2014-06-01
Malaysia is a country which is rich in natural resources and one of it is a gold. Gold has already become an important national commodity. This study is conducted to determine a model that can be well fitted with the gold production in Malaysia from the year 1995-2010. Five nonlinear models are presented in this study which are Logistic model, Gompertz, Richard, Weibull and Chapman-Richard model. These model are used to fit the cumulative gold production in Malaysia. The best model is then selected based on the model performance. The performance of the fitted model is measured by sum squares error, root mean squares error, coefficient of determination, mean relative error, mean absolute error and mean absolute percentage error. This study has found that a Weibull model is shown to have significantly outperform compare to the other models. To confirm that Weibull is the best model, the latest data are fitted to the model. Once again, Weibull model gives the lowest readings at all types of measurement error. We can concluded that the future gold production in Malaysia can be predicted according to the Weibull model and this could be important findings for Malaysia to plan their economic activities.
Inverse mathematical modelling and identification in metal powder compaction process
International Nuclear Information System (INIS)
Gakwaya, A.; Hrairi, M.; Guillot, M.
2000-01-01
An online assessment of the quality of advanced integrated computer aided manufacturing systems require the knowledge of accurate and reliable non-linear constitutive material behavior. This paper is concerned with material parameter identification based on experimental data for which non uniform distribution of stresses and deformation within the volume of the specimen is considered. Both geometric and material non linearities as well interfacial frictional contact are taken into account during the simulation. Within the framework of finite deformation theory, a multisurface multiplicative plasticity model for metal powder compaction process is presented. The model is seen to involve several parameters which are not always activated by a single state variable even though it may be technologically important in assessing the final product quality and manufacturing performance. The resulting expressions are presented in spatial setting and gradient based descent method utilizing the modified Levenberg-Marquardt scheme is used for the minimization of least square functional so as to obtain the best agreement between relevant experimental data and simulated data in a specified energy norm. The identification of a subset of material parameters of the cap model for stainless steel powder compaction is performed. The obtained parameters are validated through a simulation of an industrial part manufacturing case. A very good agreement between simulated final density and measured density is obtained thus demonstrating the practical usefulness of the proposed approach. (author)
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
The Inverse Problem of Identification of Hydrogen Permeability Model
Directory of Open Access Journals (Sweden)
Yury V. Zaika
2018-01-01
Full Text Available One of the technological challenges for hydrogen materials science is the currently active search for structural materials with important applications (including the ITER project and gas-separation plants. One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones. The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR and the surface limited regime (SLR.
Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model
Energy Technology Data Exchange (ETDEWEB)
Litvinenko, Yuri E. [Department of Mathematics, University of Waikato, P. B. 3105, Hamilton 3240 (New Zealand); Fichtner, Horst; Walter, Dominik [Institut für Theoretische Physik IV, Ruhr-Universität Bochum, Universitätsstrasse 150, D-44780 Bochum (Germany)
2017-05-20
We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatment of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.
Models of the delayed nonlinear Raman response in diatomic gases
International Nuclear Information System (INIS)
Palastro, J. P.; Antonsen, T. M. Jr.; Pearson, A.
2011-01-01
We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as O 2 and N 2 , and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas' orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.
Identification of nonlinear dynamics in power plant components using neural networks
International Nuclear Information System (INIS)
Parlos, A.G.; Fernandez, B.; Tsai, W.K.
1990-01-01
Advances in digital computer technology have enabled widespread implementation of closed-loop digital control systems in a variety of industries. In some instances, however, the complexity of the plant and the uncertainty associated with the parameters involved in the mathematical modeling narrow the range of applicability of most systematic control system design methodologies. A multiyear project has been initiated to assess the feasibility of the artificial neural networks (ANNs) technology for computerized enhanced diagnostics and control of nuclear power plant components. At this stage of the project, a new methodology, based on backpropagation learning, has been developed for identifying the nonlinear dynamic systems from a set of input-output data known as the training set
Nonlinear spherical perturbations in quintessence models of dark energy
Pratap Rajvanshi, Manvendra; Bagla, J. S.
2018-06-01
Observations have confirmed the accelerated expansion of the universe. The accelerated expansion can be modelled by invoking a cosmological constant or a dynamical model of dark energy. A key difference between these models is that the equation of state parameter w for dark energy differs from ‑1 in dynamical dark energy (DDE) models. Further, the equation of state parameter is not constant for a general DDE model. Such differences can be probed using the variation of scale factor with time by measuring distances. Another significant difference between the cosmological constant and DDE models is that the latter must cluster. Linear perturbation analysis indicates that perturbations in quintessence models of dark energy do not grow to have a significant amplitude at small length scales. In this paper we study the response of quintessence dark energy to non-linear perturbations in dark matter. We use a fully relativistic model for spherically symmetric perturbations. In this study we focus on thawing models. We find that in response to non-linear perturbations in dark matter, dark energy perturbations grow at a faster rate than expected in linear perturbation theory. We find that dark energy perturbation remains localised and does not diffuse out to larger scales. The dominant drivers of the evolution of dark energy perturbations are the local Hubble flow and a supression of gradients of the scalar field. We also find that the equation of state parameter w changes in response to perturbations in dark matter such that it also becomes a function of position. The variation of w in space is correlated with density contrast for matter. Variation of w and perturbations in dark energy are more pronounced in response to large scale perturbations in matter while the dependence on the amplitude of matter perturbations is much weaker.
Integrated identification, modeling and control with applications
Shi, Guojun
This thesis deals with the integration of system design, identification, modeling and control. In particular, six interdisciplinary engineering problems are addressed and investigated. Theoretical results are established and applied to structural vibration reduction and engine control problems. First, the data-based LQG control problem is formulated and solved. It is shown that a state space model is not necessary to solve this problem; rather a finite sequence from the impulse response is the only model data required to synthesize an optimal controller. The new theory avoids unnecessary reliance on a model, required in the conventional design procedure. The infinite horizon model predictive control problem is addressed for multivariable systems. The basic properties of the receding horizon implementation strategy is investigated and the complete framework for solving the problem is established. The new theory allows the accommodation of hard input constraints and time delays. The developed control algorithms guarantee the closed loop stability. A closed loop identification and infinite horizon model predictive control design procedure is established for engine speed regulation. The developed algorithms are tested on the Cummins Engine Simulator and desired results are obtained. A finite signal-to-noise ratio model is considered for noise signals. An information quality index is introduced which measures the essential information precision required for stabilization. The problems of minimum variance control and covariance control are formulated and investigated. Convergent algorithms are developed for solving the problems of interest. The problem of the integrated passive and active control design is addressed in order to improve the overall system performance. A design algorithm is developed, which simultaneously finds: (i) the optimal values of the stiffness and damping ratios for the structure, and (ii) an optimal output variance constrained stabilizing
Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models
Institute of Scientific and Technical Information of China (English)
Jochen Aβfalg; Frank Allg(o)wer
2007-01-01
This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.
Nonlinear flight dynamics and stability of hovering model insects
Liang, Bin; Sun, Mao
2013-01-01
Current analyses on insect dynamic flight stability are based on linear theory and limited to small disturbance motions. However, insects' aerial environment is filled with swirling eddies and wind gusts, and large disturbances are common. Here, we numerically solve the equations of motion coupled with the Navier–Stokes equations to simulate the large disturbance motions and analyse the nonlinear flight dynamics of hovering model insects. We consider two representative model insects, a model hawkmoth (large size, low wingbeat frequency) and a model dronefly (small size, high wingbeat frequency). For small and large initial disturbances, the disturbance motion grows with time, and the insects tumble and never return to the equilibrium state; the hovering flight is inherently (passively) unstable. The instability is caused by a pitch moment produced by forward/backward motion and/or a roll moment produced by side motion of the insect. PMID:23697714
Dynamics in a nonlinear Keynesian good market model
International Nuclear Information System (INIS)
Naimzada, Ahmad; Pireddu, Marina
2014-01-01
In this paper, we show how a rich variety of dynamical behaviors can emerge in the standard Keynesian income-expenditure model when a nonlinearity is introduced, both in the cases with and without endogenous government spending. A specific sigmoidal functional form is used for the adjustment mechanism of income with respect to the excess demand, in order to bound the income variation. With the aid of analytical and numerical tools, we investigate the stability conditions, bifurcations, as well as periodic and chaotic dynamics. Globally, we study multistability phenomena, i.e., the coexistence of different kinds of attractors
A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning
DEFF Research Database (Denmark)
Fraccaro, Marco; Kamronn, Simon Due; Paquet, Ulrich
2017-01-01
This paper takes a step towards temporal reasoning in a dynamically changing video, not in the pixel space that constitutes its frames, but in a latent space that describes the non-linear dynamics of the objects in its world. We introduce the Kalman variational auto-encoder, a framework...... for unsupervised learning of sequential data that disentangles two latent representations: an object’s representation, coming from a recognition model, and a latent state describing its dynamics. As a result, the evolution of the world can be imagined and missing data imputed, both without the need to generate...
Visualization of nonlinear kernel models in neuroimaging by sensitivity maps
DEFF Research Database (Denmark)
Rasmussen, Peter Mondrup; Hansen, Lars Kai; Madsen, Kristoffer Hougaard
There is significant current interest in decoding mental states from neuroimages. In this context kernel methods, e.g., support vector machines (SVM) are frequently adopted to learn statistical relations between patterns of brain activation and experimental conditions. In this paper we focus...... on visualization of such nonlinear kernel models. Specifically, we investigate the sensitivity map as a technique for generation of global summary maps of kernel classification methods. We illustrate the performance of the sensitivity map on functional magnetic resonance (fMRI) data based on visual stimuli. We...
Nonlinear model of epidemic spreading in a complex social network.
Kosiński, Robert A; Grabowski, A
2007-10-01
The epidemic spreading in a human society is a complex process, which can be described on the basis of a nonlinear mathematical model. In such an approach the complex and hierarchical structure of social network (which has implications for the spreading of pathogens and can be treated as a complex network), can be taken into account. In our model each individual has one of the four permitted states: susceptible, infected, infective, unsusceptible or dead. This refers to the SEIR model used in epidemiology. The state of an individual changes in time, depending on the previous state and the interactions with other individuals. The description of the interpersonal contacts is based on the experimental observations of the social relations in the community. It includes spatial localization of the individuals and hierarchical structure of interpersonal interactions. Numerical simulations were performed for different types of epidemics, giving the progress of a spreading process and typical relationships (e.g. range of epidemic in time, the epidemic curve). The spreading process has a complex and spatially chaotic character. The time dependence of the number of infective individuals shows the nonlinear character of the spreading process. We investigate the influence of the preventive vaccinations on the spreading process. In particular, for a critical value of preventively vaccinated individuals the percolation threshold is observed and the epidemic is suppressed.
On concurvity in nonlinear and nonparametric regression models
Directory of Open Access Journals (Sweden)
Sonia Amodio
2014-12-01
Full Text Available When data are affected by multicollinearity in the linear regression framework, then concurvity will be present in fitting a generalized additive model (GAM. The term concurvity describes nonlinear dependencies among the predictor variables. As collinearity results in inflated variance of the estimated regression coefficients in the linear regression model, the result of the presence of concurvity leads to instability of the estimated coefficients in GAMs. Even if the backfitting algorithm will always converge to a solution, in case of concurvity the final solution of the backfitting procedure in fitting a GAM is influenced by the starting functions. While exact concurvity is highly unlikely, approximate concurvity, the analogue of multicollinearity, is of practical concern as it can lead to upwardly biased estimates of the parameters and to underestimation of their standard errors, increasing the risk of committing type I error. We compare the existing approaches to detect concurvity, pointing out their advantages and drawbacks, using simulated and real data sets. As a result, this paper will provide a general criterion to detect concurvity in nonlinear and non parametric regression models.
Empirical intrinsic geometry for nonlinear modeling and time series filtering.
Talmon, Ronen; Coifman, Ronald R
2013-07-30
In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.
International Nuclear Information System (INIS)
Abe, H.; Okuda, H.
1994-06-01
We study linear and nonlinear properties of a new computer simulation model developed to study the propagation of electromagnetic waves in a dielectric medium in the linear and nonlinear regimes. The model is constructed by combining a microscopic model used in the semi-classical approximation for the dielectric media and the particle model developed for the plasma simulations. It is shown that the model may be useful for studying linear and nonlinear wave propagation in the dielectric media
Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.
2018-05-01
Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.
Modelling non-linear effects of dark energy
Bose, Benjamin; Baldi, Marco; Pourtsidou, Alkistis
2018-04-01
We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving w models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter ξ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter σv. To quantify the importance of modelling the interaction, we create mock data sets for varying values of ξ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a ξ=0 modelling, ignoring the interaction. We find the fiducial growth parameter f is generally recovered even for very large values of ξ both at z=0.5 and z=1. The ξ=0 modelling is most biased in its estimation of f for the phantom w=‑1.1 case.
Directory of Open Access Journals (Sweden)
Xingjian Wang
2016-01-01
Full Text Available Attainment of high-performance motion/velocity control objectives for the Direct-Drive Rotary (DDR torque motor should fully consider practical nonlinearities in controller design, such as dynamic friction. The LuGre model has been widely utilized to describe nonlinear friction behavior; however, parameter identification for the LuGre model remains a challenge. A new dynamic friction parameter identification method for LuGre model is proposed in this study. Static parameters are identified through a series of constant velocity experiments, while dynamic parameters are obtained through a presliding process. Novel evolutionary algorithm (NEA is utilized to increase identification accuracy. Experimental results gathered from the identification experiments conducted in the study for a practical DDR torque motor control system validate the effectiveness of the proposed method.
Nonlinear realizations and effective Lagrangian densities for nonlinear σ-models
International Nuclear Information System (INIS)
Hamilton-Charlton, Jason Dominic
2003-01-01
Nonlinear realizations of the groups SU(N), SO(m) and SO(t,s) are analysed, described by the coset spaces SU(N) / SU(N-1) x U(1), SO(m) / SO(m-1), SO(1,m-1) / SO(1,m-2) and SO(m) / SO(m-2 x SO(2). The analysis consists of determining the transformation properties of the Goldstone Bosons, constructing the most general possible Lagrangian for the realizations, and as a result identifying the coset space metric. We view the λ matrices of SU(N) as being the basis of an (N 2 - 1) dimensional real vector space, and from this we learn how to construct the basis of a Cartan Subspace associated with a vector. This results in a mathematical structure which allows us to find expressions for coset representative elements used in the analysis. This structure is not only relevant to SU(N) breaking models, but may also be used to find results in SO(m) and SO(1,m - 1) breaking models. (author)
A NONLINEAR MATHEMATICAL MODEL FOR ASTHMA: EFFECT OF ENVIRONMENTAL POLLUTION
Directory of Open Access Journals (Sweden)
NARESHA RAM
2009-04-01
Full Text Available In this paper, we explore a nonlinear mathematical model to study the spread of asthma due to inhaled pollutants from industry as well as tobacco smoke from smokers in a variable size population. The model is analyzed using stability theory of differential equations and computer simulation. It is shown that with an increase in the level of air pollutants concentration, the asthmatic (diseased population increases. It is also shown that along with pollutants present in the environment, smoking (active or passive also helps in the spread of asthma. Moreover, with the increase in the rate of interaction between susceptibles and smokers, the persistence of the spread of asthma is higher. A numerical study of the model is also performed to see the role of certain key parameters on the spread of asthma and to support the analytical results.
Fluid mechanics and heat transfer advances in nonlinear dynamics modeling
Asli, Kaveh Hariri
2015-01-01
This valuable new book focuses on new methods and techniques in fluid mechanics and heat transfer in mechanical engineering. The book includes the research of the authors on the development of optimal mathematical models and also uses modern computer technology and mathematical methods for the analysis of nonlinear dynamic processes. It covers technologies applicable to both fluid mechanics and heat transfer problems, which include a combination of physical, mechanical, and thermal techniques. The authors develop a new method for the calculation of mathematical models by computer technology, using parametric modeling techniques and multiple analyses for mechanical system. The information in this book is intended to help reduce the risk of system damage or failure. Included are sidebar discussions, which contain information and facts about each subject area that help to emphasize important points to remember.
Lectures on nonlinear sigma-models in projective superspace
International Nuclear Information System (INIS)
Kuzenko, Sergei M
2010-01-01
N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkaehler and quaternionic Kaehler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkaehler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kaehler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N= 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkaehler and quaternionic Kaehler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach. (topical review)
Lectures on nonlinear sigma-models in projective superspace
Energy Technology Data Exchange (ETDEWEB)
Kuzenko, Sergei M, E-mail: kuzenko@cyllene.uwa.edu.a [School of Physics M013, University of Western Australia, 35 Stirling Highway, Crawley WA 6009 (Australia)
2010-11-05
N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkaehler and quaternionic Kaehler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkaehler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kaehler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N= 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkaehler and quaternionic Kaehler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach. (topical review)
Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects
Directory of Open Access Journals (Sweden)
Yi Hu
2014-01-01
Full Text Available This paper suggests a generalized method of moments (GMM based estimation for dynamic panel data models with individual specific fixed effects and threshold effects simultaneously. We extend Hansen’s (Hansen, 1999 original setup to models including endogenous regressors, specifically, lagged dependent variables. To address the problem of endogeneity of these nonlinear dynamic panel data models, we prove that the orthogonality conditions proposed by Arellano and Bond (1991 are valid. The threshold and slope parameters are estimated by GMM, and asymptotic distribution of the slope parameters is derived. Finite sample performance of the estimation is investigated through Monte Carlo simulations. It shows that the threshold and slope parameter can be estimated accurately and also the finite sample distribution of slope parameters is well approximated by the asymptotic distribution.
Magnetically nonlinear dynamic model of synchronous motor with permanent magnets
International Nuclear Information System (INIS)
Hadziselimovic, Miralem; Stumberger, Gorazd; Stumberger, Bojan; Zagradisnik, Ivan
2007-01-01
This paper deals with a magnetically nonlinear two-axis dynamic model of a permanent magnet synchronous motor (PMSM). The geometrical and material properties of iron core and permanent magnets, the effects of winding distribution, saturation, cross-saturation and slotting effects are, for the first time, simultaneously accounted for in a single two-axis dynamic model of a three-phase PMSM. They are accounted for by current- and position-dependent characteristics of flux linkages. These characteristics can be determined either experimentally or by the finite element (FE) computations. The results obtained by the proposed dynamic model show a very good agreement with the measured ones and those obtained by the FE computation
Energy Technology Data Exchange (ETDEWEB)
Zhou, Ping; Song, Heda; Wang, Hong; Chai, Tianyou
2017-09-01
Blast furnace (BF) in ironmaking is a nonlinear dynamic process with complicated physical-chemical reactions, where multi-phase and multi-field coupling and large time delay occur during its operation. In BF operation, the molten iron temperature (MIT) as well as Si, P and S contents of molten iron are the most essential molten iron quality (MIQ) indices, whose measurement, modeling and control have always been important issues in metallurgic engineering and automation field. This paper develops a novel data-driven nonlinear state space modeling for the prediction and control of multivariate MIQ indices by integrating hybrid modeling and control techniques. First, to improve modeling efficiency, a data-driven hybrid method combining canonical correlation analysis and correlation analysis is proposed to identify the most influential controllable variables as the modeling inputs from multitudinous factors would affect the MIQ indices. Then, a Hammerstein model for the prediction of MIQ indices is established using the LS-SVM based nonlinear subspace identification method. Such a model is further simplified by using piecewise cubic Hermite interpolating polynomial method to fit the complex nonlinear kernel function. Compared to the original Hammerstein model, this simplified model can not only significantly reduce the computational complexity, but also has almost the same reliability and accuracy for a stable prediction of MIQ indices. Last, in order to verify the practicability of the developed model, it is applied in designing a genetic algorithm based nonlinear predictive controller for multivariate MIQ indices by directly taking the established model as a predictor. Industrial experiments show the advantages and effectiveness of the proposed approach.
Hyperbolicity of the Nonlinear Models of Maxwell's Equations
Serre, Denis
. We consider the class of nonlinear models of electromagnetism that has been described by Coleman & Dill [7]. A model is completely determined by its energy density W(B,D). Viewing the electromagnetic field (B,D) as a 3×2 matrix, we show that polyconvexity of W implies the local well-posedness of the Cauchy problem within smooth functions of class Hs with s>1+d/2. The method follows that designed by Dafermos in his book [9] in the context of nonlinear elasticity. We use the fact that B×D is a (vectorial, non-convex) entropy, and we enlarge the system from 6 to 9 equations. The resulting system admits an entropy (actually the energy) that is convex. Since the energy conservation law does not derive from the system of conservation laws itself (Faraday's and Ampère's laws), but also needs the compatibility relations divB=divD=0 (the latter may be relaxed in order to take into account electric charges), the energy density is not an entropy in the classical sense. Thus the system cannot be symmetrized, strictly speaking. However, we show that the structure is close enough to symmetrizability, so that the standard estimates still hold true.
Hazard identification based on plant functional modelling
International Nuclear Information System (INIS)
Rasmussen, B.; Whetton, C.
1993-10-01
A major objective of the present work is to provide means for representing a process plant as a socio-technical system, so as to allow hazard identification at a high level. The method includes technical, human and organisational aspects and is intended to be used for plant level hazard identification so as to identify critical areas and the need for further analysis using existing methods. The first part of the method is the preparation of a plant functional model where a set of plant functions link together hardware, software, operations, work organisation and other safety related aspects of the plant. The basic principle of the functional modelling is that any aspect of the plant can be represented by an object (in the sense that this term is used in computer science) based upon an Intent (or goal); associated with each Intent are Methods, by which the Intent is realized, and Constraints, which limit the Intent. The Methods and Constraints can themselves be treated as objects and decomposed into lower-level Intents (hence the procedure is known as functional decomposition) so giving rise to a hierarchical, object-oriented structure. The plant level hazard identification is carried out on the plant functional model using the Concept Hazard Analysis method. In this, the user will be supported by checklists and keywords and the analysis is structured by pre-defined worksheets. The preparation of the plant functional model and the performance of the hazard identification can be carried out manually or with computer support. (au) (4 tabs., 10 ills., 7 refs.)
Quasilinear Extreme Learning Machine Model Based Internal Model Control for Nonlinear Process
Directory of Open Access Journals (Sweden)
Dazi Li
2015-01-01
Full Text Available A new strategy for internal model control (IMC is proposed using a regression algorithm of quasilinear model with extreme learning machine (QL-ELM. Aimed at the chemical process with nonlinearity, the learning process of the internal model and inverse model is derived. The proposed QL-ELM is constructed as a linear ARX model with a complicated nonlinear coefficient. It shows some good approximation ability and fast convergence. The complicated coefficients are separated into two parts. The linear part is determined by recursive least square (RLS, while the nonlinear part is identified through extreme learning machine. The parameters of linear part and the output weights of ELM are estimated iteratively. The proposed internal model control is applied to CSTR process. The effectiveness and accuracy of the proposed method are extensively verified through numerical results.
Non-perturbative aspects of nonlinear sigma models
Energy Technology Data Exchange (ETDEWEB)
Flore, Raphael
2012-12-07
The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3){approx_equal}CP{sup 1} model. By the generalization of the topological
Non-perturbative aspects of nonlinear sigma models
International Nuclear Information System (INIS)
Flore, Raphael
2012-01-01
The aim of this thesis was the study and further development of non-perturbative methods of quantum field theory by means of their application to nonlinear sigma models. While a large part of the physical phenomena of quantum field theory can be successfully predicted by the perturbation theory, some aspects in the region of large coupling strengths are not definitively understood and require suited non-perturbative methods for its analysis. This thesis is concentrated on two approaches, the numerical treatment of field theories on discrete space-time lattices and the functional renormalization group (FRG) as description of the renormalization flux of effective actions. Considerations of the nonlinear O(N) models have shown that for the correct analysis of the critical properties in the framework of the FRG an approach must be chosen, which contained fourth-derivation orders. For this a covariant formalism was developed, which is based on a background-field expansion and the development of a heat kernel. Apart from a destabilizing coupling the results suggest a nontrivial fixed point and by this a non-perturbative renormalizability of these models. The resulting flow diagrams were finally still compared with the results of a numerical analysis of the renormalization flow by means of the Monte-Carlo renormalization group, and hereby qualitative agreement was found. Furthermore an alternative formulation of the FRG in phase-space coordinates was studied and their consistency tested on simple examples. Beyond this an alternative expansion of the effective action in orders of the canonical momenta was applied to the nonlinear O(N) models with the result of a stable non-trivial fixed point, the critical properties of which however show not the expected N-dependence. By means of the FRG finally still the renormalization of topological operators was studied by means of the winding number of the O(3)≅CP 1 model. By the generalization of the topological operator and the
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao
2018-04-01
We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.
Nonlinear Fuzzy Model Predictive Control for a PWR Nuclear Power Plant
Directory of Open Access Journals (Sweden)
Xiangjie Liu
2014-01-01
Full Text Available Reliable power and temperature control in pressurized water reactor (PWR nuclear power plant is necessary to guarantee high efficiency and plant safety. Since the nuclear plants are quite nonlinear, the paper presents nonlinear fuzzy model predictive control (MPC, by incorporating the realistic constraints, to realize the plant optimization. T-S fuzzy modeling on nuclear power plant is utilized to approximate the nonlinear plant, based on which the nonlinear MPC controller is devised via parallel distributed compensation (PDC scheme in order to solve the nonlinear constraint optimization problem. Improved performance compared to the traditional PID controller for a TMI-type PWR is obtained in the simulation.
Locally supersymmetric D=3 non-linear sigma models
International Nuclear Information System (INIS)
Wit, B. de; Tollsten, A.K.; Nicolai, H.
1993-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is riemannian or Kaehler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it generally decomposes, into two separate quaternionic spaces, associated with inequivalent supermultiplets. For N=5, 6, 8 there is a unique (symmetric) space for any given number of supermultiplets. Beyond that there are only theories based on a single supermultiplet for N=9, 10, 12 and 16, associated with coset spaces with the exceptional isometry groups F 4(-20) , E 6(-14) , E 7(-5) and E 8(+8) , respectively. For N=3 and N ≥ 5 the D=2 theories obtained by dimensional reduction are two-loop finite. (orig.)
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
International Nuclear Information System (INIS)
Guerra, Fabio A.; Coelho, Leandro dos S.
2008-01-01
An important problem in engineering is the identification of nonlinear systems, among them radial basis function neural networks (RBF-NN) using Gaussian activation functions models, which have received particular attention due to their potential to approximate nonlinear behavior. Several design methods have been proposed for choosing the centers and spread of Gaussian functions and training the RBF-NN. The selection of RBF-NN parameters such as centers, spreads, and weights can be understood as a system identification problem. This paper presents a hybrid training approach based on clustering methods (k-means and c-means) to tune the centers of Gaussian functions used in the hidden layer of RBF-NNs. This design also uses particle swarm optimization (PSO) for centers (local clustering search method) and spread tuning, and the Penrose-Moore pseudoinverse for the adjustment of RBF-NN weight outputs. Simulations involving this RBF-NN design to identify Lorenz's chaotic system indicate that the performance of the proposed method is superior to that of the conventional RBF-NN trained for k-means and the Penrose-Moore pseudoinverse for multi-step ahead forecasting
Experimental identification and mathematical modeling of viscoplastic material behavior
Haupt, P.; Lion, A.
1995-03-01
Uniaxial torsion and biaxial torsion-tension experiments on thin-walled tubes were carried out to investigate the viscoplastic behavior of stainless steel XCrNi18.9. A series of monotonic tests under strain and stress control shows nonlinear rate dependence and suggests the existence of equilibrium states, which are asymptotically approached during relaxation and creep processes. Strain controlled cyclic experiments display various hardening and softening phenomena that depend on strain amplitude and mean strain. All experiments indicate that the equilibrium states within the material depend on the history of the input process, whereas the history-dependence of the relaxation and creep behavior appears less significant. From the experiments the design of a constitutive model of viscoplasticity is motivated: The basic assumption is a decomposition of the total stress into an equilibrium stress and a non-equilibrium overstress: At constant strain, the overstress relaxes to zero, where the relaxation time depends on the overstress in order to account for the nonlinear rate-dependence. The equilibrium stress is assumed to be a rate independent functional of the total strain history. Classical plasticity is utilized with a kinematic hardening rule of the Armstrong-Frederick type. In order to incorporate the amplitude-dependent hardening and softening behavior, a generalized arc length representation is applied [14]. The introduction of an additional kinematic hardening variable facilitates consideration of additional hardening effects resulting from the non-radiality of the input process. Apart from the common yield and loading criterion of classical plasticity, the proposed constitutive model does not contain any further distinction of different cases. The experimental data are sufficient to identify the material parameters of the constitutive model. The results of the identification procedure demonstrate the ability of the model to represent the observed phenomena
A Non-linear Stochastic Model for an Office Building with Air Infiltration
DEFF Research Database (Denmark)
Thavlov, Anders; Madsen, Henrik
2015-01-01
This paper presents a non-linear heat dynamic model for a multi-room office building with air infiltration. Several linear and non-linear models, with and without air infiltration, are investigated and compared. The models are formulated using stochastic differential equations and the model...
Nonlinear Modeling of Forced Magnetic Reconnection with Transient Perturbations
Beidler, Matthew T.; Callen, James D.; Hegna, Chris C.; Sovinec, Carl R.
2017-10-01
Externally applied 3D magnetic fields in tokamaks can penetrate into the plasma and lead to forced magnetic reconnection, and hence magnetic islands, on resonant surfaces. Analytic theory has been reasonably successful in describing many aspects of this paradigm with regard to describing the time asymptotic-steady state. However, understanding the nonlinear evolution into a low-slip, field-penetrated state, especially how MHD events such as sawteeth and ELMs precipitate this transition, is in its early development. We present nonlinear computations employing the extended-MHD code NIMROD, building on previous work by incorporating a temporally varying external perturbation as a simple model for an MHD event that produces resonant magnetic signals. A parametric series of proof-of-principle computations and accompanying analytical theory characterize the transition into a mode-locked state with an emphasis on detailing the temporal evolution properties. Supported by DOE OFES Grants DE-FG02-92ER54139, DE-FG02-86ER53218, and the U.S. DOE FES Postdoctoral Research program administered by ORISE and managed by ORAU under DOE contract DE-SC0014664.
Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.
2015-10-01
An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit
Robust nonlinear control of nuclear reactors under model uncertainty
International Nuclear Information System (INIS)
Park, Moon Ghu
1993-02-01
A nonlinear model-based control method is developed for the robust control of a nuclear reactor. The nonlinear plant model is used to design a unique control law which covers a wide operating range. The robustness is a crucial factor for the fully automatic control of reactor power due to time-varying, uncertain parameters, and state estimation error, or unmodeled dynamics. A variable structure control (VSC) method is introduced which consists of an adaptive performance specification (fime control) after the tracking error reaches the narrow boundary-layer by a time-optimal control (coarse control). Variable structure control is a powerful method for nonlinear system controller design which has inherent robustness to parameter variations or external disturbances using the known uncertainty bounds, and it requires very low computational efforts. In spite of its desirable properties, conventional VSC presents several important drawbacks that limit its practical applicability. One of the most undesirable phenomena is chattering, which implies extremely high control activity and may excite high-frequency unmodeled dynamics. This problem is due to the neglected actuator time-delay or sampling effects. The problem was partially remedied by replacing chattering control by a smooth control inter-polation in a boundary layer neighnboring a time-varying sliding surface. But, for the nuclear reactor systems which has very fast dynamic response, the sampling effect may destroy the narrow boundary layer when a large uncertainty bound is used. Due to the very short neutron life time, large uncertainty bound leads to the high gain in feedback control. To resolve this problem, a derivative feedback is introduced that gives excellent performance by reducing the uncertainty bound. The stability of tracking error dynamics is guaranteed by the second method of Lyapunov using the two-level uncertainty bounds that are obtained from the knowledge of uncertainty bound and the estimated
Nonlinear Model-Based Predictive Control applied to Large Scale Cryogenic Facilities
Blanco Vinuela, Enrique; de Prada Moraga, Cesar
2001-01-01
The thesis addresses the study, analysis, development, and finally the real implementation of an advanced control system for the 1.8 K Cooling Loop of the LHC (Large Hadron Collider) accelerator. The LHC is the next accelerator being built at CERN (European Center for Nuclear Research), it will use superconducting magnets operating below a temperature of 1.9 K along a circumference of 27 kilometers. The temperature of these magnets is a control parameter with strict operating constraints. The first control implementations applied a procedure that included linear identification, modelling and regulation using a linear predictive controller. It did improve largely the overall performance of the plant with respect to a classical PID regulator, but the nature of the cryogenic processes pointed out the need of a more adequate technique, such as a nonlinear methodology. This thesis is a first step to develop a global regulation strategy for the overall control of the LHC cells when they will operate simultaneously....
Background field method for nonlinear σ-model in stochastic quantization
International Nuclear Information System (INIS)
Nakazawa, Naohito; Ennyu, Daiji
1988-01-01
We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model. (orig.)
Preisach hysteresis model for non-linear 2D heat diffusion
International Nuclear Information System (INIS)
Jancskar, Ildiko; Ivanyi, Amalia
2006-01-01
This paper analyzes a non-linear heat diffusion process when the thermal diffusivity behaviour is a hysteretic function of the temperature. Modelling this temperature dependence, the discrete Preisach algorithm as general hysteresis model has been integrated into a non-linear multigrid solver. The hysteretic diffusion shows a heating-cooling asymmetry in character. The presented type of hysteresis speeds up the thermal processes in the modelled systems by a very interesting non-linear way
Qualitative analysis of nonlinear incidence rate upon the behaviour of an epidemiological model
International Nuclear Information System (INIS)
Li Xiaogui.
1988-12-01
Two theorems concerning the solutions of the system of differential equations describing an epidemiological model with nonlinear incidence rate per infective individual are demonstrated. 2 refs, 1 fig
DEFF Research Database (Denmark)
Fournier, David A.; Skaug, Hans J.; Ancheta, Johnoel
2011-01-01
Many criteria for statistical parameter estimation, such as maximum likelihood, are formulated as a nonlinear optimization problem.Automatic Differentiation Model Builder (ADMB) is a programming framework based on automatic differentiation, aimed at highly nonlinear models with a large number...... of such a feature is the generic implementation of Laplace approximation of high-dimensional integrals for use in latent variable models. We also review the literature in which ADMB has been used, and discuss future development of ADMB as an open source project. Overall, the main advantages ofADMB are flexibility...
The Mathematics of Psychotherapy: A Nonlinear Model of Change Dynamics.
Schiepek, Gunter; Aas, Benjamin; Viol, Kathrin
2016-07-01
Psychotherapy is a dynamic process produced by a complex system of interacting variables. Even though there are qualitative models of such systems the link between structure and function, between network and network dynamics is still missing. The aim of this study is to realize these links. The proposed model is composed of five state variables (P: problem severity, S: success and therapeutic progress, M: motivation to change, E: emotions, I: insight and new perspectives) interconnected by 16 functions. The shape of each function is modified by four parameters (a: capability to form a trustful working alliance, c: mentalization and emotion regulation, r: behavioral resources and skills, m: self-efficacy and reward expectation). Psychologically, the parameters play the role of competencies or traits, which translate into the concept of control parameters in synergetics. The qualitative model was transferred into five coupled, deterministic, nonlinear difference equations generating the dynamics of each variable as a function of other variables. The mathematical model is able to reproduce important features of psychotherapy processes. Examples of parameter-dependent bifurcation diagrams are given. Beyond the illustrated similarities between simulated and empirical dynamics, the model has to be further developed, systematically tested by simulated experiments, and compared to empirical data.
Predicting Madura cattle growth curve using non-linear model
Widyas, N.; Prastowo, S.; Widi, T. S. M.; Baliarti, E.
2018-03-01
Madura cattle is Indonesian native. It is a composite breed that has undergone hundreds of years of selection and domestication to reach nowadays remarkable uniformity. Crossbreeding has reached the isle of Madura and the Madrasin, a cross between Madura cows and Limousine semen emerged. This paper aimed to compare the growth curve between Madrasin and one type of pure Madura cows, the common Madura cattle (Madura) using non-linear models. Madura cattles are kept traditionally thus reliable records are hardly available. Data were collected from small holder farmers in Madura. Cows from different age classes (5years) were observed, and body measurements (chest girth, body length and wither height) were taken. In total 63 Madura and 120 Madrasin records obtained. Linear model was built with cattle sub-populations and age as explanatory variables. Body weights were estimated based on the chest girth. Growth curves were built using logistic regression. Results showed that within the same age, Madrasin has significantly larger body compared to Madura (plogistic models fit better for Madura and Madrasin cattle data; with the estimated MSE for these models were 39.09 and 759.28 with prediction accuracy of 99 and 92% for Madura and Madrasin, respectively. Prediction of growth curve using logistic regression model performed well in both types of Madura cattle. However, attempts to administer accurate data on Madura cattle are necessary to better characterize and study these cattle.
Analytical model for nonlinear piezoelectric energy harvesting devices
International Nuclear Information System (INIS)
Neiss, S; Goldschmidtboeing, F; M Kroener; Woias, P
2014-01-01
In this work we propose analytical expressions for the jump-up and jump-down point of a nonlinear piezoelectric energy harvester. In addition, analytical expressions for the maximum power output at optimal resistive load and the 3 dB-bandwidth are derived. So far, only numerical models have been used to describe the physics of a piezoelectric energy harvester. However, this approach is not suitable to quickly evaluate different geometrical designs or piezoelectric materials in the harvester design process. In addition, the analytical expressions could be used to predict the jump-frequencies of a harvester during operation. In combination with a tuning mechanism, this would allow the design of an efficient control algorithm to ensure that the harvester is always working on the oscillator's high energy attractor. (paper)
Onset of the nonlinear regime in unified dark matter models
International Nuclear Information System (INIS)
Avelino, P.P.; Beca, L.M.G.; Carvalho, J.P.M. de; Martins, C.J.A.P.; Copeland, E.J.
2004-01-01
We discuss the onset of the nonlinear regime in the context of unified dark matter models involving a generalized Chaplygin gas. We show that the transition from dark-matter-like to dark-energy-like behavior will never be smooth. In some regions of space the transition will never take place while in others it may happen sooner or later than naively expected. As a result the linear theory used in previous studies may break down late in the matter dominated era even on large cosmological scales. We study the importance of this effect showing that its magnitude depends on the exact form of the equation of state in the low density regime. We expect that our results will be relevant for other unified dark matter scenarios, particularly those where the quartessence candidate is a perfect fluid
Nonlinear model predictive control for chemical looping process
Joshi, Abhinaya; Lei, Hao; Lou, Xinsheng
2017-08-22
A control system for optimizing a chemical looping ("CL") plant includes a reduced order mathematical model ("ROM") that is designed by eliminating mathematical terms that have minimal effect on the outcome. A non-linear optimizer provides various inputs to the ROM and monitors the outputs to determine the optimum inputs that are then provided to the CL plant. An estimator estimates the values of various internal state variables of the CL plant. The system has one structure adapted to control a CL plant that only provides pressure measurements in the CL loops A and B, a second structure adapted to a CL plant that provides pressure measurements and solid levels in both loops A, and B, and a third structure adapted to control a CL plant that provides full information on internal state variables. A final structure provides a neural network NMPC controller to control operation of loops A and B.
Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model
Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr
2017-10-01
Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations
Non-Linear Slosh Damping Model Development and Validation
Yang, H. Q.; West, Jeff
2015-01-01
Propellant tank slosh dynamics are typically represented by a mechanical model of spring mass damper. This mechanical model is then included in the equation of motion of the entire vehicle for Guidance, Navigation and Control (GN&C) analysis. For a partially-filled smooth wall propellant tank, the critical damping based on classical empirical correlation is as low as 0.05%. Due to this low value of damping, propellant slosh is potential sources of disturbance critical to the stability of launch and space vehicles. It is postulated that the commonly quoted slosh damping is valid only under the linear regime where the slosh amplitude is small. With the increase of slosh amplitude, the critical damping value should also increase. If this nonlinearity can be verified and validated, the slosh stability margin can be significantly improved, and the level of conservatism maintained in the GN&C analysis can be lessened. The purpose of this study is to explore and to quantify the dependence of slosh damping with slosh amplitude. Accurately predicting the extremely low damping value of a smooth wall tank is very challenging for any Computational Fluid Dynamics (CFD) tool. One must resolve thin boundary layers near the wall and limit numerical damping to minimum. This computational study demonstrates that with proper grid resolution, CFD can indeed accurately predict the low damping physics from smooth walls under the linear regime. Comparisons of extracted damping values with experimental data for different tank sizes show very good agreements. Numerical simulations confirm that slosh damping is indeed a function of slosh amplitude. When slosh amplitude is low, the damping ratio is essentially constant, which is consistent with the empirical correlation. Once the amplitude reaches a critical value, the damping ratio becomes a linearly increasing function of the slosh amplitude. A follow-on experiment validated the developed nonlinear damping relationship. This discovery can
Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.
Directory of Open Access Journals (Sweden)
Olga Kononova
2016-01-01
Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.
Core seismic behaviour: linear and non-linear models
International Nuclear Information System (INIS)
Bernard, M.; Van Dorsselaere, M.; Gauvain, M.; Jenapierre-Gantenbein, M.
1981-08-01
The usual methodology for the core seismic behaviour analysis leads to a double complementary approach: to define a core model to be included in the reactor-block seismic response analysis, simple enough but representative of basic movements (diagrid or slab), to define a finer core model, with basic data issued from the first model. This paper presents the history of the different models of both kinds. The inert mass model (IMM) yielded a first rough diagrid movement. The direct linear model (DLM), without shocks and with sodium as an added mass, let to two different ones: DLM 1 with independent movements of the fuel and radial blanket subassemblies, and DLM 2 with a core combined movement. The non-linear (NLM) ''CORALIE'' uses the same basic modelization (Finite Element Beams) but accounts for shocks. It studies the response of a diameter on flats and takes into account the fluid coupling and the wrapper tube flexibility at the pad level. Damping consists of one modal part of 2% and one part due to shocks. Finally, ''CORALIE'' yields the time-history of the displacements and efforts on the supports, but damping (probably greater than 2%) and fluid-structures interaction are still to be precised. The validation experiments were performed on a RAPSODIE core mock-up on scale 1, in similitude of 1/3 as to SPX 1. The equivalent linear model (ELM) was developed for the SPX 1 reactor-block response analysis and a specified seismic level (SB or SM). It is composed of several oscillators fixed to the diagrid and yields the same maximum displacements and efforts than the NLM. The SPX 1 core seismic analysis with a diagrid input spectrum which corresponds to a 0,1 g group acceleration, has been carried out with these models: some aspects of these calculations are presented here
McNeish, Daniel; Dumas, Denis
2017-01-01
Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study-Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.
Bergboer, N.H.; Verdult, V.; Verhaegen, M.H.G.
2002-01-01
We present a numerically efficient implementation of the nonlinear least squares and maximum likelihood identification of multivariable linear time-invariant (LTI) state-space models. This implementation is based on a local parameterization of the system and a gradient search in the resulting
Modelling female fertility traits in beef cattle using linear and non-linear models.
Naya, H; Peñagaricano, F; Urioste, J I
2017-06-01
Female fertility traits are key components of the profitability of beef cattle production. However, these traits are difficult and expensive to measure, particularly under extensive pastoral conditions, and consequently, fertility records are in general scarce and somehow incomplete. Moreover, fertility traits are usually dominated by the effects of herd-year environment, and it is generally assumed that relatively small margins are kept for genetic improvement. New ways of modelling genetic variation in these traits are needed. Inspired in the methodological developments made by Prof. Daniel Gianola and co-workers, we assayed linear (Gaussian), Poisson, probit (threshold), censored Poisson and censored Gaussian models to three different kinds of endpoints, namely calving success (CS), number of days from first calving (CD) and number of failed oestrus (FE). For models involving FE and CS, non-linear models overperformed their linear counterparts. For models derived from CD, linear versions displayed better adjustment than the non-linear counterparts. Non-linear models showed consistently higher estimates of heritability and repeatability in all cases (h 2 linear models; h 2 > 0.23 and r > 0.24, for non-linear models). While additive and permanent environment effects showed highly favourable correlations between all models (>0.789), consistency in selecting the 10% best sires showed important differences, mainly amongst the considered endpoints (FE, CS and CD). In consequence, endpoints should be considered as modelling different underlying genetic effects, with linear models more appropriate to describe CD and non-linear models better for FE and CS. © 2017 Blackwell Verlag GmbH.
A simple non-linear model of immune response
International Nuclear Information System (INIS)
Gutnikov, Sergei; Melnikov, Yuri
2003-01-01
It is still unknown why the adaptive immune response in the natural immune system based on clonal proliferation of lymphocytes requires interaction of at least two different cell types with the same antigen. We present a simple mathematical model illustrating that the system with separate types of cells for antigen recognition and patogen destruction provides more robust adaptive immunity than the system where just one cell type is responsible for both recognition and destruction. The model is over-simplified as we did not have an intention of describing the natural immune system. However, our model provides a tool for testing the proposed approach through qualitative analysis of the immune system dynamics in order to construct more sophisticated models of the immune systems that exist in the living nature. It also opens a possibility to explore specific features of highly non-linear dynamics in nature-inspired computational paradigms like artificial immune systems and immunocomputing . We expect this paper to be of interest not only for mathematicians but also for biologists; therefore we made effort to explain mathematics in sufficient detail for readers without professional mathematical background
FDTD modeling of anisotropic nonlinear optical phenomena in silicon waveguides.
Dissanayake, Chethiya M; Premaratne, Malin; Rukhlenko, Ivan D; Agrawal, Govind P
2010-09-27
A deep insight into the inherent anisotropic optical properties of silicon is required to improve the performance of silicon-waveguide-based photonic devices. It may also lead to novel device concepts and substantially extend the capabilities of silicon photonics in the future. In this paper, for the first time to the best of our knowledge, we present a three-dimensional finite-difference time-domain (FDTD) method for modeling optical phenomena in silicon waveguides, which takes into account fully the anisotropy of the third-order electronic and Raman susceptibilities. We show that, under certain realistic conditions that prevent generation of the longitudinal optical field inside the waveguide, this model is considerably simplified and can be represented by a computationally efficient algorithm, suitable for numerical analysis of complex polarization effects. To demonstrate the versatility of our model, we study polarization dependence for several nonlinear effects, including self-phase modulation, cross-phase modulation, and stimulated Raman scattering. Our FDTD model provides a basis for a full-blown numerical simulator that is restricted neither by the single-mode assumption nor by the slowly varying envelope approximation.
Lukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models
Baianu, I C
2004-01-01
A categorical and Lukasiewicz-Topos framework for Lukasiewicz Algebraic Logic models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes is proposed. Lukasiewicz Algebraic Logic models of genetic networks and signaling pathways in cells are formulated in terms of nonlinear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable 'next-state functions' is extended to a Lukasiewicz Topos with an n-valued Lukasiewicz Algebraic Logic subobject classifier description that represents non-random and nonlinear network activities as well as their transformations in developmental processes and carcinogenesis.
Modeling and Analysis of a Nonlinear Age-Structured Model for Tumor Cell Populations with Quiescence
Liu, Zijian; Chen, Jing; Pang, Jianhua; Bi, Ping; Ruan, Shigui
2018-05-01
We present a nonlinear first-order hyperbolic partial differential equation model to describe age-structured tumor cell populations with proliferating and quiescent phases at the avascular stage in vitro. The division rate of the proliferating cells is assumed to be nonlinear due to the limitation of the nutrient and space. The model includes a proportion of newborn cells that enter directly the quiescent phase with age zero. This proportion can reflect the effect of treatment by drugs such as erlotinib. The existence and uniqueness of solutions are established. The local and global stabilities of the trivial steady state are investigated. The existence and local stability of the positive steady state are also analyzed. Numerical simulations are performed to verify the results and to examine the impacts of parameters on the nonlinear dynamics of the model.
Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS
Bolker, Benjamin M.; Gardner, Beth; Maunder, Mark; Berg, Casper W.; Brooks, Mollie; Comita, Liza; Crone, Elizabeth; Cubaynes, Sarah; Davies, Trevor; de Valpine, Perry; Ford, Jessica; Gimenez, Olivier; Kéry, Marc; Kim, Eun Jung; Lennert-Cody, Cleridy; Magunsson, Arni; Martell, Steve; Nash, John; Nielson, Anders; Regentz, Jim; Skaug, Hans; Zipkin, Elise
2013-01-01
1. Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. 2. R is convenient and (relatively) easy to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. 3. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield) to specific suggestions about how to change the mathematical description of models to make them more amenable to parameter estimation. 4. A companion web site (https://groups.nceas.ucsb.edu/nonlinear-modeling/projects) presents detailed examples of application of the three tools to a variety of typical ecological estimation problems; each example links both to a detailed project report and to full source code and data.
Directory of Open Access Journals (Sweden)
YanBin Liu
2017-01-01
Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.
Campbell, Stefan F.; Kaneshige, John T.
2010-01-01
Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).
Sphalerons of O(3) nonlinear sigma model on a circle
International Nuclear Information System (INIS)
Funakubo, Koichi; Otsuki, Shoichiro; Toyoda, Fumihiko.
1989-09-01
A series of saddle point solutions of O(3) nonlinear sigma model with symmetry breaking term in 1 + 1 dimensions are obtained by imposing boundary condition either periodic or partially antiperiodic (O(3) sphalerons on a circle). Under the periodic boundary condition, classical features of the O(3) sphalerons are similar to scalar sphalerons of φ 4 model on a circle by Manton and Samols. Under the partially antiperiodic boundary condition, the lowest of the O(3) sphalerons coincides in the limit of infinite spatial domain with the O(3) sphaleron by Mottola and Wipf. In particular, zero and negative modes of them are examined in detail. An estimate of transition rate over the lowest O(3) sphaleron at finite temperature is made, and some remarks on simulating the transition on a lattice are given. One to one correspondence between these O(3) sphalerons on a circle and a series of (possible) classical solutions of SU(2) gauge-Higgs model, to which the electroweak sphaleron S and new sphaleron S* belong, is discussed. (author)
Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials
Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)
1996-01-01
There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.
Cnoidal waves as solutions of the nonlinear liquid drop model
International Nuclear Information System (INIS)
Ludu, Andrei; Sandulescu, Aureliu; Greiner Walter
1997-01-01
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equation and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equations (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by ratio of the square amplitudes in the two minima. (authors)
International Nuclear Information System (INIS)
Jacobs, William R; Dodd, Tony J; Anderson, Sean R; Wilson, Emma D; Porrill, John; Assaf, Tareq; Rossiter, Jonathan
2015-01-01
Current models of dielectric elastomer actuators (DEAs) are mostly constrained to first principal descriptions that are not well suited to the application of control design due to their computational complexity. In this work we describe an integrated framework for the identification of control focused, data driven and time-varying DEA models that allow advanced analysis of nonlinear system dynamics in the frequency-domain. Experimentally generated input–output data (voltage-displacement) was used to identify control-focused, nonlinear and time-varying dynamic models of a set of film-type DEAs. The model description used was the nonlinear autoregressive with exogenous input structure. Frequency response analysis of the DEA dynamics was performed using generalized frequency response functions, providing insight and a comparison into the time-varying dynamics across a set of DEA actuators. The results demonstrated that models identified within the presented framework provide a compact and accurate description of the system dynamics. The frequency response analysis revealed variation in the time-varying dynamic behaviour of DEAs fabricated to the same specifications. These results suggest that the modelling and analysis framework presented here is a potentially useful tool for future work in guiding DEA actuator design and fabrication for application domains such as soft robotics. (paper)
Nonlinear sigma models with compact hyperbolic target spaces
International Nuclear Information System (INIS)
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-01-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Nonlinear sigma models with compact hyperbolic target spaces
Energy Technology Data Exchange (ETDEWEB)
Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Robust and fast nonlinear optimization of diffusion MRI microstructure models.
Harms, R L; Fritz, F J; Tobisch, A; Goebel, R; Roebroeck, A
2017-07-15
Advances in biophysical multi-compartment modeling for diffusion MRI (dMRI) have gained popularity because of greater specificity than DTI in relating the dMRI signal to underlying cellular microstructure. A large range of these diffusion microstructure models have been developed and each of the popular models comes with its own, often different, optimization algorithm, noise model and initialization strategy to estimate its parameter maps. Since data fit, accuracy and precision is hard to verify, this creates additional challenges to comparability and generalization of results from diffusion microstructure models. In addition, non-linear optimization is computationally expensive leading to very long run times, which can be prohibitive in large group or population studies. In this technical note we investigate the performance of several optimization algorithms and initialization strategies over a few of the most popular diffusion microstructure models, including NODDI and CHARMED. We evaluate whether a single well performing optimization approach exists that could be applied to many models and would equate both run time and fit aspects. All models, algorithms and strategies were implemented on the Graphics Processing Unit (GPU) to remove run time constraints, with which we achieve whole brain dataset fits in seconds to minutes. We then evaluated fit, accuracy, precision and run time for different models of differing complexity against three common optimization algorithms and three parameter initialization strategies. Variability of the achieved quality of fit in actual data was evaluated on ten subjects of each of two population studies with a different acquisition protocol. We find that optimization algorithms and multi-step optimization approaches have a considerable influence on performance and stability over subjects and over acquisition protocols. The gradient-free Powell conjugate-direction algorithm was found to outperform other common algorithms in terms of
A Model Predictive Algorithm for Active Control of Nonlinear Noise Processes
Directory of Open Access Journals (Sweden)
Qi-Zhi Zhang
2005-01-01
Full Text Available In this paper, an improved nonlinear Active Noise Control (ANC system is achieved by introducing an appropriate secondary source. For ANC system to be successfully implemented, the nonlinearity of the primary path and time delay of the secondary path must be overcome. A nonlinear Model Predictive Control (MPC strategy is introduced to deal with the time delay in the secondary path and the nonlinearity in the primary path of the ANC system. An overall online modeling technique is utilized for online secondary path and primary path estimation. The secondary path is estimated using an adaptive FIR filter, and the primary path is estimated using a Neural Network (NN. The two models are connected in parallel with the two paths. In this system, the mutual disturbances between the operation of the nonlinear ANC controller and modeling of the secondary can be greatly reduced. The coefficients of the adaptive FIR filter and weight vector of NN are adjusted online. Computer simulations are carried out to compare the proposed nonlinear MPC method with the nonlinear Filter-x Least Mean Square (FXLMS algorithm. The results showed that the convergence speed of the proposed nonlinear MPC algorithm is faster than that of nonlinear FXLMS algorithm. For testing the robust performance of the proposed nonlinear ANC system, the sudden changes in the secondary path and primary path of the ANC system are considered. Results indicated that the proposed nonlinear ANC system can rapidly track the sudden changes in the acoustic paths of the nonlinear ANC system, and ensure the adaptive algorithm stable when the nonlinear ANC system is time variable.
Nonlinear time-domain modeling of balanced-armature receivers
DEFF Research Database (Denmark)
Jensen, Joe; Agerkvist, Finn T.; Harte, James
2011-01-01
Nonlinear distortion added by the loudspeaker in a hearing aid lowers the signal-to-noise ratio and may degrade the hearing aid user's ability to understand speech. The balancedarmature- type loudspeakers, predominantly used in hearing aids, are inherently nonlinear devices, as any displacement...
Sinusoidal velaroidal shell – numerical modelling of the nonlinear ...
African Journals Online (AJOL)
The nonlinearity, applied to a sinusoidal velaroidal shell with the inner radius r0, the outer variables radii from 10m to 20m and the number of waves n=8, will give rise to the investigation of its nonlinear buckling resistance. The building material is a high-performant concrete. The investigation emphasizes more on the ...
Neurobiologically Inspired Approaches to Nonlinear Process Control and Modeling
1999-12-31
incorporates second messenger reaction kinetics and calcium dynamics to represent the nonlinear dynamics and the crucial role of neuromodulation in local...reflex). The dynamic neuromodulation as a mechanism for the nonlinear attenuation is the novel result of this study. Ear- lier simulations have shown
Curvature-induced symmetry breaking in nonlinear Schrodinger models
DEFF Research Database (Denmark)
Gaididei, Yuri Borisovich; Mingaleev, S. F.; Christiansen, Peter Leth
2000-01-01
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. We show that the energy of localized states...
Non-linear scaling of a musculoskeletal model of the lower limb using statistical shape models.
Nolte, Daniel; Tsang, Chui Kit; Zhang, Kai Yu; Ding, Ziyun; Kedgley, Angela E; Bull, Anthony M J
2016-10-03
Accurate muscle geometry for musculoskeletal models is important to enable accurate subject-specific simulations. Commonly, linear scaling is used to obtain individualised muscle geometry. More advanced methods include non-linear scaling using segmented bone surfaces and manual or semi-automatic digitisation of muscle paths from medical images. In this study, a new scaling method combining non-linear scaling with reconstructions of bone surfaces using statistical shape modelling is presented. Statistical Shape Models (SSMs) of femur and tibia/fibula were used to reconstruct bone surfaces of nine subjects. Reference models were created by morphing manually digitised muscle paths to mean shapes of the SSMs using non-linear transformations and inter-subject variability was calculated. Subject-specific models of muscle attachment and via points were created from three reference models. The accuracy was evaluated by calculating the differences between the scaled and manually digitised models. The points defining the muscle paths showed large inter-subject variability at the thigh and shank - up to 26mm; this was found to limit the accuracy of all studied scaling methods. Errors for the subject-specific muscle point reconstructions of the thigh could be decreased by 9% to 20% by using the non-linear scaling compared to a typical linear scaling method. We conclude that the proposed non-linear scaling method is more accurate than linear scaling methods. Thus, when combined with the ability to reconstruct bone surfaces from incomplete or scattered geometry data using statistical shape models our proposed method is an alternative to linear scaling methods. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.
Identification of Civil Engineering Structures using Vector ARMA Models
DEFF Research Database (Denmark)
Andersen, P.
The dissertation treats the matter of systems identification and modelling of load-bearing constructions using Auto-Regressive Moving Average Vector (ARMAV) models.......The dissertation treats the matter of systems identification and modelling of load-bearing constructions using Auto-Regressive Moving Average Vector (ARMAV) models....
Application of homotopy-perturbation method to nonlinear population dynamics models
International Nuclear Information System (INIS)
Chowdhury, M.S.H.; Hashim, I.; Abdulaziz, O.
2007-01-01
In this Letter, the homotopy-perturbation method (HPM) is employed to derive approximate series solutions of nonlinear population dynamics models. The nonlinear models considered are the multispecies Lotka-Volterra equations. The accuracy of this method is examined by comparison with the available exact and the fourth-order Runge-Kutta method (RK4)
CROSS DIFFUSION AND NONLINEAR DIFFUSION PREVENTING BLOW UP IN THE KELLER–SEGEL MODEL
CARRILLO, JOSÉ ANTONIO; HITTMEIR, SABINE; JÜ NGEL, ANSGAR
2012-01-01
A parabolic-parabolic (Patlak-)Keller-Segel model in up to three space dimensions with nonlinear cell diffusion and an additional nonlinear cross-diffusion term is analyzed. The main feature of this model is that there exists a new entropy
DEFF Research Database (Denmark)
Péguin-Feissolle, Anne; Strikholm, Birgit; Teräsvirta, Timo
In this paper we propose a general method for testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form. These tests are based on a Taylor expansion of the nonlinear model around a given point in the sample space. We study the performance of our tests b...
Butcher, Mark; Masi, Alessandro
2016-01-01
The identification problem of the linear dynamic part of piezo based actuators is addressed in this paper, exploiting the use of binary signals, specifically the pseudo random binary sequences (PRBS). Due to the presence of nonlocal memory hysteretic behavior in piezoelectric active materials, the dependence of the identification results on this strongly nonlinear effect is analyzed and useful guidelines for the design of the PRBS stimulating signal are derived. Moreover, some properties of hysteresis like cancellation and congruency are experimentally analyzed and their effects on the identification process are discussed. Finally, the use of a hysteresis compensation strategy in the identification process is evaluated and discussed.
Energy Technology Data Exchange (ETDEWEB)
Butcher, Mark; Giustiniani, Alessandro, E-mail: alessandro.giustiniani@cern.ch; Masi, Alessandro
2016-04-01
The identification problem of the linear dynamic part of piezo based actuators is addressed in this paper, exploiting the use of binary signals, specifically the pseudo random binary sequences (PRBS). Due to the presence of nonlocal memory hysteretic behavior in piezoelectric active materials, the dependence of the identification results on this strongly nonlinear effect is analyzed and useful guidelines for the design of the PRBS stimulating signal are derived. Moreover, some properties of hysteresis like cancellation and congruency are experimentally analyzed and their effects on the identification process are discussed. Finally, the use of a hysteresis compensation strategy in the identification process is evaluated and discussed.
Cutoff effects in O(N) nonlinear sigma models
International Nuclear Information System (INIS)
Knechtli, Francesco; Leder, Bjoern; Wolff, Ulli
2005-01-01
In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been found before with standard discretizations and lattice spacings. Here the situation is analyzed further employing additional data for the step scaling function of the finite volume mass gap at N=3,4,8 and a large N-study of the leading as well as next-to-leading terms in 1/N. The latter exact results are demonstrated to follow Symanzik's form of the asymptotic cutoff dependence. At the same time, when fuzzed with artificial statistical errors and then fitted like the Monte Carlo results, a picture similar to N=3 emerges. We hence cannot conclude a truly anomalous cutoff dependence but only relatively large cutoff effects, where the logarithmic component is important. Their size shrinks at larger N, but the structure remains similar. The large N results are particularly interesting as we here have exact nonperturbative control over an asymptotically free model both in the continuum limit and on the lattice
Cutoff effects in O(N) nonlinear sigma models
International Nuclear Information System (INIS)
Knechtli, F.; Wolff, U.; Leder, B.
2005-06-01
In the nonlinear O(N) sigma model at N=3 unexpected cutoff effects have been found before with standard discretizations and lattice spacings. Here the situation is analyzed further employing additional data for the step scaling function of the finite volume mass gap at N=3,4,8 and a large N-study of the leading as well as next-to-leading terms in 1/N. The latter exact results are demonstrated to follow Symanzik's form of the asymptotic cutoff dependence. At the same time, when fuzzed with artificial statistical errors and then fitted like the Monte Carlo results, a picture similar to N=3 emerges. We hence cannot conclude a truly anomalous cutoff dependence but only relatively large cutoff effects, where the logarithmic component is important. Their size shrinks at larger N, but the structure remains similar. The large N results are particularly interesting as we here have exact nonperturbative control over an asymptotically free model both in the continuum limit and on the lattice. (orig.)
DEFF Research Database (Denmark)
Tornøe, Christoffer Wenzel; Agersø, Henrik; Madsen, Henrik
2004-01-01
The standard software for non-linear mixed-effect analysis of pharmacokinetic/phar-macodynamic (PK/PD) data is NONMEM while the non-linear mixed-effects package NLME is an alternative as tong as the models are fairly simple. We present the nlmeODE package which combines the ordinary differential...... equation (ODE) solver package odesolve and the non-Linear mixed effects package NLME thereby enabling the analysis of complicated systems of ODEs by non-linear mixed-effects modelling. The pharmacokinetics of the anti-asthmatic drug theophylline is used to illustrate the applicability of the nlme...
Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.
Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre
2017-10-01
We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.
A model of nonlinear strain and damage accumulation in polymer composites
Directory of Open Access Journals (Sweden)
A. N. Ruslantsev
2014-01-01
Full Text Available This paper presents a model to predict a nonlinear strain of the carbon laminate; the model is based on the relations between the theory of laminated plates and the non-linear approximation of deformation curve of unidirectional layer at the shear in the layer plane. The explicit expressions of stiffness and compliance matrices were obtained via multiplying the matrices that correspond to the elastic characteristics by the matrices, considering the non-linear properties of the laminate. The paper suggests an approximation option for the non-linear properties of the layer at the shear using an exponential function. Some considerations on damage accumulation in carbon laminates were made.
Directory of Open Access Journals (Sweden)
Nur Alam
2016-02-01
Full Text Available In this research article, we present exact solutions with parameters for two nonlinear model partial differential equations(PDEs describing microtubules, by implementing the exp(−Φ(ξ-Expansion Method. The considered models, describing highly nonlinear dynamics of microtubules, can be reduced to nonlinear ordinary differential equations. While the first PDE describes the longitudinal model of nonlinear dynamics of microtubules, the second one describes the nonlinear model of dynamics of radial dislocations in microtubules. The acquired solutions are then graphically presented, and their distinct properties are enumerated in respect to the corresponding dynamic behavior of the microtubules they model. Various patterns, including but not limited to regular, singular kink-like, as well as periodicity exhibiting ones, are detected. Being the method of choice herein, the exp(−Φ(ξ-Expansion Method not disappointing in the least, is found and declared highly efficient.
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Directory of Open Access Journals (Sweden)
Zhenhua Hu
2013-01-01
Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.
Practical Modeling and Comprehensive System Identification of a BLDC Motor
Directory of Open Access Journals (Sweden)
Changle Xiang
2015-01-01
Full Text Available The aim of this paper is to outline all the steps in a rigorous and simple procedure for system identification of BLDC motor. A practical mathematical model for identification is derived. Frequency domain identification techniques and time domain estimation method are combined to obtain the unknown parameters. The methods in time domain are founded on the least squares approximation method and a disturbance observer. Only the availability of experimental data for rotor speed and armature current are required for identification. The proposed identification method is systematically investigated, and the final identified model is validated by experimental results performed on a typical BLDC motor in UAV.
Robust input design for nonlinear dynamic modeling of AUV.
Nouri, Nowrouz Mohammad; Valadi, Mehrdad
2017-09-01
Input design has a dominant role in developing the dynamic model of autonomous underwater vehicles (AUVs) through system identification. Optimal input design is the process of generating informative inputs that can be used to generate the good quality dynamic model of AUVs. In a problem with optimal input design, the desired input signal depends on the unknown system which is intended to be identified. In this paper, the input design approach which is robust to uncertainties in model parameters is used. The Bayesian robust design strategy is applied to design input signals for dynamic modeling of AUVs. The employed approach can design multiple inputs and apply constraints on an AUV system's inputs and outputs. Particle swarm optimization (PSO) is employed to solve the constraint robust optimization problem. The presented algorithm is used for designing the input signals for an AUV, and the estimate obtained by robust input design is compared with that of the optimal input design. According to the results, proposed input design can satisfy both robustness of constraints and optimality. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids
International Nuclear Information System (INIS)
Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li
2009-01-01
A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))
Directory of Open Access Journals (Sweden)
Luis García Domínguez
2006-03-01
Full Text Available ABSTRACTKernel nonparametric nonlinear autoregression was applied to measles data from the pre-vaccination era (1944-1966. A slowly sliding time window covered 20 overlapping segments of the series. In the case of data from Birmingham the order of the model was higher than 22 for all windows and the reconstructed noise free realizations were periodic with the most probable period being equal to 3 years, though values of 2, 4 and 6 years were also obtained.For London data 6 windows were with low orders (below 5. Low order noise free realizations were chaotic. The rest presented periodic solutions corresponding to 1, 2, and 3-years cycles. Our results are consistent with views about dynamical transitions among measles data. The method is reliable and puts practically no restrictions regarding data properties. We recommend its use for further exploration of epidemic data from different origin. RESUMENPROPIEDADES NO LINEALES DE DATOS EPIDEMIOLÓGICOS DE SARAMPIÓN EVALUADAS MEDIANTE UN ENFOQUE DE IDENTIFICACIÓN NO LINEAL POR NÚCLEOS.Se aplicó un método de auto-regresión no lineal por núcleos a datos de incidencia de sarampión correspondientes a la época previa a la vacunación (1944-1966. Una ventana de tiempo que se desplazaba lentamente cubrió 20 segmentos de serie temporal que se solapaban. En el caso de los datos correspondientes a Birmingham el orden del modelo era mayor de 22 para todas las ventanas y las realizaciones libres de ruido reconstruidas eran periódicas con la duración del periodo más probable igual a 3 años, aunque también se obtuvieron valores de 2, 4 y 6 años.Para los datos de Londres, se observaron 6 ventanas con órdenes inferiores a 5. Las realizaciones libres de ruido con órdenes bajos eran caóticas. El resto de las ventanas mostraron ciclos de 1, 2 y tres años. Nuestros resultados son concordantes con la idea de la presencia de transiciones de fase en series de sarampión. El método es confiable y no
Directory of Open Access Journals (Sweden)
Yacouba Simporé
2016-01-01
Full Text Available We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.
A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors
Shi, H.; Yang, B.; Thomson, M.; Fang, H.
2011-01-01
This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.
Ho Pham Huy Anh; Nguyen Thanh Nam
2012-01-01
In this paper, a novel forward adaptive neural MIMO NARX model is used for modelling and identifying the forward kinematics of an industrial 3‐DOF robot arm system. The nonlinear features of the forward kinematics of the industrial robot arm drive are thoroughly modelled based on the forward adaptive neural NARX model‐based identification process using experimental input‐output training data. This paper proposes a novel use of a back propagation (BP) algorithm to generate the forward neural M...
Sampled-data models for linear and nonlinear systems
Yuz, Juan I
2014-01-01
Sampled-data Models for Linear and Nonlinear Systems provides a fresh new look at a subject with which many researchers may think themselves familiar. Rather than emphasising the differences between sampled-data and continuous-time systems, the authors proceed from the premise that, with modern sampling rates being as high as they are, it is becoming more appropriate to emphasise connections and similarities. The text is driven by three motives: · the ubiquity of computers in modern control and signal-processing equipment means that sampling of systems that really evolve continuously is unavoidable; · although superficially straightforward, sampling can easily produce erroneous results when not treated properly; and · the need for a thorough understanding of many aspects of sampling among researchers and engineers dealing with applications to which they are central. The authors tackle many misconceptions which, although appearing reasonable at first sight, are in fact either p...
Li, Guang
2017-01-01
This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.
Modeling the SAR Signature of Nonlinear Internal Waves
National Research Council Canada - National Science Library
Lettvin, Ellen E
2008-01-01
Nonlinear Internal Waves are pervasive globally, particularly in coastal waters. The currents and displacements associated with internal waves influence acoustic propagation and underwater navigation, as well as ocean transport and mixing...
A nonlinear inversion for the velocity background and perturbation models
Wu, Zedong; Alkhalifah, Tariq Ali
2015-01-01
Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect
Stabilization and Control Models of Systems With Hysteresis Nonlinearities
Directory of Open Access Journals (Sweden)
Mihail E. Semenov
2012-05-01
Full Text Available Mechanical and economic systems with hysteresis nonlinearities are studied in article. Dissipativity condition of inverted pendulum under the hysteresis control is obtained. The solution of the optimal production strategy problem was found where price has hysteresis behaviour.
The spectral cell method in nonlinear earthquake modeling
Giraldo, Daniel; Restrepo, Doriam
2017-12-01
This study examines the applicability of the spectral cell method (SCM) to compute the nonlinear earthquake response of complex basins. SCM combines fictitious-domain concepts with the spectral-version of the finite element method to solve the wave equations in heterogeneous geophysical domains. Nonlinear behavior is considered by implementing the Mohr-Coulomb and Drucker-Prager yielding criteria. We illustrate the performance of SCM with numerical examples of nonlinear basins exhibiting physically and computationally challenging conditions. The numerical experiments are benchmarked with results from overkill solutions, and using MIDAS GTS NX, a finite element software for geotechnical applications. Our findings show good agreement between the two sets of results. Traditional spectral elements implementations allow points per wavelength as low as PPW = 4.5 for high-order polynomials. Our findings show that in the presence of nonlinearity, high-order polynomials (p ≥ 3) require mesh resolutions above of PPW ≥ 10 to ensure displacement errors below 10%.
Strategies for fitting nonlinear ecological models in R, AD Model Builder, and BUGS
DEFF Research Database (Denmark)
Bolker, B.M.; Gardner, B.; Maunder, M.
2013-01-01
Ecologists often use nonlinear fitting techniques to estimate the parameters of complex ecological models, with attendant frustration. This paper compares three open-source model fitting tools and discusses general strategies for defining and fitting models. R is convenient and (relatively) easy...... to learn, AD Model Builder is fast and robust but comes with a steep learning curve, while BUGS provides the greatest flexibility at the price of speed. Our model-fitting suggestions range from general cultural advice (where possible, use the tools and models that are most common in your subfield...
NSLS-II: Nonlinear Model Calibration for Synchrotrons
Energy Technology Data Exchange (ETDEWEB)
Bengtsson, J.
2010-10-08
This tech note is essentially a summary of a lecture we delivered to the Acc. Phys. Journal Club Apr, 2010. However, since the estimated accuracy of these methods has been naive and misleading in the field of particle accelerators, i.e., ignores the impact of noise, we will elaborate on this in some detail. A prerequisite for a calibration of the nonlinear Hamiltonian is that the quadratic part has been understood, i.e., that the linear optics for the real accelerator has been calibrated. For synchrotron light source operations, this problem has been solved by the interactive LOCO technique/tool (Linear Optics from Closed Orbits). Before that, in the context of hadron accelerators, it has been done by signal processing of turn-by-turn BPM data. We have outlined how to make a basic calibration of the nonlinear model for synchrotrons. In particular, we have shown how this was done for LEAR, CERN (antiprotons) in the mid-80s. Specifically, our accuracy for frequency estimation was {approx} 1 x 10{sup -5} for 1024 turns (to calibrate the linear optics) and {approx} 1 x 10{sup -4} for 256 turns for tune footprint and betatron spectrum. For a comparison, the estimated tune footprint for stable beam for NSLS-II is {approx}0.1. Since the transverse damping time is {approx}20 msec, i.e., {approx}4,000 turns. There is no fundamental difference for: antiprotons, protons, and electrons in this case. Because the estimated accuracy for these methods in the field of particle accelerators has been naive, i.e., ignoring the impact of noise, we have also derived explicit formula, from first principles, for a quantitative statement. For e.g. N = 256 and 5% noise we obtain {delta}{nu} {approx} 1 x 10{sup -5}. A comparison with the state-of-the-arts in e.g. telecomm and electrical engineering since the 60s is quite revealing. For example, Kalman filter (1960), crucial for the: Ranger, Mariner, and Apollo (including the Lunar Module) missions during the 60s. Or Claude Shannon et al
NSLS-II: Nonlinear Model Calibration for Synchrotrons
International Nuclear Information System (INIS)
Bengtsson, J.
2010-01-01
This tech note is essentially a summary of a lecture we delivered to the Acc. Phys. Journal Club Apr, 2010. However, since the estimated accuracy of these methods has been naive and misleading in the field of particle accelerators, i.e., ignores the impact of noise, we will elaborate on this in some detail. A prerequisite for a calibration of the nonlinear Hamiltonian is that the quadratic part has been understood, i.e., that the linear optics for the real accelerator has been calibrated. For synchrotron light source operations, this problem has been solved by the interactive LOCO technique/tool (Linear Optics from Closed Orbits). Before that, in the context of hadron accelerators, it has been done by signal processing of turn-by-turn BPM data. We have outlined how to make a basic calibration of the nonlinear model for synchrotrons. In particular, we have shown how this was done for LEAR, CERN (antiprotons) in the mid-80s. Specifically, our accuracy for frequency estimation was ∼ 1 x 10 -5 for 1024 turns (to calibrate the linear optics) and ∼ 1 x 10 -4 for 256 turns for tune footprint and betatron spectrum. For a comparison, the estimated tune footprint for stable beam for NSLS-II is ∼0.1. Since the transverse damping time is ∼20 msec, i.e., ∼4,000 turns. There is no fundamental difference for: antiprotons, protons, and electrons in this case. Because the estimated accuracy for these methods in the field of particle accelerators has been naive, i.e., ignoring the impact of noise, we have also derived explicit formula, from first principles, for a quantitative statement. For e.g. N = 256 and 5% noise we obtain (delta)ν ∼ 1 x 10 -5 . A comparison with the state-of-the-arts in e.g. telecomm and electrical engineering since the 60s is quite revealing. For example, Kalman filter (1960), crucial for the: Ranger, Mariner, and Apollo (including the Lunar Module) missions during the 60s. Or Claude Shannon et al since the 40s for that matter. Conclusion: what
Nonlinear economic dynamics and financial modelling: essays in honour of Carl Chiarella
Dieci, R.; He, X.Z.; Hommes, C.
2014-01-01
This book reflects the state of the art on nonlinear economic dynamics, financial market modelling and quantitative finance. It contains eighteen papers with topics ranging from disequilibrium macroeconomics, monetary dynamics, monopoly, financial market and limit order market models with boundedly
Study of the critical behavior of the O(N) linear and nonlinear sigma models
International Nuclear Information System (INIS)
Graziani, F.R.
1983-01-01
A study of the large N behavior of both the O(N) linear and nonlinear sigma models is presented. The purpose is to investigate the relationship between the disordered (ordered) phase of the linear and nonlinear sigma models. Utilizing operator product expansions and stability analyses, it is shown that for 2 - (lambda/sub R/(M) is the dimensionless renormalized quartic coupling and lambda* is the IR fixed point) limit of the linear sigma model which yields the nonlinear sigma model. It is also shown that stable large N linear sigma models with lambda 0) and nonlinear models are trivial. This result (i.e., triviality) is well known but only for one and two component models. Interestingly enough, the lambda< d = 4 linear sigma model remains nontrivial and tachyonic free
Identification of nonlinear coupling in wave turbulence at the surface of water
Campagne, Antoine; Hassaini, Roumaissa; Redor, Ivan; Aubourg, Quentin; Sommeria, Joël; Mordant, Nicolas
2017-11-01
The Weak Turbulence Theory is a theory, in the limit of vanishing nonlinearity, that derive analytically statistical features of wave turbulence. The stationary spectrum for the surface elevation in the case of gravity waves, is predicted to E(k) k - 5 / 2 . This spectral exponent -5/2 remains elusive in all experiments. in which the measured exponent is systematically lower than the prediction. Furthermore in the experiments the weaker the nonlinearity the further the spectral exponent is from the prediction. In order to investigate the reason for this observation we developed an experiment in the CORIOLIS facility in Grenoble. It is a 13m-diameter circular pool filled with water with a 70 cm depth. We generate wave turbulence by using two wedge wavemakers. Surface elevation measurements are performed by a stereoscopic optical technique and by capacitive probes. The nonlinear coupling at work in this system are analyzed by computing 3- and 4-wave correlations of the Fourier wave amplitudes in frequency. Theory predicts that coupling should occur through 4-wave resonant interaction. In our data, strong 3-wave correlations are observed in addition to the 4-wave correlation. Most our observations are consistent with field observation in the Black Sea (Leckler et al. 2015). This project has received funding from the European Research Council (ERC, Grant Agreement No 647018-WATU).
2013-01-01
This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.
An efficient flexible-order model for 3D nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole
2009-01-01
The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal......, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental...
A Monte Carlo Investigation of the Box-Cox Model and a Nonlinear Least Squares Alternative.
Showalter, Mark H
1994-01-01
This paper reports a Monte Carlo study of the Box-Cox model and a nonlinear least squares alternative. Key results include the following: the transformation parameter in the Box-Cox model appears to be inconsistently estimated in the presence of conditional heteroskedasticity; the constant term in both the Box-Cox and the nonlinear least squares models is poorly estimated in small samples; conditional mean forecasts tend to underestimate their true value in the Box-Cox model when the transfor...
A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation
Rajeswaran, Jeevanantham; Blackstone, Eugene H.
2014-01-01
In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830
Global sea surface temperature (SST) anomalies can affect terrestrial precipitation via ocean-atmosphere interaction known as climate teleconnection. Non-stationary and non-linear characteristics of the ocean-atmosphere system make the identification of the teleconnection signals...
Applicability of linear and non-linear potential flow models on a Wavestar float
DEFF Research Database (Denmark)
Bozonnet, Pauline; Dupin, Victor; Tona, Paolino
2017-01-01
as a model based on non-linear potential flow theory and weakscatterer hypothesis are successively considered. Simple tests, such as dip tests, decay tests and captive tests enable to highlight the improvements obtained with the introduction of nonlinearities. Float motion under wave actions and without...... control action, limited to small amplitude motion with a single float, is well predicted by the numerical models, including the linear one. Still, float velocity is better predicted by accounting for non-linear hydrostatic and Froude-Krylov forces.......Numerical models based on potential flow theory, including different types of nonlinearities are compared and validated against experimental data for the Wavestar wave energy converter technology. Exact resolution of the rotational motion, non-linear hydrostatic and Froude-Krylov forces as well...
Mohammadzadeh, Ardashir; Ghaemi, Sehraneh
2015-09-01
This paper proposes a novel approach for training of proposed recurrent hierarchical interval type-2 fuzzy neural networks (RHT2FNN) based on the square-root cubature Kalman filters (SCKF). The SCKF algorithm is used to adjust the premise part of the type-2 FNN and the weights of defuzzification and the feedback weights. The recurrence property in the proposed network is the output feeding of each membership function to itself. The proposed RHT2FNN is employed in the sliding mode control scheme for the synchronization of chaotic systems. Unknown functions in the sliding mode control approach are estimated by RHT2FNN. Another application of the proposed RHT2FNN is the identification of dynamic nonlinear systems. The effectiveness of the proposed network and its learning algorithm is verified by several simulation examples. Furthermore, the universal approximation of RHT2FNNs is also shown. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Gørgens, Tue; Skeels, Christopher L.; Wurtz, Allan
This paper explores estimation of a class of non-linear dynamic panel data models with additive unobserved individual-specific effects. The models are specified by moment restrictions. The class includes the panel data AR(p) model and panel smooth transition models. We derive an efficient set...... of moment restrictions for estimation and apply the results to estimation of panel smooth transition models with fixed effects, where the transition may be determined endogenously. The performance of the GMM estimator, both in terms of estimation precision and forecasting performance, is examined in a Monte...
Nonlinear dynamics and modelling of various wooden toys with impact and friction
Leine, R.I.; Campen, van D.H.; Glocker, C.
2003-01-01
In this paper, we study bifurcations in systems with impact and friction, modeled with a rigid multibody approach. Knowledge from the field of nonlinear dynamics is therefore combined with theory from the field of non-smooth mechanics. We study the nonlinear dynamics of three commercial wooden toys.
Nonlinear modeling of a rotational MR damper via an enhanced Bouc–Wen model
International Nuclear Information System (INIS)
Miah, Mohammad S; Chatzi, Eleni N; Dertimanis, Vasilis K; Weber, Felix
2015-01-01
The coupling of magnetorheological (MR) dampers with semi-active control schemes has proven to be an effective and failsafe approach for vibration mitigation of low-damped structures. However, due to the nonlinearities inherently relating to such damping devices, the characterization of the associated nonlinear phenomena is still a challenging task. Herein, an enhanced phenomenological modeling approach is proposed for the description of a rotational-type MR damper, which comprises a modified Bouc–Wen model coupled with an appropriately selected sigmoid function. In a first step, parameter optimization is performed on the basis of individual models in an effort to approximate the experimentally observed response for varying current levels and actuator force characteristics. In a second step, based on the previously identified parameters, a generalized best-fit model is proposed by performing a regression analysis. Finally, model validation is carried out via implementation on different sets of experimental data. The proposed model indeed renders an improved representation of the actually observed nonlinear behavior of the tested rotational MR damper. (paper)
Directory of Open Access Journals (Sweden)
Ryś Maciej
2014-09-01
Full Text Available In this work, a macroscopic material model for simulation two distinct dissipative phenomena taking place in FCC metals and alloys at low temperatures: plasticity and phase transformation, is presented. Plastic yielding is the main phenomenon occurring when the yield stress is reached, resulting in nonlinear response of the material during loading. The phase transformation process leads to creation of two-phase continuum, where the parent phase coexists with the inclusions of secondary phase. An identification of the model parameters, based on uniaxial tension test at very low temperature, is also proposed.
Search-based model identification of smart-structure damage
Glass, B. J.; Macalou, A.
1991-01-01
This paper describes the use of a combined model and parameter identification approach, based on modal analysis and artificial intelligence (AI) techniques, for identifying damage or flaws in a rotating truss structure incorporating embedded piezoceramic sensors. This smart structure example is representative of a class of structures commonly found in aerospace systems and next generation space structures. Artificial intelligence techniques of classification, heuristic search, and an object-oriented knowledge base are used in an AI-based model identification approach. A finite model space is classified into a search tree, over which a variant of best-first search is used to identify the model whose stored response most closely matches that of the input. Newly-encountered models can be incorporated into the model space. This adaptativeness demonstrates the potential for learning control. Following this output-error model identification, numerical parameter identification is used to further refine the identified model. Given the rotating truss example in this paper, noisy data corresponding to various damage configurations are input to both this approach and a conventional parameter identification method. The combination of the AI-based model identification with parameter identification is shown to lead to smaller parameter corrections than required by the use of parameter identification alone.
System identification and the modeling of sailing yachts
Legursky, Katrina
This research represents an exploration of sailing yacht dynamics with full-scale sailing motion data, physics-based models, and system identification techniques. The goal is to provide a method of obtaining and validating suitable physics-based dynamics models for use in control system design on autonomous sailing platforms, which have the capacity to serve as mobile, long range, high endurance autonomous ocean sensing platforms. The primary contributions of this study to the state-of-the-art are the formulation of a five degree-of-freedom (DOF) linear multi-input multi-output (MIMO) state space model of sailing yacht dynamics, the process for identification of this model from full-scale data, a description of the maneuvers performed during on-water tests, and an analysis method to validate estimated models. The techniques and results described herein can be directly applied to and tested on existing autonomous sailing platforms. A full-scale experiment on a 23ft monohull sailing yacht is developed to collect motion data for physics-based model identification. Measurements include 3 axes of accelerations, velocities, angular rates, and attitude angles in addition to apparent wind speed and direction. The sailing yacht herein is treated as a dynamic system with two control inputs, the rudder angle, deltaR, and the mainsail angle, delta B, which are also measured. Over 20 hours of full scale sailing motion data is collected, representing three sail configurations corresponding to a range of wind speeds: the Full Main and Genoa (abbrev. Genoa) for lower wind speeds, the Full Main and Jib (abbrev. Jib) for mid-range wind speeds, and the Reefed Main and Jib (abbrev. Reef) for the highest wind speeds. The data also covers true wind angles from upwind through a beam reach. A physics-based non-linear model to describe sailing yacht motion is outlined, including descriptions of methods to model the aerodynamics and hydrodynamics of a sailing yacht in surge, sway, roll, and
On the Nonlinear Structural Analysis of Wind Turbine Blades using Reduced Degree-of-Freedom Models
DEFF Research Database (Denmark)
Holm-Jørgensen, Kristian; Larsen, Jesper Winther; Nielsen, Søren R.K.
2008-01-01
, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based...... on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response...... of the small number of included modes. The qualitative erratic response and stability prediction of the reduced order models take place at frequencies slightly above normal operation. However, for normal operation of the wind turbine without resonance excitation 4 modes in the reduced-degree-of-freedom model...
Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives
Yao, Jianyong
2018-06-01
Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.
Calibration of the Nonlinear Accelerator Model at the Diamond Storage Ring
Bartolini, Riccardo; Rowland, James; Martin, Ian; Schmidt, Frank
2010-01-01
The correct implementation of the nonlinear ring model is crucial to achieve the top performance of a synchrotron light source. Several dynamics quantities can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these methods are based on the analysis of turn-by-turn data of excited betatron oscillations. We present the experimental results of the campaign of measurements carried out at the Diamond. A combination of Frequency Map Analysis (FMA) and detuning with momentum measurements has allowed a precise calibration of the nonlinear model capable of reproducing the nonlinear beam dynamics in the storage ring
Nonlinear dynamics approach of modeling the bifurcation for aircraft wing flutter in transonic speed
DEFF Research Database (Denmark)
Matsushita, Hiroshi; Miyata, T.; Christiansen, Lasse Engbo
2002-01-01
The procedure of obtaining the two-degrees-of-freedom, finite dimensional. nonlinear mathematical model. which models the nonlinear features of aircraft flutter in transonic speed is reported. The model enables to explain every feature of the transonic flutter data of the wind tunnel tests...... conducted at National Aerospace Laboratory in Japan for a high aspect ratio wing. It explains the nonlinear features of the transonic flutter such as the subcritical Hopf bifurcation of a limit cycle oscillation (LCO), a saddle-node bifurcation, and an unstable limit cycle as well as a normal (linear...
A Comparison Between Mıcrosoft Excel Solver and Ncss, Spss Routines for Nonlinear Regression Models
Directory of Open Access Journals (Sweden)
Didem Tetik Küçükelçi
2018-02-01
Full Text Available In this study we have tried to compare the results obtained by Microsoft Excel Solver program with those of NCSS and SPSS in some nonlinear regression models. We fit some nonlinear models to data present in http//itl.nist.gov/div898/strd/nls/nls_main.shtml by the three packages. Although EXCEL did not succeed as well as the other packages, we conclude that Microsoft Excel Solver provides us a cheaper and a more interactive way of studying nonlinear models.
Nonlinear Kalman filtering in affine term structure models
DEFF Research Database (Denmark)
Christoffersen, Peter; Dorion, Christian; Jacobs, Kris
2014-01-01
The extended Kalman filter, which linearizes the relationship between security prices and state variables, is widely used in fixed-income applications. We investigate whether the unscented Kalman filter should be used to capture nonlinearities and compare the performance of the Kalman filter...... with that of the particle filter. We analyze the cross section of swap rates, which are mildly nonlinear in the states, and cap prices, which are highly nonlinear. When caps are used to filter the states, the unscented Kalman filter significantly outperforms its extended counterpart. The unscented Kalman filter also...... performs well when compared with the much more computationally intensive particle filter. These findings suggest that the unscented Kalman filter may be a good approach for a variety of problems in fixed-income pricing....
Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.
Humphrey, V F
2000-03-01
In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.
The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model
Energy Technology Data Exchange (ETDEWEB)
Lei Min [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)], E-mail: leimin@sjtu.edu.cn; Meng Guang [State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiao Tong University, Shanghai 200030 (China)
2008-04-15
This paper studies the influence of noises on Volterra-Wiener-Korenberg (VWK) nonlinear test model. Our numerical results reveal that different types of noises lead to different behavior of VWK model detection. For dynamic noise, it is difficult to distinguish chaos from nonchaotic but nonlinear determinism. For time series, measure noise has no impact on chaos determinism detection. This paper also discusses various behavior of VWK model detection with surrogate data for different noises.
Hamed Kharrati; Sohrab Khanmohammadi; Witold Pedrycz; Ghasem Alizadeh
2012-01-01
This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB) systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA) is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy m...
Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo
2013-01-01
We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.
International Nuclear Information System (INIS)
Fujii, Akira; Kluemper, Andreas
1999-01-01
We derive the non-linear integral equations determining the free energy of the three-state pure bosonic Uimin-Sutherland model. In order to find a complete set of auxiliary functions, the anti-symmetric fusion procedure is utilized. We solve the non-linear integral equations numerically and see that the low-temperature behavior coincides with that predicted by conformal field theory. The magnetization and magnetic susceptibility are also calculated by means of the non-linear integral equation
Identification of cow milk in goat milk by nonlinear chemical fingerprint technique.
Ma, Yong-Jie; Dong, Wen-Bin; Fan, Cheng; Wang, Er-Dan
2017-10-01
The objective of this paper was to develop a nonlinear chemical fingerprint technique for identifying and detecting adulteration of goat milk with cow milk. In this study, by taking the Belousov-Zhabotinsky oscillatory chemical reaction using acetone and substrates in goat milk or cow milk as main dissipative substances, when the same dosage of goat milk and cow milk was introduced to the "H + + Mn 2+ + BrO 3 - + acetone" oscillating system respectively, nonlinear chemical fingerprints were obtained for goat milk and cow milk from the same origin. The results showed that inductive time value and the content of cow milk in goat milk had a linear relationship in the range of 0-100% and the corresponding regression coefficient was 0.9991. A detection limit of 0.0107 g/g was obtained, and the content of cow milk in mixed milk was calculated. The proposed method in this study was simple, economical and effective. In addition, the method did not need the pretreatment and separation of samples for identifying and evaluating cow milk adulteration in goat milk. Copyright © 2017. Published by Elsevier B.V.
Decuyper, J.; De Troyer, T.; Runacres, M. C.; Tiels, K.; Schoukens, J.
2018-01-01
The flow-induced vibration of bluff bodies is an important problem of many marine, civil, or mechanical engineers. In the design phase of such structures, it is vital to obtain good predictions of the fluid forces acting on the structure. Current methods rely on computational fluid dynamic simulations (CFD), with a too high computational cost to be effectively used in the design phase or for control applications. Alternative methods use heuristic mathematical models of the fluid forces, but these lack the accuracy (they often assume the system to be linear) or flexibility to be useful over a wide operating range. In this work we show that it is possible to build an accurate, flexible and low-computational-cost mathematical model using nonlinear system identification techniques. This model is data driven: it is trained over a user-defined region of interest using data obtained from experiments or simulations, or both. Here we use a Van der Pol oscillator as well as CFD simulations of an oscillating circular cylinder to generate the training data. Then a discrete-time polynomial nonlinear state-space model is fit to the data. This model relates the oscillation of the cylinder to the force that the fluid exerts on the cylinder. The model is finally validated over a wide range of oscillation frequencies and amplitudes, both inside and outside the so-called lock-in region. We show that forces simulated by the model are in good agreement with the data obtained from CFD.
Finite element modeling of nonlinear piezoelectric energy harvesters with magnetic interaction
International Nuclear Information System (INIS)
Upadrashta, Deepesh; Yang, Yaowen
2015-01-01
Piezoelectric energy harvesting from ambient vibrations is a potential technology for powering wireless sensors and low power electronic devices. The conventional linear harvesters suffer from narrow operational bandwidth. Many attempts have been made especially using the magnetic interaction to broaden the bandwidth of harvesters. The finite element (FE) modeling has been used only for analyzing the linear harvesters in the literature. The main difficulties in extending the FE modeling to analyze the nonlinear harvesters involving magnetic interaction are developing the mesh needed for magnetic interaction in dynamic problems and the high demand on computational resource needed for solving the coupled electrical–mechanical–magnetic problem. In this paper, an innovative method is proposed to model the magnetic interaction without inclusion of the magnetic module. The magnetic force is modeled using the nonlinear spring element available in ANSYS finite element analysis (FEA) package, thus simplifying the simulation of nonlinear piezoelectric energy harvesters as an electromechanically coupled problem. Firstly, an FE model of a monostable nonlinear harvester with cantilever configuration is developed and the results are validated with predictions from the theoretical model. Later, the proposed technique of FE modeling is extended to a complex 2-degree of freedom nonlinear energy harvester for which an accurate analytical model is difficult to derive. The performance predictions from FEA are compared with the experimental results. It is concluded that the proposed modeling technique is able to accurately analyze the behavior of nonlinear harvesters with magnetic interaction. (paper)