NONLINEAR DATA RECONCILIATION METHOD BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
In the industrial process situation, principal component analysis (PCA) is a general method in data reconciliation.However, PCA sometime is unfeasible to nonlinear feature analysis and limited in application to nonlinear industrial process.Kernel PCA (KPCA) is extension of PCA and can be used for nonlinear feature analysis.A nonlinear data reconciliation method based on KPCA is proposed.The basic idea of this method is that firstly original data are mapped to high dimensional feature space by nonlinear function, and PCA is implemented in the feature space.Then nonlinear feature analysis is implemented and data are reconstructed by using the kernel.The data reconciliation method based on KPCA is applied to ternary distillation column.Simulation results show that this method can filter the noise in measurements of nonlinear process and reconciliated data can represent the true information of nonlinear process.
Online Fault Diagnosis Method Based on Nonlinear Spectral Analysis
Institute of Scientific and Technical Information of China (English)
WEI Rui-xuan; WU Li-xun; WANG Yong-chang; HAN Chong-zhao
2005-01-01
The fault diagnosis based on nonlinear spectral analysis is a new technique for the nonlinear fault diagnosis, but its online application could be limited because of the enormous compution requirements for the estimation of general frequency response functions. Based on the fully decoupled Volterra identification algorithm, a new online fault diagnosis method based on nonlinear spectral analysis is presented, which can availably reduce the online compution requirements of general frequency response functions. The composition and working principle of the method are described, the test experiments have been done for damping spring of a vehicle suspension system by utilizing the new method, and the results indicate that the method is efficient.
Nonlinear fault diagnosis method based on kernel principal component analysis
Institute of Scientific and Technical Information of China (English)
Yan Weiwu; Zhang Chunkai; Shao Huihe
2005-01-01
To ensure the system run under working order, detection and diagnosis of faults play an important role in industrial process. This paper proposed a nonlinear fault diagnosis method based on kernel principal component analysis (KPCA). In proposed method, using essential information of nonlinear system extracted by KPCA, we constructed KPCA model of nonlinear system under normal working condition. Then new data were projected onto the KPCA model. When new data are incompatible with the KPCA model, it can be concluded that the nonlinear system isout of normal working condition. Proposed method was applied to fault diagnosison rolling bearings. Simulation results show proposed method provides an effective method for fault detection and diagnosis of nonlinear system.
A New Nonlinear Compound Forecasting Method Based on ANN
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
In this paper the compound-forecasting method is discussed. The compound-forecasting method is one of the hotspots in the current predication. Firstly, the compound-forecasting method is introduced and various existing compound-forecasting methods arediscussed. Secondly, the Artificial Neural Network (ANN) is brought in compound-prediction research and a nonlinear compound-prediction model based on ANN is presented. Finally, inorder to avoid irregular weight, a new method is presented which uses principal component analyses to increase the availability of compound-forecasting information. Higherforecasting precision is achieved in practice.
Simple noise-reduction method based on nonlinear forecasting
Tan, James P. L.
2017-03-01
Nonparametric detrending or noise reduction methods are often employed to separate trends from noisy time series when no satisfactory models exist to fit the data. However, conventional noise reduction methods depend on subjective choices of smoothing parameters. Here we present a simple multivariate noise reduction method based on available nonlinear forecasting techniques. These are in turn based on state-space reconstruction for which a strong theoretical justification exists for their use in nonparametric forecasting. The noise reduction method presented here is conceptually similar to Schreiber's noise reduction method using state-space reconstruction. However, we show that Schreiber's method has a minor flaw that can be overcome with forecasting. Furthermore, our method contains a simple but nontrivial extension to multivariate time series. We apply the method to multivariate time series generated from the Van der Pol oscillator, the Lorenz equations, the Hindmarsh-Rose model of neuronal spiking activity, and to two other univariate real-world data sets. It is demonstrated that noise reduction heuristics can be objectively optimized with in-sample forecasting errors that correlate well with actual noise reduction errors.
Nonlinear diffusion methods based on robust statistics for noise removal
Institute of Scientific and Technical Information of China (English)
JIA Di-ye; HUANG Feng-gang; SU Han
2007-01-01
A novel smoothness term of Bayesian regularization framework based on M-estimation of robust statistics is proposed, and from this term a class of fourth-order nonlinear diffusion methods is proposed. These methods attempt to approximate an observed image with a piecewise linear image, which looks more natural than piecewise constant image used to approximate an observed image by P-M[1] model. It is known that M-estimators and W-estimators are essentially equivalent and solve the same minimization problem. Then, we propose PL bilateral filter from equivalent W-estimator. This new model is designed for piecewise linear image filtering,which is more effective than normal bilateral filter.
An Agent Interaction Based Method for Nonlinear Process Plan Scheduling
Institute of Scientific and Technical Information of China (English)
GAO Qinglu; WU Bo; GUO Guang
2006-01-01
This article puts forward a scheduling method for nonlinear process plan shop floor. Task allocation and load balance are realized by bidding mechanism. Though the agent interaction process, the execution of tasks is determined and the coherence of manufacturing decision is verified. The employment of heuristic index can help to optimize the system performance.
Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods
Perumal, Muthiah; Tayfur, Gokmen; Rao, C. Madhusudana; Gurarslan, Gurhan
2017-03-01
Two variants of the Muskingum flood routing method formulated for accounting nonlinearity of the channel routing process are investigated in this study. These variant methods are: (1) The three-parameter conceptual Nonlinear Muskingum (NLM) method advocated by Gillin 1978, and (2) The Variable Parameter McCarthy-Muskingum (VPMM) method recently proposed by Perumal and Price in 2013. The VPMM method does not require rigorous calibration and validation procedures as required in the case of NLM method due to established relationships of its parameters with flow and channel characteristics based on hydrodynamic principles. The parameters of the conceptual nonlinear storage equation used in the NLM method were calibrated using the Artificial Intelligence Application (AIA) techniques, such as the Genetic Algorithm (GA), the Differential Evolution (DE), the Particle Swarm Optimization (PSO) and the Harmony Search (HS). The calibration was carried out on a given set of hypothetical flood events obtained by routing a given inflow hydrograph in a set of 40 km length prismatic channel reaches using the Saint-Venant (SV) equations. The validation of the calibrated NLM method was investigated using a different set of hypothetical flood hydrographs obtained in the same set of channel reaches used for calibration studies. Both the sets of solutions obtained in the calibration and validation cases using the NLM method were compared with the corresponding solutions of the VPMM method based on some pertinent evaluation measures. The results of the study reveal that the physically based VPMM method is capable of accounting for nonlinear characteristics of flood wave movement better than the conceptually based NLM method which requires the use of tedious calibration and validation procedures.
A new method based on the harmonic balance method for nonlinear oscillators
Energy Technology Data Exchange (ETDEWEB)
Chen, Y.M. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China); Liu, J.K. [Department of Mechanics, Zhongshan University, Guangzhou 510275 (China)], E-mail: jikeliu@hotmail.com
2007-08-27
The harmonic balance (HB) method as an analytical approach is widely used for nonlinear oscillators, in which the initial conditions are generally simplified by setting velocity or displacement to be zero. Based on HB, we establish a new theory to address nonlinear conservative systems with arbitrary initial conditions, and deduce a set of over-determined algebraic equations. Since these deduced algebraic equations are not solved directly, a minimization problem is constructed instead and an iterative algorithm is employed to seek the minimization point. Taking Duffing and Duffing-harmonic equations as numerical examples, we find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
A Nonlinear Physics-Based Optimal Control Method for Magnetostrictive Actuators
Smith, Ralph C.
1998-01-01
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
An extended harmonic balance method based on incremental nonlinear control parameters
Khodaparast, Hamed Haddad; Madinei, Hadi; Friswell, Michael I.; Adhikari, Sondipon; Coggon, Simon; Cooper, Jonathan E.
2017-02-01
A new formulation for calculating the steady-state responses of multiple-degree-of-freedom (MDOF) non-linear dynamic systems due to harmonic excitation is developed. This is aimed at solving multi-dimensional nonlinear systems using linear equations. Nonlinearity is parameterised by a set of 'non-linear control parameters' such that the dynamic system is effectively linear for zero values of these parameters and nonlinearity increases with increasing values of these parameters. Two sets of linear equations which are formed from a first-order truncated Taylor series expansion are developed. The first set of linear equations provides the summation of sensitivities of linear system responses with respect to non-linear control parameters and the second set are recursive equations that use the previous responses to update the sensitivities. The obtained sensitivities of steady-state responses are then used to calculate the steady state responses of non-linear dynamic systems in an iterative process. The application and verification of the method are illustrated using a non-linear Micro-Electro-Mechanical System (MEMS) subject to a base harmonic excitation. The non-linear control parameters in these examples are the DC voltages that are applied to the electrodes of the MEMS devices.
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
Nonlinear Spline Kernel-based Partial Least Squares Regression Method and Its Application
Institute of Scientific and Technical Information of China (English)
JIA Jin-ming; WEN Xiang-jun
2008-01-01
Inspired by the traditional Wold's nonlinear PLS algorithm comprises of NIPALS approach and a spline inner function model,a novel nonlinear partial least squares algorithm based on spline kernel(named SK-PLS)is proposed for nonlinear modeling in the presence of multicollinearity.Based on the iuner-product kernel spanned by the spline basis functions with infinite numher of nodes,this method firstly maps the input data into a high dimensional feature space,and then calculates a linear PLS model with reformed NIPALS procedure in the feature space and gives a unified framework of traditional PLS"kernel"algorithms in consequence.The linear PLS in the feature space corresponds to a nonlinear PLS in the original input (primal)space.The good approximating property of spline kernel function enhances the generalization ability of the novel model,and two numerical experiments are given to illustrate the feasibility of the proposed method.
Improved nonlinear prediction method
Adenan, Nur Hamiza; Md Noorani, Mohd Salmi
2014-06-01
The analysis and prediction of time series data have been addressed by researchers. Many techniques have been developed to be applied in various areas, such as weather forecasting, financial markets and hydrological phenomena involving data that are contaminated by noise. Therefore, various techniques to improve the method have been introduced to analyze and predict time series data. In respect of the importance of analysis and the accuracy of the prediction result, a study was undertaken to test the effectiveness of the improved nonlinear prediction method for data that contain noise. The improved nonlinear prediction method involves the formation of composite serial data based on the successive differences of the time series. Then, the phase space reconstruction was performed on the composite data (one-dimensional) to reconstruct a number of space dimensions. Finally the local linear approximation method was employed to make a prediction based on the phase space. This improved method was tested with data series Logistics that contain 0%, 5%, 10%, 20% and 30% of noise. The results show that by using the improved method, the predictions were found to be in close agreement with the observed ones. The correlation coefficient was close to one when the improved method was applied on data with up to 10% noise. Thus, an improvement to analyze data with noise without involving any noise reduction method was introduced to predict the time series data.
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation an
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
Intrusion detection method based on nonlinear correlation measure
Ambusaidi, Mohammed A.; Tan, Zhiyuan; He, Xiangjian; Nanda, Priyadarsi; Lu, Liang Fu; Jamdagni, Aruna
2014-01-01
Cyber crimes and malicious network activities have posed serious threats to the entire internet and its users. This issue is becoming more critical, as network-based services, are more widespread and closely related to our daily life. Thus, it has raised a serious concern in individual internet user
An iterative regularization method for nonlinear problems based on Bregman projections
Maaß, Peter; Strehlow, Robin
2016-11-01
In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237-62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.
Diffusion Geometry Based Nonlinear Methods for Hyperspectral Change Detection
2010-05-12
Schaum and A. Stocker, “Hyperspectral change detection and supervised matched filtering based on covariance equalization,” Proceedings of the SPIE, vol...5425, pp. 77- 90 (2004). 10. A. Schaum and A. Stocker, “Linear chromodynamics models for hyperspectral target detection,” Proceedings of the IEEE...Aerospace Conference (February 2003). 11. A. Schaum and A. Stocker, “Linear chromodynamics models for hyperspectral target detection
Yelve, Nitesh P; Mitra, Mira; Mujumdar, P M; Ramadas, C
2016-08-01
A new hybrid method based upon nonlinear Lamb wave response in time and frequency domains is introduced to locate a delamination in composite laminates. In Lamb wave based nonlinear method, the presence of damage is shown by the appearance of higher harmonics in the Lamb wave response. The proposed method not only uses this spectral information but also the corresponding temporal response data, for locating the delamination. Thus, the method is termed as a hybrid method. The paper includes formulation of the method and its application to locate a Barely Visible Impact Damage (BVID) induced delamination in a Carbon Fiber Reinforced Polymer (CFRP) laminate. The method gives the damage location fairly well. It is a baseline free method, as it does not need data from the pristine specimen.
Image quality assessment method based on nonlinear feature extraction in kernel space
Institute of Scientific and Technical Information of China (English)
Yong DING‡; Nan LI; Yang ZHAO; Kai HUANG
2016-01-01
To match human perception, extracting perceptual features effectively plays an important role in image quality assessment. In contrast to most existing methods that use linear transformations or models to represent images, we employ a complex mathematical expression of high dimensionality to reveal the statistical characteristics of the images. Furthermore, by introducing kernel methods to transform the linear problem into a nonlinear one, a full-reference image quality assessment method is proposed based on high-dimensional nonlinear feature extraction. Experiments on the LIVE, TID2008, and CSIQ databases demonstrate that nonlinear features offer competitive performance for image inherent quality representation and the proposed method achieves a promising performance that is consistent with human subjective evaluation.
Directory of Open Access Journals (Sweden)
Kohei Arai
2013-01-01
Full Text Available Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to the conventional methods in terms of prediction accuracy.
Directory of Open Access Journals (Sweden)
Mahsa Khoeiniha
2012-01-01
Full Text Available This paper investigated study of dynamics of nonlinear electrical circuit by means of modern nonlinear techniques and the control of a class of chaotic system by using backstepping method based on Lyapunov function. The behavior of such nonlinear system when they are under the influence of external sinusoidal disturbances with unknown amplitudes has been considered. The objective is to analyze the performance of this system at different amplitudes of disturbances. We illustrate the proposed approach for controlling duffing oscillator problem to stabilize this system at the equilibrium point. Also Genetic Algorithm method (GA for computing the parameters of controller has been used. GA can be successfully applied to achieve a better controller. Simulation results have shown the effectiveness of the proposed method.
Measurement of heart rate variability by methods based on nonlinear dynamics.
Huikuri, Heikki V; Mäkikallio, Timo H; Perkiömäki, Juha
2003-01-01
Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of HR dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear HR dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional HR variability indexes. In particular, short-term fractal scaling exponent measured by detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of HR dynamics, which describes the complexity of R-R interval behavior, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indexes, eg, Lyapunov exponent and correlation dimensions, which also give information on the characteristics of HR dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of HR behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.
Li, Xingfeng; Coyle, Damien; Maguire, Liam; McGinnity, Thomas M; Benali, Habib
2011-07-01
In this paper a model selection algorithm for a nonlinear system identification method is proposed to study functional magnetic resonance imaging (fMRI) effective connectivity. Unlike most other methods, this method does not need a pre-defined structure/model for effective connectivity analysis. Instead, it relies on selecting significant nonlinear or linear covariates for the differential equations to describe the mapping relationship between brain output (fMRI response) and input (experiment design). These covariates, as well as their coefficients, are estimated based on a least angle regression (LARS) method. In the implementation of the LARS method, Akaike's information criterion corrected (AICc) algorithm and the leave-one-out (LOO) cross-validation method were employed and compared for model selection. Simulation comparison between the dynamic causal model (DCM), nonlinear identification method, and model selection method for modelling the single-input-single-output (SISO) and multiple-input multiple-output (MIMO) systems were conducted. Results show that the LARS model selection method is faster than DCM and achieves a compact and economic nonlinear model simultaneously. To verify the efficacy of the proposed approach, an analysis of the dorsal and ventral visual pathway networks was carried out based on three real datasets. The results show that LARS can be used for model selection in an fMRI effective connectivity study with phase-encoded, standard block, and random block designs. It is also shown that the LOO cross-validation method for nonlinear model selection has less residual sum squares than the AICc algorithm for the study.
A New UKF Based Fault Detection Method in Non-linear Systems
Institute of Scientific and Technical Information of China (English)
GE Zhe-xue; YANG Yong-min; HU Zheng
2006-01-01
To detect the bias fault in stochastic non-linear dynamic systems, a new Unscented Kalman Filtering(UKF) based real-time recursion detection method is brought forward with the consideration of the flaws of traditional Extended Kalman Filtering(EKF). It uses the UKF as the residual generation method and the Weighted-Sum Squared Residual (WSSR) as the fault detection strategy. The simulation results are provided which demonstrate better effectiveness and a higher detection ratio of the developed methods.
A LQP BASED INTERIOR PREDICTION-CORRECTION METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEMS
Institute of Scientific and Technical Information of China (English)
Bing-sheng He; Li-zhi Liao; Xiao-ming Yuan
2006-01-01
To solve nonlinear complementarity problems (NCP), at each iteration, the classical proximal point algorithm solves a well-conditioned sub-NCP while the LogarithmicQuadratic Proximal (LQP) method solves a system of nonlinear equations (LQP system). This paper presents a practical LQP method-based prediction-correction method for NCP.The predictor is obtained via solving the LQP system approximately under significantly relaxed restriction, and the new iterate (the corrector) is computed directly by an explicit formula derived from the original LQP method. The implementations are very easy to be carried out. Global convergence of the method is proved under the same mild assumptions as the original LQP method. Finally, numerical results for traffic equilibrium problems are provided to verify that the method is effective for some practical problems.
NONLINEAR FILTER METHOD OF GPS DYNAMIC POSITIONING BASED ON BANCROFT ALGORITHM
Institute of Scientific and Technical Information of China (English)
ZHANGQin; TAOBen-zao; ZHAOChao-ying; WANGLi
2005-01-01
Because of the ignored items after linearization, the extended Kalman filter (EKF) becomes a form of suboptimal gradient descent algorithm. The emanative tendency exists in GPS solution when the filter equations are ill-posed. The deviation in the estimation cannot be avoided. Furthermore, the true solution may be lost in pseudorange positioning because the linearized pseudorange equations are partial solutions. To solve the above problems in GPS dynamic positioning by using EKF, a closed-form Kalman filter method called the two-stage algorithm is presented for the nonlinear algebraic solution of GPS dynamic positioning based on the global nonlinear least squares closed algorithm--Bancroft numerical algorithm of American. The method separates the spatial parts from temporal parts during processing the GPS filter problems, and solves the nonlinear GPS dynamic positioning, thus getting stable and reliable dynamic positioning solutions.
Directory of Open Access Journals (Sweden)
Suxiang He
2014-01-01
Full Text Available An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
Directory of Open Access Journals (Sweden)
Shaolong Chen
2016-01-01
Full Text Available Parameter estimation is an important problem in nonlinear system modeling and control. Through constructing an appropriate fitness function, parameter estimation of system could be converted to a multidimensional parameter optimization problem. As a novel swarm intelligence algorithm, chicken swarm optimization (CSO has attracted much attention owing to its good global convergence and robustness. In this paper, a method based on improved boundary chicken swarm optimization (IBCSO is proposed for parameter estimation of nonlinear systems, demonstrated and tested by Lorenz system and a coupling motor system. Furthermore, we have analyzed the influence of time series on the estimation accuracy. Computer simulation results show it is feasible and with desirable performance for parameter estimation of nonlinear systems.
A quadrature based method of moments for nonlinear Fokker-Planck equations
Otten, Dustin L.; Vedula, Prakash
2011-09-01
Fokker-Planck equations which are nonlinear with respect to their probability densities and occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, fermions and bosons can be challenging to solve numerically. To address some underlying challenges, we propose the application of the direct quadrature based method of moments (DQMOM) for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations (NLFPEs). In DQMOM, probability density (or other distribution) functions are represented using a finite collection of Dirac delta functions, characterized by quadrature weights and locations (or abscissas) that are determined based on constraints due to evolution of generalized moments. Three particular examples of nonlinear Fokker-Planck equations considered in this paper include descriptions of: (i) the Shimizu-Yamada model, (ii) the Desai-Zwanzig model (both of which have been developed as models of muscular contraction) and (iii) fermions and bosons. Results based on DQMOM, for the transient and stationary solutions of the nonlinear Fokker-Planck equations, have been found to be in good agreement with other available analytical and numerical approaches. It is also shown that approximate reconstruction of the underlying probability density function from moments obtained from DQMOM can be satisfactorily achieved using a maximum entropy method.
Nonlinear Multiantenna Detection Methods
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Chen Sheng
2004-01-01
Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.
Nonlinear approximation method in Lagrangian relaxation-based algorithms for hydrothermal scheduling
Energy Technology Data Exchange (ETDEWEB)
Guan, X. [Pacific Gas and Electric, San Francisco, CA (United States); Luh, P.B.; Zhang, L. [Univ. of Connecticut, Storrs, CT (United States). Dept. of Electrical and Systems Engineering
1995-05-01
When the Lagrangian relaxation technique is used to solve hydrothermal scheduling problems, many subproblems have linear stage-wise cost functions. A well recognized difficulty is that the solutions to these subproblems may oscillate between maximum and minimum generations with slight changes of the multipliers. Furthermore, the subproblem solutions may become singular, i.e., they are un-determined when the linear coefficients become zero. This may result in large differences between subproblem solutions and the optimal primal schedule. In this paper, a nonlinear approximation method is presented which utilizes nonlinear functions, quadratic in this case, to approximate relevant linear cost functions. The analysis shows that the difficulty associated with solution oscillation is reduced, and singularity is avoided. Extensive testing based on Northeast Utilities data indicates that the method consistently generates better schedules than the standard Lagrangian relaxation method.
Soft sensor modeling based on variable partition ensemble method for nonlinear batch processes
Wang, Li; Chen, Xiangguang; Yang, Kai; Jin, Huaiping
2017-01-01
Batch processes are always characterized by nonlinear and system uncertain properties, therefore, the conventional single model may be ill-suited. A local learning strategy soft sensor based on variable partition ensemble method is developed for the quality prediction of nonlinear and non-Gaussian batch processes. A set of input variable sets are obtained by bootstrapping and PMI criterion. Then, multiple local GPR models are developed based on each local input variable set. When a new test data is coming, the posterior probability of each best performance local model is estimated based on Bayesian inference and used to combine these local GPR models to get the final prediction result. The proposed soft sensor is demonstrated by applying to an industrial fed-batch chlortetracycline fermentation process.
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Ahad Zeinali
2007-12-01
Full Text Available Introduction: Because of the importance of vertebral compressive fracture (VCF role in increasing the patients’ death rate and reducing their quality of life, many studies have been conducted for a noninvasive prediction of vertebral compressive strength based on bone mineral density (BMD determination and recently finite element analysis. In this study, QCT-voxel based nonlinear finite element method is used for predicting vertebral compressive strength. Material and Methods: Four thoracolumbar vertebrae were excised from 3 cadavers with an average age of 42 years. They were then put in a water phantom and were scanned using the QCT. Using a computer program prepared in MATLAB, detailed voxel based geometry and mechanical characteristics of the vertebra were extracted from the CT images. The three dimensional finite element models of the samples were created using ANSYS computer program. The compressive strength of each vertebra body was calculated based on a linearly elastic-linearly plastic model and large deformation analysis in ANSYS and was compared to the value measured experimentally for that sample. Results: Based on the obtained results the QCT-voxel based nonlinear finite element method (FEM can predict vertebral compressive strength more effectively and accurately than the common QCT-voxel based linear FEM. The difference between the predicted strength values using this method and the measured ones was less than 1 kN for all the samples. Discussion and Conclusion: It seems that the QCT-voxel based nonlinear FEM used in this study can predict more effectively and accurately the vertebral strengths based on every vertebrae specification by considering their detailed geometric and densitometric characteristics.
Goldsworthy, Ray L.; Greenberg, Julie E.
2004-12-01
The Speech Transmission Index (STI) is a physical metric that is well correlated with the intelligibility of speech degraded by additive noise and reverberation. The traditional STI uses modulated noise as a probe signal and is valid for assessing degradations that result from linear operations on the speech signal. Researchers have attempted to extend the STI to predict the intelligibility of nonlinearly processed speech by proposing variations that use speech as a probe signal. This work considers four previously proposed speech-based STI methods and four novel methods, studied under conditions of additive noise, reverberation, and two nonlinear operations (envelope thresholding and spectral subtraction). Analyzing intermediate metrics in the STI calculation reveals why some methods fail for nonlinear operations. Results indicate that none of the previously proposed methods is adequate for all of the conditions considered, while four proposed methods produce qualitatively reasonable results and warrant further study. The discussion considers the relevance of this work to predicting the intelligibility of cochlear-implant processed speech. .
Institute of Scientific and Technical Information of China (English)
ZHANG Suying; DENG Zichen
2005-01-01
Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system.
Institute of Scientific and Technical Information of China (English)
ZHANG Juliang; ZHANG Xiangsun
2001-01-01
In this paper, we use the smoothing penalty function proposed in [1] as the merit function of SQP method for nonlinear optimization with inequality constraints. The global convergence of the method is obtained.
A new method of determining the optimal embedding dimension based on nonlinear prediction
Institute of Scientific and Technical Information of China (English)
Meng Qing-Fang; Peng Yu-Hua; Xue Pei-Jun
2007-01-01
A new method is proposed to determine the optimal embedding dimension from a scalar time series in this paper. This method determines the optimal embedding dimension by optimizing the nonlinear autoregressive prediction model parameterized by the embedding dimension and the nonlinear degree. Simulation results show the effectiveness of this method. And this method is applicable to a short time series, stable to noise, computationally efficient, and without any purposely introduced parameters.
Directory of Open Access Journals (Sweden)
Taochang Li
2014-01-01
Full Text Available Automatic steering control is the key factor and essential condition in the realization of the automatic navigation control of agricultural vehicles. In order to get satisfactory steering control performance, an adaptive sliding mode control method based on a nonlinear integral sliding surface is proposed in this paper for agricultural vehicle steering control. First, the vehicle steering system is modeled as a second-order mathematic model; the system uncertainties and unmodeled dynamics as well as the external disturbances are regarded as the equivalent disturbances satisfying a certain boundary. Second, a transient process of the desired system response is constructed in each navigation control period. Based on the transient process, a nonlinear integral sliding surface is designed. Then the corresponding sliding mode control law is proposed to guarantee the fast response characteristics with no overshoot in the closed-loop steering control system. Meanwhile, the switching gain of sliding mode control is adaptively adjusted to alleviate the control input chattering by using the fuzzy control method. Finally, the effectiveness and the superiority of the proposed method are verified by a series of simulation and actual steering control experiments.
Determining the minimum embedding dimension of nonlinear time series based on prediction method
Institute of Scientific and Technical Information of China (English)
Bian Chun-Hua; Ning Xin-Bao
2004-01-01
Determining the embedding dimension of nonlinear time series plays an important role in the reconstruction of nonlinear dynamics. The paper first summarizes the current methods for determining the embedding dimension.Then, inspired by the fact that the optimum modelling dimension of nonlinear autoregressive (NAR) prediction model can characterize the embedding feature of the dynamics, the paper presents a new idea that the optimum modelling dimension of the NAR model can be taken as the minimum embedding dimension. Some validation examples and results are given and the present method shows its advantage for short data series.
Motulsky, Harvey J; Brown, Ronald E
2006-03-09
Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1-3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.
Directory of Open Access Journals (Sweden)
Motulsky Harvey J
2006-03-01
Full Text Available Abstract Background Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. Results We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely one or more outlier in only about 1–3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. Conclusion Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.
Crouseilles, Nicolas; Lemou, Mohammed
2016-01-01
We introduce a new numerical strategy to solve a class of oscillatory transport PDE models which is able to captureaccurately the solutions without numerically resolving the high frequency oscillations {\\em in both space and time}.Such PDE models arise in semiclassical modeling of quantum dynamics with band-crossings, and otherhighly oscillatory waves. Our first main idea is to use the nonlinear geometric optics ansatz, which builds theoscillatory phase into an independent variable. We then choose suitable initial data, based on the Chapman-Enskog expansion, for the new model. For a scalar model, we prove that so constructed model will have certain smoothness, and consequently, for a first order approximation scheme we prove uniform error estimates independent of the (possibly small) wave length. The method is extended to systems arising from a semiclassical model for surface hopping, a non-adiabatic quantum dynamic phenomenon. Numerous numerical examples demonstrate that the method has the desired properties...
Institute of Scientific and Technical Information of China (English)
GUYanfeng; ZHANGYe; QUANTaifan
2003-01-01
A challenging problem in using hyper-spectral data is to eliminate redundancy and preserve useful spectral information for applications. In this pa-per, a kernel-based nonlinear subspace projection (KNSP)method is proposed for feature extraction and dimension-ality reduction in hyperspectral images. The proposed method includes three key steps: subspace partition of hyperspectral data, feature extraction using kernel-based principal component analysis (KPCA) and feature selec-tion based on class separability in the subspaces. Accord-ing to the strong correlation between neighboring bands,the whole data space is partitioned to requested subspaces.In each subspace, the KPCA method is used to effectively extract spectral feature and eliminate redundancies. A criterion function based on class discrimination and sepa-rability is used for the transformed feature selection. For the purpose of testifying its effectiveness, the proposed new method is compared with the classical principal component analysis (PCA) and segmented principal component trans-formation (SPCT). A hyperspectral image classification is performed on AVIRIS data. which have 224 svectral bands.Experimental results show that KNSP is very effective for feature extraction and dimensionality reduction of hyper-spectral data and provides significant improvement over classical PCA and current SPCT technique.
A nonlinear combination forecasting method based on the fuzzy inference system
Institute of Scientific and Technical Information of China (English)
董景荣; YANG; Jun; 等
2002-01-01
It has been shown in recent economic and statistical studies that combining forecasts may produce more accurate forecasts than individual ones,However,the literature on combining forecasts has almost exclusively focused on linear combining forecasts.In this paper,a new nonlinear combination forecasting method based on fuzzy inference system is present to overcome the difficulties and drawbacks in linear combination modeling of non-stationary time series.Furthermore,the optimization algorithm based on a hierarchical structure of learning automata is used to identify the parameters of the fuzzy system.Experiment results related to numerical examples demonstrate that the new technique has excellent identification performances and forecasting accuracy superior to other existing linear combining forecasts.
Directory of Open Access Journals (Sweden)
Hui Cao
2014-01-01
Full Text Available Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.
Cao, Hui; Yan, Xingyu; Li, Yaojiang; Wang, Yanxia; Zhou, Yan; Yang, Sanchun
2014-01-01
Quantitative analysis for the flue gas of natural gas-fired generator is significant for energy conservation and emission reduction. The traditional partial least squares method may not deal with the nonlinear problems effectively. In the paper, a nonlinear partial least squares method with extended input based on radial basis function neural network (RBFNN) is used for components prediction of flue gas. For the proposed method, the original independent input matrix is the input of RBFNN and the outputs of hidden layer nodes of RBFNN are the extension term of the original independent input matrix. Then, the partial least squares regression is performed on the extended input matrix and the output matrix to establish the components prediction model of flue gas. A near-infrared spectral dataset of flue gas of natural gas combustion is used for estimating the effectiveness of the proposed method compared with PLS. The experiments results show that the root-mean-square errors of prediction values of the proposed method for methane, carbon monoxide, and carbon dioxide are, respectively, reduced by 4.74%, 21.76%, and 5.32% compared to those of PLS. Hence, the proposed method has higher predictive capabilities and better robustness.
Directory of Open Access Journals (Sweden)
Wang Pidong
2016-01-01
Full Text Available Blind source separation is a hot topic in signal processing. Most existing works focus on dealing with linear combined signals, while in practice we always encounter with nonlinear mixed signals. To address the problem of nonlinear source separation, in this paper we propose a novel algorithm using radial basis function neutral network, optimized by multi-universe parallel quantum genetic algorithm. Experiments show the efficiency of the proposed method.
Directory of Open Access Journals (Sweden)
Chen Xiong
2016-01-01
Full Text Available Although the structured light system that uses digital fringe projection has been widely implemented in three-dimensional surface profile measurement, the measurement system is susceptible to non-linear error. In this work, we propose a convenient look-up-table-based (LUT-based method to compensate for the non-linear error in captured fringe patterns. Without extra calibration, this LUT-based method completely utilizes the captured fringe pattern by recording the full-field differences. Then, a phase compensation map is established to revise the measured phase. Experimental results demonstrate that this method works effectively.
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Ćosić Mladen
2014-01-01
Full Text Available This paper presents the original method of controlled building damage mechanisms based on Nonlinear Static Pushover Analysis (NSPA-DMBD. The optimal building damage mechanism is determined based on the solution of the Capacity Design Method (CDM, and the response of the building is considered in incremental situations. The development of damage mechanism of a system in such incremental situations is being controlled on the strain level, examining the relationship of current and limit strains in concrete and reinforcement steel. Since the procedure of the system damage mechanism analysis according to the NSPA-DMBD method is being iteratively implemented and designing checked after the strain reaches the limit, for this analysis a term Iterative-Interactive Design (IID has been introduced. By selecting, monitoring and controlling the optimal damage mechanism of the system and by developed NSPA-DMBD method, damage mechanism of the building is being controlled and the level of resistance to an early collapse is being increased. [Projekat Ministarstva nauke Republike Srbije, br. TR 36043
Multiscale Study of the Nonlinear Behavior of Heterogeneous Clayey Rocks Based on the FFT Method
Jiang, Tao; Xu, Weiya; Shao, Jianfu
2015-03-01
A multiscale model based on the fast Fourier transform (FFT) is applied to study the nonlinear mechanical behavior of Callovo-Oxfordian (COx) argillite, a typical heterogeneous clayey rocks. COx argillite is modeled as a three-phase composite with a clay matrix and two types of mineral inclusions. The macroscopic mechanical behavior of argillite samples with different mineralogical compositions are satisfactorily predicted by unified local constitutive models and material parameters. Moreover, the numerical implementation of the FFT-based nonlinear homogenization is easier than direct homogenization, such as the FEM-based homogenization, because it automatically satisfies the periodic boundary condition.
Institute of Scientific and Technical Information of China (English)
WANG Zi-yang; WU Gang; CHEN Wei
2007-01-01
A new model predictive control (MPC) algorithm for nonlinear systems is presented, its stabilizing property is proved, and its attractive regions are estimated. The presented method is based on the feasible solution,which makes the attractive regions much larger than those of the normal MPC controller that is based on the optimal solution.
Energy Technology Data Exchange (ETDEWEB)
Meili, G.; Dubroca, G.; Pasquier, M.; Thepenier, J.
1982-06-01
The paper discusses a method for the mechanical testing of casebonded composite modified double base charges (CMDB) subjected to thermal cycling. The method proposed to determine stresses and safety margins takes into account the non-linear viscoelastic behaviour and the compressibility of the propellant. The non-linear behaviour is derived from tensile testing. The equations of equilibrium are solved numerically by deviding the grain web into many layers. The nonlinearities mainly concern the modulus; a multiaxial criterion and the time-temperature shift factors are used. At each time-step and for each layer the temperature, the reduced time, the non-linear factor, the Poisson's ratio and the damage according to the concept of Farris are calculated. Different charges (star, wagon wheel, finocyl) were subjected to various types of thermal cycles. The comparison between prediction and experimentation is acceptable even for complex histories in strain and temperature.
Hosen, Md. Alal; Chowdhury, M. S. H.; Ali, Mohammad Yeakub; Ismail, Ahmad Faris
In the present paper, a novel analytical approximation technique has been proposed based on the energy balance method (EBM) to obtain approximate periodic solutions for the focus generalized highly nonlinear oscillators. The expressions of the natural frequency-amplitude relationship are obtained using a novel analytical way. The accuracy of the proposed method is investigated on three benchmark oscillatory problems, namely, the simple relativistic oscillator, the stretched elastic wire oscillator (with a mass attached to its midpoint) and the Duffing-relativistic oscillator. For an initial oscillation amplitude A0 = 100, the maximal relative errors of natural frequency found in three oscillators are 2.1637%, 0.0001% and 1.201%, respectively, which are much lower than the errors found using the existing methods. It is highly remarkable that an excellent accuracy of the approximate natural frequency has been found which is valid for the whole range of large values of oscillation amplitude as compared with the exact ones. Very simple solution procedure and high accuracy that is found in three benchmark problems reveal the novelty, reliability and wider applicability of the proposed analytical approximation technique.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Short-term pollution forecasts based on linear and nonlinear methods of time series analysis
Russo, A.; Trigo, R. M.
2012-04-01
Urban air pollution is a complex mixture of toxic components, which may induce acute and chronic responses from sensitive groups, such as children and people with previous heart and respiratory insufficiencies. However, air pollution, presents a highly chaotic and non-linear behavior. In this work we analyzed several pollutants time series recorded in the urban area of Lisbon (Portugal) for the 2002-2006 period. Linear and nonlinear methods were applied in order to assess NO2, PM10 and O3 main trends and fluctuations and finally, to produce daily forecasts of the referred pollutants. Here we evaluate the potential of linear and non-linear neural networks (NN) to produce short-term forecasts, and also the contribution of meteorological variables (daily mean temperature, radiation, wind speed and direction, boundary layer height, humidity) to pollutants dispersion. Additionally, we assess the role of large-scale circulation patterns, usually referred as Weather types (WT) (from the ERA40/ECMWF and ECMWF SLP database) towards the occurrence of critical pollution events identified previously. The presence and importance of trends and fluctuation is addressed by means of two modelling approaches: (1) raw data modelling; (2) residuals modelling (after the removal of the trends from the original data). The relative importance of two periodic components, the weekly and the monthly cycles, is addressed. For the three pollutants, the approach based on the removal of the weekly cycle presents the best results, comparatively to the removal of the monthly cycle or to the use of the raw data. The best predictors are chosen independently for each monitoring station and pollutant through an objective procedure (backward stepwise regression). The analysis reveals that the most significant variables in predicting NO2 concentration are several NO2 measures, wind direction and speed and global radiation, while for O3 correspond to several O3 measures, O3 precursors and WT
Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method
Institute of Scientific and Technical Information of China (English)
Chen Yimei; Han Zhengzhi; Tang Houjun
2006-01-01
The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.
Nonlinearity measurements of solar cells with an LED-based combinatorial flux addition method.
Hamadani, Behrang H; Shore, Andrew; Roller, John; Yoon, Howard W; Campanelli, Mark
2016-02-01
We present a light emitting diode (LED)-based system utilizing a combinatorial flux addition method to investigate the nonlinear relationship in solar cells between the output current of the cell and the incident irradiance level. The magnitude of the light flux is controlled by the supplied currents to two LEDs (or two sets of them) in a combinatorial fashion. The signals measured from the cell are arranged within a related overdetermined linear system of equations derived from an appropriately chosen N(th) degree polynomial representing the relationship between the measured signals and the incident fluxes. The flux values and the polynomial coefficients are then solved for by linear least squares to obtain the best fit. The technique can be applied to any solar cell, under either monochromatic or broadband spectrum. For the unscaled solution, no reference detectors or prior calibrations of the light flux are required. However, if at least one calibrated irradiance value is known, then the entire curve can be scaled to an appropriate spectral responsivity value. Using this technique, a large number of data points can be obtained in a relatively short time scale over a large signal range.
Cai, Lanlan; Li, Peng; Luo, Qi; Zhai, Pengcheng; Zhang, Qingjie
2017-03-01
As no single thermoelectric material has presented a high figure-of-merit (ZT) over a very wide temperature range, segmented thermoelectric generators (STEGs), where the p- and n-legs are formed of different thermoelectric material segments joined in series, have been developed to improve the performance of thermoelectric generators. A crucial but difficult problem in a STEG design is to determine the optimal values of the geometrical parameters, like the relative lengths of each segment and the cross-sectional area ratio of the n- and p-legs. Herein, a multi-parameter and nonlinear optimization method, based on the Improved Powell Algorithm in conjunction with the discrete numerical model, was implemented to solve the STEG's geometrical optimization problem. The multi-parameter optimal results were validated by comparison with the optimal outcomes obtained from the single-parameter optimization method. Finally, the effect of the hot- and cold-junction temperatures on the geometry optimization was investigated. Results show that the optimal geometry parameters for maximizing the specific output power of a STEG are different from those for maximizing the conversion efficiency. Data also suggest that the optimal geometry parameters and the interfacial temperatures of the adjacent segments optimized for maximum specific output power or conversion efficiency vary with changing hot- and cold-junction temperatures. Through the geometry optimization, the CoSb3/Bi2Te3-based STEG can obtain a maximum specific output power up to 1725.3 W/kg and a maximum efficiency of 13.4% when operating at a hot-junction temperature of 823 K and a cold-junction temperature of 298 K.
Teaching Numerical Methods for Non-linear Equations with GeoGebra-Based Activities
Directory of Open Access Journals (Sweden)
Ana M. Martín-Caraballo
2015-08-01
Full Text Available but even in University. To be more precise, our main goal consists in putting forward the usefulness of GeoGebra as working tool so that our students manipulate several numerical (both recursive and iterative methods to solve nonlinear equations. In this sense, we show how Interactive Geometry Software makes possible to deal with these methods by means of their geometrical interpretation and to visualize their behavior and procedure. In our opinion, visualization is absolutely essential for first-year students in the University, since they must change their perception about Mathematics and start considering a completely formal and argued way to work the notions, methods and problems explained and stated. Concerning these issues, we present some applets developed using GeoGebra to explain and work with numerical methods for nonlinear equations. Moreover, we indicate how these applets are applied to our teaching. In fact, the methods selected to be dealt with this paper are those with important geometric interpretations, namely: the bisection method, the secant method, the regula-falsi (or false-position method and the tangent (or Newton-Raphson method, this last as example of fixed-point methods.
Gorban, A. N.; Karlin, I.V.
2003-01-01
Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation, Phenomenology and Quasi-chemical representation of the Boltzmann equation, Kinetic models, Discrete velocity models, Direct simulation, Lattice Gas and Lattice Boltzmann models, Minimal Boltzmann models for flows at low Knudsen number, Other kinetic equati...
Directory of Open Access Journals (Sweden)
V. E. Markevich
2017-01-01
Full Text Available A method of analytical synthesis of an optimal controller for the terminal control task of supersonic unmanned aerial vehicles based on synergetic approach to the design of control systems for nonlinear multidimensional dynamic objects is considered.The article provides analytical expressions describing the algorithm for control the velocity vector position of a supersonic UAV, the simulation results and the comparative analysis of the proposed control algorithm with the modified method of proportional navigation.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Nonlinear fractal dynamics of human colonic pressure activity based upon the box-counting method.
Yan, Rongguo; Guo, Xudong
2013-01-01
The computational fractal dimension of human colonic pressure activity acquired by a telemetric capsule robot under normal physiological conditions was studied using the box-counting method. The fractal dimension is a numeric value that quantifies to measure how rough the signal is from nonlinear dynamics, rather than its amplitude or other linear statistical features. The colonic pressure activities from the healthy subject during three typical periods were analysed. The results showed that the activity might be fractal with a non-integer fractal dimension after it being integrated over time using the cumsum method, which was never revealed before. Moreover, the activity (after it being integrated) acquired soon after wakening up was the roughest (also the most complex one) with the largest fractal dimension, closely followed by that acquired during sleep with that acquired long time after awakening up (in the daytime) ranking third with the smallest fractal dimension. Fractal estimation might provide a new method to learn the nonlinear dynamics of human gastrointestinal pressure recordings.
Institute of Scientific and Technical Information of China (English)
Fan Yuxin; Xia Jian
2014-01-01
A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute tran-sient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute infla-tion is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES) method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hil-ber–Hughes–Taylor (HHT) time integration method is employed. For the fluid dynamic simula-tions, the Roe and HLLC (Harten–Lax–van Leer contact) scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS) approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Directory of Open Access Journals (Sweden)
Fan Yuxin
2014-12-01
Full Text Available A fluid–structure interaction method combining a nonlinear finite element algorithm with a preconditioning finite volume method is proposed in this paper to simulate parachute transient dynamics. This method uses a three-dimensional membrane–cable fabric model to represent a parachute system at a highly folded configuration. The large shape change during parachute inflation is computed by the nonlinear Newton–Raphson iteration and the linear system equation is solved by the generalized minimal residual (GMRES method. A membrane wrinkling algorithm is also utilized to evaluate the special uniaxial tension state of membrane elements on the parachute canopy. In order to avoid large time expenses during structural nonlinear iteration, the implicit Hilber–Hughes–Taylor (HHT time integration method is employed. For the fluid dynamic simulations, the Roe and HLLC (Harten–Lax–van Leer contact scheme has been modified and extended to compute flow problems at all speeds. The lower–upper symmetric Gauss–Seidel (LU-SGS approximate factorization is applied to accelerate the numerical convergence speed. Finally, the test model of a highly folded C-9 parachute is simulated at a prescribed speed and the results show similar characteristics compared with experimental results and previous literature.
Dattoli, Giuseppe
2005-01-01
The coherent synchrotron radiation (CSR) is one of the main problems limiting the performance of high intensity electron accelerators. A code devoted to the analysis of this type of problems should be fast and reliable: conditions that are usually hardly achieved at the same time. In the past, codes based on Lie algebraic techniques have been very efficient to treat transport problem in accelerators. The extension of these method to the non-linear case is ideally suited to treat CSR instability problems. We report on the development of a numerical code, based on the solution of the Vlasov equation, with the inclusion of non-linear contribution due to wake field effects. The proposed solution method exploits an algebraic technique, using exponential operators implemented numerically in C++. We show that the integration procedure is capable of reproducing the onset of an instability and effects associated with bunching mechanisms leading to the growth of the instability itself. In addition, parametric studies a...
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates
Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma
2016-10-01
This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.
Directory of Open Access Journals (Sweden)
Ignat’ev Aleksandr Vladimirovich
2016-02-01
Full Text Available The most widely used numerical method used in linear calculation of building structures is finite element method in traditional form of displacements. Different software is developed on its basis. Though it is only possible to check the certainty of these numerical solutions, especially of non-linear tasks of engineering structures’ deformation by the coincidence of the results obtained by two different methods. The authors solved geometrically nonlinear task of the static deformation of a flat hinged-rod system consisting of five linear elastic rods undergoing great tension-compression strains. The solution was obtained basing on the finite element method in the form of classical mixed method developed by the authors. The set of all equilibrium states of the system, both stable and unstable, and all the limit points were found. The certainty of the solution was approved by the coincidence of the results obtained by other authors basing on traditional finite element method in displacements.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A new noise reduction method for nonlinear signal based on maximum variance unfolding(MVU)is proposed.The noisy sig- nal is firstly embedded into a high-dimensional phase space based on phase space reconstruction theory,and then the manifold learning algorithm MVU is used to perform nonlinear dimensionality reduction on the data of phase space in order to separate low-dimensional manifold representing the attractor from noise subspace.Finally,the noise-reduced signal is obtained through reconstructing the low-dimensional manifold.The simulation results of Lorenz system show that the proposed MVU-based noise reduction method outperforms the KPCA-based method and has the advantages of simple parameter estimation and low parameter sensitivity.The proposed method is applied to fault detection of a vibration signal from rotor-stator of aero engine with slight rubbing fault.The denoised results show that the slight rubbing features overwhelmed by noise can be effectively extracted by the proposed noise reduction method.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Institute of Scientific and Technical Information of China (English)
2011-01-01
In this paper mathematical model of single inverted pendulum established based on Lagrange method. Stability of the inverted pendulum system is analyzed. Single inverted pendulum can be controlled by modem control theory, pole assignment method and Linear-quadratic regulator theory, effectually but only in small angle range. In order to obtain the larger controllable angle, the fuzzy method has been accepted to treat with this system. The idea behind of fuzzy control method in this paper is to divide the operating region of nonlinear system into small area, and treated as a collection of local linear systems which can be controlled. Global bounded property of the fuzzy method has been proven success, and according the simulation results of fuzzy servo system controllable angle is extended.
Institute of Scientific and Technical Information of China (English)
ZHOU Rong-yi; LIU Ai-qun; LI Shu-qing
2007-01-01
Directing at the non-linear dynamic characteristics of water inrush from coal seam floor and by the analysis of the shortages of current forecast methods for water inrush from coal seam floor,a new forecast method was raised based on wavelet neural network(WNN)that was a model combining wavelet function with artificiaI neural network.Firstly basic principle of WNN was described.then a forecast model for water inrush from coal seam floor based on WNN was established and analyzed,finally an example of forecasting the quantity of water inrush from coal floor was illustrated to verify the feasibility and superiority of this method.Conclusions show that the forecast result based on WNN is more precise and that using WNN model to forecast the quantity of water inrush from coal seam floor is feasible and practical.
Muniz, Rodrigo A; Martin, Ivar
2011-09-16
We theoretically study the effect that stripelike superconducting inclusions would have on the nonlinear resistivity in single crystals. Even if the stripe orientation varies throughout the sample between two orthogonal directions due to twinning, we predict that there should be a universal dependence of the nonlinear resistivity on the angle between the applied current and the crystal axes. This prediction can be used to test the existence of superconducting stripes at and above the superconducting transition temperature in cuprate superconductors.
Heli Hu; Dan Zhao; Qingling Zhang
2013-01-01
The sliding mode control and optimization are investigated for a class of nonlinear neutral systems with the unmatched nonlinear term. In the framework of Lyapunov stability theory, the existence conditions for the designed sliding surface and the stability bound ${\\alpha }^{\\ast }$ are derived via twice transformations. The further results are to develop an efficient sliding mode control law with tuned parameters to attract the state trajectories onto the sliding surface in finit...
DEFF Research Database (Denmark)
Lu, Kaiyuan; Rasmussen, Peter Omand; Ritchie, Ewen
2011-01-01
This paper presents a new method for computation of the nonlinear flux linkage in 3-D finite-element models (FEMs) of electrical machines. Accurate computation of the nonlinear flux linkage in 3-D FEM is not an easy task. Compared to the existing energy-perturbation method, the new technique......-perturbation method. The new method proposed is validated using experimental results on two different permanent magnet machines....
DEFF Research Database (Denmark)
Tatu, Aditya Jayant
defined subspace, the N-links bicycle chain space, i.e. the space of curves with equidistant neighboring landmark points. This in itself is a useful shape space for medical image analysis applications. The Histogram of Gradient orientation based features are many in number and are widely used......This thesis deals with two unrelated issues, restricting curve evolution to subspaces and computing image patches in the equivalence class of Histogram of Gradient orientation based features using nonlinear projection methods. Curve evolution is a well known method used in various applications like...... specific requirements like shape priors or a given data model, and due to limitations of the computer, the computed curve evolution forms a path in some finite dimensional subspace of the space of curves. We give methods to restrict the curve evolution to a finite dimensional linear or implicitly defined...
Zhang, Li-Guo; Zhang, Xin; Ni, Li-Jun; Xue, Zhi-Bin; Gu, Xin; Huang, Shi-Xin
2014-02-15
More than 800 representative milk samples, which consisted of 287 raw cow milk samples from different pastures surrounding Shanghai of China and 526 adulteration milk samples containing different pseudo proteins and thickeners, were collected and designed to demonstrate a method for rapidly discriminating adulterated milks based on near infrared (NIR) spectra. The NIR classification models were built by two non-linear supervised pattern recognition methods of improved support vector machine (I-SVM) and improved and simplified K nearest neighbours (IS-KNN). Uniform design theory was applied to optimize the parameters of SVM and thus the computation amount was reduced 90%. Both two methods exhibit good adaptability in discriminating adulterated milks from raw cow milks. Further investigation showed that the correction ratio for discriminating milk samples increased with the increasing of adulteration solutions' level in the adulterated milk. The concentration of adulterants is an important factor of influencing milk discrimination results of the NIR pattern recognition models. The results demonstrated the usefulness of NIR spectra combined with non-linear pattern recognition methods as an objective and rapid method for the authentication of complicated raw cow milks.
Entropy viscosity method for nonlinear conservation laws
Guermond, Jean-Luc
2011-05-01
A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entropy inequalities and does not depend on the mesh type and polynomial approximation. Various benchmark problems are solved with finite elements, spectral elements and Fourier series to illustrate the capability of the proposed method. © 2010 Elsevier Inc.
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
Zhao, Yifan; Mehnen, Jörn; Sirikham, Adisorn; Roy, Rajkumar
2017-02-01
This paper introduces a new method to improve the reliability and confidence level of defect depth measurement based on pulsed thermographic inspection by addressing the over-fitting problem. Different with existing methods using a fixed model structure for all pixels, the proposed method adaptively detects the optimal model structure for each pixel thus targeting to achieve better model fitting while using less model terms. Results from numerical simulations and real experiments suggest that (a) the new method is able to measure defect depth more accurately without a pre-set model structure (error is usually within 1 % when SNR>32 dB) in comparison with existing methods, (b) the number of model terms should be 8 for signals with SNR∈ [ 30 dB , 40 dB ] , 8-10 for SNR>40 dB and 5-8 for SNR<30 dB, and (c) a data length with at least 100 data points and 2-3 times of the characteristic time usually produces the best results.
Scarselli, G.; Ciampa, F.; Ginzburg, D.; Meo, M.
2015-04-01
Nonlinear ultrasonic non-destructive evaluation (NDE) methods can be used for the identification of defects within adhesive bonds as they rely on the detection of nonlinear elastic features for the evaluation of the bond strength. In this paper the nonlinear content of the structural response of a single lap joint subjected to ultrasonic harmonic excitation is both numerically and experimentally evaluated to identify and characterize the defects within the bonded region. Different metallic samples with the same geometry were experimentally tested in order to characterize the debonding between two plates by using two surface bonded piezoelectric transducers in pitch-catch mode. The dynamic response of the damaged samples acquired by the single receiver sensor showed the presence of higher harmonics (2nd and 3rd) and subharmonics of the fundamental frequencies. These nonlinear elastic phenomena are clearly due to nonlinear effects induced by the poor adhesion between the two plates. A new constitutive model aimed at representing the nonlinear material response generated by the interaction of the ultrasonic waves with the adhesive joint is also presented. Such a model is implemented in an explicit FE software and uses a nonlinear user defined traction-displacement relationship implemented by means of a cohesive material user model interface. The developed model is verified for the different geometrical and material configurations. Good agreement between the experimental and numerical nonlinear response showed that this model can be used as a simple and useful tool for understanding the quality of the adhesive joint.
Institute of Scientific and Technical Information of China (English)
GE Jian-Ya; WANG Rui-Min; DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, by means of the variable-coefficient mapping method based on elliptical equation, we obtain explicit solutions of nonlinear Schr(o)dinger equation with variable-coefficient. These solutions include Jacobian elliptic function solutions, solitary wave solutions, soliton-like solutions, and trigonometric function solutions, among which some are found for the first time. Six figures are given to illustrate some features of these solutions. The method can be applied to other nonlinear evolution equations in mathematical physics.
Adaptive explicit Magnus numerical method for nonlinear dynamical systems
Institute of Scientific and Technical Information of China (English)
LI Wen-cheng; DENG Zi-chen
2008-01-01
Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group,an efficient numerical method is proposed for nonlinear dynamical systems.To improve computational efficiency,the integration step size can be adaptively controlled.Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system,the van der Pol system with strong stiffness,and the nonlinear Hamiltonian pendulum system.
Statistical methods in nonlinear dynamics
Indian Academy of Sciences (India)
K P N Murthy; R Harish; S V M Satyanarayana
2005-03-01
Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.
Fu, Libi; Song, Weiguo; Lo, Siuming
2017-01-01
Emergencies involved in mass events are related to a variety of factors and processes. An important factor is the transmission of information on danger that has an influence on nonlinear crowd dynamics during the process of crowd dispersion. Due to much uncertainty in this process, there is an urgent need to propose a method to investigate the influence. In this paper, a novel fuzzy-theory-based method is presented to study crowd dynamics under the influence of information transmission. Fuzzy functions and rules are designed for the ambiguous description of human states. Reasonable inference is employed to decide the output values of decision making such as pedestrian movement speed and directions. Through simulation under four-way pedestrian situations, good crowd dispersion phenomena are achieved. Simulation results under different conditions demonstrate that information transmission cannot always induce successful crowd dispersion in all situations. This depends on whether decision strategies in response to information on danger are unified and effective, especially in dense crowds. Results also suggest that an increase in drift strength at low density and the percentage of pedestrians, who choose one of the furthest unoccupied Von Neumann neighbors from the dangerous source as the drift direction at high density, is helpful in crowd dispersion. Compared with previous work, our comprehensive study improves an in-depth understanding of nonlinear crowd dynamics under the effect of information on danger.
Institute of Scientific and Technical Information of China (English)
Xiang Li; Serge Cescotto; Barbara Rossi
2009-01-01
The natural neighbour method can be considered as one of many variants of the meshless methods. In the present paper, a new approach based on the Fraeijs de Veubeke (FdV) functional, which is initially developed for linear elasticity, is extended to the case of geometrically linear but materially non-linear solids. The new approach provides an original treatment to two classical problems: the numerical evaluation of the integrals over the domain A and the enforcement of boundary conditions of the type ui = uion Su. In the absence of body forces (Fi = 0), it will be shown that the calculation of integrals of the type fA .dA can be avoided and that boundary conditions of the type ui = ui on Su can be imposed in the average sense in general and exactly if ui is linear between two contour nodes, which is obviously the case for ui = 0.
Cernuda, Carlos; Lughofer, Edwin; Klein, Helmut; Forster, Clemens; Pawliczek, Marcin; Brandstetter, Markus
2017-01-01
During the production process of beer, it is of utmost importance to guarantee a high consistency of the beer quality. For instance, the bitterness is an essential quality parameter which has to be controlled within the specifications at the beginning of the production process in the unfermented beer (wort) as well as in final products such as beer and beer mix beverages. Nowadays, analytical techniques for quality control in beer production are mainly based on manual supervision, i.e., samples are taken from the process and analyzed in the laboratory. This typically requires significant lab technicians efforts for only a small fraction of samples to be analyzed, which leads to significant costs for beer breweries and companies. Fourier transform mid-infrared (FT-MIR) spectroscopy was used in combination with nonlinear multivariate calibration techniques to overcome (i) the time consuming off-line analyses in beer production and (ii) already known limitations of standard linear chemometric methods, like partial least squares (PLS), for important quality parameters Speers et al. (J I Brewing. 2003;109(3):229-235), Zhang et al. (J I Brewing. 2012;118(4):361-367) such as bitterness, citric acid, total acids, free amino nitrogen, final attenuation, or foam stability. The calibration models are established with enhanced nonlinear techniques based (i) on a new piece-wise linear version of PLS by employing fuzzy rules for local partitioning the latent variable space and (ii) on extensions of support vector regression variants (-PLSSVR and ν-PLSSVR), for overcoming high computation times in high-dimensional problems and time-intensive and inappropriate settings of the kernel parameters. Furthermore, we introduce a new model selection scheme based on bagged ensembles in order to improve robustness and thus predictive quality of the final models. The approaches are tested on real-world calibration data sets for wort and beer mix beverages, and successfully compared to
μ Synthesis Method for Robust Control of Uncertain Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
μ synthesis method for robust control of uncertain nonlinear systems is propored, which is based on feedback linearization. First, nonlinear systems are linearized as controllable linear systems by I/O linearization,such that uncertain nonlinear systems are expressed as the linear fractional transformations (LFTs) on the generalized linearized plants and uncertainty.Then,linear robust controllers are obtained for the LFTs usingμsynthesis method based on H∞ optimization.Finally,the nonlinear robust controllers are constructed by combining the linear robust controllers and the nonlinear feedback.An example is given to illustrate the design.
Stenvall, A.; Tarhasaari, T.
2010-07-01
Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T - phiv formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.
Energy Technology Data Exchange (ETDEWEB)
Stenvall, A; Tarhasaari, T, E-mail: antti.stenvall@tut.f [Electromagnetics, Tampere University of Technology, PO Box 692, 33101 Tampere (Finland)
2010-07-15
Due to the rapid development of personal computers from the beginning of the 1990s, it has become a reality to simulate current penetration, and thus hysteresis losses, in superconductors with other than very simple one-dimensional (1D) Bean model computations or Norris formulae. Even though these older approaches are still usable, they do not consider, for example, multifilamentary conductors, local critical current dependency on magnetic field or varying n-values. Currently, many numerical methods employing different formulations are available. The problem of hysteresis losses can be scrutinized via an eddy current formulation of the classical theory of electromagnetism. The difficulty of the problem lies in the non-linear resistivity of the superconducting region. The steep transition between the superconducting and the normal states often causes convergence problems for the most common finite element method based programs. The integration methods suffer from full system matrices and, thus, restrict the number of elements to a few thousands at most. The so-called T - {psi} formulation and the use of edge elements, or more precisely Whitney 1-forms, within the finite element method have proved to be a very suitable method for hysteresis loss simulations of different geometries. In this paper we consider making such finite element method software from first steps, employing differential geometry and forms.
Lo, Men-Tzung; Novak, Vera; Peng, C-K; Liu, Yanhui; Hu, Kun
2009-06-01
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently proposed multimodal pressure flow (MMPF) analysis that is based on Hilbert-Huang transform (HHT)-an advanced nonlinear decomposition algorithm. We considered three types of nonstationarities that are often presented in physical and physiological signals: (i) missing segments of data, (ii) linear and step-function trends embedded in data, and (iii) multiple chaotic oscillatory components at different frequencies in data. By generating two coupled oscillatory signals with an assigned phase shift, we quantify the change in the estimated phase shift after imposing artificial nonstationarities into the oscillatory signals. We found that all three types of nonstationarities affect the performances of the Fourier-based and the HHT-based phase analyses, introducing bias and random errors in the estimation of the phase shift between two oscillatory signals. We also provided examples of nonstationarities in real physiological data (cerebral blood flow and blood pressure) and showed how nonstationarities can complicate result interpretation. Furthermore, we propose certain strategies that can be implemented in the TFA and the MMPF methods to reduce the effects of nonstationarities, thus improving the performances of the two methods.
Computer-Aided Design Methods for Model-Based Nonlinear Engine Control Systems Project
National Aeronautics and Space Administration — Traditional design methods for aircraft turbine engine control systems have relied on the use of linearized models and linear control theory. While these controllers...
Scalable nonlinear iterative methods for partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Cai, X-C
2000-10-29
We conducted a six-month investigation of the design, analysis, and software implementation of a class of singularity-insensitive, scalable, parallel nonlinear iterative methods for the numerical solution of nonlinear partial differential equations. The solutions of nonlinear PDEs are often nonsmooth and have local singularities, such as sharp fronts. Traditional nonlinear iterative methods, such as Newton-like methods, are capable of reducing the global smooth nonlinearities at a nearly quadratic convergence rate but may become very slow once the local singularities appear somewhere in the computational domain. Even with global strategies such as line search or trust region the methods often stagnate at local minima of {parallel}F{parallel}, especially for problems with unbalanced nonlinearities, because the methods do not have built-in machinery to deal with the unbalanced nonlinearities. To find the same solution u* of F(u) = 0, we solve, instead, an equivalent nonlinearly preconditioned system G(F(u*)) = 0 whose nonlinearities are more balanced. In this project, we proposed and studied a nonlinear additive Schwarz based parallel nonlinear preconditioner and showed numerically that the new method converges well even for some difficult problems, such as high Reynolds number flows, when a traditional inexact Newton method fails.
Nonlinear structural analysis using integrated force method
Indian Academy of Sciences (India)
N R B Krishnam Raju; J Nagabhushanam
2000-08-01
Though the use of the integrated force method for linear investigations is well-recognised, no efforts were made to extend this method to nonlinear structural analysis. This paper presents the attempts to use this method for analysing nonlinear structures. General formulation of nonlinear structural analysis is given. Typically highly nonlinear bench-mark problems are considered. The characteristic matrices of the elements used in these problems are developed and later these structures are analysed. The results of the analysis are compared with the results of the displacement method. It has been demonstrated that the integrated force method is equally viable and efficient as compared to the displacement method.
Directory of Open Access Journals (Sweden)
Wenqi Wu
2012-06-01
Full Text Available In Compass/INS integrated navigation systems, feedback inertial navigation solutions to baseband tracking loops may eliminate receiver dynamic effects, and effectively improve the tracking accuracy and sensitivity. In the conventional inertially-aided tracking loop, the satellite-receiver line-of-sight velocity is used directly to adjust local carrier frequency. However, if the inertial solution drifts, the phase tracking error will be enlarged. By using Kalman filter based carrier phase tracking loop, this paper introduces a new inertial aid method, in which the line-of-sight jerk obtained from inertial acceleration by a nonlinear tracking differentiator is used to adjust relevant parameters of the Kalman filter’s process noise matrix. Validation is achieved through high dynamic Compass B3 signal with line-of-sight jerk of 10 g/s collected by a GNSS simulator. Experimental results indicate that the new inertial aid method proposed in this paper is free of the impact of the receiver dynamic and inertial errors. Therefore, when the integrated navigation system is starting or re-tracking after losing lock, the inertial error is absent from the navigation solution correction that induces large drift, and the new aid method proposed in this paper can track highly dynamic signals.
Guo, Yao; Wu, Wenqi; Tang, Kanghua
2012-01-01
In Compass/INS integrated navigation systems, feedback inertial navigation solutions to baseband tracking loops may eliminate receiver dynamic effects, and effectively improve the tracking accuracy and sensitivity. In the conventional inertially-aided tracking loop, the satellite-receiver line-of-sight velocity is used directly to adjust local carrier frequency. However, if the inertial solution drifts, the phase tracking error will be enlarged. By using Kalman filter based carrier phase tracking loop, this paper introduces a new inertial aid method, in which the line-of-sight jerk obtained from inertial acceleration by a nonlinear tracking differentiator is used to adjust relevant parameters of the Kalman filter's process noise matrix. Validation is achieved through high dynamic Compass B3 signal with line-of-sight jerk of 10 g/s collected by a GNSS simulator. Experimental results indicate that the new inertial aid method proposed in this paper is free of the impact of the receiver dynamic and inertial errors. Therefore, when the integrated navigation system is starting or re-tracking after losing lock, the inertial error is absent from the navigation solution correction that induces large drift, and the new aid method proposed in this paper can track highly dynamic signals.
Vibrations of Nonlinear Systems. The Method of Integral Equations,
Many diverse applied methods of investigating oscillations of nonlinear systems often in different mathematical formulations and outwardly not...parameter classical methods and the methods of investigating nonlinear systems of automatic control based on the so-called filter hypothesis, and to
FFT-Based Methods for Nonlinear Image Restoration in Confocal Microscopy
Roerdink, J.B.T.M.
1994-01-01
Recently we developed a new method for attenuation correction in 3D imaging by a confocal scanning laser microscope (CSLM) in the (epi)fluorescence mode. The fundamental element in our approach consisted of multiplying the measured fluorescent intensity by a correction factor involving a convolution
Sheta, B.; M. Elhabiby; Sheimy, N.
2012-01-01
A robust scale and rotation invariant image matching algorithm is vital for the Visual Based Navigation (VBN) of aerial vehicles, where matches between an existing geo-referenced database images and the real-time captured images are used to georeference (i.e. six transformation parameters - three rotation and three translation) the real-time captured image from the UAV through the collinearity equations. The georeferencing information is then used in aiding the INS integration Kalman filter a...
Bds/gps Integrated Positioning Method Research Based on Nonlinear Kalman Filtering
Ma, Y.; Yuan, W.; Sun, H.
2017-09-01
In order to realize fast and accurate BDS/GPS integrated positioning, it is necessary to overcome the adverse effects of signal attenuation, multipath effect and echo interference to ensure the result of continuous and accurate navigation and positioning. In this paper, pseudo-range positioning is used as the mathematical model. In the stage of data preprocessing, using precise and smooth carrier phase measurement value to promote the rough pseudo-range measurement value without ambiguity. At last, the Extended Kalman Filter(EKF), the Unscented Kalman Filter(UKF) and the Particle Filter(PF) algorithm are applied in the integrated positioning method for higher positioning accuracy. The experimental results show that the positioning accuracy of PF is the highest, and UKF is better than EKF.
Karimi, Hossein; Nikmehr, Saeid; Khodapanah, Ehsan
2016-09-01
In this paper, we develop a B-spline finite-element method (FEM) based on a locally modal wave propagation with anisotropic perfectly matched layers (PMLs), for the first time, to simulate nonlinear and lossy plasmonic waveguides. Conventional approaches like beam propagation method, inherently omit the wave spectrum and do not provide physical insight into nonlinear modes especially in the plasmonic applications, where nonlinear modes are constructed by linear modes with very close propagation constant quantities. Our locally modal B-spline finite element method (LMBS-FEM) does not suffer from the weakness of the conventional approaches. To validate our method, first, propagation of wave for various kinds of linear, nonlinear, lossless and lossy materials of metal-insulator plasmonic structures are simulated using LMBS-FEM in MATLAB and the comparisons are made with FEM-BPM module of COMSOL Multiphysics simulator and B-spline finite-element finite-difference wide angle beam propagation method (BSFEFD-WABPM). The comparisons show that not only our developed numerical approach is computationally more accurate and efficient than conventional approaches but also it provides physical insight into the nonlinear nature of the propagation modes.
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
Zingan, Valentin Nikolaevich
This work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.
Some geometrical iteration methods for nonlinear equations
Institute of Scientific and Technical Information of China (English)
LU Xing-jiang; QIAN Chun
2008-01-01
This paper describes geometrical essentials of some iteration methods (e.g. Newton iteration,secant line method,etc.) for solving nonlinear equations and advances some geomet-rical methods of iteration that are flexible and efficient.
Identification methods for nonlinear stochastic systems.
Fullana, Jose-Maria; Rossi, Maurice
2002-03-01
Model identifications based on orbit tracking methods are here extended to stochastic differential equations. In the present approach, deterministic and statistical features are introduced via the time evolution of ensemble averages and variances. The aforementioned quantities are shown to follow deterministic equations, which are explicitly written within a linear as well as a weakly nonlinear approximation. Based on such equations and the observed time series, a cost function is defined. Its minimization by simulated annealing or backpropagation algorithms then yields a set of best-fit parameters. This procedure is successfully applied for various sampling time intervals, on a stochastic Lorenz system.
Convergence of some asynchronous nonlinear multisplitting methods
Szyld, Daniel B.; Xu, Jian-Jun
2000-09-01
Frommer's nonlinear multisplitting methods for solving nonlinear systems of equations are extended to the asynchronous setting. Block methods are extended to include overlap as well. Several specific cases are discussed. Sufficient conditions to guarantee their local convergence are given. A numerical example is presented illustrating the performance of the new approach.
A new method of binary addition scheme with massive use of non-linear material based system
Institute of Scientific and Technical Information of China (English)
Kuladeep Roy Chowdhury; Sourangshu Mukhopadhyay
2003-01-01
The limitations in electronics in arithmetic, algebraic & logic processing are well known. Very high speedperformance (above GHz) are not expected at all in conventional electronic mechanism. To achieve highspeed performance we may think on the introduction of optics instead of electronics for information pro-cessing and computing. Non-linear optical material is a successful candidate in this regard to play a majorrole in the optically controlled switching systems and therefore in all-optical parallel computation thesematerials can show a very good potential aspect. In this paper, we have proposed a new method of anoptical half adder as well as full adder circuit for binary addition using non-linear and linear optical ma-terials.
Domnisoru, L.; Modiga, A.; Gasparotti, C.
2016-08-01
At the ship's design, the first step of the hull structural assessment is based on the longitudinal strength analysis, with head wave equivalent loads by the ships' classification societies’ rules. This paper presents an enhancement of the longitudinal strength analysis, considering the general case of the oblique quasi-static equivalent waves, based on the own non-linear iterative procedure and in-house program. The numerical approach is developed for the mono-hull ships, without restrictions on 3D-hull offset lines non-linearities, and involves three interlinked iterative cycles on floating, pitch and roll trim equilibrium conditions. Besides the ship-wave equilibrium parameters, the ship's girder wave induced loads are obtained. As numerical study case we have considered a large LPG liquefied petroleum gas carrier. The numerical results of the large LPG are compared with the statistical design values from several ships' classification societies’ rules. This study makes possible to obtain the oblique wave conditions that are inducing the maximum loads into the large LPG ship's girder. The numerical results of this study are pointing out that the non-linear iterative approach is necessary for the computation of the extreme loads induced by the oblique waves, ensuring better accuracy of the large LPG ship's longitudinal strength assessment.
Nonlinear modal methods for crack localization
Sutin, Alexander; Ostrovsky, Lev; Lebedev, Andrey
2003-10-01
A nonlinear method for locating defects in solid materials is discussed that is relevant to nonlinear modal tomography based on the signal cross-modulation. The scheme is illustrated by a theoretical model in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). A crack is considered as a small contact-type defect which does not perturb the modal structure of sound in linear approximation but creates combinational-frequency components whose amplitudes depend on their closeness to a resonance and crack position. Using different crack models, including the hysteretic ones, the nonlinear part of its volume variations under the given stress and then the combinational wave components in the bar can be determined. Evidently, their amplitude depends strongly on the crack position with respect to the peaks or nodes of the corresponding linear signals which can be used for localization of the crack position. Exciting the sample by sweeping ultrasound frequencies through several resonances (modes) reduces the ambiguity in the localization. Some aspects of inverse problem solution are also discussed, and preliminary experimental results are presented.
一类完全模糊非线性系统同伦法求解%Solving a class of fuzzy nonlinear systems based on homotopy method
Institute of Scientific and Technical Information of China (English)
彭晓华; 贾美珍; 王磊
2015-01-01
Based on the triangular fuzzy number and fuzzy rules, a class of full fuzzy nonlinear systems can be trans-formed into equivalent crisp nonlinear systems by parameters transform method. Then the approximate solutions of full fuzzy nonlinear systems are obtained also. One illustrated example is provided.%在现有三角模糊数表示及模糊运算规则基础上，采用参数变换法对一类模糊非线性系统做变换，得到同解的确定非线性系统。采用同伦法求解该确定非线性系统，进而给出原模糊非线性系统的近似解，并给出了具体算例。
Iterative regularization methods for nonlinear ill-posed problems
Scherzer, Otmar; Kaltenbacher, Barbara
2008-01-01
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Nonlinear calculating method of pile settlement
Institute of Scientific and Technical Information of China (English)
贺炜; 王桂尧; 王泓华
2008-01-01
To study calculating method of settlement on top of extra-long large-diameter pile, the relevant research results were summarized. The hyperbola model, a nonlinear load transfer function, was introduced to establish the basic differential equation with load transfer method. Assumed that the displacement of pile shaft was the high order power series of buried depth, through merging the same orthometric items and arranging the relevant coefficients, the solution which could take the nonlinear pile-soil interaction and stratum properties of soil into account was solved by power series. On the basis of the solution, by determining the load transfer depth with criterion of settlement on pile tip, the method by making boundary conditions compatible was advised to solve the load-settlement curve of pile. The relevant flow chart and mathematic expressions of boundary conditions were also listed. Lastly, the load transfer methods based on both two-broken-line model and hyperbola model were applied to analyzing a real project. The related coefficients of fitting curves by hyperbola were not less than 0.96, which shows that the hyperbola model is truthfulness, and is propitious to avoid personal error. The calculating value of load-settlement curve agrees well with the measured one, which indicates that it can be applied in engineering practice and making the theory that limits the design bearing capacity by settlement on pile top comes true.
Reproducing Kernel Particle Method for Non-Linear Fracture Analysis
Institute of Scientific and Technical Information of China (English)
Cao Zhongqing; Zhou Benkuan; Chen Dapeng
2006-01-01
To study the non-linear fracture, a non-linear constitutive model for piezoelectric ceramics was proposed, in which the polarization switching and saturation were taken into account. Based on the model, the non-linear fracture analysis was implemented using reproducing kernel particle method (RKPM). Using local J-integral as a fracture criterion, a relation curve of fracture loads against electric fields was obtained. Qualitatively, the curve is in agreement with the experimental observations reported in literature. The reproducing equation, the shape function of RKPM, and the transformation method to impose essential boundary conditions for meshless methods were also introduced. The computation was implemented using object-oriented programming method.
New nonlinear optical materials based on ferrofluids
Energy Technology Data Exchange (ETDEWEB)
Huang, J P [Department of Physics, Fudan University, Shanghai 200433 (China); Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz (Germany); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Yu, K W [Department of Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China); Institute of Theoretical Physics, Chinese University of Hong Kong, Shatin, NT, Hong Kong (China)
2006-01-01
We exploit theoretically a new class of magneto-controlled nonlinear optical material based on ferrofluids in which ferromagnetic nanoparticles are coated with a nonmagnetic metallic nonlinear shell. Such an optical material can have anisotropic nonlinear optical properties and a giant enhancement of nonlinearity, as well as an attractive figure of merit.
TAYLOR EXPANSION METHOD FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
HE Yin-nian
2005-01-01
A new numerical method of integrating the nonlinear evolution equations, namely the Taylor expansion method, was presented. The standard Galerkin method can be viewed as the 0-th order Taylor expansion method; while the nonlinear Galerkin method can be viewed as the 1-st order modified Taylor expansion method. Moreover, the existence of the numerical solution and its convergence rate were proven. Finally, a concrete example,namely, the two-dimensional Navier-Stokes equations with a non slip boundary condition,was provided. The result is that the higher order Taylor expansion method is of the higher convergence rate under some assumptions about the regularity of the solution.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
LI ChengJin; SUN WenYui
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
ACCELERATION METHODS OF NONLINEAR ITERATION FOR NONLINEAR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
Guang-wei Yuan; Xu-deng Hang
2006-01-01
This paper discusses the accelerating iterative methods for solving the implicit scheme of nonlinear parabolic equations. Two new nonlinear iterative methods named by the implicit-explicit quasi-Newton (IEQN) method and the derivative free implicit-explicit quasi-Newton (DFIEQN) method are introduced, in which the resulting linear equations from the linearization can preserve the parabolic characteristics of the original partial differential equations. It is proved that the iterative sequence of the iteration method can converge to the solution of the implicit scheme quadratically. Moreover, compared with the Jacobian Free Newton-Krylov (JFNK) method, the DFIEQN method has some advantages, e.g., its implementation is easy, and it gives a linear algebraic system with an explicit coefficient matrix, so that the linear (inner) iteration is not restricted to the Krylov method. Computational results by the IEQN, DFIEQN, JFNK and Picard iteration meth-ods are presented in confirmation of the theory and comparison of the performance of these methods.
An SQP Algorithm for Recourse-based Stochastic Nonlinear Programming
Directory of Open Access Journals (Sweden)
Xinshun Ma
2016-05-01
Full Text Available The stochastic nonlinear programming problem with completed recourse and nonlinear constraints is studied in this paper. We present a sequential quadratic programming method for solving the problem based on the certainty extended nonlinear model. This algorithm is obtained by combing the active set method and filter method. The convergence of the method is established under some standard assumptions. Moreover, a practical design is presented and numerical results are provided.
Nonlinear Process Fault Diagnosis Based on Serial Principal Component Analysis.
Deng, Xiaogang; Tian, Xuemin; Chen, Sheng; Harris, Chris J
2016-12-22
Many industrial processes contain both linear and nonlinear parts, and kernel principal component analysis (KPCA), widely used in nonlinear process monitoring, may not offer the most effective means for dealing with these nonlinear processes. This paper proposes a new hybrid linear-nonlinear statistical modeling approach for nonlinear process monitoring by closely integrating linear principal component analysis (PCA) and nonlinear KPCA using a serial model structure, which we refer to as serial PCA (SPCA). Specifically, PCA is first applied to extract PCs as linear features, and to decompose the data into the PC subspace and residual subspace (RS). Then, KPCA is performed in the RS to extract the nonlinear PCs as nonlinear features. Two monitoring statistics are constructed for fault detection, based on both the linear and nonlinear features extracted by the proposed SPCA. To effectively perform fault identification after a fault is detected, an SPCA similarity factor method is built for fault recognition, which fuses both the linear and nonlinear features. Unlike PCA and KPCA, the proposed method takes into account both linear and nonlinear PCs simultaneously, and therefore, it can better exploit the underlying process's structure to enhance fault diagnosis performance. Two case studies involving a simulated nonlinear process and the benchmark Tennessee Eastman process demonstrate that the proposed SPCA approach is more effective than the existing state-of-the-art approach based on KPCA alone, in terms of nonlinear process fault detection and identification.
2006-08-31
Orientation Layer Type - Woven/ Nonwoven Layer Type - Woven/ Nonwoven Figure 29. A completed design model for fiber-reinforced composites 0 2 4 6 8 10 12 14...crew survivability of tactical wheeled vehicles subject to mine blast. However, these CPK’s were based on a conventional steel/aluminum construction
LINEARIZATION AND CORRECTION METHOD FOR NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
何吉欢
2002-01-01
A new perturbation-like technique called linearization and correction method is proposed. Contrary to the traditional perturbation techniques, the present theory does not assume that the solution is expressed in the form of a power series of small parameter. To obtain an asymptotic solution of nonlinear system, the technique first searched for a solution for the linearized system, then a correction was added to the linearized solution. So the obtained results are uniformly valid for both weakly and strongly nonlinear equations.
Method for conducting nonlinear electrochemical impedance spectroscopy
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Method for conducting nonlinear electrochemical impedance spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Adler, Stuart B.; Wilson, Jamie R.; Huff, Shawn L.; Schwartz, Daniel T.
2015-06-02
A method for conducting nonlinear electrochemical impedance spectroscopy. The method includes quantifying the nonlinear response of an electrochemical system by measuring higher-order current or voltage harmonics generated by moderate-amplitude sinusoidal current or voltage perturbations. The method involves acquisition of the response signal followed by time apodization and fast Fourier transformation of the data into the frequency domain, where the magnitude and phase of each harmonic signal can be readily quantified. The method can be implemented on a computer as a software program.
Advances in iterative methods for nonlinear equations
Busquier, Sonia
2016-01-01
This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations...
A Numerical Embedding Method for Solving the Nonlinear Optimization Problem
Institute of Scientific and Technical Information of China (English)
田保锋; 戴云仙; 孟泽红; 张建军
2003-01-01
A numerical embedding method was proposed for solving the nonlinear optimization problem. By using the nonsmooth theory, the existence and the continuation of the following path for the corresponding homotopy equations were proved. Therefore the basic theory for the algorithm of the numerical embedding method for solving the non-linear optimization problem was established. Based on the theoretical results, a numerical embedding algorithm was designed for solving the nonlinear optimization problem, and prove its convergence carefully. Numerical experiments show that the algorithm is effective.
Numerical methods for nonlinear partial differential equations
Bartels, Sören
2015-01-01
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Yu, Xiang-xiang; Wang, Yu-hua
2014-01-13
Silver nanoparticles synthesized in a synthetic sapphire matrix were fabricated by ion implantation using the metal vapor vacuum arc ion source. The optical absorption spectrum of the Ag: Al2O3 composite material has been measured. The analysis of the supercontinuum spectrum displayed the nonlinear refractive property of this kind of sample. Nonlinear optical refraction index was identified at 800 nm excitation using the Kerr-lens autocorrelation (KLAC) technique. The spectrum showed that the material possessed self-defocusing property (n(2) = -1.1 × 10(-15) cm(2)W). The mechanism of nonlinear refraction has been discussed.
Nonlinear variations of forest leaf area index over China during 1982-2010 based on EEMD method
Yin, Yunhe; Ma, Danyang; Wu, Shaohong; Dai, Erfu; Zhu, Zaichun; Myneni, Ranga B.
2016-11-01
Variations in leaf area index (LAI) are critical to research on forest ecosystem structure and function, especially carbon and water cycle, and their responses to climate change. Using the ensemble empirical mode decomposition (EEMD) method and global inventory modeling and mapping studies (GIMMS) LAI3g dataset from 1982 to 2010, we analyzed the nonlinear feature and spatial difference of forest LAI variability over China for the past 29 years in this paper. Results indicated that the national-averaged forest LAI was characterized by quasi-3- and quasi-7-year oscillations, which generally exhibited a rising trend with an increasing rate. When compared with 1982, forest LAI change by 2010 was more evident than that by 1990 and 2000. The largest increment of forest LAI occurred in Central and South China, while along the southeastern coastal areas LAI increased at the fastest pace. During the study period, forest LAI experienced from decrease to increase or vice versa across much of China and varied monotonically for only a few areas. Focusing on regional-averaged trend processes, almost all eco-geographical regions showed continuously increasing trends in forest LAI with different magnitudes and speeds, other than tropical humid region and temperate humid/subhumid region, where LAI decreased initially and increased afterwards.
A granular computing method for nonlinear convection-diffusion equation
Directory of Open Access Journals (Sweden)
Tian Ya Lan
2016-01-01
Full Text Available This paper introduces a method of solving nonlinear convection-diffusion equation (NCDE, based on the combination of granular computing (GrC and characteristics finite element method (CFEM. The key idea of the proposed method (denoted as GrC-CFEM is to reconstruct the solution from coarse-grained layer to fine-grained layer. It first gets the nonlinear solution on the coarse-grained layer, and then the function (Taylor expansion is applied to linearize the NCDE on the fine-grained layer. Switch to the fine-grained layer, the linear solution is directly derived from the nonlinear solution. The full nonlinear problem is solved only on the coarse-grained layer. Numerical experiments show that the GrC-CFEM can accelerate the convergence and improve the computational efficiency without sacrificing the accuracy.
Femtosecond nonlinear polarization evolution based on cascade quadratic nonlinearities.
Liu, X; Ilday, F O; Beckwitt, K; Wise, F W
2000-09-15
We experimentally demonstrate that one can exploit nonlinear phase shifts produced in type I phase-mismatched second-harmonic generation to produce intensity-dependent polarization evolution with 100-fs pulses. An amplitude modulator based on nonlinear polarization rotation provides passive amplitude-modulation depth of up to ~50%. Applications of the amplitude and phase modulations to mode locking of femtosecond bulk and fiber lasers are promising and are discussed.
Yu, XiaoChun; Bai, YuGuang; Cui, Miao; Gao, XiaoWei
2013-05-01
This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) analysis based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.
Cohen, J.; Shukhman, I. G.; Karp, M.; Philip, J.
2010-10-01
Recent experimental and numerical studies have shown that the interaction between a localized vortical disturbance and the shear of an external base flow can lead to the formation of counter-rotating vortex pairs and hairpin vortices that are frequently observed in wall bounded and free turbulent shear flows as well as in subcritical shear flows. In this paper an analytical-based solution method is developed. The method is capable of following (numerically) the evolution of finite-amplitude localized vortical disturbances embedded in shear flows. Due to their localization in space, the surrounding base flow is assumed to have homogeneous shear to leading order. The method can solve in a novel way the interaction between a general family of unbounded planar homogeneous shear flows and any localized disturbance. The solution is carried out using Lagrangian variables in Fourier space which is convenient and enables fast computations. The potential of the method is demonstrated by following the evolved structures of large amplitude disturbances in three canonical base flows, including simple shear, plane stagnation (extensional) and pure rotation flows, and a general case. The results obtained by the current method for plane stagnation and simple shear flows are compared with the published results. The proposed method could be extended to other flows (e.g. geophysical and rotating flows) and to include periodic disturbances as well.
Tensor methods for large sparse systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Bouaricha, A. [Argonne National Lab., IL (United States). Mathematics and Computer Science Div.; Schnabel, R.B. [Colorado Univ., Boulder, CO (United States). Dept. of Computer Science
1996-12-31
This paper introduces censor methods for solving, large sparse systems of nonlinear equations. Tensor methods for nonlinear equations were developed in the context of solving small to medium- sized dense problems. They base each iteration on a quadratic model of the nonlinear equations. where the second-order term is selected so that the model requires no more derivative or function information per iteration than standard linear model-based methods, and hardly more storage or arithmetic operations per iteration. Computational experiments on small to medium-sized problems have shown censor methods to be considerably more efficient than standard Newton-based methods, with a particularly large advantage on singular problems. This paper considers the extension of this approach to solve large sparse problems. The key issue that must be considered is how to make efficient use of sparsity in forming and solving the censor model problem at each iteration. Accomplishing this turns out to require an entirely new way of solving the tensor model that successfully exploits the sparsity of the Jacobian, whether the Jacobian is nonsingular or singular. We develop such an approach and, based upon it, an efficient tensor method for solving large sparse systems of nonlinear equations. Test results indicate that this tensor method is significantly more efficient and robust than an efficient sparse Newton-based method. in terms of iterations, function evaluations. and execution time.
Monotone method for nonlinear nonlocal hyperbolic problems
Directory of Open Access Journals (Sweden)
Azmy S. Ackleh
2003-02-01
Full Text Available We present recent results concerning the application of the monotone method for studying existence and uniqueness of solutions to general first-order nonlinear nonlocal hyperbolic problems. The limitations of comparison principles for such nonlocal problems are discussed. To overcome these limitations, we introduce new definitions for upper and lower solutions.
Review of Nonlinear Methods and Modelling
Borg, F G
2005-01-01
The first part of this Review describes a few of the main methods that have been employed in non-linear time series analysis with special reference to biological applications (biomechanics). The second part treats the physical basis of posturogram data (human balance) and EMG (electromyography, a measure of muscle activity).
Nonlinear Dimensionality Reduction Methods in Climate Data Analysis
Ross, Ian
2008-01-01
Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mappin...
Direct Perturbation Method for Derivative Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
CHENG Xue-Ping; LIN Ji; HAN Ping
2008-01-01
We extend Lou's direct perturbation method for solving the nonlinear SchrSdinger equation to the case of the derivative nonlinear Schrodinger equation (DNLSE). By applying this method, different types of perturbation solutions axe obtained. Based on these approximate solutions, the analytical forms of soliton parameters, such as the velocity, the width and the initial position, are carried out and the effects of perturbation on solitons are analyzed at the same time. A numerical simulation of perturbed DNLSE finally verifies the results of the perturbation method.
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Pakniat, R.; Tavassoly, M. K.; Zandi, M. H.
2017-01-01
In this paper, we outline a scheme for entanglement swapping based on the concept of cavity QED. The atom-field entangled state in our study is produced in the nonlinear regime. In this scheme, the exploited cavities are prepared in a hybrid entangled state (a combination of coherent and number states) and the swapping process is investigated using two different methods, i.e., detecting and Bell-state measurement methods through the cavity QED. Then, we make use of the atom-field entangled state obtained by detecting method to show that how the atom-atom entanglement as well as atomic and field states teleportation can be achieved with complete fidelity.
Nonlinear signal-based control with an error feedback action for nonlinear substructuring control
Enokida, Ryuta; Kajiwara, Koichi
2017-01-01
A nonlinear signal-based control (NSBC) method utilises the 'nonlinear signal' that is obtained from the outputs of a controlled system and its linear model under the same input signal. Although this method has been examined in numerical simulations of nonlinear systems, its application in physical experiments has not been studied. In this paper, we study an application of NSBC in physical experiments and incorporate an error feedback action into the method to minimise the error and enhance the feasibility in practice. Focusing on NSBC in substructure testing methods, we propose nonlinear substructuring control (NLSC), that is a more general form of linear substructuring control (LSC) developed for dynamical substructured systems. In this study, we experimentally and numerically verified the proposed NLSC via substructuring tests on a rubber bearing used in base-isolated structures. In the examinations, NLSC succeeded in gaining accurate results despite significant nonlinear hysteresis and unknown parameters in the substructures. The nonlinear signal feedback action in NLSC was found to be notably effective in minimising the error caused by nonlinearity or unknown properties in the controlled system. In addition, the error feedback action in NLSC was found to be essential for maintaining stability. A stability analysis based on the Nyquist criterion, which is used particularly for linear systems, was also found to be efficient for predicting the instability conditions of substructuring tests with NLSC and useful for the error feedback controller design.
Nonlinear modal method of crack localization
Ostrovsky, Lev; Sutin, Alexander; Lebedev, Andrey
2004-05-01
A simple scheme for crack localization is discussed that is relevant to nonlinear modal tomography based on the cross-modulation of two signals at different frequencies. The scheme is illustrated by a theoretical model, in which a thin plate or bar with a single crack is excited by a strong low-frequency wave and a high-frequency probing wave (ultrasound). The crack is assumed to be small relative to all wavelengths. Nonlinear scattering from the crack is studied using a general matrix approach as well as simplified models allowing one to find the nonlinear part of crack volume variations under the given stress and then the combinational wave components in the tested material. The nonlinear response strongly depends on the crack position with respect to the peaks or nodes of the corresponding interacting signals which can be used for determination of the crack position. Juxtaposing various resonant modes interacting at the crack it is possible to retrieve both crack location and orientation. Some aspects of inverse problem solutions are also discussed, and preliminary experimental results are presented.
Multigrid Methods for Nonlinear Problems: An Overview
Energy Technology Data Exchange (ETDEWEB)
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Institute of Scientific and Technical Information of China (English)
黄道平; 龚婷婷; 曾辉
2009-01-01
Nonlinear principal component analysis (NLPCA) fault detection method achieves good detection results especially in a nonlinear process. Signed directed graph (SDG) model is based on deep-going information, which excels in fault interpretation. In this work, an NLPCA-SDG fault diagnosis method was proposed. SDG model was used to interpret the residual contributions produced by NLPCA. This method could overcome the shortcomings of traditional principal component analysis (PCA) method in fault detection of a nonlinear process and the shortcomings of traditional SDG method in single variable statistics in discriminating node conditions and threshold values. The application to a distillation unit of a petrochemical plant illustrated its validity in nonlinear process fault diagnosis.%@@引言 化工过程通常具有变量多、非线性程度高、难以获得准确的数学模型、故障样本少等特点.
Directory of Open Access Journals (Sweden)
Qian Xie
2016-07-01
Full Text Available This paper pays attention to magnetic flux linkage optimization of a direct-driven surface-mounted permanent magnet synchronous generator (D-SPMSG. A new compact representation of the D-SPMSG nonlinear dynamic differential equations to reduce system parameters is established. Furthermore, the nonlinear dynamic characteristics of new D-SPMSG equations in the process of varying magnetic flux linkage are considered, which are illustrated by Lyapunov exponent spectrums, phase orbits, Poincaré maps, time waveforms and bifurcation diagrams, and the magnetic flux linkage stable region of D-SPMSG is acquired concurrently. Based on the above modeling and analyses, a novel method of magnetic flux linkage optimization is presented. In addition, a 2 MW D-SPMSG 2D/3D model is designed by ANSYS software according to the practical design requirements. Finally, five cases of D-SPMSG models with different magnetic flux linkages are simulated by using the finite element analysis (FEA method. The nephograms of magnetic flux density are agreement with theoretical analysis, which both confirm the correctness and effectiveness of the proposed approach.
DEFF Research Database (Denmark)
Lu, Kaiyuan; Lei, Xiao; Blaabjerg, Frede
2013-01-01
The back EMF-based sensorless control method is very popular for permanent magnet synchronous machines (PMSMs) in the medium- to high-speed operation range due to its simple structure. In this speed range, the accuracy of the estimated position is mainly affected by the inductance, which varies...... on the estimated position error, and gives a deep insight into this problem. It also provides a simple approach to achieve a globally minimized position error. A proper choice of the artificial machine inductance may reduce the maximum position error by 50% without considering the actual inductance variation...
Chen, Hao; Zhong, Shouming; Li, Min; Liu, Xingwen; Adu-Gyamfi, Fehrs
2016-07-01
In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and nonlinear perturbations. Based on the common ratio α, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Li, Cheng; Zhao, Tianlun; Li, Cong; Mei, Lei; Yu, En; Dong, Yating; Chen, Jinhong; Zhu, Shuijin
2017-04-15
Near infrared (NIR) spectroscopy combined with Monte Carlo uninformative variable elimination (MC-UVE) and nonlinear calibration methods employed to determine gossypol content in cottonseeds were investigated. The reference method was performed by high performance liquid chromatography coupled to an ultraviolet detector (HPLC-UV). MC-UVE was employed to extract the effective information from the full NIR spectra. Nonlinear calibration methods were applied to establish the models compared with the linear method. The optimal model for gossypol content was obtained by MC-UVE-WLS-SVM, with root mean squares error of prediction (RMSEP) of 0.0422, coefficient of determination (R(2)) of 0.9331, and residual predictive deviation (RPD) of 3.8374, respectively, which was accurate and robust enough to substitute for traditional gossypol measurements. The nonlinear methods performed more reliable than linear method during the development of calibration models. Furthermore, MC-UVE could provide better and simpler calibration models than full spectra.
Nonlinear ordinary differential equations analytical approximation and numerical methods
Hermann, Martin
2016-01-01
The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...
APPLICATION OF MODIFIED CONVERSION METHOD TO A NONLINEAR DYNAMICAL SYSTEM
Directory of Open Access Journals (Sweden)
G.I. Melnikov
2015-01-01
Full Text Available The paper deals with a mathematical model of dynamical system with single degree of freedom, presented in the form of ordinary differential equations with nonlinear parts in the form of polynomials with constant and periodic coefficients. A modified method for the study of self-oscillations of nonlinear mechanical systems is presented. A refined method of transformation and integration of the equation, based on Poincare-Dulac normalization method has been developed. Refinement of the method lies in consideration of higher order nonlinear terms by Chebyshev economization technique that improves the accuracy of the calculations. Approximation of the higher order remainder terms by homogeneous forms of lower orders is performed; in the present case, it is done by cubic forms. An application of the modified method for the Van-der-Pol equation is considered as an example; the expressions for the amplitude and the phase of the oscillations are obtained in an analytical form. The comparison of the solution of the Van-der-Pol equation obtained by the developed method and the exact solution is performed. The error of the solution obtained by the modified method equals to 1%, which shows applicability of the developed method for analysis of self-oscillations of nonlinear dynamic systems with constant and periodic parameters.
DEFF Research Database (Denmark)
Kragh, Knud Abildgaard; Thomsen, Jon Juel; Tcherniak, Dmitri
2010-01-01
exists. The present study suggests a framework for the detection of structural nonlinearities. Two methods for detection are compared, the homogeneity method and a Hilbert transform based method. Based on these two methods, a nonlinearity index is suggested. Through simulations and laboratory experiments...
Seismic base isolation by nonlinear mode localization
Energy Technology Data Exchange (ETDEWEB)
Wang, Y. [University of Illinois, Department of Civil and Environmental Engineering, Urbana, IL (United States); Washington University, Department of Civil and Environmental Engineering, St. Louis, MO (United States); McFarland, D.M. [University of Illinois, Department of Aerospace Engineering, Urbana, IL (United States); Vakakis, A.F. [National Technical University of Athens, Division of Mechanics (Greece); Bergman, L.A. [University of Illinois, Department of Mechanical and Industrial Engineering, Urbana, IL (United States)
2005-03-01
In this paper, the performance of a nonlinear base-isolation system, comprised of a nonlinearly sprung subfoundation tuned in a 1:1 internal resonance to a flexible mode of the linear primary structure to be isolated, is examined. The application of nonlinear localization to seismic isolation distinguishes this study from other base-isolation studies in the literature. Under the condition of third-order smooth stiffness nonlinearity, it is shown that a localized nonlinear normal mode (NNM) is induced in the system, which confines energy to the subfoundation and away from the primary or main structure. This is followed by a numerical analysis wherein the smooth nonlinearity is replaced by clearance nonlinearity, and the system is excited by ground motions representing near-field seismic events. The performance of the nonlinear system is compared with that of the corresponding linear system through simulation, and the sensitivity of the isolation system to several design parameters is analyzed. These simulations confirm the existence of the localized NNM, and show that the introduction of simple clearance nonlinearity significantly reduces the seismic energy transmitted to the main structure, resulting in significant attenuation in the response. (orig.)
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Method for Measuring Small Nonlinearities of Electric Characteristics
DEFF Research Database (Denmark)
Guldbrandsen, Tom; Meyer, Niels I; Schjær-Jacobsen, Jørgen
1965-01-01
A method is described for measuring very small deviations from linearity in electric characteristics. The measurement is based on the harmonics generated by the nonlinear element when subjected to a sine wave signal. A special bridge circuit is used to balance out the undesired harmonics...... of the signal generator together with the first harmonic frequency. The set-up measures the small-signal value and the first and second derivative with respect to voltage. The detailed circuits are given for measuring nonlinearities in Ohmic and capacitive components. In the Ohmic case, a sensitivity...
Optimal Variational Method for Truly Nonlinear Oscillators
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Vasile Marinca
2013-01-01
Full Text Available The Optimal Variational Method (OVM is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.
Nonlinear Analysis Methods for Evaluating Seismic Performance of Multi-Story RC Buildings
Tayyebi, Saeid Moussavi
2014-01-01
ABSTRACT: A major challenge in performance-based earthquake engineering is to develop simple and practical methods for estimating capacity level and seismic demand on structures by taking into account their inelastic behavior. Researchers and engineers certainly prefer to use nonlinear static methods over complicated nonlinear time-history methods. However, in Nonlinear Static procedure both predetermined target displacement and force distribution pattern are based on a false assumption that ...
Directory of Open Access Journals (Sweden)
Gaosheng Luo
2014-01-01
Full Text Available A robust adaptive control method with full-state feedback is proposed based on the fact that the elbow joint of a seven-function hydraulic manipulator with double-screw-pair transmission features the following control characteristics: a strongly nonlinear hydraulic system, parameter uncertainties susceptible to temperature and pressure changes of the external environment, and unknown outer disturbances. Combined with the design method of the back-stepping controller, the asymptotic stability of the control system in the presence of disturbances from uncertain systematic parameters and unknown external disturbances was demonstrated using Lyapunov stability theory. Based on the elbow joint of the seven-function master-slave hydraulic manipulator for the 4500 m Deep-Sea Working System as the research subject, a comparative study was conducted using the control method presented in this paper for unknown external disturbances. Simulations and experiments of different unknown outer disturbances showed that (1 the proposed controller could robustly track the desired reference trajectory with satisfactory dynamic performance and steady accuracy and that (2 the modified parameter adaptive laws could also guarantee that the estimated parameters are bounded.
Elsawy, Mahmoud M R
2016-01-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a nonlinear metamaterial core of Kerr-type embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assumed that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and the nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical, it is based on the finite-element method in which all the components of the electric field are considered in the Kerr-type nonlinearity with no presumptions on the nonlinear refractive index change. Our finite-element based model is valid beyond weak nonlinearity regime and generalize the well-known single-component fixed...
Wavelet neural network based fault diagnosis in nonlinear analog circuits
Institute of Scientific and Technical Information of China (English)
Yin Shirong; Chen Guangju; Xie Yongle
2006-01-01
The theories of diagnosing nonlinear analog circuits by means of the transient response testing are studied. Wavelet analysis is made to extract the transient response signature of nonlinear circuits and compress the signature dada. The best wavelet function is selected based on the between-category total scatter of signature. The fault dictionary of nonlinear circuits is constructed based on improved back-propagation(BP) neural network. Experimental results demonstrate that the method proposed has high diagnostic sensitivity and fast fault identification and deducibility.
A simplified NARMAX method using nonlinear input-output data
Institute of Scientific and Technical Information of China (English)
Jie CHEN; Sheng FENG
2007-01-01
A system identification method for nonlinear systems with unknown structure is presented using short input-output data. The method simplifies the original NARMAX method. It introduces more general model structures for nonlinear systems. The group method of data handling (GMDH) method is employed to obtain the model terms and parameters. Effectiveness of the proposed method is illustrated by a typical nonlinear system with unknown structure and deficient input-output data.
Discretization analysis of bifurcation based nonlinear amplifiers
Feldkord, Sven; Reit, Marco; Mathis, Wolfgang
2017-09-01
Recently, for modeling biological amplification processes, nonlinear amplifiers based on the supercritical Andronov-Hopf bifurcation have been widely analyzed analytically. For technical realizations, digital systems have become the most relevant systems in signal processing applications. The underlying continuous-time systems are transferred to the discrete-time domain using numerical integration methods. Within this contribution, effects on the qualitative behavior of the Andronov-Hopf bifurcation based systems concerning numerical integration methods are analyzed. It is shown exemplarily that explicit Runge-Kutta methods transform the truncated normalform equation of the Andronov-Hopf bifurcation into the normalform equation of the Neimark-Sacker bifurcation. Dependent on the order of the integration method, higher order terms are added during this transformation.A rescaled normalform equation of the Neimark-Sacker bifurcation is introduced that allows a parametric design of a discrete-time system which corresponds to the rescaled Andronov-Hopf system. This system approximates the characteristics of the rescaled Hopf-type amplifier for a large range of parameters. The natural frequency and the peak amplitude are preserved for every set of parameters. The Neimark-Sacker bifurcation based systems avoid large computational effort that would be caused by applying higher order integration methods to the continuous-time normalform equations.
Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng
2015-01-01
The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.
Directory of Open Access Journals (Sweden)
Jun Wang
2015-01-01
Full Text Available The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.
Hu, Juju; Hu, Haijiang; Ji, Yinghua
2010-03-15
Periodic nonlinearity that ranges from tens of nanometers to a few nanometers in heterodyne interferometer limits its use in high accuracy measurement. A novel method is studied to detect the nonlinearity errors based on the electrical subdivision and the analysis method of statistical signal in heterodyne Michelson interferometer. Under the movement of micropositioning platform with the uniform velocity, the method can detect the nonlinearity errors by using the regression analysis and Jackknife estimation. Based on the analysis of the simulations, the method can estimate the influence of nonlinearity errors and other noises for the dimensions measurement in heterodyne Michelson interferometer.
Directory of Open Access Journals (Sweden)
Orlando Soriano-Vargas
2016-12-01
Full Text Available Spinodal decomposition was studied during aging of Fe-Cr alloys by means of the numerical solution of the linear and nonlinear Cahn-Hilliard differential partial equations using the explicit finite difference method. Results of the numerical simulation permitted to describe appropriately the mechanism, morphology and kinetics of phase decomposition during the isothermal aging of these alloys. The growth kinetics of phase decomposition was observed to occur very slowly during the early stages of aging and it increased considerably as the aging progressed. The nonlinear equation was observed to be more suitable for describing the early stages of spinodal decomposition than the linear one.
Slope stability analysis using limit equilibrium method in nonlinear criterion.
Lin, Hang; Zhong, Wenwen; Xiong, Wei; Tang, Wenyu
2014-01-01
In slope stability analysis, the limit equilibrium method is usually used to calculate the safety factor of slope based on Mohr-Coulomb criterion. However, Mohr-Coulomb criterion is restricted to the description of rock mass. To overcome its shortcomings, this paper combined Hoek-Brown criterion and limit equilibrium method and proposed an equation for calculating the safety factor of slope with limit equilibrium method in Hoek-Brown criterion through equivalent cohesive strength and the friction angle. Moreover, this paper investigates the impact of Hoek-Brown parameters on the safety factor of slope, which reveals that there is linear relation between equivalent cohesive strength and weakening factor D. However, there are nonlinear relations between equivalent cohesive strength and Geological Strength Index (GSI), the uniaxial compressive strength of intact rock σ ci , and the parameter of intact rock m i . There is nonlinear relation between the friction angle and all Hoek-Brown parameters. With the increase of D, the safety factor of slope F decreases linearly; with the increase of GSI, F increases nonlinearly; when σ ci is relatively small, the relation between F and σ ci is nonlinear, but when σ ci is relatively large, the relation is linear; with the increase of m i , F decreases first and then increases.
2009-01-01
Phase interactions among signals of physical and physiological systems can provide useful information about the underlying control mechanisms of the systems. Physical and biological recordings are often noisy and exhibit nonstationarities that can affect the estimation of phase interactions. We systematically studied effects of nonstationarities on two phase analyses including (i) the widely used transfer function analysis (TFA) that is based on Fourier decomposition and (ii) the recently pro...
STABILITY ANALYSIS OF RUNGE-KUTTA METHODS FOR NONLINEAR SYSTEMS OF PANTOGRAPH EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yue-xin Yu; Shou-fu Li
2005-01-01
This paper is concerned with numerical stability of nonlinear systems of pantograph equations. Numerical methods based on (k, l)-algebraically stable Runge-Kutta methods are suggested. Global and asymptotic stability conditions for the presented methods are derived.
Institute of Scientific and Technical Information of China (English)
丁先文; 徐亮; 林金官
2012-01-01
经验似然方法已经被广泛用于线性模型和广义线性模型.本文基于经验似然方法对非线性回归模型进行统计诊断.首先得到模型参数的极大经验似然估计；其次基于经验似然研究了三种不同的影响曲率度量；最后通过一个实际例子,说明了诊断方法的有效性.%The empirical likelihood method has been extensively applied to linear regression and generalized linear regression models. In this paper, the diagnostic measures for nonlinear regression models are studied based on the empirical likelihood method. First, the maximum empirical likelihood estimate of the parameters are obtained. Then, three different measures of influence curvatures are studied. Last, real data analysis are given to illustrate the validity of statistical diagnostic measures.
Shuttle entry guidance revisited using nonlinear geometric methods
Mease, Kenneth D.; Kremer, Jean-Paul
1994-11-01
The entry guidance law for the space shuttle orbiter is revisited using nonlinear geometric methods. The shuttle guidance concept is to track a reference drag trajectory that has been designed to lead a specified range and velocity. It is shown that the approach taken in the original derivation of the shuttle entry guidance has much in common with the more recently developed feedback linearization method of differential geometric control. Using the feedback linearization method, however, an alternative, potentially superior, guidance law was formulated. Comparing the two guidance laws based performance domains in state space, taking into account the nonlinear dynamics, the alternative guidance law achieves the desired performance over larger domains in state space; the stability domain of the laws are similar. With larger operating domain for the shuttle or some other entry vehicle, the alternative guidance law should be considered.
Directory of Open Access Journals (Sweden)
Margaret A. Ryan
2005-12-01
Full Text Available The Jet Propulsion Laboratory has recently developed and built an electronic nose(ENose using a polymer-carbon composite sensing array. This ENose is designed to be usedfor air quality monitoring in an enclosed space, and is designed to detect, identify andquantify common contaminants at concentrations in the parts-per-million range. Itscapabilities were demonstrated in an experiment aboard the National Aeronautics and SpaceAdministrationÃ¢Â€Â™s Space Shuttle Flight STS-95. This paper describes a modified nonlinearleast-squares based algorithm developed to analyze data taken by the ENose, and itsperformance for the identification and quantification of single gases and binary mixtures oftwelve target analytes in clean air. Results from laboratory-controlled events demonstrate theeffectiveness of the algorithm to identify and quantify a gas event if concentration exceedsthe ENose detection threshold. Results from the flight test demonstrate that the algorithmcorrectly identifies and quantifies all registered events (planned or unplanned, as singles ormixtures with no false positives and no inconsistencies with the logged events and theindependent analysis of air samples.
Kernel-Based Nonlinear Discriminant Analysis for Face Recognition
Institute of Scientific and Technical Information of China (English)
LIU QingShan (刘青山); HUANG Rui (黄锐); LU HanQing (卢汉清); MA SongDe (马颂德)
2003-01-01
Linear subspace analysis methods have been successfully applied to extract features for face recognition. But they are inadequate to represent the complex and nonlinear variations of real face images, such as illumination, facial expression and pose variations, because of their linear properties. In this paper, a nonlinear subspace analysis method, Kernel-based Nonlinear Discriminant Analysis (KNDA), is presented for face recognition, which combines the nonlinear kernel trick with the linear subspace analysis method - Fisher Linear Discriminant Analysis (FLDA).First, the kernel trick is used to project the input data into an implicit feature space, then FLDA is performed in this feature space. Thus nonlinear discriminant features of the input data are yielded. In addition, in order to reduce the computational complexity, a geometry-based feature vectors selection scheme is adopted. Another similar nonlinear subspace analysis is Kernel-based Principal Component Analysis (KPCA), which combines the kernel trick with linear Principal Component Analysis (PCA). Experiments are performed with the polynomial kernel, and KNDA is compared with KPCA and FLDA. Extensive experimental results show that KNDA can give a higher recognition rate than KPCA and FLDA.
Bayesian Methods for Nonlinear System Identification of Civil Structures
Directory of Open Access Journals (Sweden)
Conte Joel P.
2015-01-01
Full Text Available This paper presents a new framework for the identification of mechanics-based nonlinear finite element (FE models of civil structures using Bayesian methods. In this approach, recursive Bayesian estimation methods are utilized to update an advanced nonlinear FE model of the structure using the input-output dynamic data recorded during an earthquake event. Capable of capturing the complex damage mechanisms and failure modes of the structural system, the updated nonlinear FE model can be used to evaluate the state of health of the structure after a damage-inducing event. To update the unknown time-invariant parameters of the FE model, three alternative stochastic filtering methods are used: the extended Kalman filter (EKF, the unscented Kalman filter (UKF, and the iterated extended Kalman filter (IEKF. For those estimation methods that require the computation of structural FE response sensitivities with respect to the unknown modeling parameters (EKF and IEKF, the accurate and computationally efficient direct differentiation method (DDM is used. A three-dimensional five-story two-by-one bay reinforced concrete (RC frame is used to illustrate the performance of the framework and compare the performance of the different filters in terms of convergence, accuracy, and robustness. Excellent estimation results are obtained with the UKF, EKF, and IEKF. Because of the analytical linearization used in the EKF and IEKF, abrupt and large jumps in the estimates of the modeling parameters are observed when using these filters. The UKF slightly outperforms the EKF and IEKF.
Modified extended tanh-function method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Department of Physics, Faculty of Science, Theoretical Research Group, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-03-15
Based on computerized symbolic computation, modified extended tanh-method for constructing multiple travelling wave solutions of nonlinear evolution equations is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some nonlinear evolution equations in mathematical physics such as the nonlinear partial differential equation, nonlinear Fisher-type equation, ZK-BBM equation, generalized Burgers-Fisher equation and Drinfeld-Sokolov system. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods.
Comparative study of homotopy continuation methods for nonlinear algebraic equations
Nor, Hafizudin Mohamad; Ismail, Ahmad Izani Md.; Majid, Ahmad Abd.
2014-07-01
We compare some recent homotopy continuation methods to see which method has greater applicability and greater accuracy. We test the methods on systems of nonlinear algebraic equations. The results obtained indicate the superior accuracy of Newton Homotopy Continuation Method (NHCM).
Institute of Scientific and Technical Information of China (English)
崔霞
2002-01-01
Alternating direction finite element (ADFE) scheme for d-dimensional nonlinear system of parabolic integro-differential equations is studied. By using a local approximation based on patches of finite elements to treat the capacity term qi(u), decomposition of the coefficient matrix is realized; by using alternating direction, the multi-dimensional problem is reduced to a family of single space variable problems, calculation work is simplified; by using finite element method, high accuracy for space variant is kept; by using inductive hypothesis reasoning, the difficulty coming from the nonlinearity of the coefficients and boundary conditions is treated; by introducing Ritz-Volterra projection, the difficulty coming from the memory term is solved. Finally, by using various techniques for priori estimate for differential equations, the unique resolvability and convergence properties for both FE and ADFE schemes are rigorously demonstrated, and optimal H1 and L2norm space estimates and O((△t)2) estimate for time variant are obtained.
Chen, Jianxin; Zhuo, Shuangmu; Luo, Tianshu; Liu, Dingzhong; Zhao, Jingjun
2008-08-01
Collagen and elastin are the most important proteins of the connective tissues in higher vertebrates. In this paper, we present a combined nonlinear optical imaging technique of second-harmonic generation and two-photon excited fluorescence to simultaneously observe the collagen and elastic fiber of dermis in a freshly excised human skin and rabbit aorta using a two-channel synchronized detection method. The obtained two-channel overlay image in the backward direction can clearly distinguish the morphological structure and distribution of collagen and elastic fibers. Tissue spectrum further confirms the obtained structural information. These results suggest that the combined nonlinear optical imaging technique coupled with two-channel synchronized detection method can be an effective tool for detecting collage and elastic fibers without any invasive tissue procedure of slicing, embedding, fixation and staining when two structural proteins are simultaneously present in the biological tissue.
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
A new method to solve the damped nonlinear Klein-Gordon equation
Institute of Scientific and Technical Information of China (English)
2008-01-01
This paper discusses a damped nonlinear Klein-Gordon equation in the reproducing kernel space and provides a new method for solving the damped nonlinear Klein-Gordon equation based on the reproducing kernel space.Two numerical examples are given for illustrating the feasibility and accuracy of the method.
Elsawy, Mahmoud M. R.; Renversez, Gilles
2017-07-01
Two distinct models are developed to investigate the transverse magnetic stationary solutions propagating in one-dimensional anisotropic nonlinear plasmonic structures made from a Kerr-type nonlinear metamaterial core embedded between two semi-infinite metal claddings. The first model is semi-analytical, in which we assume that the anisotropic nonlinearity depends only on the transverse component of the electric field and that the nonlinear refractive index modification is small compared to the linear one. This method allows us to derive analytically the field profiles and nonlinear dispersion relations in terms of the Jacobi elliptical functions. The second model is fully numerical and is based on the finite element method in which all the components of the electric field are considered in the Kerr-type nonlinearity, with no presumptions as to the nonlinear refractive index change. Our finite-element-based model is valid beyond the weak nonlinearity regime and generalizes the well-known single-component fixed power algorithm that is usually used. Examples of the main cases are investigated, including those with strong spatial nonlinear effects at low power. Loss issues are reduced through the use of a gain medium in the nonlinear metamaterial core. Using anisotropic nonlinear FDTD simulations, we provide some results for the properties of the main solution.
Nonlinear Ultrasonic Characterization Using the Noncollinear Method
Croxford, A. J.; Drinkwater, B. W.; Wilcox, P. D.
2011-06-01
The measurement of material non-linearity using ultrasound is an attractive concept, offering the potential to detect fatigue damage earlier than is possible with conventional techniques. Despite this advantage and much work in the field the currently developed approaches are primarily limited to the lab environment. This is due to the difficulty in separating the material nonlinearity from that generated by equipment. This paper reports on an approach that eliminates this problem. When two shear waves interact a third wave is generated due to the material nonlinearity. This paper shows how this interaction can be used to measure material properties in damaged specimens. It goes on to show that this approach can be used to make measurements of material non-linearity both across a specimen.
The simplex method for nonlinear sliding mode control
Directory of Open Access Journals (Sweden)
Bartolini G.
1998-01-01
Full Text Available General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
The energy balance to nonlinear oscillations via Jacobi collocation method
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M.K. Yazdi
2015-06-01
Full Text Available This study develops the energy balance based on Jacobi collocation method for accurate prediction of conservative nonlinear oscillator models with a single collocation point. The node points are taken as the roots of Jacobi orthogonal polynomials. Several examples are included to demonstrate the applicability and accuracy of the proposed algorithm, and some comparisons are made with the existing results. The method is suitable and the approximate frequencies are valid for small as well as large amplitudes of oscillation. Excellent agreement with exact ones is presented for the first order approximation.
Controller Design of Complex System Based on Nonlinear Strength
Directory of Open Access Journals (Sweden)
Rongjun Mu
2015-01-01
Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.
An hp symplectic pseudospectral method for nonlinear optimal control
Peng, Haijun; Wang, Xinwei; Li, Mingwu; Chen, Biaosong
2017-01-01
An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
A Hybrid of DL and WYL Nonlinear Conjugate Gradient Methods
Directory of Open Access Journals (Sweden)
Shengwei Yao
2014-01-01
Full Text Available The conjugate gradient method is an efficient method for solving large-scale nonlinear optimization problems. In this paper, we propose a nonlinear conjugate gradient method which can be considered as a hybrid of DL and WYL conjugate gradient methods. The given method possesses the sufficient descent condition under the Wolfe-Powell line search and is globally convergent for general functions. Our numerical results show that the proposed method is very robust and efficient for the test problems.
Auxiliary equation method for solving nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Sirendaoreji,; Jiong, Sun
2003-03-31
By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation.
Nonlinear oscillations in coriolis based gyroscopes
Directory of Open Access Journals (Sweden)
Dag Kristiansen
1999-01-01
Full Text Available In this paper we model and analyze nonlinear oscillations which are known to exist in some Coriolis based gyroscopes due to large amplitude excitation in the drive loop. A detailed derivation of a dynamic model for a cylinder gyroscope which includes geometric nonlinearities is given, and energy transfer between the system's modes are analyzed using perturbation theory and by proposing a simplified model. The model is also simulated, and the results are shown to give an accurate description of the experimental results. This work is done in order to gain a better understanding of the gyroscope's dynamics, and is intended to be a starting point for designing nonlinear observers and vibration controllers for the gyroscope in order to increase the performance.
Diagnosis of multiple sclerosis from EEG signals using nonlinear methods.
Torabi, Ali; Daliri, Mohammad Reza; Sabzposhan, Seyyed Hojjat
2017-09-08
EEG signals have essential and important information about the brain and neural diseases. The main purpose of this study is classifying two groups of healthy volunteers and Multiple Sclerosis (MS) patients using nonlinear features of EEG signals while performing cognitive tasks. EEG signals were recorded when users were doing two different attentional tasks. One of the tasks was based on detecting a desired change in color luminance and the other task was based on detecting a desired change in direction of motion. EEG signals were analyzed in two ways: EEG signals analysis without rhythms decomposition and EEG sub-bands analysis. After recording and preprocessing, time delay embedding method was used for state space reconstruction; embedding parameters were determined for original signals and their sub-bands. Afterwards nonlinear methods were used in feature extraction phase. To reduce the feature dimension, scalar feature selections were done by using T-test and Bhattacharyya criteria. Then, the data were classified using linear support vector machines (SVM) and k-nearest neighbor (KNN) method. The best combination of the criteria and classifiers was determined for each task by comparing performances. For both tasks, the best results were achieved by using T-test criterion and SVM classifier. For the direction-based and the color-luminance-based tasks, maximum classification performances were 93.08 and 79.79% respectively which were reached by using optimal set of features. Our results show that the nonlinear dynamic features of EEG signals seem to be useful and effective in MS diseases diagnosis.
Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
Full Text Available We introduce a nonlinearization procedure that replaces the system potential energy by an equivalent representation form that is used to derive analytical solutions of strongly nonlinear conservative oscillators. We illustrate the applicability of this method by finding the approximate solutions of two strongly nonlinear oscillators and show that this procedure provides solutions that follow well the numerical integration solutions of the corresponding equations of motion.
Dynamic decoupling nonlinear control method for aircraft gust alleviation
Lv, Yang; Wan, Xiaopeng; Li, Aijun
2008-10-01
A dynamic decoupling nonlinear control method for MIMO system is presented in this paper. The dynamic inversion method is used to decouple the multivariable system. The nonlinear control method is used to overcome the poor decoupling effect when the system model is inaccurate. The nonlinear control method has correcting function and is expressed in analytic form, it is easy to adjust the parameters of the controller and optimize the design of the control system. The method is used to design vertical transition mode of active control aircraft for gust alleviation. Simulation results show that the designed vertical transition mode improves the gust alleviation effect about 34% comparing with the normal aircraft.
Cardiovascular Response Identification Based on Nonlinear Support Vector Regression
Wang, Lu; Su, Steven W.; Chan, Gregory S. H.; Celler, Branko G.; Cheng, Teddy M.; Savkin, Andrey V.
This study experimentally investigates the relationships between central cardiovascular variables and oxygen uptake based on nonlinear analysis and modeling. Ten healthy subjects were studied using cycle-ergometry exercise tests with constant workloads ranging from 25 Watt to 125 Watt. Breath by breath gas exchange, heart rate, cardiac output, stroke volume and blood pressure were measured at each stage. The modeling results proved that the nonlinear modeling method (Support Vector Regression) outperforms traditional regression method (reducing Estimation Error between 59% and 80%, reducing Testing Error between 53% and 72%) and is the ideal approach in the modeling of physiological data, especially with small training data set.
Robust methods and asymptotic theory in nonlinear econometrics
Bierens, Herman J
1981-01-01
This Lecture Note deals with asymptotic properties, i.e. weak and strong consistency and asymptotic normality, of parameter estimators of nonlinear regression models and nonlinear structural equations under various assumptions on the distribution of the data. The estimation methods involved are nonlinear least squares estimation (NLLSE), nonlinear robust M-estimation (NLRME) and non linear weighted robust M-estimation (NLWRME) for the regression case and nonlinear two-stage least squares estimation (NL2SLSE) and a new method called minimum information estimation (MIE) for the case of structural equations. The asymptotic properties of the NLLSE and the two robust M-estimation methods are derived from further elaborations of results of Jennrich. Special attention is payed to the comparison of the asymptotic efficiency of NLLSE and NLRME. It is shown that if the tails of the error distribution are fatter than those of the normal distribution NLRME is more efficient than NLLSE. The NLWRME method is appropriate ...
A method of nonlinear correction of thermocouple based on function%一种基于函数型的热电偶非线性校正方法
Institute of Scientific and Technical Information of China (English)
何晓文; 周雪纯
2016-01-01
由于热电偶的输出信号只有几十毫伏,并且存在较大的非线性,因此测温时需要进行非线性校正.热电偶的非线性校正方法多种多样,以K型热电偶为例,介绍一种基于函数型的热电偶非线性校正方法,可将热电偶1%左右的非线性误差降至0.2%以内,具有校准精度高、实时性好等特点,该方法可广泛应用于各种类型热电偶的非线性校正电路中.%The output signal of the thermocouple was only a few tens of millivolts, due to its large nonlinear, so the result must be corrected. There are various corrected methods of thermocouple, K type as an example, the method based on the function is introduced, the nonlinearity error from 1% down to 0.2% or less, it has high precision, good real-time, and it is also applicable to correction method of other types of thermocouples nonlinear. The method can be widely used in various types of the thermocouple non-linear correction circuit.
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have been...
Numerical Methods for Nonlinear PDEs in Finance
DEFF Research Database (Denmark)
Mashayekhi, Sima
Nonlinear Black-Scholes equations arise from considering parameters such as feedback and illiquid markets eects or large investor preferences, volatile portfolio and nontrivial transaction costs into option pricing models to have more accurate option price. Here some nite dierence schemes have be...
Immersion and Invariance Based Nonlinear Adaptive Flight Control
Sonneveldt, L.; Van Oort, E.R.; Chu, Q.P.; Mulder, J.A.
2010-01-01
In this paper a theoretical framework for nonlinear adaptive flight control is developed and applied to a simplified, over-actuated nonlinear fighter aircraft model. The framework is based on a modular adaptive backstepping scheme with a new type of nonlinear estimator. The nonlinear estimator is
Immersion and Invariance Based Nonlinear Adaptive Flight Control
Sonneveldt, L.; Van Oort, E.R.; Chu, Q.P.; Mulder, J.A.
2010-01-01
In this paper a theoretical framework for nonlinear adaptive flight control is developed and applied to a simplified, over-actuated nonlinear fighter aircraft model. The framework is based on a modular adaptive backstepping scheme with a new type of nonlinear estimator. The nonlinear estimator is co
Modified Homotopy Analysis Method for Nonlinear Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
D. Ziane
2017-05-01
Full Text Available In this paper, a combined form of natural transform with homotopy analysis method is proposed to solve nonlinear fractional partial differential equations. This method is called the fractional homotopy analysis natural transform method (FHANTM. The FHANTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHANTM is an appropriate method for solving nonlinear fractional partial differentia equation.
Hyperbolic function method for solving nonlinear differential-different equations
Institute of Scientific and Technical Information of China (English)
Zhu Jia-Min
2005-01-01
An algorithm is devised to obtained exact travelling wave solutions of differential-different equations by means of hyperbolic function. For illustration, we apply the method to solve the discrete nonlinear (2+1)-dimensional Toda lattice equation and the discretized nonlinear mKdV lattice equation, and successfully constructed some explicit and exact travelling wave solutions.
A SELF-ADAPTIVE TECHNIQUE FOR A KIND OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
王丽平
2004-01-01
Conjugate gradient methods. are a class of important methods for unconstrained optimization, especially when the dimension is large. In 2001, Dai and Liao have proposed a new conjugate condition, based on it two nonlinear conjugate gradient methods are constructed. With trust region idea, this paper gives a self-adaptive technique for the two methods. The numerical results show that this technique works well for the given nonlinear optimization test problems.
Indian Academy of Sciences (India)
Zaiyun Zhang; Jianhua Huang; Juan Zhong; Sha-Sha Dou; Jiao Liu; Dan Peng; Ting Gao
2014-06-01
In this paper, we construct the travelling wave solutions to the perturbed nonlinear Schrödinger’s equation (NLSE) with Kerr law non-linearity by the extended (′/)-expansion method. Based on this method, we obtain abundant exact travelling wave solutions of NLSE with Kerr law nonlinearity with arbitrary parameters. The travelling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.
Face Recognition Based on Nonlinear Feature Approach
Directory of Open Access Journals (Sweden)
Eimad E.A. Abusham
2008-01-01
Full Text Available Feature extraction techniques are widely used to reduce the complexity high dimensional data. Nonlinear feature extraction via Locally Linear Embedding (LLE has attracted much attention due to their high performance. In this paper, we proposed a novel approach for face recognition to address the challenging task of recognition using integration of nonlinear dimensional reduction Locally Linear Embedding integrated with Local Fisher Discriminant Analysis (LFDA to improve the discriminating power of the extracted features by maximize between-class while within-class local structure is preserved. Extensive experimentation performed on the CMU-PIE database indicates that the proposed methodology outperforms Benchmark methods such as Principal Component Analysis (PCA, Fisher Discrimination Analysis (FDA. The results showed that 95% of recognition rate could be obtained using our proposed method.
Adaptive Observer-Based Fault Estimate for Nonlinear Systems
Institute of Scientific and Technical Information of China (English)
ZONG Qun; LIU Wenjing; LIU Li
2006-01-01
An approach for adaptive observer-based fault estimate for nonlinear system is proposed.H-infinity theory is applied to analyzing the design method and stable conditions of the adaptive observer,from which both system state and fault can be estimated.It is proved that the fault estimate error is related to the given H-infinity track performance indexes,as well as to the changing rate of the fault and the Lipschitz constant of the nonlinear item.The design steps of the adaptive observer are proposed.The simulation results show that the observer has good performance for fault estimate even when the system includes nonlinear terms,which confirms the effectiveness of the method.
Peng, Haijun; Wang, Xinwei; Zhang, Sheng; Chen, Biaosong
2017-07-01
Nonlinear state-delayed optimal control problems have complex nonlinear characters. To solve this complex nonlinear problem, an iterative symplectic pseudospectral method based on quasilinearization techniques, the dual variational principle and pseudospectral methods is proposed in this paper. First, the proposed method transforms the original nonlinear optimal control problem into a series of linear quadratic optimal control problems. Then, a symplectic pseudospectral method is developed to solve these converted linear quadratic state-delayed optimal control problems. Coefficient matrices in the proposed method are sparse and symmetric since the dual variational principle is used, which makes the proposed method highly efficient. Converged numerical solutions with high precision can be obtained after a few iterations due to the benefit of the local pseudospectral method and quasilinearization techniques. In the numerical simulations, other numerical methods were used for comparisons. The numerical simulation results show that the proposed method is highly accurate, efficient and robust.
GHM method for obtaining rationalsolutions of nonlinear differential equations.
Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo
2015-01-01
In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.
On the freezing method for nonlinear nonautonomous systems with delay
Directory of Open Access Journals (Sweden)
Michael I. Gil'
2001-01-01
Full Text Available Nonlinear nonautonomous differential systems with delaying argument are considered. Explicit conditions for absolute stability are derived. The proposed approach is based on the generalization of the freezing method for ordinary differential equations.
Analysis of factors influencing fire damage to concrete using nonlinear resonance vibration method
Energy Technology Data Exchange (ETDEWEB)
Park, Gang Kyu; Park, Sun Jong; Kwak, Hyo Gyoung [Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, KAIST, Daejeon (Korea, Republic of); Yim, Hong Jae [Dept. of Construction and Disaster Prevention Engineering, Kyungpook National University, Sangju (Korea, Republic of)
2015-04-15
In this study, the effects of different mix proportions and fire scenarios (exposure temperatures and post-fire-curing periods) on fire-damaged concrete were analyzed using a nonlinear resonance vibration method based on nonlinear acoustics. The hysteretic nonlinearity parameter was obtained, which can sensitively reflect the damage level of fire-damaged concrete. In addition, a splitting tensile strength test was performed on each fire-damaged specimen to evaluate the residual property. Using the results, a prediction model for estimating the residual strength of fire-damaged concrete was proposed on the basis of the correlation between the hysteretic nonlinearity parameter and the ratio of splitting tensile strength.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
A novel method for extracting acoustic nonlinearity parameters with diffraction corrections
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyunjo [Wonkwang University, Iksan (Korea, Republic of); Zhang, Shuzeng; Li, Xiongbing [Central South University, Changsha (China)
2016-02-15
A new method for determining the acoustic nonlinearity parameter using a nonlinear data fitting method is proposed. Based on the quasilinear theory of Westervelt's equation, the fundamental and second harmonic beam fields are expressed as a multi-Gaussian beam model that separates the attenuation and diffraction correction terms from the propagating plane waves. A nonlinear least squares curve fitting method is developed to extract the nonlinearity parameter without knowing the attenuation coefficients of the material being tested. The nonlinearity parameter of water is determined using the proposed method, and the result agrees well with the literature value. The attenuation coefficients of the fundamental and the second harmonic are also extracted and discussed.
Ultrasound Tomography in Circular Measurement Configuration using Nonlinear Reconstruction Method
Directory of Open Access Journals (Sweden)
Tran Quang-Huy
2015-12-01
Full Text Available Ultrasound tomography offers the potential for detecting of very small tumors whose sizes are smaller than the wavelength of the incident pressure wave without ionizing radiation. Based on inverse scattering technique, this imaging modality uses some material properties such as sound contrast and attenuation in order to detect small objects. One of the most commonly used methods in ultrasound tomography is the Distorted Born Iterative Method (DBIM. The compressed sensing technique was applied in the DBIM as a promising approach for the image reconstruction quality improvement. Nevertheless, the random measurement configuration of transducers in this method is very difficult to set up in practice. Therefore, in this paper, we take advantages of simpler sparse uniform measurement configuration set-up of transducers and high-quality image reconstruction of 1 non-linear regularization in sparse scattering domain. The simulation results demonstrate the high performance of the proposed approach in terms of tremendously reduced total runtime and normalized error.
Cluster-based control of nonlinear dynamics
Kaiser, Eurika; Spohn, Andreas; Cattafesta, Louis N; Morzynski, Marek
2016-01-01
The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. Here, a cluster-based control framework is proposed to determine optimal control laws with respect to a cost function for unsteady flows. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a Markov model. The Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is de...
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
COMPARISON OF NONLINEAR DYNAMICS OPTIMIZATION METHODS FOR APS-U
Energy Technology Data Exchange (ETDEWEB)
Sun, Y.; Borland, Michael
2017-06-25
Many different objectives and genetic algorithms have been proposed for storage ring nonlinear dynamics performance optimization. These optimization objectives include nonlinear chromaticities and driving/detuning terms, on-momentum and off-momentum dynamic acceptance, chromatic detuning, local momentum acceptance, variation of transverse invariant, Touschek lifetime, etc. In this paper, the effectiveness of several different optimization methods and objectives are compared for the nonlinear beam dynamics optimization of the Advanced Photon Source upgrade (APS-U) lattice. The optimized solutions from these different methods are preliminarily compared in terms of the dynamic acceptance, local momentum acceptance, chromatic detuning, and other performance measures.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A trial equation method to nonlinear evolution equation with rank inhomogeneous is given. As applications, the exact traveling wave solutions to some higher-order nonlinear equations such as generalized Boussinesq equation,generalized Pochhammer-Chree equation, KdV-Burgers equation, and KS equation and so on, are obtained. Among these, some results are new. The proposed method is based on the idea of reduction of the order of ODE. Some mathematical details of the proposed method are discussed.
Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping
2013-01-01
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic ...
Fast nonlinear regression method for CT brain perfusion analysis.
Bennink, Edwin; Oosterbroek, Jaap; Kudo, Kohsuke; Viergever, Max A; Velthuis, Birgitta K; de Jong, Hugo W A M
2016-04-01
Although computed tomography (CT) perfusion (CTP) imaging enables rapid diagnosis and prognosis of ischemic stroke, current CTP analysis methods have several shortcomings. We propose a fast nonlinear regression method with a box-shaped model (boxNLR) that has important advantages over the current state-of-the-art method, block-circulant singular value decomposition (bSVD). These advantages include improved robustness to attenuation curve truncation, extensibility, and unified estimation of perfusion parameters. The method is compared with bSVD and with a commercial SVD-based method. The three methods were quantitatively evaluated by means of a digital perfusion phantom, described by Kudo et al. and qualitatively with the aid of 50 clinical CTP scans. All three methods yielded high Pearson correlation coefficients ([Formula: see text]) with the ground truth in the phantom. The boxNLR perfusion maps of the clinical scans showed higher correlation with bSVD than the perfusion maps from the commercial method. Furthermore, it was shown that boxNLR estimates are robust to noise, truncation, and tracer delay. The proposed method provides a fast and reliable way of estimating perfusion parameters from CTP scans. This suggests it could be a viable alternative to current commercial and academic methods.
Institute of Scientific and Technical Information of China (English)
WangLin; NiQiao; HuangYuying
2003-01-01
This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.
Institute of Scientific and Technical Information of China (English)
郭亚红; 吴保奎
2011-01-01
Studying control theory of induction motor nonlinear control method is the development direction. For nonlinear control method of induction motor, there are mainly three forms-feedback linearization method, passivity-based control method and backstepping method. Based on the introduction the basic control principle, and comparisons among the different control methods were made through simulation experiments, the results show that the passivity-based control method with stronger robustness is more beneficial to design.%非线性控制方法是感应电机控制理论研究的发展方向.感应电机的非线性控制方法主要有反馈线性化法、无源性控制法和反步法三种,在介绍其基本控制原理的基础上,通过仿真实验对不同的控制方法进行比较,结果表明无源性控制方法有较强的鲁棒性,更利于设计.
A NUMERICAL CALCULATION METHOD FOR EIGENVALUE PROBLEMS OF NONLINEAR INTERNAL WAVES
Institute of Scientific and Technical Information of China (English)
SHI Xin-gang; FAN Zhi-song; LIU Hai-long
2009-01-01
Generally speaking, the background shear current U(z)must be taken into account in eigenvalue problems of nonlinear internal waves in ocean, as is different from those of linear internal waves. A numerical calculation method for eigenvalue problems of nonlinear internal waves is presented in this paper on the basis of the Thompson-Haskell's calculation method. As an application of this method, at a station (21°N, 117°15′E) in the South China Sea, a modal structure and parameters of nonlinear internal waves are calculated, and the results closely agree with the calculated results based on observation by Yang et al..
A Hybrid Method for Nonlinear Least Squares Problems
Institute of Scientific and Technical Information of China (English)
Zhongyi Liu; Linping Sun
2007-01-01
A negative curvature method is applied to nonlinear least squares problems with indefinite Hessian approximation matrices. With the special structure of the method,a new switch is proposed to form a hybrid method. Numerical experiments show that this method is feasible and effective for zero-residual,small-residual and large-residual problems.
Ren, Shijin
2003-01-01
Response surface models based on multiple linear regression had previously been developed for the toxicity of aromatic chemicals to Tetrahymena pyriformis. However, a nonlinear relationship between toxicity and one of the molecular descriptors in the response surface model was observed. In this study, response surface models were established using six nonlinear modeling methods to handle the nonlinearity exhibited in the aromatic chemicals data set. All models were validated using the method of cross-validation, and prediction accuracy was tested on an external data set. Results showed that response surface models based on locally weighted regression scatter plot smoothing (LOESS), multivariate adaptive regression splines (MARS), neural networks (NN), and projection pursuit regression (PPR) provided satisfactory power of model fitting and prediction and had similar applicabilities. The response surface models based on nonlinear methods were difficult to interpret and conservative in discriminating toxicity mechanisms.
Nonlinear inverse modeling of sensor based on back-propagation fuzzy logical system
Institute of Scientific and Technical Information of China (English)
Li Jun; Liu Junhua
2007-01-01
Objective To correct the nonlinear error of sensor output, a new approach to sensor inverse modeling based on Back-Propagation Fuzzy Logical System (BP FS) is presented. Methods The BP FS is a computationally efficient nonlinear universal approximator, which is capable of implementing complex nonlinear mapping from its input pattern space to the output with fast convergence speed. Results The neuro-fuzzy hybrid system, i.e. BP FS, is then applied to construct nonlinear inverse model of pressure sensor. The experimental results show that the proposed inverse modeling method automatically compensates the associated nonlinear error in pressure estimation, and thus the performance of pressure sensor is significantly improved. Conclusion The proposed method can be widely used in nonlinearity correction of various kinds of sensors to compensate the effects of nonlinearity and temperature on sensor output.
GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems
Directory of Open Access Journals (Sweden)
W. L. Chiang
2008-11-01
Full Text Available Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC or an adaptive fuzzy sliding mode controller (AFSMC capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.
Institute of Scientific and Technical Information of China (English)
QIN Xinqiang; MA Yichen; GONG Chunqiong
2004-01-01
A two-grid method for solving nonlinear convection-dominated diffusion equations is presented. The method use discretizations based on a characteristic mixed finite-element method and give the linearization for nonlinear systems by two steps. The error analysis shows that the two-grid scheme combined with the characteristic mixed finite-element method can decrease numerical oscillation caused by dominated convections and solve nonlinear advection-dominated diffusion problems efficiently.
Nonlinear Circuit Analysis via Perturbation Methods and Hardware Prototyping
Directory of Open Access Journals (Sweden)
K. Odame
2010-01-01
Full Text Available Nonlinear signal processing is necessary in many emerging applications where form factor and power are at a premium. In order to make such complex computation feasible under these constraints, it is necessary to implement the signal processors as analog circuits. Since analog circuit design is largely based on a linear systems perspective, new tools are being introduced to circuit designers that allow them to understand and exploit circuit nonlinearity for useful processing. This paper discusses two such tools, which represent nonlinear circuit behavior in a graphical way, making it easy to develop a qualitative appreciation for the circuits under study.
NOLB: Nonlinear Rigid Block Normal Mode Analysis Method
Hoffmann, Alexandre; Grudinin, Sergei
2017-01-01
International audience; We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velo...
Directory of Open Access Journals (Sweden)
J. Prakash
2016-03-01
Full Text Available In this paper, a numerical algorithm based on a modified He-Laplace method (MHLM is proposed to solve space and time nonlinear fractional differential-difference equations (NFDDEs arising in physical phenomena such as wave phenomena in fluids, coupled nonlinear optical waveguides and nanotechnology fields. The modified He-Laplace method is a combined form of the fractional homotopy perturbation method and Laplace transforms method. The nonlinear terms can be easily decomposed by the use of He’s polynomials. This algorithm has been tested against time-fractional differential-difference equations such as the modified Lotka Volterra and discrete (modified KdV equations. The proposed scheme grants the solution in the form of a rapidly convergent series. Three examples have been employed to illustrate the preciseness and effectiveness of the proposed method. The achieved results expose that the MHLM is very accurate, efficient, simple and can be applied to other nonlinear FDDEs.
LIMITED MEMORY BFGS METHOD FOR NONLINEAR MONOTONE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Weijun Zhou; Donghui Li
2007-01-01
In this paper, we propose an algorithm for solving nonlinear monotone equations by combining the limited memory BFGS method (L-BFGS) with a projection method. We show that the method is globally convergent if the equation involves a Lipschitz continuous monotone function. We also present some preliminary numerical results.
A simple harmonic balance method for solving strongly nonlinear oscillators
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2016-10-01
Full Text Available In this paper, a simple harmonic balance method (HBM is proposed to obtain higher-order approximate periodic solutions of strongly nonlinear oscillator systems having a rational and an irrational force. With the proposed procedure, the approximate frequencies and the corresponding periodic solutions can be easily determined. It gives high accuracy for both small and large amplitudes of oscillations and better result than those obtained by other existing results. The main advantage of the present method is that its simplicity and the second-order approximate solutions almost coincide with the corresponding numerical solutions (considered to be exact. The method is illustrated by examples. The present method is very effective and convenient method for solving strongly nonlinear oscillator systems arising in nonlinear science and engineering.
H∞ Synthesis Method for Control of Non-linear Flexible Joint Models
Axelsson, Patrik; Pipeleers, Goele; Helmersson, Anders; Norrlöf, Mikael
2014-01-01
An H∞ synthesis method for control of a flexible joint, with non-linear spring characteristic, is proposed. The first step of the synthesis method is to extend the joint model with an uncertainty description of the stiffness parameter. In the second step, a non-linear optimisation problem, based on nominal performance and robust stability requirements, has to be solved. Using the Lyapunov shaping paradigm and a change of variables, the non-linear optimisation problem can be rewritten as a con...
Stabilization of discrete nonlinear systems based on control Lyapunov functions
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
The stabilization of discrete nonlinear systems is studied.Based on control Lyapunov functions,asufficient and necessary condition for a quadratic function to be a control Lyapunov function is given.From this condition,a continuous state feedback law is constructed explicitly.It can globally asymptotically stabilize the equilibrium of the closed-loop system.A simulation example shows the effectiveness of the proposed method.
CONVERGENCE OF NONLINEAR CONJUGATE GRADIENT METHODS
Institute of Scientific and Technical Information of China (English)
Yu-hong Dai
2001-01-01
This paper proves that a simplified Armijo-type line search can ensure the global con vergences of the Fletcher-Reeves method and the Polak-Ribiére-Polyak method for un constrained optimization. Although it seems not possible to verify that the PRP method using the generalized Armijo line search converges globally for generally problems, it can be shown that in this case the PRP method always solves uniformly convex problems.
Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin
2016-08-01
This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.
Improved HPC method for nonlinear wave tank
DEFF Research Database (Denmark)
Zhu, Wenbo; Greco, Marilena; Shao, Yanlin
2017-01-01
The recently developed Harmonic Polynomial Cell (HPC) method has been proved to be a promising choice for solving potential-flow Boundary Value Problem (BVP). In this paper, a flux method is proposed to consistently deal with the Neumann boundary condition of the original HPC method and enhance...
A new method for parameter estimation in nonlinear dynamical equations
Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao
2015-01-01
Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Nonlinear Methods in Riemannian and Kählerian Geometry
Jost, Jürgen
1991-01-01
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps ...
Adaptive control method for nonlinear time-delay processes
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Two complex properties,varying time-delay and block-oriented nonlinearity,are very common in chemical engineering processes and not easy to be controlled by routine control methods.Aimed at these two complex properties,a novel adaptive control algorithm the basis of nonlinear OFS(orthonormal functional series) model is proposed.First,the hybrid model which combines OFS and Volterra series is introduced.Then,a stable state feedback strategy is used to construct a nonlinear adaptive control algorithm that can guarantee the closed-loop stability and can track the set point curve without steady-state errors.Finally,control simulations and experiments on a nonlinear process with varying time-delay are presented.A number of experimental results validate the efficiency and superiority of this algorithm.
Optimal Variational Asymptotic Method for Nonlinear Fractional Partial Differential Equations.
Baranwal, Vipul K; Pandey, Ram K; Singh, Om P
2014-01-01
We propose optimal variational asymptotic method to solve time fractional nonlinear partial differential equations. In the proposed method, an arbitrary number of auxiliary parameters γ 0, γ 1, γ 2,… and auxiliary functions H 0(x), H 1(x), H 2(x),… are introduced in the correction functional of the standard variational iteration method. The optimal values of these parameters are obtained by minimizing the square residual error. To test the method, we apply it to solve two important classes of nonlinear partial differential equations: (1) the fractional advection-diffusion equation with nonlinear source term and (2) the fractional Swift-Hohenberg equation. Only few iterations are required to achieve fairly accurate solutions of both the first and second problems.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
The optical nonlinearity of gold nanoparticles prepared by bioreduction method
Balbuena Ortega, A.; Arroyo Carrasco, M. L.; Gayou, V. L.; Orduña Díaz, A.; Delgado Macuil, R.; Rojas López, Marlon
2013-11-01
Nonlinear optical and electronic properties of nanosized metal particles have drawn considerable attention because of their strong and size-dependent plasmon resonance absorption. In a metal nanoparticle system such as gold dispersed in a transparent matrix, an absorption peak due to surface plasmon resonance is usually observed in the visible spectral region. Metal nanoparticles are of special interest as nonlinear materials for optical switching and computing because of their relatively large third-order nonlinearity (χ3) and ultrafast response time. The purpose of this study was to analyze the nonlinear optical properties of biosynthesized gold nanoparticles. The samples were prepared by biosynthesis method using yeast extract as reducing agent and the nonlinear optical properties of the nanoparticles were investigated using a single beam Z-scan technique with a beam power of 20 mW and operated at wavelength of 514 nm. The reaction between metal ions and yeast extracts were monitored by UV-visible spectra of Au nanoparticles in aqueous solution with different pH (3-6). The surface plasmon peak position was shifted from 528 nm to 573 nm, according to of pH variation 4 to 6. The average particle size was calculated by the absorption peak position using the Fernig method, from 42 to 103 nm. The z-scan curves showed a negative nonlocal nonlinear refractive index with a magnitude dependent on the nanoparticle size.
基于流形学习的非线性维数约简方法%Nonlinear Dimensionality Reduction Method Based on Manifold Learning
Institute of Scientific and Technical Information of China (English)
段志臣; 芮小平; 张立媛
2012-01-01
流形学习是一种新的非线性维数约简方法,近年来正引起可视化等领域研究者的高度重视.为加深对流形学习的理解,介绍了流形学习的基本原理,总结了其研究进展和分类方法,最后阐述了几种常用的流形学习方法的基本思想、算法步骤和各自的优缺点.通过在人工数据集Swiss-Roll上进行实验,将各类方法在近邻值选取和噪声影响等方面进行了对比分析,结果表明:与传统的线性维数约简方法相比,流形学习方法能够有效地发现观测样本的低维结构.最后对流形学习未来的研究方向作出展望,以期在这一领域取得更大进展.%As a new kind of nonlinear dimensionality reduction method, manifold learning is capturing increasing interests of researchers. To understand manifold learning better, the principle is firstly introduced, and then its development history and different representations are summarized, finally several major method are introduced, whose basic thoughts, steps and advantages are pointed out respectively. By the experiments on Swiss-Roll, the selection of neighbors and noise effect are analyzed, the results shows: compared with traditional linear method, manifold learning can discover the intrinsic structure of the samples better. Finally the prospect of manifold learning was discussed for more developments.
THE MORTAR ELEMENT METHOD FOR A NONLINEAR BIHARMONIC EQUATION
Institute of Scientific and Technical Information of China (English)
Zhong-ci Shi; Xue-jun Xu
2005-01-01
The mortar element method is a new domain decomposition method(DDM) with nonoverlapping subdomains. It can handle the situation where the mesh on different subdomains need not align across interfaces, and the matching of discretizations on adjacent subdomains is only enforced weakly. But until now there has been very little work for nonlinear PDEs. In this paper, we will present a mortar-type Morley element method for a nonlinear biharmonic equation which is related to the well-known Navier-Stokes equation. Optimal energy and H1-norm estimates are obtained under a reasonable elliptic regularity assumption.
Applications of Automation Methods for Nonlinear Fracture Test Analysis
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
Using automated and standardized computer tools to calculate the pertinent test result values has several advantages such as: 1. allowing high-fidelity solutions to complex nonlinear phenomena that would be impractical to express in written equation form, 2. eliminating errors associated with the interpretation and programing of analysis procedures from the text of test standards, 3. lessening the need for expertise in the areas of solid mechanics, fracture mechanics, numerical methods, and/or finite element modeling, to achieve sound results, 4. and providing one computer tool and/or one set of solutions for all users for a more "standardized" answer. In summary, this approach allows a non-expert with rudimentary training to get the best practical solution based on the latest understanding with minimum difficulty.Other existing ASTM standards that cover complicated phenomena use standard computer programs: 1. ASTM C1340/C1340M-10- Standard Practice for Estimation of Heat Gain or Loss Through Ceilings Under Attics Containing Radiant Barriers by Use of a Computer Program 2. ASTM F 2815 - Standard Practice for Chemical Permeation through Protective Clothing Materials: Testing Data Analysis by Use of a Computer Program 3. ASTM E2807 - Standard Specification for 3D Imaging Data Exchange, Version 1.0 The verification, validation, and round-robin processes required of a computer tool closely parallel the methods that are used to ensure the solution validity for equations included in test standard. The use of automated analysis tools allows the creation and practical implementation of advanced fracture mechanics test standards that capture the physics of a nonlinear fracture mechanics problem without adding undue burden or expense to the user. The presented approach forms a bridge between the equation-based fracture testing standards of today and the next generation of standards solving complex problems through analysis automation.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Institute of Scientific and Technical Information of China (English)
Pan Jun-Ting; Gong Lun-Xun
2008-01-01
Based on a first order nonlinear ordinary differential equation with at most a sixth-degree nonlinear term which is extended from a type of elliptic equation,and by converting it into a new expansion form,this paper proposes a new algebraic method to construct exact solutions for nonlinear evolution equations.Being concise and straightforward,themethod is applied to modified Benjamin-Bona-Mahony (mBBM) model,and some new exact solutions to the system are obtained.The algorithm is of important significance in exploring exact solutions for other nonlinear evolution equations.
New Efficient Fourth Order Method for Solving Nonlinear Equations
Directory of Open Access Journals (Sweden)
Farooq Ahmad
2013-12-01
Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems
Directory of Open Access Journals (Sweden)
Daniel Olvera
2014-01-01
Full Text Available We introduce a new approach called the enhanced multistage homotopy perturbation method (EMHPM that is based on the homotopy perturbation method (HPM and the usage of time subintervals to find the approximate solution of differential equations with strong nonlinearities. We also study the convergence of our proposed EMHPM approach based on the value of the control parameter h by following the homotopy analysis method (HAM. At the end of the paper, we compare the derived EMHPM approximate solutions of some nonlinear physical systems with their corresponding numerical integration solutions obtained by using the classical fourth order Runge-Kutta method via the amplitude-time response curves.
An averaging method for nonlinear laminar Ekman layers
DEFF Research Database (Denmark)
Andersen, Anders Peter; Lautrup, B.; Bohr, T.
2003-01-01
We study steady laminar Ekman boundary layers in rotating systems using,an averaging method similar to the technique of von Karman and Pohlhausen. The method allows us to explore nonlinear corrections to the standard Ekman theory even at large Rossby numbers. We consider both the standard self...
Liu, Jingwei; Liu, Yi; Xu, Meizhi
2015-01-01
Parameter estimation method of Jelinski-Moranda (JM) model based on weighted nonlinear least squares (WNLS) is proposed. The formulae of resolving the parameter WNLS estimation (WNLSE) are derived, and the empirical weight function and heteroscedasticity problem are discussed. The effects of optimization parameter estimation selection based on maximum likelihood estimation (MLE) method, least squares estimation (LSE) method and weighted nonlinear least squares estimation (WNLSE) method are al...
Dehghan, Mehdi; Mohammadi, Vahid
2017-08-01
In this research, we investigate the numerical solution of nonlinear Schrödinger equations in two and three dimensions. The numerical meshless method which will be used here is RBF-FD technique. The main advantage of this method is the approximation of the required derivatives based on finite difference technique at each local-support domain as Ωi. At each Ωi, we require to solve a small linear system of algebraic equations with a conditionally positive definite matrix of order 1 (interpolation matrix). This scheme is efficient and its computational cost is same as the moving least squares (MLS) approximation. A challengeable issue is choosing suitable shape parameter for interpolation matrix in this way. In order to overcome this matter, an algorithm which was established by Sarra (2012), will be applied. This algorithm computes the condition number of the local interpolation matrix using the singular value decomposition (SVD) for obtaining the smallest and largest singular values of that matrix. Moreover, an explicit method based on Runge-Kutta formula of fourth-order accuracy will be applied for approximating the time variable. It also decreases the computational costs at each time step since we will not solve a nonlinear system. On the other hand, to compare RBF-FD method with another meshless technique, the moving kriging least squares (MKLS) approximation is considered for the studied model. Our results demonstrate the ability of the present approach for solving the applicable model which is investigated in the current research work.
Analysis of Nonlinear Dynamics by Square Matrix Method
Energy Technology Data Exchange (ETDEWEB)
Yu, Li Hua [Brookhaven National Lab. (BNL), Upton, NY (United States). Energy and Photon Sciences Directorate. National Synchrotron Light Source II
2016-07-25
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. And more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.
Observer-Based Nonlinear Control of A Torque Motor with Perturbation Estimation
Institute of Scientific and Technical Information of China (English)
J Chen; E Prempain; Q H Wu
2006-01-01
This paper presents an observer-based nonlinear control method that was developed and implemented to provide accurate tracking control of a limited angle torque motor following a 50Hz reference waveform. The method is based on a robust nonlinear observer, which is used to estimate system states and perturbations and then employ input-output feedback linearization to compensate for the system nonlinearities and uncertainties. The estimation of system states and perturbations allows input-output linearization of the nonlinear system without an accurate mathematical model of nominal plant. The simulation results show that the observer-based nonlinear control method is superior in comparison with the conventional model-based state feedback linearizing controller.
Nonlinear Direct Robust Adaptive Control Using Lyapunov Method
Directory of Open Access Journals (Sweden)
Chunbo Xiu
2013-07-01
Full Text Available The problem of robust adaptive stabilization of a class of multi-input nonlinear systems with arbitrary unknown parameters and unknown structure of bounded variation have been considered. By employing the direct adaptive and control Lyapunov function method, a robust adaptive controller is designed to complete the globally adaptive stability of the system states. By employing our result, a kind of nonlinear system is analyzed, the concrete form of the control law is given and the meaningful quadratic control Lyapunov function for the system is constructed. Simulation of parallel manipulator is provided to illustrate the effectiveness of the proposed method.
Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.
Zhang, Yanjun; Tao, Gang; Chen, Mou
2016-09-01
This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.
Non-linear time series analysis: methods and applications to atrial fibrillation.
Hoekstra, B P; Diks, C G; Allessie, M A; Degoede, J
2001-01-01
We apply methods from non-linear statistical time series analysis to characterize electrograms of atrial fibrillation. These are based on concepts originating from the theory of non-linear dynamical systems and use the empirical reconstruction density in reconstructed phase space. Application of these methods is not restricted to deterministic chaos but is valid in a general time series context. We illustrate this by applying three recently proposed non-linear time series methods to fibrillation electrograms: 1) a test for time reversibility in atrial electrograms during paroxysmal atrial fibrillation in patients; 2) a test to detect differences in the dynamical behaviour during the pharmacological conversion of sustained atrial fibrillation in instrumented conscious goats; 3) a test for general Granger causality to identify couplings and information transport in the atria during fibrillation. We conclude that a characterization of the dynamics via the reconstruction density offers a useful framework for the non-linear analysis of electrograms of atrial fibrillation.
Nonlinear feature identification of impedance-based structural health monitoring
Energy Technology Data Exchange (ETDEWEB)
Rutherford, A. C. (Amanda C.); Park, G. H. (Gyu Hae); Sohn, H. (Hoon); Farrar, C. R. (Charles R.)
2004-01-01
The impedance-based structural health monitoring technique, which utilizes electromechanical coupling properties of piezoelectric materials, has shown feasibility for use in a variety of structural health monitoring applications. Relying on high frequency local excitations (typically > 30 kHz), this technique is very sensitive to minor changes in structural integrity in the near field of piezoelectric sensors. Several damage sensitive features have been identified and used coupled with the impedance methods. Most of these methods are, however, limited to linearity assumptions of a structure. This paper presents the use of experimentally identified nonlinear features, combined with impedance methods, for structural health monitoring. Their applicability to damage detection in various frequency ranges is demonstrated using actual impedance signals measured from a portal frame structure. The performance of the nonlinear feature is compared with those of conventional impedance methods. This paper reinforces the utility of nonlinear features in structural health monitoring and suggests that their varying sensitivity in different frequency ranges may be leveraged for certain applications.
Application of new novel energy balance method to strongly nonlinear oscillator systems
Directory of Open Access Journals (Sweden)
Md. Abdur Razzak
2015-01-01
Full Text Available In this paper, a new novel energy balance method based on the harmonic balance method is proposed to obtain higher-order approximations of strongly nonlinear problems arising in engineering. Especially, second-order approximation is considered in this paper. Results found in this paper are compared with the exact result and other existing results. The results show that the proposed method gives better result for both small and large amplitudes of oscillation than other existing results. The method is illustrated by examples. It has been shown that the proposed method is very effective, convenient and quite accurate to nonlinear engineering problems.
Nonvolatile Memory Based on Nonlinear Magnetoelectric Effects
Shen, Jianxin; Cong, Junzhuang; Chai, Yisheng; Shang, Dashan; Shen, Shipeng; Zhai, Kun; Tian, Ying; Sun, Young
2016-08-01
The magnetoelectric effects in multiferroics have a great potential in creating next-generation memory devices. We use an alternative concept of nonvolatile memory based, on a type of nonlinear magnetoelectric effects showing a butterfly-shaped hysteresis loop. The principle is to utilize the states of the magnetoelectric coefficient, instead of magnetization, electric polarization, or resistance, to store binary information. Our experiments in a device made of the PMN-PT/Terfenol-D multiferroic heterostructure clearly demonstrate that the sign of the magnetoelectric coefficient can be repeatedly switched between positive and negative by applying electric fields, confirming the feasibility of this principle. This kind of nonvolatile memory has outstanding practical virtues such as simple structure, easy operation in writing and reading, low power, fast speed, and diverse materials available.
Control design for the nonlinear benchmark problem via the output regulation method
Institute of Scientific and Technical Information of China (English)
Jie HUANG; Guoqiang HU
2004-01-01
The problem of designing a feedback controller to achieve asymptotic disturbance rejection / attenuation while maintaining good transient response in the RTAC system is known as a benchmark nonlinear control problem, which has been an intensive research subject since 1995. In this paper, we will further investigate the solvability of the robust disturbance rejection problem of the RTAC system by the measurement output feedback control based on the robust output regulation method. We have obtained a design by overcoming two major obstacles: find a closed-form solution of the regulator equations; and devise a nonlinear internal model to account for non-polynomial nonlinearities.
An Analytical Approximation Method for Strongly Nonlinear Oscillators
Directory of Open Access Journals (Sweden)
Wang Shimin
2012-01-01
Full Text Available An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring force. The nonlinear restoring force is expressed as a spring with varying stiffness that depends on the vibration amplitude. That is, for stationary vibration, the restoring force linearly depends on the displacement, but the stiffness of the spring varies with the vibration amplitude for nonstationary oscillations. The varied stiffness is constructed by means of the first and second averaged derivatives of the restoring force with respect to the displacement. Then, this stiffness gives the amplitude frequency and the phase frequency characteristics of the oscillator. Various examples show that this method can be applied extensively to oscillators with nonlinear restoring force, and that the solving process is extremely simple.
Implementing Kernel Methods Incrementally by Incremental Nonlinear Projection Trick.
Kwak, Nojun
2016-05-20
Recently, the nonlinear projection trick (NPT) was introduced enabling direct computation of coordinates of samples in a reproducing kernel Hilbert space. With NPT, any machine learning algorithm can be extended to a kernel version without relying on the so called kernel trick. However, NPT is inherently difficult to be implemented incrementally because an ever increasing kernel matrix should be treated as additional training samples are introduced. In this paper, an incremental version of the NPT (INPT) is proposed based on the observation that the centerization step in NPT is unnecessary. Because the proposed INPT does not change the coordinates of the old data, the coordinates obtained by INPT can directly be used in any incremental methods to implement a kernel version of the incremental methods. The effectiveness of the INPT is shown by applying it to implement incremental versions of kernel methods such as, kernel singular value decomposition, kernel principal component analysis, and kernel discriminant analysis which are utilized for problems of kernel matrix reconstruction, letter classification, and face image retrieval, respectively.
Application of nonlinear methods to the study of ionospheric plasma
Chernyshov, A. A.; Mogilevsky, M. M.; Kozelov, B. V.
2015-01-01
Most of the processes taking place in the auroral region of Earth's ionosphere are reflected in a variety of dynamic forms of the aurora borealis. In order to study these processes it is necessary to consider temporary and spatial variations of the characteristics of ionospheric plasma. Most traditional methods of classical physics are applicable mainly for stationary or quasi-stationary phenomena, but dynamic regimes, transients, fluctuations, selfsimilar scaling could be considered using the methods of nonlinear dynamics. Special interest is the development of the methods for describing the spatial structure and the temporal dynamics of auroral ionosphere based on the ideas of percolation theory and fractal geometry. The fractal characteristics (the Hausdorff fractal dimension and the index of connectivity) of Hall and Pedersen conductivities are used to the description of fractal patterns in the ionosphere. To obtain the self-consistent estimates of the parameters the Hausdorff fractal dimension and the index of connectivity in the auroral zone, an additional relation describing universal behavior of the fractal geometry of percolation at the critical threshold is applied. Also, it is shown that Tsallis statistics can be used to study auroral ionosphere
Microcrack Identification in Cement-Based Materials Using Nonlinear Acoustic Waves
Chen, X. J.; Kim, J.-Y.; Qu, J.; Kurtis, K. E.; Wu, S. C.; Jacobs, L. J.
2007-03-01
This paper presents results from tests that use nonlinear acoustic waves to distinguish microcracks in cement-based materials. Portland cement mortar samples prepared with alkali-reactive aggregate were exposed to an aggressive environment to induce cracking were compared to control samples, of the same composition, but which were not exposed to aggressive conditions. Two nonlinear ultrasonic methods were used to characterize the samples, with the aim of identifying the time and extent of microcracking; these techniques were a nonlinear acoustical modulation (NAM) method and a harmonic amplitude relation (HAR) method. These nonlinear acoustic results show that both methods can distinguish damaged samples from undamaged ones, demonstrating the potential of nonlinear acoustic waves to provide a quantitative evaluation of the deterioration of cement-based materials.
Linear Algebraic Method for Non-Linear Map Analysis
Energy Technology Data Exchange (ETDEWEB)
Yu,L.; Nash, B.
2009-05-04
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Application of homotopy analysis method for solving nonlinear Cauchy problem
Directory of Open Access Journals (Sweden)
V.G. Gupta
2012-11-01
Full Text Available In this paper, by means of the homotopy analysis method (HAM, the solutions of some nonlinear Cauchy problem of parabolic-hyperbolic type are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter \\hbar that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear examples to obtain the exact solutions. The results reveal that the proposed method is very effective and simple.
Applications of non-linear methods in astronomy
Martens, P.C.H.
1984-01-01
In this review I discuss catastrophes, bifurcations and strange attractors in a non-mathematical manner by giving very simple examples that st ill contain the essence of the phenomenon. The salientresults of the applications of these non-linear methods in astrophysics are reviewed and include such d
Method and system for training dynamic nonlinear adaptive filters which have embedded memory
Rabinowitz, Matthew (Inventor)
2002-01-01
Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.
Acceleration of the AFEN method by two-node nonlinear iteration
Energy Technology Data Exchange (ETDEWEB)
Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-12-31
A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)
Li, Bing-Xuan; Wei, Yong; Huang, Cheng-Hui; Zhuang, Feng-Jiang; Zhang, Ge; Guo, Guo-Cong
2014-01-01
In the present paper the authors report a research on testing the nonlinear optical performance of optical materials in visible and infrared band. Based on the second order nonlinear optic principle and the photoelectric signal detection technology, the authors have proposed a new testing scheme in which a infrared OPO laser and a method for separating the beams arising from frequency matching and the light produced by other optical effects were used. The OPO laser is adopted as light source to avoid the error of measurement caused by absorption because the double frequency signal of the material is in the transmittance band Our research work includes testing system composition, operational principle and experimental method. The experimental results of KTP, KDP, AGS tested by this method were presented. In the experiment several new infrared non-linear materials were found. This method possesses the merits of good stability and reliability, high sensitivity, simple operation and good reproducibility, which can effectively make qualitative and semi-quantitative test for optical material's nonlinear optical properties from visible to infrared. This work provides an important test -method for the research on second order nonlinear optical materials in visible, infrared and ultraviolet bands.
Comparison of alternative improved perturbative methods for nonlinear oscillations
Energy Technology Data Exchange (ETDEWEB)
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico)]. E-mail: paolo@ucol.mx; Raya, Alfredo [Facultad de Ciencias, Universidad de Colima, Bernal Diaz del Castillo 340, Colima (Mexico); Fernandez, Francisco M. [INIFTA (Conicet, UNLP), Diag. 113 y 64 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2005-06-06
We discuss and compare two alternative perturbation approaches for the calculation of the period of nonlinear systems based on the Lindstedt-Poincare technique. As illustrative examples we choose one-dimensional anharmonic oscillators and the Van der Pol equation. Our results show that each approach is better for just one type of model considered here.
A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem
Directory of Open Access Journals (Sweden)
Meixia Li
2012-01-01
Full Text Available Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.
Various Newton-type iterative methods for solving nonlinear equations
Directory of Open Access Journals (Sweden)
Manoj Kumar
2013-10-01
Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.
GLOBAL FINITE ELEMENT NONLINEAR GALERKIN METHOD FOR THE PENALIZED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yin-nian He; Yan-ren Hou; Li-quan Mei
2001-01-01
A global finite element nonlinear Galerkin method for the penalized Navier-Stokes equations is presented. This method is based on two finite element spaces XH and Xh,defined respectively on one coarse grid with grid size H and one fine grid with grid size h ＜＜ H. Comparison is also made with the finite element Galerkin method. If we choose H = O(ε-1/4h1/2), ε＞ 0 being the penalty parameter, then two methods are of the same order of approximation. However, the global finite element nonlinear Galerkin method is much cheaper than the standard finite element Galerkin method. In fact, in the finite element Galerkin method the nonlinearity is treated on the fine grid finite element space Xh and while in the global finite element nonlinear Galerkin method the similar nonlinearity is treated on the coarse grid finite element space XH and only the linearity needs to be treated on the fine grid increment finite element space Wh. Finally, we provide numerical test which shows above results stated.
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
A new method for observing the running states of a single-variable nonlinear system.
Meng, Yu; Chen, Hong; Chen, Cheng
2015-03-01
In order to timely grasp a single variable nonlinear system running states, a new method called Scatter Point method is put forward in this paper. It can be used to observe or monitor the running states of a single variable nonlinear system in real-time. In this paper, the definition of the method is given at first, and then its working principle is expounded theoretically, after this, some physical experiments based on Chua's nonlinear system are conducted. At the same time, many scatter point graphs are measured by a general analog oscilloscope. The motion, number, and distribution of these scatter points shown on the oscilloscope screen can directly reflect the current states of the tested system. The experimental results further confirm that the method is effective and practical, in which the system running states are not easily lost. In addition, this method is not only suitable for single variable systems but also for multivariable systems.
Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
A Filter Method for Nonlinear Semidefinite Programming with Global Convergence
Institute of Scientific and Technical Information of China (English)
Zhi Bin ZHU; Hua Li ZHU
2014-01-01
In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the suffi cient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is eff ective.
Nonlinear dynamics based digital logic and circuits.
Kia, Behnam; Lindner, John F; Ditto, William L
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two.
Perturbation and harmonic balance methods for nonlinear panel flutter.
Kuo, C.-C.; Morino, L.; Dugundji, J.
1972-01-01
A systematic way of applying both perturbation methods and harmonic balance methods to nonlinear panel flutter problems is developed here. Results obtained by both these methods for two-dimensional simply supported and three-dimensional clamped-clamped plates with six modes agree well with those obtained by the straightforward direct integration method, yet require less computer time and provide better insight into the solutions. Effects of viscoelastic structural damping on the flutter stability boundary are generally found to be destabilizing and the postflutter behavior becomes more explosive. The methods developed here may be of interest in related vibration problems.
Multi-level damage detection with nonlinear ultrasonic methods
Matlack, Kathryn H.; Kim, Jin-Yeon; Jacobs, Laurence J.; Qu, Jianmin
2013-01-01
The nonlinear ultrasonic method of second harmonic generation is used to detect multiple levels of damage on a single specimen. There is a breadth of research in the literature that measures the second harmonic and the resulting nonlinear parameter to monitor increasing amounts of uniform damage, but for this method to be applicable as an in situ technique, it must be able to scan an area of a structure with varying amounts of damage over a region. To investigate this, an aluminum alloy sample is shot-peened to two intensity levels along its length, to produce different sections of cold work and residual stress as a function of spatial location. Previous research has shown that the residual stress and cold work introduced in a material from shot peening causes an increase in the nonlinear parameter. Rayleigh waves are generated in the sample and the first and second harmonic amplitudes are measured at increasing propagation distances that encompass an undamaged section and two sections, each with different levels of shot peening. Results show that the nonlinear parameter increases as the Rayleigh wedge sensor is scanned over the shot peening sections.
Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems
Directory of Open Access Journals (Sweden)
Huiling Xi
2014-11-01
Full Text Available In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.
Zhao, Zhanqi; Guttmann, Josef; Möller, Knut
2012-01-01
The objective of this paper is to introduce and evaluate the adaptive SLICE method (ASM) for continuous determination of intratidal nonlinear dynamic compliance and resistance. The tidal volume is subdivided into a series of volume intervals called slices. For each slice, one compliance and one resistance are calculated by applying a least-squares-fit method. The volume window (width) covered by each slice is determined based on the confidence interval of the parameter estimation. The method was compared to the original SLICE method and evaluated using simulation and animal data. The ASM was also challenged with separate analysis of dynamic compliance during inspiration. If the signal-to-noise ratio (SNR) in the respiratory data decreased from +∞ to 10 dB, the relative errors of compliance increased from 0.1% to 22% for the ASM and from 0.2% to 227% for the SLICE method. Fewer differences were found in resistance. When the SNR was larger than 40 dB, the ASM delivered over 40 parameter estimates (42.2 ± 1.3). When analyzing the compliance during inspiration separately, the estimates calculated with the ASM were more stable. The adaptive determination of slice bounds results in consistent and reliable parameter values. Online analysis of nonlinear respiratory mechanics will profit from such an adaptive selection of interval size.
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
Directory of Open Access Journals (Sweden)
Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
Switching behaviour of nonlinear Mach–Zehnder interferometer based on photonic crystal geometry
Indian Academy of Sciences (India)
Man Mohan Gupta; S Medhekar
2014-06-01
Nonlinear Mach–Zehnder interferometer (NMZI) created with photonic crystal waveguides (PCW) and with Kerr-type nonlinearity has been investigated in this paper. The NMZI has been simulated using two-dimensional finite difference time domain (2D-FDTD) method. Input verses output (I/O) characteristics have been obtained for different lengths of the nonlinear arm, nonlinear coefficients of the nonlinear arm, wavelengths of the input beam, sizes of defect rods and NMZI offset. The results obtained are compared with earlier published results of NMZI created with conventional step index waveguides (SIW). It is shown that all useful features of light switching offered by SIW-based NMZIs are also possible with PCW-based NMZIs of extremely small dimensions. Moreover, PCW-based NMZIs offer additional useful feature not available with SIW-based NMZIs.
Institute of Scientific and Technical Information of China (English)
张丽燕; 鲍长春; 刘鑫; 张兴涛
2013-01-01
A bandwidth extension method based on audio classification was proposed. Time series of audio signals were classified into four types based on recurrence plot and recurrence quantification analysis, and the fine spectrums were re-covered by taking advantage of four methods respectively. In addition, the spectrum envelope and energy gain were ad-justed by Gaussian mixture model and codebook mapping on the basis of soft decision respectively. Subjective and ob-jective testing results indicate that the proposed method has good quality compared with conventional blind bandwidth extension methods, and the performance of ITU-T G.722.1 codec with the proposed algorithm is better than that of G.722.1C codec at the same bit rate.%提出了一种基于非线性音频分类的频带扩展方法，即利用递归图和定量递归分析将音频信号的时间序列分成4类，并分别采用4种方法恢复高频频谱细节，最终利用高斯混合模型和基于软判决的码书映射调整频谱包络和能量增益。主客观测试表明，该方法优于传统的盲目式频带扩展方法，且应用到ITU-T G.722.1编解码器时，音频质量优于同码率下的G.722.1C编解码器。
Institute of Scientific and Technical Information of China (English)
柴天佑; 张亚军
2011-01-01
针对一类不确定的离散时间零动态不稳定的单输入-单输出(Single-input single-output,SISO)非线性系统,提出了一种基于未建模动态补偿的非线性控制器.采用自适应神经模糊推理系统(Adaptive-network-based fuzzy inference system,ANFIS)和一一映射相结合的方法估计未建模动态在此基础上,提出了由线性自适应控制器、非线性自适应空制器以及切换机制组成的自适应切换控制方法该方法通过对上述两种控制器的切换,保证闭环系统输入输出信号有界的同时,改善系统性能.本文将要求未建模动态全局有界的条件放宽为线性增长,建立了所提自适应控制方法的稳定性和收敛性分析.通过仿真比较和水箱的液位控制实验,验证了所提方法的有效性.%This paper presents a nonlinear controller based on unmodeled dynamics compensation for a class of uncertain and discrete-time single-input single-output (SISO) nonlinear systems with unstable zero-dynamics. By combining an adaptive-network-based fuzzy inference system (ANFIS) with "one-to-one mapping", a compensator for unmodeled dynamics is constructed. With the above development, an adaptive switching control method is proposed that consists of a linear adaptive controller, a nonlinear adaptive controller and a switching mechanism. By using switching between the above two controllers, it has been shown that both an improved performance and stability can be achieved simultaneously. The paper assumes the unmodeled dynamics of the systems to satisfy a linear growth condition, which relaxes the widely used global bounded ness condition on the unmodeled dynamics. The analysis on stability and convergence of the adaptive control method are established. Finally, through the simulation based comparative study and the experiment of the proposed control on a tank level adaptive control system, the effectiveness of the proposed method is justified.
Stabilization of nonlinear systems based on robust control Lyapunov function
Institute of Scientific and Technical Information of China (English)
CAI Xiu-shan; HAN Zheng-zhi; LU Gan-yun
2007-01-01
This paper deals with the robust stabilization problem for a class of nonlinear systems with structural uncertainty. Based on robust control Lyapunov function, a sufficient and necessary condition for a function to be a robust control Lyapunov function is given. From this condition, simply sufficient condition for the robust stabilization (robust practical stabilization) is deduced. Moreover, if the equilibrium of the closed-loop system is unique, the existence of such a robust control Lyapunov function will also imply robustly globally asymptotical stabilization. Then a continuous state feedback law can be constructed explicitly. The simulation shows the effectiveness of the method.
Nonlinear properties of the lattice network-based nonlinear CRLH transmission lines
Institute of Scientific and Technical Information of China (English)
王正斌; 吴昭质; 高超
2015-01-01
The nonlinear properties of lattice network-based (LNB) composite right-/left-handed transmission lines (CRLH TLs) with nonlinear capacitors are experimentally investigated. Harmonic generation, subharmonic generation, and parametric excitation are clearly observed in an unbalanced LNB CRLH TL separately. While the balanced design of the novel nonlinear TL shows that the subharmonic generation and parametric processes can be suppressed, and almost the same power level of the higher harmonics can be achieved over a wide bandwidth range, which are difficult to find in the conventional CRLH TLs.
Simplified Methods Applied to Nonlinear Motion of Spar Platforms
Energy Technology Data Exchange (ETDEWEB)
Haslum, Herbjoern Alf
2000-07-01
Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.
Network-Based Practical Consensus of Heterogeneous Nonlinear Multiagent Systems.
Ding, Lei; Zheng, Wei Xing
2016-09-07
This paper studies network-based practical leader-following consensus problem of heterogeneous multiagent systems with Lipschitz nonlinear dynamics under both fixed and switching topologies. Considering the effect of network-induced delay, a network-based leader-following consensus protocol with heterogeneous gain matrix is proposed for each follower agent. By employing Lyapunov-Krasovskii method, a sufficient condition for designing the network-based consensus controller gain is derived such that the leader-following consensus error exponentially converges to a bounded region under a fixed topology. Correspondingly, the proposed design approach is then extended to the case of switching topology. Two numerical examples with networked Chua's circuits are given to show the efficiency of the design method proposed in this paper.
Institute of Scientific and Technical Information of China (English)
孔亮亮; 江建慧; 肖杰; 蒋园园
2012-01-01
为了快速而准确地估计ARM处理器上的程序执行时间,研究了基于模拟的非线性程序执行时间估计器的结构.它由程序功能剖面生成模块和程序执行时间预测模块串联而成.程序功能剖面生成模块直接用精确指令模拟器Sim-profile实现；而基于程序执行中的动态指令数与执行时间在处理器上的非线性关系,对于程序执行时间预测模块的实现,首先设计了一种人工神经网络方案,再根据对人工神经网络局限性的判断,如局部最优问题、不适于解决小样本的回归、网络拓扑结构依赖先验知识等缺点,又提出了基于最小二乘支持向量机的方法.实验证明,这些非线性方法,特别是基于最小二乘支持向量机的方法,可以用较低的模拟代价获得较高的程序执行时间估计精度.%In order to accurately estimate execution cycles of programs running on ARM architectures as soon as possible, a simulation-based non-linear estimator is proposed. The estimator consists of two cascade modules: profiling program function module and program execution time prediction module. The module of profiling program function can be directly implemented by Sim-profile, an instruction-accurate simulator. According to the non-linear behavior of the program execution time in advanced processors and the dynamic instruction counts during program executions, the program execution time prediction module is implemented by an artificial neural network (ANN). However, besides the problem of local minimization, ANN is not suited to solve small-sample set regression. It depends on the priori knowledge of designers, which could determine the topology of the model and finally impact its performance. In order to conquer the limitations of ANN, a non-linear method based on the least squares support vector machine (LS-SVM) is further proposed to map the number of executed instructions into execution cycle counts. Experimental results show
Kamalian, Morteza; Prilepsky, Jaroslaw E; Le, Son Thai; Turitsyn, Sergei K
2016-08-08
In this work, we introduce the periodic nonlinear Fourier transform (PNFT) method as an alternative and efficacious tool for compensation of the nonlinear transmission effects in optical fiber links. In the Part I, we introduce the algorithmic platform of the technique, describing in details the direct and inverse PNFT operations, also known as the inverse scattering transform for periodic (in time variable) nonlinear Schrödinger equation (NLSE). We pay a special attention to explaining the potential advantages of the PNFT-based processing over the previously studied nonlinear Fourier transform (NFT) based methods. Further, we elucidate the issue of the numerical PNFT computation: we compare the performance of four known numerical methods applicable for the calculation of nonlinear spectral data (the direct PNFT), in particular, taking the main spectrum (utilized further in Part II for the modulation and transmission) associated with some simple example waveforms as the quality indicator for each method. We show that the Ablowitz-Ladik discretization approach for the direct PNFT provides the best performance in terms of the accuracy and computational time consumption.
Shi, Zhong-Ke; Wu, Fang-Xiang
2013-06-01
A common assumption is that the model structure is known for modelling high performance aircraft. In practice, this is not the case. Actually, structure identification plays the most important role in the processing of nonlinear system modelling. The integration of mode structure identification and parameter estimation is an efficient method to construct the model for high performance aircraft, which is nonlinear and also contains uncertainties. This article presents an efficient method for identifying nonlinear model structure and estimating parameters for high-performance aircraft model, which contains uncertainties. The parameters associated with nonlinear terms are considered one after the other if they should be included in the nonlinear model until a stopping criterion is met, which is based on Akaike's information criterion. A numerically efficient U-D factorisation is presented to avoid complex computation of high-order matrices. The proposed method is applied to flight test data of a high-performance aircraft. The results demonstrate that the proposed method could obtain the good aircraft model with a reasonably good fidelity based on the comparison with flight test data.
Multi-crack imaging using nonclassical nonlinear acoustic method
Zhang, Lue; Zhang, Ying; Liu, Xiao-Zhou; Gong, Xiu-Fen
2014-10-01
Solid materials with cracks exhibit the nonclassical nonlinear acoustical behavior. The micro-defects in solid materials can be detected by nonlinear elastic wave spectroscopy (NEWS) method with a time-reversal (TR) mirror. While defects lie in viscoelastic solid material with different distances from one another, the nonlinear and hysteretic stress—strain relation is established with Preisach—Mayergoyz (PM) model in crack zone. Pulse inversion (PI) and TR methods are used in numerical simulation and defect locations can be determined from images obtained by the maximum value. Since false-positive defects might appear and degrade the imaging when the defects are located quite closely, the maximum value imaging with a time window is introduced to analyze how defects affect each other and how the fake one occurs. Furthermore, NEWS-TR-NEWS method is put forward to improve NEWS-TR scheme, with another forward propagation (NEWS) added to the existing phases (NEWS and TR). In the added phase, scanner locations are determined by locations of all defects imaged in previous phases, so that whether an imaged defect is real can be deduced. NEWS-TR-NEWS method is proved to be effective to distinguish real defects from the false-positive ones. Moreover, it is also helpful to detect the crack that is weaker than others during imaging procedure.
Institute of Scientific and Technical Information of China (English)
常乃超; 陈来军; 侯云鹤
2014-01-01
分析了电力系统非线性的数学性质,指出电力系统非线性是一种有界非线性。在此基础上,将反馈主导方法(feedback domination method, FDM)引入多机电力系统非线性控制。该方法与反馈线性化方法不同；反馈线性化方法是通过反馈将原非线性系统转化为线性系统,反馈主导方法则是通过反馈将原非线性系统转换为特定形式的非线性系统,该特定形式的非线性系统的动态由反馈引入的非线性部分主导。以多机系统非线性汽门控制问题为例,设计了反馈主导非线性汽门控制器,该控制器仅包含本地量测量,易于实现。数值仿真表明,多机系统反馈主导非线性汽门控制器可显著提高电力系统暂态稳定性。%Mathematical characteristics of power system nonlinearity are analyzed. It is shown that the nonlinearity between generator output power and node voltage is a kind of bounded nonlinearity. According to the bounded nonlinearity, we introduce the feedback domination method (FDM) for controlling the nonlinear multi-machine power systems. Being different from the feedback linearization method (FLM) which transforms a nonlinear system into a linear system through nonlinear feedback, FDM transforms a nonlinear system into another nonlinear system with a particular form through nonlinear feedback. The dynamics of the transformed nonlinear system is dominated by the nonlinear part in the feedback loop. As an example, feedback domination method (FDM) is applied to design the nonlinear turbine valve control in multi-machine power systems. The nonlinear valve control law constructed for generators only includes local measurements, so that it is easy to be implemented. Numerical simulations demonstrate that the nonlinear valve control law based on FDM effectively improves transient stability in power system.
Optical limiter based on two-dimensional nonlinear photonic crystals
Belabbas, Amirouche; Lazoul, Mohamed
2016-04-01
The aim behind this work is to investigate the capabilities of nonlinear photonic crystals to achieve ultra-fast optical limiters based on third order nonlinear effects. The purpose is to combine the actions of nonlinear effects with the properties of photonic crystals in order to activate the photonic band according to the magnitude of the nonlinear effects, themselves a function of incident laser power. We are interested in designing an optical limiter based nonlinear photonic crystal operating around 1064 nm and its second harmonic at 532 nm. Indeed, a very powerful solid-state laser that can blind or destroy optical sensors and is widely available and easy to handle. In this work, we perform design and optimization by numerical simulations to determine the better structure for the nonlinear photonic crystal to achieve compact and efficient integrated optical limiter. The approach consists to analyze the band structures in Kerr-nonlinear two-dimensional photonic crystals as a function of the optical intensity. We confirm that these bands are dynamically red-shifted with regard to the bands observed in linear photonic crystals or in the case of weak nonlinear effects. The implemented approach will help to understand such phenomena as intensitydriven optical limiting with Kerr-nonlinear photonic crystals.
Condition Monitoring of Turbines Using Nonlinear Mapping Method
Institute of Scientific and Technical Information of China (English)
Liao Guang-lan; Shi Tie-lin; Jiang Nan
2004-01-01
Aiming at the non-linear nature of the signals generated from turbines, curvilinear component analysis (CCA), a novel nonlinear projection method that favors local topology conservation is presented for turbines conditions monitoring. This is accomplished in two steps. Time domain features are extracted from raw vibration signals, and then they are projected into a two-dimensional output space by using CCA method and form regions indicative of specific conditions, which helps classify and identify turbine states visually. Therefore, the variation of turbine conditions can be observed clearly with the trajectory of image points for the feature data in the two-dimensional space, and the occurrence and development of failures can be monitored in time.
Application of the homotopy perturbation method to the nonlinear pendulum
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Hernandez, A; Belendez, T; Neipp, C; Marquez, A [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)
2007-01-15
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130{sup 0}. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics; although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that the present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics.
Lavrentiev regularization method for nonlinear ill-posed problems
Kinh, N V
2002-01-01
In this paper we shall be concerned with Lavientiev regularization method to reconstruct solutions x sub 0 of non ill-posed problems F(x)=y sub o , where instead of y sub 0 noisy data y subdelta is an element of X with absolut(y subdelta-y sub 0) X is an accretive nonlinear operator from a real reflexive Banach space X into itself. In this regularization method solutions x subalpha supdelta are obtained by solving the singularly perturbed nonlinear operator equation F(x)+alpha(x-x*)=y subdelta with some initial guess x*. Assuming certain conditions concerning the operator F and the smoothness of the element x*-x sub 0 we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the regularization parameter alpha has been chosen properly.
Noninteracting control of nonlinear systems based on relaxed control
Jayawardhana, B.
2010-01-01
In this paper, we propose methodology to solve noninteracting control problem for general nonlinear systems based on the relaxed control technique proposed by Artstein. For a class of nonlinear systems which cannot be stabilized by smooth feedback, a state-feedback relaxed control can be designed to
Institute of Scientific and Technical Information of China (English)
陈涛; 陈自凯; 段利斌; 王彬; 成艾国
2015-01-01
针对等效静载荷法(Equivalent static loads method，ESLM)求解大变形和多变量结构动态非线性优化问题难以收敛与效率较低的不足，结合结构静态线性优化方法与最速下降法(Steepest descent method，SDM)提出一种高效的基于梯度的等效静载荷法(Equivalent static loads method based on gradient，ESLMG)，根据结构动态非线性分析计算得到基于节点位移等效的静态载荷，从而将结构动态非线性优化问题转化为以等效载荷及节点位移为输入条件的结构静态线性优化问题(内层循环)；利用内层循环最优解处的梯度信息，同时结合 SDM 方法更新设计变量(外层循环)；将更新的设计变量值作为下一次迭代内层循环的初始值，直到满足收敛条件为止。该方法在保证算法收敛性的前提下，提高了收敛速度。算例表明，该方法对于处理大变形及多变量结构动态非线性优化问题非常有效，在收敛速度方面相比ESLM方法和数值优化算法具有很大的优势。%Combined with structure static linear optimization and the steepest descent method(SDM), an equivalent static loads method based on gradient(ESLMG)is proposed to overcome the disadvantages of difficulty to achieve convergence and low efficiency of equivalent static loads method(ESLM) when solving large deformation and multi-variable structure nonlinear dynamic optimization, equivalent static loads based on node displacement are calculated according to structure nonlinear dynamic analysis and then structural dynamic nonlinear optimization problem will be transformed into structure static linear optimization problem with the obtalned equivalent loads and node displacement as input conditions, which is called inner iteration. The design variables are updated efficiently according to the method of SDM and the gradient information of optimal solution, which is called outer iteration. The updated variables are used as the
Wu, Hao; Noé, Frank
2011-03-01
Diffusion processes are relevant for a variety of phenomena in the natural sciences, including diffusion of cells or biomolecules within cells, diffusion of molecules on a membrane or surface, and diffusion of a molecular conformation within a complex energy landscape. Many experimental tools exist now to track such diffusive motions in single cells or molecules, including high-resolution light microscopy, optical tweezers, fluorescence quenching, and Förster resonance energy transfer (FRET). Experimental observations are most often indirect and incomplete: (1) They do not directly reveal the potential or diffusion constants that govern the diffusion process, (2) they have limited time and space resolution, and (3) the highest-resolution experiments do not track the motion directly but rather probe it stochastically by recording single events, such as photons, whose properties depend on the state of the system under investigation. Here, we propose a general Bayesian framework to model diffusion processes with nonlinear drift based on incomplete observations as generated by various types of experiments. A maximum penalized likelihood estimator is given as well as a Gibbs sampling method that allows to estimate the trajectories that have caused the measurement, the nonlinear drift or potential function and the noise or diffusion matrices, as well as uncertainty estimates of these properties. The approach is illustrated on numerical simulations of FRET experiments where it is shown that trajectories, potentials, and diffusion constants can be efficiently and reliably estimated even in cases with little statistics or nonequilibrium measurement conditions.
Adomian decomposition method for nonlinear Sturm-Liouville problems
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Sennur Somali
2007-09-01
Full Text Available In this paper the Adomian decomposition method is applied to the nonlinear Sturm-Liouville problem-y" + y(tp=λy(t, y(t > 0, t ∈ I = (0, 1, y(0 = y(1 = 0, where p > 1 is a constant and λ > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfuctions of the problem are demonstrated.
Method of Green’s function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations be-came nonlinear ordinary differential equations with regard to time. The ampli-tude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.
Method of Green's function of nonlinear vibration of corrugated shallow shells
Institute of Scientific and Technical Information of China (English)
YUAN Hong
2008-01-01
Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution,the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated.The nonlinear partial differential equations of shallow shell were re-duced to the nonlinear integral-differential equations by using the method of Green's function.To solve the integral-differential equations,the expansion method was used to obtain Green's function.Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green's function as a series of characteristic function.Therefore,the integral-differential equations be-came nonlinear ordinary differential equations with regard to time.The ampli-tude-frequency relation,with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force,were obtained by considering single mode vibration.As a numerical example,nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied.The obtained solutions are available for reference to the design of corrugated shells.
Institute of Scientific and Technical Information of China (English)
查翔; 倪世宏; 张鹏
2015-01-01
对于一类非线性信号的去噪问题,该文提出一种基于奇异值分解(Singular Value Decomposition, SVD)的有效迭代方法.对现有奇异值差分谱方法在两类不同非线性信号上的去噪效果进行了对比,指出在信号不具有明显特征频率、非周期性变化时这一方法并不适用,并分析了现象产生的原因;然后针对该类信号的特点重新定义了Hankel矩阵结构,给出有效奇异值的确定方式,并通过SVD多次迭代过程实现对该类信号的有效去噪.对实际飞行数据去噪的实验结果表明,该方法对提出的一类信号对象不仅去噪效果良好,而且可提高运算效率.%To solve a class of nonlinear signal denoising, an effective iteration method based on the Singular Value Decomposition (SVD) is proposed. When the signals have no obvious characteristic frequency and non-periodic change, the current difference spectrum method is not applicable by comparing the results on the two class of nonlinear signal, and then the corresponding reason is analyzed. According to the signal feature, the structure of the Hankel matrix is defined again and the valid singular values are determined. The effective denoising is realized by the repeated iteration which is based on the SVD. The results of the flight data demonstrate that the proposed method can effectively reduce the noise and improve the computing efficiency as well.
Reproducing wavelet kernel method in nonlinear system identification
Institute of Scientific and Technical Information of China (English)
WEN Xiang-jun; XU Xiao-ming; CAI Yun-ze
2008-01-01
By combining the wavelet decomposition with kernel method, a practical approach of universal multi-scale wavelet kernels constructed in reproducing kernel Hilbert space (RKHS) is discussed, and an identifica-tion scheme using wavelet support vector machines ( WSVM ) estimator is proposed for nonlinear dynamic sys-tems. The good approximating properties of wavelet kernel function enhance the generalization ability of the pro-posed method, and the comparison of some numerical experimental results between the novel approach and some existing methods is encouraging.
Recursive prediction error methods for online estimation in nonlinear state-space models
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Dag Ljungquist
1994-04-01
Full Text Available Several recursive algorithms for online, combined state and parameter estimation in nonlinear state-space models are discussed in this paper. Well-known algorithms such as the extended Kalman filter and alternative formulations of the recursive prediction error method are included, as well as a new method based on a line-search strategy. A comparison of the algorithms illustrates that they are very similar although the differences can be important for the online tracking capabilities and robustness. Simulation experiments on a simple nonlinear process show that the performance under certain conditions can be improved by including a line-search strategy.
Stability for a class of nonlinear time-delay systems via Hamiltonian functional method
Institute of Scientific and Technical Information of China (English)
YANG RenMing; WANG YuZhen
2012-01-01
This paper investigates the stability of a class of nonlinear time-delay systems via Hamiltonian functional method,and proposes a number of new results on generalized Hamiltonian realization (GHR) and stability analysis for this class of systems.Firstly,the concept of GHR of general nonlinear time-delay systems is proposed,and several new GHR methods are given.Then,based on the new GHR methods obtained,the stability of time-delay systems is investigated,and several delay-dependent sufficient conditions in term of matrix inequalities are derived for the stability analysis by constructing suitable Lyapunov-Krasovskii (L-K) functionals.Finally,an illustrative example shows that the results obtained in this paper have less conservatism,and work very well in the stability analysis of some nonlinear time-delay Hamiltonian systems.
The First Integral Method to the Nonlinear Schrodinger Equations in Higher Dimensions
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Shoukry Ibrahim Atia El-Ganaini
2013-01-01
Full Text Available The first integral method introduced by Feng is adopted for solving some important nonlinear partial differential equations, including the (2 + 1-dimensional hyperbolic nonlinear Schrodinger (HNLS equation, the generalized nonlinear Schrodinger (GNLS equation with a source, and the higher-order nonlinear Schrodinger equation in nonlinear optical fibers. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner.
Stupishin, L.; Nikitin, K.; Kolesnikov, A.
2017-05-01
A methodology for shell stability research and determining buckling load, based on the mixed finite element method are proposed. Axisymmetric geometrically nonlinear shallow shells made of orthotropic material are considered. The results of numerical research of stability by changing the shape of shells, ratio of elastic modulus of the material and parameters of the support contour are presented.
Van Dijk, N.P.
2012-01-01
This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.
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Khaled A. Gepreel
2012-01-01
Full Text Available We modified the rational Jacobi elliptic functions method to construct some new exact solutions for nonlinear differential difference equations in mathematical physics via the lattice equation, the discrete nonlinear Schrodinger equation with a saturable nonlinearity, the discrete nonlinear Klein-Gordon equation, and the quintic discrete nonlinear Schrodinger equation. Some new types of the Jacobi elliptic solutions are obtained for some nonlinear differential difference equations in mathematical physics. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
Hu, Zhan; Zheng, Gangtie
2016-08-01
A combined analysis method is developed in the present paper for studying the dynamic properties of a type of geometrically nonlinear vibration isolator, which is composed of push-pull configuration rings. This method combines the geometrically nonlinear theory of curved beams and the Harmonic Balance Method to overcome the difficulty in calculating the vibration and vibration transmissibility under large deformations of the ring structure. Using the proposed method, nonlinear dynamic behaviors of this isolator, such as the lock situation due to the coulomb damping and the usual jump resulting from the nonlinear stiffness, can be investigated. Numerical solutions based on the primary harmonic balance are first verified by direct integration results. Then, the whole procedure of this combined analysis method is demonstrated and validated by slowly sinusoidal sweeping experiments with different amplitudes of the base excitation. Both numerical and experimental results indicate that this type of isolator behaves as a hardening spring with increasing amplitude of the base excitation, which makes it suitable for isolating both steady-state vibrations and transient shocks.
Nonlinear error testing method based on sine wave click rate technology%基于正弦波点击率的非线性误差测试方法
Institute of Scientific and Technical Information of China (English)
杨景阳; 刘路扬; 吕兵
2016-01-01
针对ADC在通讯和多媒体技术上的应用需求，研究了基于正弦波点击率的ADC非线性误差测试方法，实现了正弦波点击率技术在ADC非线性误差测试中的应用。向ADC输入正弦波信号，对输出数字码进行标准化处理，补偿正弦波形电压分布的不均匀性，通过点击率算法推算 ADC 的微分非线性误差，并在大规模数模混合测试设备Catalyst-200上验证了算法的可靠性和精确性。实验结果表明，该算法能够精确地估算 ADC非线性误差，完整地表征了ADC线性度和丢码率，为ADC在通讯和多媒体技术上的应用提供了重要的参数依据，具有较强的工程实用性和市场前景性。%To fulfill the ADC applied on communication and imedia technology,this article researches the ADC’s Nonlinear error testing method based on Sine Wave click rate technology,and realizes the application of Sine wave click technology in ADC’s nonlinearity error testing.Put the sine wave into ADC’s input,deal the output data with normalized conduct to compensate the uneven distribution of sine waveform voltage,and then,calculate the ADC’s differential Nonlinearity Error by means of click rate algorithm,at the end,verify reliability and accuracy of the algorithm at the e-scale mixed-signal test equipment Catalyst-200.The experimental results show that this algorithm can estimate the ADC’s nonlinearity error accurately,represent the ADC’s linearity and dropout rate entirely,provide important parameter to the application of ADC on communication and imedia technology.it has a strong engineering practicality and a fine market outlook.
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Directory of Open Access Journals (Sweden)
Ebrahim Parcham
2014-07-01
Full Text Available Classifying similar images is one of the most interesting and essential image processing operations. Presented methods have some disadvantages like: low accuracy in analysis step and low speed in feature extraction process. In this paper, a new method for image classification is proposed in which similarity weight is revised by means of information in related and unrelated images. Based on researchers’ idea, most of real world similarity measurement systems are nonlinear. Thus, traditional linear methods are not capable of recognizing nonlinear relationship and correlation in such systems. Undoubtedly, Self Organizing Map neural networks are strongest networks for data mining and nonlinear analysis of sophisticated spaces purposes. In our proposed method, we obtain images with the most similarity measure by extracting features of our target image and comparing them with the features of other images. We took advantage of NLPCA algorithm for feature extraction which is a nonlinear algorithm that has the ability to recognize the smallest variations even in noisy images. Finally, we compare the run time and efficiency of our proposed method with previous proposed methods.
Mapping deformation method and its application to nonlinear equations
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李画眉
2002-01-01
An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinearpartial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraicmapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein-Gordon equation. This isapplied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained,including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.
Method of guiding functions in problems of nonlinear analysis
Obukhovskii, Valeri; Van Loi, Nguyen; Kornev, Sergei
2013-01-01
This book offers a self-contained introduction to the theory of guiding functions methods, which can be used to study the existence of periodic solutions and their bifurcations in ordinary differential equations, differential inclusions and in control theory. It starts with the basic concepts of nonlinear and multivalued analysis, describes the classical aspects of the method of guiding functions, and then presents recent findings only available in the research literature. It describes essential applications in control theory, the theory of bifurcations, and physics, making it a valuable resource not only for “pure” mathematicians, but also for students and researchers working in applied mathematics, the engineering sciences and physics.
High-Order Energy Balance Method to Nonlinear Oscillators
Seher Durmaz; Metin Orhan Kaya
2012-01-01
Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated fo...
High-Order Energy Balance Method to Nonlinear Oscillators
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Seher Durmaz
2012-01-01
Full Text Available Energy balance method (EBM is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.
EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM
Institute of Scientific and Technical Information of China (English)
XU Zi-xiang; ZHOU De-yun; DENG Zi-chen
2006-01-01
To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control,multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.
Institute of Scientific and Technical Information of China (English)
林海军; 王震宇; 林亚平; 汪鲁才
2013-01-01
电阻应变式称重传感器存在严重的非线性误差,直接影响称重结果的准确度。本文首先阐述了称重传感器的非线性误差机理与误差补偿原理,提出了一种基于导数约束的称重传感器非线性误差补偿方法。该方法根据称重传感器输入-输出特性曲线的单调递增性,构造神经网络补偿模型训练的约束条件,完成神经网络优化设计,弥补了因训练样本不足导致的网络泛化误差大的缺陷,同时讨论了惩罚因子对网络性能的影响。实验表明,采用这种基于导数约束神经网络补偿方法( DCNN方法)的称重传感器的非线性误差远小于补偿前的误差；同时当训练样本不足时,DCNN方法比传统训练方法(仅利用数据样本训练神经网络,DINN)具有更好的泛化能力,称重准确度更高。%The nonlinear error of the resistance strain gauge load cell has heavy nonlinear error,which will lead to the low accuracy of weighing results. In this paper,the mechanism of the load cell's nonlinear error is introduced and a method for compensation on the load cell's nonlinear error based on derivatives constraints neural network ( DCNN) is proposed. In this method,the monotonically increasing characteristic of load cell's input-output function is used to construct the constraint conditions of training and optimizing the error compensation model with neural network,which can decrease the model's generalization error because of the lack of its training samples. On the other hand,the model's performance affected by the punishing factor is discussed. The experimental results show that the nonlinear error of load cell with this proposed method is far less than that without compensation,and the DCNN's generalization ability is more advantageous than the DINN( i. e. training neural network by only using data samples and not any constraint condition) ,and the weighing results of load cell with DCNN are more accurate.
A new method for nonlinear optimization - experimental results
Energy Technology Data Exchange (ETDEWEB)
Loskovska, S.; Percinkova, B.
1994-12-31
In this paper an application of a new method for nonlinear optimization problems suggested and presented by B. Percinkova is performed. The method is originally developed and applicated on nonlinear systems. Basis of the method is following: A system of n-nonlinear equations gives as F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = 0; 1 = 1, 2, ..., n and solution domain x{sub pi} {<=} x{sub i} {<=} x{sub ki} i = 1, 2, ..., n is modified by introducing a new variable z. The new system is given by: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) = z; i = 1, 2, ..., n. The system defines a curve in (n + 1) dimensional space. System`s point X = (x{sub i}, x{sub 2}, x{sub 3}, ..., x{sub n}, z) that, the solution of the system is obtained using an interative procedure moving along the curve until the point with z = 0 is reached. In order to applicate method on optimization problems, a basic optimization model given with (min, max)F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) with the following optimization space: F{sub i}(x{sub 1}, x{sub 2}, x{sub 3}, ..., x{sub n}) ({<=}{>=})0 : i = 1, 2, ..., n is transformed into a system equivalent to system (2) by (dF/dx{sub i}) = z; i - 1, 2, ..., n. The main purpose of this work is to make relevant evaluation of the method by standard test problems.
Dynamic Simulations of Nonlinear Multi-Domain Systems Based on Genetic Programming and Bond Graphs
Institute of Scientific and Technical Information of China (English)
DI Wenhui; SUN Bo; XU Lixin
2009-01-01
A dynamic simulation method for non-linear systems based on genetic programming (GP) and bond graphs (BG) was developed to improve the design of nonlinear multi-domain energy conversion sys-tems. The genetic operators enable the embryo bond graph to evolve towards the target graph according to the fitness function. Better simulation requires analysis of the optimization of the eigenvalue and the filter circuit evolution. The open topological design and space search ability of this method not only gives a more optimized convergence for the operation, but also reduces the generation time for the new circuit graph for the design of nonlinear multi-domain systems.
Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.
Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong
2016-12-13
In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.
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Aijia Ouyang
2015-01-01
Full Text Available Nonlinear Muskingum models are important tools in hydrological forecasting. In this paper, we have come up with a class of new discretization schemes including a parameter θ to approximate the nonlinear Muskingum model based on general trapezoid formulas. The accuracy of these schemes is second order, if θ≠1/3, but interestingly when θ=1/3, the accuracy of the presented scheme gets improved to third order. Then, the present schemes are transformed into an unconstrained optimization problem which can be solved by a hybrid invasive weed optimization (HIWO algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the present methods. The numerical results substantiate the fact that the presented methods have better precision in estimating the parameters of nonlinear Muskingum models.
Pulse wave attenuation measurement by linear and nonlinear methods in nonlinearly elastic tubes.
Bertram, C D; Pythoud, F; Stergiopulos, N; Meister, J J
1999-04-01
Reasons for the continuing difficulty in making definitive measurements of pulse wave attenuation in elastic tubes and arteries in the presence of reflections are sought. The measurement techniques available were re-examined in elastic tubes mimicking the arterial compliance nonlinearity, under conditions of strong reflection. The pulse was of physiological shape, and two different pulse amplitudes in the physiological range were used. Measurements of pressure, flow-rate and diameter pulsation allowed the deployment of four of the classical linear methods of analysis. In addition, a method of separating the forward- and backward-travelling waves that does not require linearising assumptions was used, and the attenuation in the forward and reverse directions was calculated from the resulting waveforms. Overall, the results obtained here suggest that a fully satisfactory way of measuring arterial attenuation has yet to be devised. The classical linear methods all provided comparable attenuation estimates in terms of average value and degree of scatter across frequency. Increased scatter was generally found at the higher pulse amplitude. When the forward waveforms from the separation were similarly compared in terms of frequency components, the average value at energetic harmonics was similar to both the value indicated by the linear methods and the values predicted from linear theory on the basis of estimated viscous and viscoelastic parameter data. The backward waveforms indicated a physically unreasonable result, attributed as the expression for this technique of the same difficulties that normally manifest in scatter. Data in the literature suggesting that one of the classical methods, the three-point, systematically over-estimates attenuation were not supported, but it was confirmed that this method becomes prone to negative attenuation estimates at low harmonics as pulse amplitude increases. Although the goal of definitive attenuation measurement remains elusive
Approximation-Based Adaptive Tracking Control for MIMO Nonlinear Systems With Input Saturation.
Zhou, Qi; Shi, Peng; Tian, Yang; Wang, Mingyu
2015-10-01
In this paper, an approximation-based adaptive tracking control approach is proposed for a class of multiinput multioutput nonlinear systems. Based on the method of neural network, a novel adaptive controller is designed via backstepping design process. Furthermore, by introducing Nussbaum function, the issue of unknown control directions is handled. In the backstepping design process, the dynamic surface control technique is employed to avoid differentiating certain nonlinear functions repeatedly. Moreover, in order to reduce the number of adaptation laws, we do not use the neural networks to directly approximate the unknown nonlinear functions but the desired control signals. Finally, we provide two examples to illustrate the effectiveness of the proposed approach.
Optimization-Based Robust Nonlinear Control
2006-08-01
IEEE Transactions on Automatic Control , vol. 51, no. 4, pp. 661...systems with two time scales", A.R. Teel, L. Moreau and D. Nesic, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1526-1544, September 2003...Turner, L. Zaccarian, IEEE Transactions on Automatic Control , vol. 48, no. 9, pp. 1509- 1525, September 2003. 5. "Nonlinear Scheduled anti-windup
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper presents a method on non-linear correction of broadband LFMCW signal utilizing its relativenonlinear error. The deriving procedure and the results simulated by a computer and tested by a practical system arealso introduced. The method has two obvious advantages compared with the previous methods: (1) Correction has norelation with delay time td and sweep bandwidth B; (2) The inherent non-linear error of VCO has no influence on thecorrection and its last results.
FBFN-based adaptive repetitive control of nonlinearly parameterized systems
Institute of Scientific and Technical Information of China (English)
Wenli Sun; Hong Cai; Fu Zhao
2013-01-01
An adaptive repetitive control scheme is presented for a class of nonlinearly parameterized systems based on the fuzzy ba-sis function network (FBFN). The parameters of the fuzzy rules are tuned with adaptive schemes. To attenuate chattering effectively, the discontinuous control term is approximated by an adaptive PI control structure. The bound of the discontinuous control term is assumed to be unknown and estimated by an adaptive mecha-nism. Based on the Lyapunov stability theory, an adaptive repeti-tive control law is proposed to guarantee the closed-loop stability and the tracking performance. By means of FBFNs, which avoid the nonlinear parameterization from entering into the adaptive repetitive control, the control er singularity problem is solved. The proposed approach does not require an exact structure of the sys-tem dynamics, and the proposed control er is utilized to control a model of permanent-magnet linear synchronous motor subject to significant disturbances and parameter uncertainties. The simula-tion results demonstrate the effectiveness of the proposed method.
Prediction of biodegradation kinetics using a nonlinear group contribution method
Energy Technology Data Exchange (ETDEWEB)
Tabak, H.H. (Environmental Protection Agency, Cincinnati, OH (United States)); Govind, R. (Univ. of Cincinnati, OH (United States))
1993-02-01
The fate of organic chemicals in the environment depends on their susceptibility to biodegradation. Hence, development of regulations concerning their manufacture and use requires information on the extent and rate of biodegradation. Recent studies have attempted to correlate the kinetics of biodegradation with the molecular structure of the compound. This has led to the development of structure-biodegradation relationships (SBRs) using the group contribution approach. Each defined group present in the chemical structure of the compound is assigned a unique numerical contribution toward the calculation of the biodegradation kinetic constants. In this paper, a nonlinear group contribution method has been developed using neural networks; it is trained using literature data on the first-order biodegradation kinetic rate constant for a number of priority pollutants. The trained neural network is then used to predict the biodegradation kinetic constant for a new list of compounds, and results have been compared with the experimental values and the predictions obtained from a linear group contribution method. It has been shown that the nonlinear group contribution method using neural networks is able to provide a superior fit to the training set data and test data set and produce a lower prediction error than the previous linear method.
Energy Technology Data Exchange (ETDEWEB)
Hagstrom, T. [Univ. of New Mexico, Albuquerque, NM (United States); Radhakrishnan, K. [Sverdrup Technology, Brook Park, OH (United States)
1994-12-31
The authors report on some iterative methods which they have tested for use in combustion simulations. In particular, they have developed a code to solve zero Mach number reacting flow equations with complex reaction and diffusion physics. These equations have the form of a nonlinear parabolic system coupled with constraints. In semi-discrete form, one obtains DAE`s of index two or three depending on the number of spatial dimensions. The authors have implemented a fourth order (fully implicit) BDF method in time, coupled with a suite of fourth order explicit and implicit spatial difference approximations. Most codes they know of for simulating reacting flows use a splitting strategy to march in time. This results in a sequence of nonlinear systems to solve, each of which has a simpler structure than the one they are faced with. The rapid and robust solution of the coupled system is the essential requirement for the success of their approach. They have implemented and analyzed nonlinear generalizations of conjugate gradient-like methods for nonsymmetric systems, including CGS and the quasi-Newton based method of Eirola and Nevanlinna. They develop a general framework for the nonlinearization of linear methods in terms of the acceleration of fixed-point iterations, where the latter is assumed to include the {open_quote}preconditioning{open_quote}. Their preconditioning is a single step of a split method, using lower order spatial difference approximations as well as simplified (Fickian) approximations of the diffusion physics.
An assessment of a semi analytical AG method for solving nonlinear oscillators
Directory of Open Access Journals (Sweden)
Hadi Mirgolbabaee
2016-02-01
Based on the comparison between AGM and numerical methods, AGM can be successfully applied for a broad range of nonlinear equations. One of the important reasons of selecting AGM for solving differential equations in miscellaneous fields not only in vibrations but also in different fields of sciences for instance fluid mechanics, solid mechanics, chemical engineering, etc. The main benefit of this method in comparison with the other approaches are as follows: normally according to the order of differential equations, we need boundary conditions so in the case of the number of boundary conditions is less than the order of the differential equation, AGM can create additional new boundary conditions in regard to the own differential equation and its derivatives. Results illustrate that method is efficient and has enough accuracy in comparison with other semi analytical and numerical methods because of the simplicity of this method. Moreover results demonstrate that AGM could be applicable through other methods in nonlinear problems with high nonlinearity. Furthermore convergence problems for solving nonlinear equations by using AGM appear small.
On approximation of nonlinear boundary integral equations for the combined method
Energy Technology Data Exchange (ETDEWEB)
Gregus, M.; Khoromsky, B.N.; Mazurkevich, G.E.; Zhidkov, E.P.
1989-09-22
The nonlinear boundary integral equations that arise in research of nonlinear magnetostatic problems are investigated in combined formulation on an unbounded domain. Approximations of the derived operator equations are studied based on the Galerkin method. The investigated boundary operators are strongly monotone, Lipschitz-continuous, potential and have a symmetrical Gateaux derivative. The error estimates of the Galerkin's approximation in Sobolev spaces of fractional powers are obtained using the above-mentioned properties of the operators, too. The problem has been studied on surfaces in two and three-dimensional spaces. We answer also some questions on convergence connected with the discretized systems of equations. 21 refs.
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
Energy Technology Data Exchange (ETDEWEB)
Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir [Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of); The Laboratory of Quantum Information Processing, Yazd University, Yazd (Iran, Islamic Republic of); Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir [Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of); The Laboratory of Quantum Information Processing, Yazd University, Yazd (Iran, Islamic Republic of); Cattani, C., E-mail: ccattani@unisa.it [Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano (Italy); Maalek Ghaini, F.M., E-mail: maalek@yazd.ac.ir [Faculty of Mathematics, Yazd University, Yazd (Iran, Islamic Republic of); The Laboratory of Quantum Information Processing, Yazd University, Yazd (Iran, Islamic Republic of)
2015-02-15
Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
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...
Similar Constructive Method for Solving a nonlinearly Spherical Percolation Model
Directory of Open Access Journals (Sweden)
WANG Yong
2013-01-01
Full Text Available In the view of nonlinear spherical percolation problem of dual porosity reservoir, a mathematical model considering three types of outer boundary conditions: closed, constant pressure, infinity was established in this paper. The mathematical model was linearized by substitution of variable and became a boundary value problem of ordinary differential equation in Laplace space by Laplace transformation. It was verified that such boundary value problem with one type of outer boundary had a similar structure of solution. And a new method: Similar Constructive Method was obtained for solving such boundary value problem. By this method, solutions with similar structure in other two outer boundary conditions were obtained. The Similar Constructive Method raises efficiency of solving such percolation model.
A nonlinear analytic function expansion nodal method for transient calculations
Energy Technology Data Exchange (ETDEWEB)
Joo, Han Gyn; Park, Sang Yoon; Cho, Byung Oh; Zee, Sung Quun [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)
1998-12-31
The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation of the solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized, In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of application to the NEACRP PWR rod ejection benchmark problems. 6 refs., 2 figs., 1 tab. (Author)
Suppression of beam halo-chaos using nonlinear feedback discrete control method
Fang Jin Qing; Chen Guan Rong; Luo Xiao Shu; Weng Jia Qiang
2002-01-01
Based on nonlinear feedback control method, wavelet-based feedback controller as a especial nonlinear feedback function is designed for controlling beam halo-chaos in high-current accelerators of driven clean nuclear power system. PIC simulations show that suppression of beam halo-chaos are realized effectively after discrete control of wavelet-based feed-back is applied to five kinds of the initial proton beam distributions, respectively. The beam halo strength factor is quickly reduced to zero, and other statistical physical quantities of beam halo-chaos are more than doubly reduced. These performed PIC simulation results demonstrate that the developed methods are very effective for control of beam halo-chaos. Potential application of the beam halo-chaos control methods is discussed finally
CAD—Oriented Noise Analysis Method of Nonlinear Microwave Chircuits
Institute of Scientific and Technical Information of China (English)
WANGJun; TANGGaodi; CHENHuilian
2003-01-01
A general method is introduced which is capable of making accurate,quantitative predictions about the noise of different type of nonlinear microwave circuits.This new approach also elucidates several design criteria for making it suitable to CAD-oriented analysis via identifying the mechanisms by which intrinsic device noise and external noise sources contribute to the total equivalent noise.In particular,it explains the details of how noise spectrum at the interesting port is obtained.And the theory also naturally leads to additional important design insights.In the illustrative experiments,excellent agreement among theory,simulations,and measurements is observed.
Method of the Logistic Function for Finding Analytical Solutions of Nonlinear Differential Equations
Kudryashov, N. A.
2015-01-01
The method of the logistic function is presented for finding exact solutions of nonlinear differential equations. The application of the method is illustrated by using the nonlinear ordinary differential equation of the fourth order. Analytical solutions obtained by this method are presented. These solutions are expressed via exponential functions.logistic function, nonlinear wave, nonlinear ordinary differential equation, Painlev´e test, exact solution
Institute of Scientific and Technical Information of China (English)
唐圣金; 郭晓松; 于传强; 周志杰; 周召发; 张邦成
2014-01-01
Real time remaining useful life (RUL) prediction based on condition monitoring is an essential part in condition based maintenance (CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item’s individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.
Nonlinear system identification and control based on modular neural networks.
Puscasu, Gheorghe; Codres, Bogdan
2011-08-01
A new approach for nonlinear system identification and control based on modular neural networks (MNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This is obtained using a partitioning algorithm. Each local nonlinear model is associated with a nonlinear controller. These are also implemented by neural networks. The switching between the neural controllers is done by a dynamical switcher, also implemented by neural networks, that tracks the different operating points. The proposed multiple modelling and control strategy has been successfully tested on simulated laboratory scale liquid-level system.
Institute of Scientific and Technical Information of China (English)
SUN LiYing; WANG YuZhen
2009-01-01
This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonlan function method.Firstly,based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback,two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation,and a sufficient condition for two closed-loop systems to be impulse-free is given.The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique,based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems.Secondly,the case of more than two nonlinear descriptor systems is investigated,and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization,respectively.Finally,an illustrative example is studied by using the results proposed in this paper,and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.
A modal method for ﬁnite amplitude, nonlinear sloshing
Indian Academy of Sciences (India)
P N Shankar; R Kidambi
2002-10-01
A modal method is used to calculate the two-dimensional sloshing motion of an inviscid liquid in a rectangular container. The full nonlinear problem is reduced to the solution of a system of nonlinear ordinary differential equations for the time varying coefﬁcients in the expansions of the interface and the potential. The effects of capillarity are included in the formulation. The simplicity, generality and power of the method are exhibited not only by recovering the earlier results obtained, for example, by Penney and Price [1], Tadjbakhsh and Keller [2] and Faltinsen et al [3], but also by obtaining new and interesting results of the effects of capillarity and shallow depth, which would be difﬁcult to obtain otherwise. For example, it is found that for the initial interface proﬁle considered here, parasitic capillary waves, borne by the higher number wave modes, are generated for moderate capillarity but disappear for larger values of the parameter. The method can be extended to other simple geometries.
Directory of Open Access Journals (Sweden)
Kyung-Tae Nam
2015-12-01
Full Text Available In this paper, we consider the state estimation problem for flexible joint manipulators that involve nonlinear characteristics in their stiffness. The two key ideas of our design are that (a an accelerometer is used in order that the estimation error dynamics do not depend on nonlinearities at the link part of the manipulators and (b the model of the nonlinear stiffness is indeed a Lipschitz function. Based on the measured acceleration, we propose a nonlinear observer under the Lipschitz condition of the nonlinear stiffness. In addition, in order to effectively compensate for the estimation error, the gain of the proposed observer is chosen from the ARE (algebraic Riccati equations which depend on the Lipschitz constant. Comparative experimental results verify the effectiveness of the proposed method.
Modeling and Backstepping-based Nonlinear Control Strategy for a 6 DOF Quadrotor Helicopter
Institute of Scientific and Technical Information of China (English)
Ashfaq Ahmad Mian; Wang Daobo
2008-01-01
In this article,a nonlinear model of an underactuated six degrees of freedom (6 DOF) quadrotor helicopter is derived on the basis of the Newton-Euler formalism.The derivation comprises determining equations of the motion of the quadrotor in three dimensions andapproximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics.The derived modelcomposed of translatioual and rotational subsystems is dynamically unstable,so a sequential nonlinear control strategy is used.The con-trol strategy includes feedback linearization coupled with a PD controller for the translational subsystem and a backstepping-based PID nonlinear controller for the rotational subsystem of the quadrotor.The performances of the nonlinear control method are evaluated by nonlinear simulation and the results demonstrate the effectiveness of the proposed control strategy for the quadrotor helicopter inquasi-stationary flights.
A new Liu-Storey type nonlinear conjugate gradient method for unconstrained optimization problems
Zhang, Li
2009-03-01
Although the Liu-Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak-Ribière-Polyak (PRP) and Hestenes-Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo-Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported.
On-line Weighted Least Squares Kernel Method for Nonlinear Dynamic Modeling
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Support vector machines (SVM) have been widely used in pattern recognition and have also drawn considerable interest in control areas. Based on rolling optimization method and on-line learning strategies, a novel approach based on weighted least squares support vector machines (WLS-SVM) is proposed for nonlinear dynamic modeling.The good robust property of the novel approach enhances the generalization ability of kernel method-based modeling and some experimental results are presented to illustrate the feasibility of the proposed method.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Hybrid discretization method for time-delay nonlinear systems
Energy Technology Data Exchange (ETDEWEB)
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
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.
Homotopy deform method for reproducing kernel space for nonlinear boundary value problems
Indian Academy of Sciences (India)
MIN-QIANG XU; YING-ZHEN LIN
2016-10-01
In this paper, the combination of homotopy deform method (HDM) and simplified reproducing kernel method (SRKM) is introduced for solving the boundary value problems (BVPs) of nonlinear differential equations. The solution methodology is based on Adomian decomposition and reproducing kernel method (RKM). By the HDM, the nonlinear equations can be converted into a series of linear BVPs. After that, the simplified reproducing kernel method, which not only facilitates the reproducing kernel but also avoids the time-consuming Schmidt orthogonalization process, is proposed to solve linear equations. Some numerical test problems including ordinary differential equations and partial differential equations are analysed to illustrate the procedure and confirm the performance of the proposed method. The results faithfully reveal that our algorithm is considerably accurate and effective as expected.
An Object Detection Method Using Wavelet Optical Flow and Hybrid Linear-Nonlinear Classifier
Directory of Open Access Journals (Sweden)
Pengcheng Han
2013-01-01
Full Text Available We propose a new computational intelligence method using wavelet optical flow and hybrid linear-nonlinear classifier for object detection. With the existing optical flow methods, it is difficult to accurately estimate moving objects with diverse speeds. We propose a wavelet-based optical flow method, which uses wavelet decomposition in optical flow motion estimation. The algorithm can accurately detect moving objects with variable speeds in a scene. In addition, we use the hybrid linear-nonlinear classifier (HLNLC to classify moving objects and static background. HLNLC transforms a nonoptimal scalar variable into its likelihood ratio and uses a scalar quantity as the decision variable. This approach is appropriate for the classification of optical flow feature vectors with unequal variance matrices. The experimental results confirm that our proposed object detection method has an improved accuracy and computation efficiency over other state-of-the-art methods.
Analytic treatment of nonlinear evolution equations using ﬁrst integral method
Indian Academy of Sciences (India)
Ahmet Bekir; Ömer Ünsal
2012-07-01
In this paper, we show the applicability of the ﬁrst integral method to combined KdV-mKdV equation, Pochhammer–Chree equation and coupled nonlinear evolution equations. The power of this manageable method is conﬁrmed by applying it for three selected nonlinear evolution equations. This approach can also be applied to other nonlinear differential equations.
The tanh-coth method combined with the Riccati equation for solving non-linear equation
Energy Technology Data Exchange (ETDEWEB)
Bekir, Ahmet [Dumlupinar University, Art-Science Faculty, Department of Mathematics, Kuetahya (Turkey)], E-mail: abekir@dumlupinar.edu.tr
2009-05-15
In this work, we established abundant travelling wave solutions for some non-linear evolution equations. This method was used to construct solitons and traveling wave solutions of non-linear evolution equations. The tanh-coth method combined with Riccati equation presents a wider applicability for handling non-linear wave equations.
Optimization of nonlinear structural resonance using the incremental harmonic balance method
DEFF Research Database (Denmark)
Dou, Suguang; Jensen, Jakob Søndergaard
2015-01-01
We present an optimization procedure for tailoring the nonlinear structural resonant response with time-harmonic loads. A nonlinear finite element method is used for modeling beam structures with a geometric nonlinearity and the incremental harmonic balance method is applied for accurate nonlinea...
NOLB : Non-linear rigid block normal mode analysis method.
Hoffmann, Alexandre; Grudinin, Sergei
2017-04-05
We present a new conceptually simple and computationally efficient method for non-linear normal mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a non-linear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions. For example, NOLB detects the spiral sliding motion of the TALE protein, which is capable of rapid diffusion along its target DNA. Overall, our method produces better structures compared to the standard approach, especially at large deformation amplitudes, as we demonstrate by visual inspection, energy and topology analyses, and also by the MolProbity service validation. Finally, our method is scalable and can be applied to very large molecular systems, such as ribosomes. Standalone executables of the NOLB normal mode analysis method are available at https://team.inria.fr/nano-d/software/nolb-normal-modes. A graphical user interfaces created for the SAMSON software platform will be made available at https: //www.samson-connect.net.
Reliability-based design optimization for nonlinear energy harvesters
Seong, Sumin; Lee, Soobum; Hu, Chao
2015-03-01
The power output of a vibration energy harvesting device is highly sensitive to uncertainties in materials, manufacturing, and operating conditions. Although the use of a nonlinear spring (e.g., snap-through mechanism) in energy harvesting device has been reported to reduce the sensitivity of power output with respect to the excitation frequency, the nonlinear spring characteristic remains significantly sensitive and it causes unreliable power generation. In this paper, we present a reliability-based design optimization (RBDO) study of vibration energy harvesters. For a nonlinear harvester, a purely mechanical nonlinear spring design implemented in the middle of cantilever beam harvester is considered in the study. This design has the curved section in the center of beam that causes bi-stable configuration. When vibrating, the inertia of the tip mass activates the curved shell to cause snap-through buckling and make the nature of vibration nonlinear. In this paper, deterministic optimization (DO) is performed to obtain deterministic optimum of linear and nonlinear energy harvester configuration. As a result of the deterministic optimization, an optimum bi-stable vibration configuration of nonlinear harvester can be obtained for reliable power generation despite uncertainty on input vibration condition. For the linear harvester, RBDO is additionally performed to find the optimum design that satisfies a target reliability on power generation, while accounting for uncertainty in material properties and geometric parameters.
Pan, Shoukui; Okano, Y.; Tsunekawa, S.; Fukuda, T.
1993-03-01
The Kyropoulus method was used to grow nonlinear optical organic crystals ABP (4-aminobenzophenone). The crystals were characterized by nonlinear optical measurements and had a large effect of frequency doubling.
Simulation-based optimal Bayesian experimental design for nonlinear systems
Huan, Xun
2013-01-01
The optimal selection of experimental conditions is essential to maximizing the value of data for inference and prediction, particularly in situations where experiments are time-consuming and expensive to conduct. We propose a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models; in particular, we focus on finding sets of experiments that provide the most information about targeted sets of parameters.Our framework employs a Bayesian statistical setting, which provides a foundation for inference from noisy, indirect, and incomplete data, and a natural mechanism for incorporating heterogeneous sources of information. An objective function is constructed from information theoretic measures, reflecting expected information gain from proposed combinations of experiments. Polynomial chaos approximations and a two-stage Monte Carlo sampling method are used to evaluate the expected information gain. Stochastic approximation algorithms are then used to make optimization feasible in computationally intensive and high-dimensional settings. These algorithms are demonstrated on model problems and on nonlinear parameter inference problems arising in detailed combustion kinetics. © 2012 Elsevier Inc.
A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging
Desmal, Abdulla
2015-03-01
A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.
Finite Volume Evolution Galerkin Methods for Nonlinear Hyperbolic Systems
Lukáčová-Medvid'ová, M.; Saibertová, J.; Warnecke, G.
2002-12-01
We present new truly multidimensional schemes of higher order within the frame- work of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Coupled nonlinear-diffusion color image sharpening based on the chromaticity-brightness model
Saito, Takahiro; Nosaka, Reina; Komatsu, Takashi
2006-01-01
Previously we have presented a selective image sharpening method based on the coupled nonlinear diffusion process composed of a nonlinear diffusion term, a fidelity term and an isotropic peaking term, and it can sharpen only blurred edges without increasing the noise visibility. Our previously presented prototypal color-image sharpening methods based on the coupled nonlinear-diffusion process have been formulated on the linear color models, namely, the channel-bychannel model and the 3D vectorial model. Our prototypal methods can sharpen blurred color step edges, but they do not necessarily enhance contrasts of signal variations in complex texture image regions so well as in simple step-edge regions. To remedy the drawback, this paper extends our coupled nonlinear-diffusion color-image sharpening method to the nonlinear non-flat color model, namely, the chromaticity-brightness model, which is known to be closely relating to human color perception. We modify our time-evolution PDE's for the non-flat space of the chromaticity vector and present its digital implementations. Through experimental simulations, we compare our new color-image sharpening method based on the chromaticity-brightness model with our prototypal color-image sharpening methods based on the linear color models.
A Theoretical Method for Characterizing Nonlinear Effects in Paul Traps with Added Octopole Field.
Xiong, Caiqiao; Zhou, Xiaoyu; Zhang, Ning; Zhan, Lingpeng; Chen, Yongtai; Chen, Suming; Nie, Zongxiu
2015-08-01
In comparison with numerical methods, theoretical characterizations of ion motion in the nonlinear Paul traps always suffer from low accuracy and little applicability. To overcome the difficulties, the theoretical harmonic balance (HB) method was developed, and was validated by the numerical fourth-order Runge-Kutta (4th RK) method. Using the HB method, analytical ion trajectory and ion motion frequency in the superimposed octopole field, ε, were obtained by solving the nonlinear Mathieu equation (NME). The obtained accuracy of the HB method was comparable with that of the 4th RK method at the Mathieu parameter, q = 0.6, and the applicable q values could be extended to the entire first stability region with satisfactory accuracy. Two sorts of nonlinear effects of ion motion were studied, including ion frequency shift, Δβ, and ion amplitude variation, Δ(C(2n)/C0) (n ≠ 0). New phenomena regarding Δβ were observed, although extensive studies have been performed based on the pseudo-potential well (PW) model. For instance, the |Δβ| at ε = 0.1 and ε = -0.1 were found to be different, but they were the same in the PW model. This is the first time the nonlinear effects regarding Δ(C(2n)/C0) (n ≠ 0) are studied, and the associated study has been a challenge for both theoretical and numerical methods. The nonlinear effects of Δ(C(2n)/C0) (n ≠ 0) and Δβ were found to share some similarities at q < 0.6: both of them were proportional to ε, and the square of the initial ion displacement, z(0)(2).
Novak, Antonin; Simon, Laurent; Lotton, Pierrick
2010-12-01
A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.
Directory of Open Access Journals (Sweden)
Novak Antonin
2010-01-01
Full Text Available A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.
A Kernel Time Structure Independent Component Analysis Method for Nonlinear Process Monitoring☆
Institute of Scientific and Technical Information of China (English)
Lianfang Cai; Xuemin Tian; Ni Zhang
2014-01-01
Kernel independent component analysis (KICA) is a newly emerging nonlinear process monitoring method, which can extract mutually independent latent variables cal ed independent components (ICs) from process var-iables. However, when more than one IC have Gaussian distribution, it cannot extract the IC feature effectively and thus its monitoring performance will be degraded drastical y. To solve such a problem, a kernel time struc-ture independent component analysis (KTSICA) method is proposed for monitoring nonlinear process in this paper. The original process data are mapped into a feature space nonlinearly and then the whitened data are calculated in the feature space by the kernel trick. Subsequently, a time structure independent component analysis algorithm, which has no requirement for the distribution of ICs, is proposed to extract the IC feature. Finally, two monitoring statistics are built to detect process faults. When some fault is detected, a nonlinear fault identification method is developed to identify fault variables based on sensitivity analysis. The proposed monitoring method is applied in the Tennessee Eastman benchmark process. Applications demonstrate the superiority of KTSICA over KICA.
Conditions on Structural Controllability of Nonlinear Systems: Polynomial Method
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Qiang Ma
2011-03-01
Full Text Available In this paper the structural controllability of a class of a nonlinear system is investigated. The transfer function (matrix of nonlinear systems is obtained by putting the nonlinear system model on non-commutative ring. Conditions of structural controllability of nonlinear systems are presented according to the criterion of linear systems structural controllability in frequency domain. An example is used to testify the presented conditions finally.
Energy Technology Data Exchange (ETDEWEB)
Cho, Seung Hyun; Park, Choon Su; Seo, Dae Cheol [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of); Cho, Seung Wan [Dept. of Mechanical Engineering, Sunngkyunkwan University, Suwon (Korea, Republic of); Jhang, Kyung Young [Dept. of Mechanical Engineering, Hanyang University, Seoul (Korea, Republic of)
2014-08-15
Recently, much attention has been paid to nonlinear ultrasonic technology as a potential tool to assess hidden damages that cannot be detected by conventional ultrasonic testing. One nonlinear ultrasonic technique is measurement of the resonance frequency shift, which is based on the hysteresis of the material elasticity. Sophisticated measurement of resonance frequency is required, because the change in resonance frequency is usually quite small. In this investigation, the nonlinear electromagnetic acoustic resonance (NEMAR) method was employed. The NEMAR method uses noncontact electromagnetic acoustic transducers (EMATs) in order to minimize the effect of the transducer on the frequency response of the object. Aluminum plate specimens that underwent three point bending fatigue were tested witha shear wave EMAT. The hysteretic nonlinear parameter α, a key indicator of damage, was calculated from the resonance frequency shift at several levels of input voltage. The hysteretic nonlinear parameter of a damaged sample was compared to that of an intact one, showing a difference in the values.
Institute of Scientific and Technical Information of China (English)
吴雨珊; 江驹; 甄子洋; 顾臣风
2016-01-01
In this paper, an intelligence nonlinear control scheme is proposed based on the backstepping method to solve the difficulty of the stable tracking control of the hypersonic morphing vehicle, considering compound disturb⁃ances as well as the influence of model uncertainties and unknown outside disturbances. First, the aerodynamic pa⁃rameters of the morphing vehicle are replaced with a curve⁃fitted approximation in order to build an accurate hyper⁃sonic model. Then, the feedback linearization approach is used to transform the nonlinear vehicle model into a strict feedback multi⁃input/multi⁃output nonlinear system. The nonlinear system is divided into three subsystems accord⁃ing to the features of the state variables and the virtual control signals are calculated for every subsystem. Next, the radial basis function ( RBF) is proved to have excellent capability in restraining unknown disturbances, and a dy⁃namic surface control strategy is employed to eliminate the explosion terms. The simulation results show that the pro⁃posed method can ensure the integral stability of the closed⁃loop system, as well as can have excellent tracing per⁃formance and robustness.%针对可变翼高超声速飞行器的外环稳定跟踪控制问题，考虑可变翼对建模的影响、模型参数不确定和外界未知干扰对跟踪控制性能的影响，提出基于回馈递推的智能非线性控制策略。本文首先利用巡航段气动参数的插值数据建立精确的纵向模型；然后采用输入－输出反馈线性化方法对飞行器纵向模型进行非线性映射，并根据状态变量特性将飞行器划分为三个子系统，利用回馈递推依次求取控制信号，采用RBF神经网络对未知干扰进行逼近，保证鲁棒性能。针对回馈递推设计过程中微分膨胀的问题，加入动态面控制思想进行改进。通过仿真表明，该方法可以保证闭环系统的全局稳定，并且拥有良好的跟踪性能和鲁棒性能。
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Envelope based nonlinear blind deconvolution approach for ultrasound imaging
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L.T. Chira
2012-06-01
Full Text Available The resolution of ultrasound medical images is yet an important problem despite of the researchers efforts. In this paper we presents a nonlinear blind deconvolution to eliminate the blurring effect based on the measured radio-frequency signal envelope. This algorithm is executed in two steps. Firslty we make an estimation for Point Spread Function (PSF and, secondly we use the estimated PSF to remove, iteratively their effect. The proposed algorithm is a greedy algorithm, called also matching pursuit or CLEAN. The use of this algorithm is motivated beacause theorically it avoid the so called inverse problem, which usually needs regularization to obtain an optimal solution. The results are presented using 1D simulated signals in term of visual evaluation and nMSE in comparison with the two most kwown regularisation solution methods for least square problem, Thikonov regularization or l2-norm and Total Variation or l1 norm.
A New Method to Solve Numeric Solution of Nonlinear Dynamic System
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Min Hu
2016-01-01
Full Text Available It is well known that the cubic spline function has advantages of simple forms, good convergence, approximation, and second-order smoothness. A particular class of cubic spline function is constructed and an effective method to solve the numerical solution of nonlinear dynamic system is proposed based on the cubic spline function. Compared with existing methods, this method not only has high approximation precision, but also avoids the Runge phenomenon. The error analysis of several methods is given via two numeric examples, which turned out that the proposed method is a much more feasible tool applied to the engineering practice.
Automated seeding-based nuclei segmentation in nonlinear optical microscopy.
Medyukhina, Anna; Meyer, Tobias; Heuke, Sandro; Vogler, Nadine; Dietzek, Benjamin; Popp, Jürgen
2013-10-01
Nonlinear optical (NLO) microscopy based, e.g., on coherent anti-Stokes Raman scattering (CARS) or two-photon-excited fluorescence (TPEF) is a fast label-free imaging technique, with a great potential for biomedical applications. However, NLO microscopy as a diagnostic tool is still in its infancy; there is a lack of robust and durable nuclei segmentation methods capable of accurate image processing in cases of variable image contrast, nuclear density, and type of investigated tissue. Nonetheless, such algorithms specifically adapted to NLO microscopy present one prerequisite for the technology to be routinely used, e.g., in pathology or intraoperatively for surgical guidance. In this paper, we compare the applicability of different seeding and boundary detection methods to NLO microscopic images in order to develop an optimal seeding-based approach capable of accurate segmentation of both TPEF and CARS images. Among different methods, the Laplacian of Gaussian filter showed the best accuracy for the seeding of the image, while a modified seeded watershed segmentation was the most accurate in the task of boundary detection. The resulting combination of these methods followed by the verification of the detected nuclei performs high average sensitivity and specificity when applied to various types of NLO microscopy images.
Nonlinear system modeling based on experimental data
Energy Technology Data Exchange (ETDEWEB)
PAEZ,THOMAS L.; HUNTER,NORMAN F.
2000-02-02
The canonical variate analysis technique is used in this investigation, along with a data transformation algorithm, to identify a system in a transform space. The transformation algorithm involves the preprocessing of measured excitation/response data with a zero-memory-nonlinear transform, specifically, the Rosenblatt transform. This transform approximately maps the measured excitation and response data from its own space into the space of uncorrelated, standard normal random variates. Following this transform, it is appropriate to model the excitation/response relation as linear since Gaussian inputs excite Gaussian responses in linear structures. The linear model is identified in the transform space using the canonical variate analysis approach, and system responses in the original space are predicted using inverse Rosenblatt transformation. An example is presented.
Nonlinear Differential Geometry Method and Its Application in Induction Motor Decoupling Control
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Linyuan Fan
2016-05-01
Full Text Available An alternating current induction motor is a nonlinear, multi-variable, and strong-coupled system that is difficult to control. To address this problem, a novel control strategy based on nonlinear differential geometry theory was proposed. First, a five-order affine mathematical model for an alternating current induction motor was provided. Then, the feedback linearization method was used to realize decoupling and full linearization of the system model. Moreover, a general and simplified control law was adopted to facilitate practical applications. Finally, a controller was designed using the pole assignment method. Simulation results show that the proposed method can decouple the system model into two independent subsystems, and that the closed-loop system exhibits good dynamic and static performances. The proposed decoupling control method is useful to reduce the system complexity of an induction motor and to improve its control performance, thereby providing a new and feasible dynamic decoupling control for an alternating current induction motor.
Liu, Qian; OuYang, Liangfei; Liang, Heng; Li, Nan; Geng, Xindu
2012-06-01
A novel thermodynamic state recursion (TSR) method, which is based on nonequilibrium thermodynamic path described by the Lagrangian-Eulerian representation, is presented to simulate the whole chromatographic process of frontal analysis using the spatial distribution of solute bands in time series like as a series of images. TSR differs from the current numerical methods using the partial differential equations in Eulerian representation. The novel method is used to simulate the nonideal, nonlinear hydrophobic interaction chromatography (HIC) processes of lysozyme and myoglobin under the discrete complex boundary conditions. The results show that the simulated breakthrough curves agree well with the experimental ones. The apparent diffusion coefficient and the Langmuir isotherm parameters of the two proteins in HIC are obtained by the state recursion inverse method. Due to its the time domain and Markov characteristics, TSR is applicable to the design and online control of the nonlinear multicolumn chromatographic systems.
An analysis of the stress formula for energy-momentum methods in nonlinear elastodynamics
Romero, Ignacio
2012-11-01
The energy-momentum method, a space-time discretization strategy for elastic problems in nonlinear solid, structural, and multibody mechanics relies critically on a discrete derivative operation that defines an approximation of the internal forces that guarantees the discrete conservation of energy and momenta. In the case of nonlinear elastodynamics, the formulation for general hyperelastic materials is due to Simo and Gonzalez, dating back to the mid-nineties. In this work we show that there are actually infinite second order energy-momentum methods for elastodynamics, all of them deriving from a modified midpoint integrator by an appropriate redefinition of the stress tensor at equilibrium. Such stress tensors can be interpreted as the solutions to local convex projections, whose precise definitions lead to different methods. The mathematical requirements of such projections are identified. Based on this geometrical interpretation several conserving methods are examined.
Institute of Scientific and Technical Information of China (English)
LI Hua-Mei
2003-01-01
In this paper, we extend the mapping deformation method proposed by Lou. It is used to find new exacttravelling wave solutions of nonlinear partial differential equation or coupled nonlinear partial differential equations(PDEs). Based on the idea of the homogeneous balance method, we construct the general mapping relation betweenthe solutions of the PDEs and those of the cubic nonlinear Klein-Gordon (NKG) equation. By using this relation andthe abundant solutions of the cubic NKG equation, many explicit and exact travelling wave solutions of three systemsof coupled PDEs, which contain solitary wave solutions, trigonometric function solutions, Jacobian elliptic functionsolutions, and rational solutions, are obtained.
Leader-Based Consensus of Heterogeneous Nonlinear Multiagent Systems
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Tairen Sun
2014-01-01
Full Text Available This paper considers the leader-based consensus of heterogeneous multiple agents with nonlinear uncertain systems. Based on the information obtained from the following agents’ neighbors, leader observers are designed by the following agents to estimate the leader’s states and nonlinear dynamics. Then, to achieve leader-based consensus, adaptive distributed controllers are designed for the following agents to track the designed corresponding leader observers. The effectiveness of the leader observers and distributed consensus controllers are illustrated by formal proof and simulation results.
A method to measure the nonlinear force caused emittance growth in a RF photoinjector
Institute of Scientific and Technical Information of China (English)
Li Zheng-Hong; Yang Zhen-Ping
2006-01-01
Based on the multi-slit method, a new method is introduced to measure the non linear force caused emittance growth in a RF photoinjector. It is possible to reconstruct the phase space of a beam under some conditions by the multi-slit method. Based on the reconstructed phase space, besides the emittance, the emittance growth from the distortion of the phase space can also be measured. The emittance growth results from the effects of nonlinear force acting on electron, which is very important for the high quality beam in a RF photoinjector.
Institute of Scientific and Technical Information of China (English)
巫世晶; 刘振皓; 王晓笋; 朱恩涌
2011-01-01
为揭示多问隙作用下Ravigneaux型复合行星齿轮传动系统的非线性动力学行为,建立考虑时变啮合刚度、齿侧间隙与综合啮合误差的系统纯扭转强非线性动力学模型.将齿侧问隙非线性函数表达为描述函数的形式,运用谐波平衡法(Harmonic balance method,HBM)将方程组转化为非线性代数方程组,使用逆Broyden秩1法进行迭代求解,得到系统的基频稳态响应.通过改变时变啮合刚度、齿侧间隙与综合啮合误差的大小,分析参数变化对系统非线性动态特性的影响.研究发现,由于齿侧间隙的影响,系统动态特性曲线出现幅值跳跃与多值解等典型非线性特征,系统出现复杂的冲击现象;齿侧间隙、啮合刚度波动与误差波动的耦合使系统的非线性程度得以强化.基于描述函数的HBM法可用于求解更加复杂模型的基频稳态响应,为深入研究复合行星齿轮系统的动态特性提供了一种方法.%A purely rotational model of Ravigneaux compound planetary gear train sets including time-varying mesh stiffness,synthetic mesh errors and gear backlashes is developed to show the nonlinear dynamic behavior of the system with the action of multi-clearances. The gap function is expressed as describing function and harmonic balance method (HBM) is used to convert the differential equations to nonlinear algebraic equations, which is solved iteratively by single rank inverse Broyden method. The steady state response of fundamental frequency is obtained. The influences of gear backlashes, time-varying mesh stiffness and synthetic mesh errors are analyzed by changing the value of the parameter. It is showed from the research that multiple value and amplitude jump discontinuities are presented on the dynamic curves, there the impact phenomenon is reflected. Meanwhile the nonlinearity degree of the system is increased by the coupling of stiffness fluctuation, mesh errors and backlashes. The HBM based on
Directory of Open Access Journals (Sweden)
Marcelo A. Silva
2006-01-01
Full Text Available The goal of this paper is to propose a nonlinear dynamic model based on experimental data and NBR-6123-87 to accomplish a nonlinear dynamic analysis of slender structures subjected to wind loading. At first we compute the static answer given by the mean wind speed. In this part of the problem we consider the concept of effective stiffness to represent the physical nonlinearity of material and a P-Delta method to represent the geometrical nonlinearity. Considering the final stiffness obtained in that P-Delta method, we compute the dynamic answer given by the floating wind speed, according to the discrete dynamic model given by NBR-6123-87. A 40 m RC telecommunication tower was analyzed, and the results obtained were compared with those given by linear static and dynamic models.
Observer-based robust control of one-sided Lipschitz nonlinear systems.
Ahmad, Sohaira; Rehan, Muhammad; Hong, Keum-Shik
2016-11-01
This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young's inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.
Constrained predictive control based on T-S fuzzy model for nonlinear systems
Institute of Scientific and Technical Information of China (English)
Su Baili; Chen Zengqiang; Yuan Zhuzhi
2007-01-01
A constrained generalized predictive control (GPC) algorithm based on the T-S fuzzy model is presented for the nonlinear system. First, a Takagi-Sugeno (T-S) fuzzy model based on the fuzzy cluster algorithm and the orthogonal least square method is constructed to approach the nonlinear system. Since its consequence is linear, it can divide the nonlinear system into a number of linear or nearly linear subsystems. For this T-S fuzzy model, a GPC algorithm with input constraints is presented.This strategy takes into account all the constraints of the control signal and its increment, and does not require the calculation of the Diophantine equations. So it needs only a small computer memory and the computational speed is high. The simulation results show a good performance for the nonlinear systems.
Kernel Based Nonlinear Dimensionality Reduction and Classification for Genomic Microarray
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Lan Shu
2008-07-01
Full Text Available Genomic microarrays are powerful research tools in bioinformatics and modern medicinal research because they enable massively-parallel assays and simultaneous monitoring of thousands of gene expression of biological samples. However, a simple microarray experiment often leads to very high-dimensional data and a huge amount of information, the vast amount of data challenges researchers into extracting the important features and reducing the high dimensionality. In this paper, a nonlinear dimensionality reduction kernel method based locally linear embedding(LLE is proposed, and fuzzy K-nearest neighbors algorithm which denoises datasets will be introduced as a replacement to the classical LLEÃ¢Â€Â™s KNN algorithm. In addition, kernel method based support vector machine (SVM will be used to classify genomic microarray data sets in this paper. We demonstrate the application of the techniques to two published DNA microarray data sets. The experimental results confirm the superiority and high success rates of the presented method.
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Tudor Barbu
2014-06-01
Full Text Available A nonlinear diffusion based image denoising technique is introduced in this paper. The proposed PDE denoising and restoration scheme is based on a novel diffusivity function that uses an automatically detected conductance parameter. A robust mathematical treatment is also provided for our anisotropic diffusion model. We demonstrate that edge-stopping function model is properly chosen, explaining the mathematical reasons behind it. Also, we perform a rigorous mathematical investigation on of the existence and uniqueness of the solution of our nonlinear diffusion equation. This PDE-based noise removal approach outperforms most diffusion-based methods, producing considerably better smoothing results and providing a much better edge preservation.
Implementation of neural network based non-linear predictive control
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1999-01-01
of non-linear systems. GPC is model based and in this paper we propose the use of a neural network for the modeling of the system. Based on the neural network model, a controller with extended control horizon is developed and the implementation issues are discussed, with particular emphasis...
Jing, Xingjian
2015-01-01
This book is a systematic summary of some new advances in the area of nonlinear analysis and design in the frequency domain, focusing on the application oriented theory and methods based on the GFRF concept, which is mainly done by the author in the past 8 years. The main results are formulated uniformly with a parametric characteristic approach, which provides a convenient and novel insight into nonlinear influence on system output response in terms of characteristic parameters and thus facilitate nonlinear analysis and design in the frequency domain. The book starts with a brief introduction to the background of nonlinear analysis in the frequency domain, followed by recursive algorithms for computation of GFRFs for different parametric models, and nonlinear output frequency properties. Thereafter the parametric characteristic analysis method is introduced, which leads to the new understanding and formulation of the GFRFs, and nonlinear characteristic output spectrum (nCOS) and the nCOS based analysis a...
Parallel algorithm of trigonometric collocation method in nonlinear dynamics of rotors
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Musil T.
2007-11-01
Full Text Available A parallel algorithm of a numeric procedure based on a method of trigonometric collocation is presented for investigating an unbalance response of a rotor supported by journal bearings. After a condensation process the trigonometric collocation method results in a set of nonlinear algebraic equations which is solved by the Newton-Raphson method. The order of the set is proportional to the number of nonlinear bearing coordinates and terms of the finite Fourier series. The algorithm, realized in the MATLAB parallel computing environment (DCT/DCE, uses message passing technique for interacting among processes on nodes of a parallel computer. This technique enables portability of the source code both on parallel computers with distributed and shared memory. Tests, made on a Beowulf cluster and a symmetric multiprocessor, have revealed very good speed-up and scalability of this algorithm.
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S. S. Motsa
2014-01-01
Full Text Available This paper presents a new application of the homotopy analysis method (HAM for solving evolution equations described in terms of nonlinear partial differential equations (PDEs. The new approach, termed bivariate spectral homotopy analysis method (BISHAM, is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. The applicability of the new approach has been demonstrated by application on several examples of nonlinear evolution PDEs, namely, Fisher’s, Burgers-Fisher’s, Burger-Huxley’s, and Fitzhugh-Nagumo’s equations. Comparison with known exact results from literature has been used to confirm accuracy and effectiveness of the proposed method.
STUDY ON PREDICTION METHODS FOR DYNAMIC SYSTEMS OF NONLINEAR CHAOTIC TIME SERIES
Institute of Scientific and Technical Information of China (English)
马军海; 陈予恕; 辛宝贵
2004-01-01
The prediction methods for nonlinear dynamic systems which are decided by chaotic time series are mainly studied as well as structures of nonlinear self-related chaotic models and their dimensions.By combining neural networks and wavelet theories,the structures of wavelet transform neural networks were studied and also a wavelet neural networks learning method was given.Based on wavelet networks,a new method for parameter identification was suggested,which can be used selectively to extract different scales of frequency and time in time series in order to realize prediction of tendencies or details of original time series.Through pre-treatment and comparison of results before and after the treatment,several useful conclusions are reached:High accurate identification can be guaranteed by applying wavelet networks to identify parameters of self-related chaotic models and more valid prediction of the chaotic time series including noise can be achieved accordingly.
Color image encryption based on Coupled Nonlinear Chaotic Map
Energy Technology Data Exchange (ETDEWEB)
Mazloom, Sahar [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: sahar.mazloom@gmail.com; Eftekhari-Moghadam, Amir Masud [Faculty of Electrical, Computer and IT Engineering, Qazvin Islamic Azad University, Qazvin (Iran, Islamic Republic of)], E-mail: eftekhari@qazviniau.ac.ir
2009-11-15
Image encryption is somehow different from text encryption due to some inherent features of image such as bulk data capacity and high correlation among pixels, which are generally difficult to handle by conventional methods. The desirable cryptographic properties of the chaotic maps such as sensitivity to initial conditions and random-like behavior have attracted the attention of cryptographers to develop new encryption algorithms. Therefore, recent researches of image encryption algorithms have been increasingly based on chaotic systems, though the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. This paper proposes a Coupled Nonlinear Chaotic Map, called CNCM, and a novel chaos-based image encryption algorithm to encrypt color images by using CNCM. The chaotic cryptography technique which used in this paper is a symmetric key cryptography with a stream cipher structure. In order to increase the security of the proposed algorithm, 240 bit-long secret key is used to generate the initial conditions and parameters of the chaotic map by making some algebraic transformations to the key. These transformations as well as the nonlinearity and coupling structure of the CNCM have enhanced the cryptosystem security. For getting higher security and higher complexity, the current paper employs the image size and color components to cryptosystem, thereby significantly increasing the resistance to known/chosen-plaintext attacks. The results of several experimental, statistical analysis and key sensitivity tests show that the proposed image encryption scheme provides an efficient and secure way for real-time image encryption and transmission.
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
A method for regulating strong nonlinear vibration energy of the flexible arm
Yushu Bian; Ming Wang; Zhihui Gao; Baofeng Yuan; Ming Fan
2015-01-01
For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration ab...
A hybrid nonlinear programming method for design optimization
Rajan, S. D.
1986-01-01
Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.
Dynamic properties of the cubic nonlinear Schr(o)dinger equation by symplectic method
Institute of Scientific and Technical Information of China (English)
Liu Xue-Shen; Wei Jia-Yu; Ding Pei-Zhu
2005-01-01
The dynamic properties of a cubic nonlinear Schrodinger equation are investigated numerically by using the symplectic method with different space approximations. The behaviours of the cubic nonlinear Schrodinger equation are discussed with different cubic nonlinear parameters in the harmonically modulated initial condition. We show that the conserved quantities will be preserved for long-time computation but the system will exhibit different dynamic behaviours in space difference approximation for the strong cubic nonlinearity.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
Femtosecond Fiber Lasers Based on Dissipative Processes for Nonlinear Microscopy
Wise, Frank W.
2012-01-01
Recent progress in the development of femtosecond-pulse fiber lasers with parameters appropriate for nonlinear microscopy is reviewed. Pulse-shaping in lasers with only normal-dispersion components is briefly described, and the performance of the resulting lasers is summarized. Fiber lasers based on the formation of dissipative solitons now offer performance competitive with that of solid-state lasers, but with the benefits of the fiber medium. Lasers based on self-similar pulse evolution in the gain section of a laser also offer a combination of short pulse duration and high pulse energy that will be attractive for applications in nonlinear bioimaging. PMID:23869163
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
Pulse-Shaping-Based Nonlinear Microscopy: Development and Applications
Flynn, Daniel Christopher
The combination of optical microscopy and ultrafast spectroscopy make the spatial characterization of chemical kinetics on the femtosecond time scale possible. Commercially available octave-spanning Ti:Sapphire oscillators with sub-8 fs pulse durations can drive a multitude of nonlinear transitions across a significant portion of the visible spectrum with minimal average power. Unfortunately, dispersion from microscope objectives broadens pulse durations, decreases temporal resolution and lowers the peak intensities required for driving nonlinear transitions. In this dissertation, pulse shaping is used to compress laser pulses after the microscope objective. By using a binary genetic algorithm, pulse-shapes are designed to enable selective two-photon excitation. The pulse-shapes are demonstrated in two-photon fluorescence of live COS-7 cells expressing GFP-variants mAmetrine and tdTomato. The pulse-shaping approach is applied to a new multiphoton fluorescence resonance energy transfer (FRET) stoichiometry method that quantifies donor and acceptor molecules in complex, as well as the ratio of total donor to acceptor molecules. Compared to conventional multi-photon imaging techniques that require laser tuning or multiple laser systems to selectively excite individual fluorophores, the pulse-shaping approach offers rapid selective multifluorphore imaging at biologically relevant time scales. By splitting the laser beam into two beams and building a second pulse shaper, a pulse-shaping-based pump-probe microscope is developed. The technique offers multiple imaging modalities, such as excited state absorption (ESA), ground state bleach (GSB), and stimulated emission (SE), enhancing contrast of structures via their unique quantum pathways without the addition of contrast agents. Pulse-shaping based pump-probe microscopy is demonstrated for endogenous chemical-contrast imaging of red blood cells. In the second section of this dissertation, ultrafast spectroscopic
K-Profiles: A Nonlinear Clustering Method for Pattern Detection in High Dimensional Data
Directory of Open Access Journals (Sweden)
Kai Wang
2015-01-01
Full Text Available With modern technologies such as microarray, deep sequencing, and liquid chromatography-mass spectrometry (LC-MS, it is possible to measure the expression levels of thousands of genes/proteins simultaneously to unravel important biological processes. A very first step towards elucidating hidden patterns and understanding the massive data is the application of clustering techniques. Nonlinear relations, which were mostly unutilized in contrast to linear correlations, are prevalent in high-throughput data. In many cases, nonlinear relations can model the biological relationship more precisely and reflect critical patterns in the biological systems. Using the general dependency measure, Distance Based on Conditional Ordered List (DCOL that we introduced before, we designed the nonlinear K-profiles clustering method, which can be seen as the nonlinear counterpart of the K-means clustering algorithm. The method has a built-in statistical testing procedure that ensures genes not belonging to any cluster do not impact the estimation of cluster profiles. Results from extensive simulation studies showed that K-profiles clustering not only outperformed traditional linear K-means algorithm, but also presented significantly better performance over our previous General Dependency Hierarchical Clustering (GDHC algorithm. We further analyzed a gene expression dataset, on which K-profile clustering generated biologically meaningful results.
Ondra, V.; Sever, I. A.; Schwingshackl, C. W.
2017-01-01
This paper presents a method for detection and characterisation of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and artificial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on different numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterising non-linear behaviour from a single frequency response function.
Dynamic neural network-based robust observers for uncertain nonlinear systems.
Dinh, H T; Kamalapurkar, R; Bhasin, S; Dixon, W E
2014-12-01
A dynamic neural network (DNN) based robust observer for uncertain nonlinear systems is developed. The observer structure consists of a DNN to estimate the system dynamics on-line, a dynamic filter to estimate the unmeasurable state and a sliding mode feedback term to account for modeling errors and exogenous disturbances. The observed states are proven to asymptotically converge to the system states of high-order uncertain nonlinear systems through Lyapunov-based analysis. Simulations and experiments on a two-link robot manipulator are performed to show the effectiveness of the proposed method in comparison to several other state estimation methods.
The Fourier decomposition method for nonlinear and non-stationary time series analysis.
Singh, Pushpendra; Joshi, Shiv Dutt; Patney, Rakesh Kumar; Saha, Kaushik
2017-03-01
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of 'Fourier intrinsic band functions' (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time-frequency-energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
Demonstration of a Chip-based Nonlinear Optical Isolator
Hua, Shiyue; Jiang, Xiaoshun; Hua, Qian; Jiang, Liang; Xiao, Min
2016-01-01
Despite fundamentally challenging in integrated (nano)photonics, achieving chip-based light nonreciprocity becomes increasingly urgent in signal processing and optical communications. Because of material incompatibilities in conventional approaches based on Faraday effects, alternative solutions have resorted to nonlinear processes to obtain one-way transmission. However, revealed dynamic reciprocity in a recent theoretical analysis has pinned down the functionalities of these nonlinear isolators. To overcome this dynamic reciprocity, we here report the first demonstration of a nonlinear optical isolator on a silicon chip enforced by phase-matched parametric amplification. Using a high-Q microtoroid resonator, we realize highly nonreciprocal transport at the 1,550 nm wavelength when waves are simultaneously launched in both forward and backward directions. Our design, compatible with current CMOS technique, yields convincing isolation performance with sufficiently low insertion loss for a wide range of input ...
Directory of Open Access Journals (Sweden)
Haitao Che
2011-01-01
Full Text Available We investigate a H1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based on H1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.
Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter
Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling
2017-07-01
The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.
Fatigue Life Prediction of Metallic Materials Based on the Combined Nonlinear Ultrasonic Parameter
Zhang, Yuhua; Li, Xinxin; Wu, Zhenyong; Huang, Zhenfeng; Mao, Hanling
2017-08-01
The fatigue life prediction of metallic materials is always a tough problem that needs to be solved in the mechanical engineering field because it is very important for the secure service of mechanical components. In this paper, a combined nonlinear ultrasonic parameter based on the collinear wave mixing technique is applied for fatigue life prediction of a metallic material. Sweep experiments are first conducted to explore the influence of driving frequency on the interaction of two driving signals and the fatigue damage of specimens, and the amplitudes of sidebands at the difference frequency and sum frequency are tracked when the driving frequency changes. Then, collinear wave mixing tests are carried out on a pair of cylindrically notched specimens with different fatigue damage to explore the relationship between the fatigue damage and the relative nonlinear parameters. The experimental results show when the fatigue degree is below 65% the relative nonlinear parameter increases quickly, and the growth rate is approximately 130%. If the fatigue degree is above 65%, the increase in the relative nonlinear parameter is slow, which has a close relationship with the microstructure evolution of specimens. A combined nonlinear ultrasonic parameter is proposed to highlight the relationship of the relative nonlinear parameter and fatigue degree of specimens; the fatigue life prediction model is built based on the relationship, and the prediction error is below 3%, which is below the prediction error based on the relative nonlinear parameters at the difference and sum frequencies. Therefore, the combined nonlinear ultrasonic parameter using the collinear wave mixing method can effectively estimate the fatigue degree of specimens, which provides a fast and convenient method for fatigue life prediction.
A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS
Institute of Scientific and Technical Information of China (English)
Xiong Yuanbo; Long Shuyao; Hu De'an; Li Guangyao
2005-01-01
Nonlinear formulations of the meshless local Petrov-Galerkin (MLPG) method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation are imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.
A Non-smooth Nonlinear Conjugate Gradient Method for Interactive Contact Force Problems
DEFF Research Database (Denmark)
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2010-01-01
of a nonlinear complementarity problem (NCP), which can be solved using an iterative splitting method, such as the projected Gauss–Seidel (PGS) method. We present a novel method for solving the NCP problem by applying a Fletcher–Reeves type nonlinear nonsmooth conjugate gradient (NNCG) type method. We analyze...
Energy Technology Data Exchange (ETDEWEB)
Zhao Xiqiang [Department of Mathematics, Ocean University of China, Qingdao Shandong 266071 (China)] e-mail: zhaodss@yahoo.com.cn; Wang Limin [Shandong University of Technology, Zibo Shandong 255049 (China); Sun Weijun [Shandong University of Technology, Zibo Shandong 255049 (China)
2006-04-01
In this letter, a new method, called the repeated homogeneous balance method, is proposed for seeking the traveling wave solutions of nonlinear partial differential equations. The Burgers-KdV equation is chosen to illustrate our method. It has been confirmed that more traveling wave solutions of nonlinear partial differential equations can be effectively obtained by using the repeated homogeneous balance method.
Wang, Zhe; Li, Lizhi; Ni, Weidou; Li, Zheng
2011-01-01
A multivariate dominant factor based non-linearized PLS model is proposed. The intensities of different lines were taken to construct a multivariate dominant factor model, which describes the dominant concentration information of the measured species. In constructing such a multivariate model, non-linear transformation of multi characteristic line intensities according to the physical mechanisms of lased induced plasma spectrum were made, combined with linear-correlation-based PLS method, to model the nonlinear self-absorption and inter-element interference effects. This enables the linear PLS method to describe non-linear relationship more accurately and provides the statistics-based PLS method with physical backgrounds. Moreover, a secondary PLS is applied utilizing the whole spectra information to further correct the model results. Experiments were conducted using standard brass samples. Taylor expansion was applied to make the nonlinear transformation to describe the self-absorption effect of Cu. Then, li...
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of nonlinear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest that the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an efficient tool to investigate the nonlinear problems.
Cigeroglu, Ender; Samandari, Hamed
2014-11-01
Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.
Institute of Scientific and Technical Information of China (English)
钟伟民; 何国龙; 皮道映; 孙优贤
2005-01-01
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection.
H∞ consensus and synchronization of nonlinear systems based on a novel fuzzy model.
Zhao, Yan; Li, Bing; Qin, Jiahu; Gao, Huijun; Karimi, Hamid Reza
2013-12-01
This paper investigates the H∞ consensus control problem of nonlinear multiagent systems under an arbitrary topological structure. A novel Takagi-Sukeno (T-S) fuzzy modeling method is proposed to describe the problem of nonlinear follower agents approaching a time-varying leader, i.e., the error dynamics between the follower agents and the leader, whose dynamics is evolving according to an isolated unforced nonlinear agent model, is described as a set of T-S fuzzy models. Based on the model, a leader-following consensus algorithm is designed so that, under an arbitrary network topology, all the follower agents reach consensus with the leader subject to external disturbances, preserving a guaranteed H(∞) performance level. In addition, we obtain a sufficient condition for choosing the pinned nodes to make the entire multiagent network reach consensus. Moreover, the fuzzy modeling method is extended to solve the synchronization problem of nonlinear systems, and a fuzzy H(∞) controller is designed so that two nonlinear systems reach synchronization with a prescribed H(∞) performance level. The controller design procedure is greatly simplified by utilization of the proposed fuzzy modeling method. Finally, numerical simulations on chaotic systems and arbitrary nonlinear functions are provided to illustrate the effectiveness of the obtained theoretical results.
Study of Super-Twisting sliding mode control for U model based nonlinear system
Directory of Open Access Journals (Sweden)
Jianhua ZHANG
2016-08-01
Full Text Available The Super-Twisting control algorithm is adopted to analyze the U model based nonlinear control system in order to solve the controller design problems of non-affine nonlinear systems. The non-affine nonlinear systems are studied, the neural network approximation of the nonlinear function is performed, and the Super-Twisting control algorithm is used to control. The convergence of the Super-Twisting algorithm is proved by selecting an appropriate Lyapunov function. The Matlab simulation is carried out to verify the feasibility and effectiveness of the described method. The result shows that the output of the controlled system can be tracked in a very short time by using the designed Super-Twisting controller, and the robustness of the controlled system is significantly improved as well.
Data-based identification and control of nonlinear systems via piecewise affine approximation.
Lai, Chow Yin; Xiang, Cheng; Lee, Tong Heng
2011-12-01
The piecewise affine (PWA) model represents an attractive model structure for approximating nonlinear systems. In this paper, a procedure for obtaining the PWA autoregressive exogenous (ARX) (autoregressive systems with exogenous inputs) models of nonlinear systems is proposed. Two key parameters defining a PWARX model, namely, the parameters of locally affine subsystems and the partition of the regressor space, are estimated, the former through a least-squares-based identification method using multiple models, and the latter using standard procedures such as neural network classifier or support vector machine classifier. Having obtained the PWARX model of the nonlinear system, a controller is then derived to control the system for reference tracking. Both simulation and experimental studies show that the proposed algorithm can indeed provide accurate PWA approximation of nonlinear systems, and the designed controller provides good tracking performance.
NONLINEAR OPTICAL MOLECULAR CRYSTAL BASED ON 2,6-DIAMINOPYRIDINE: SYNTHESIS AND CHARACTERIZATION
Directory of Open Access Journals (Sweden)
I. M. Pavlovetc
2014-05-01
Full Text Available The paper deals with investigation of a new nonlinear optical material based on nonlinear optical chromophore (4-Nitrophenol and aminopyridine (2,6-Diaminopyridine. Calculation results are presented for molecular packing in the crystalline compound, based on the given components. According to these results the finite material must have a noncentrosymmetric lattice, which determines the presence of the second order nonlinear optical response. Investigations carried out in this work confirm these calculations. Results of experiments are given describing the co-crystallization of these components and the following re-crystallization of the obtained material. In order to get a monocrystal form, the optimal conditions for the synthesis of molecular crystals based on these components are determined. Sufficiently large homogeneous crystals are obtained, that gave the possibility to record their spectra in the visible and near infrared parts of the spectrum, to determine their nonlinear optical properties and the level of homogeneity. Their optical (optical transmission and optical laser damage threshold and nonlinear optical properties are presented. For observation and measurement of the nonlinear optical properties an installation was built which implements the comparative method for measurements of nonlinear optical properties. A potassium titanyl oxide phosphate crystal was used as a sample for comparison. Results are given for the conversion efficiency of the primary laser radiation in the second optical harmonic relative to the signal obtained on the potassium titanyl oxide phosphate crystal. Obtained results show that the molecular co-crystal based on 2,6-Diaminopyridine is a promising nonlinear optical material for generating the second optical harmonic on the Nd: YAG laser (532 nm.
Directory of Open Access Journals (Sweden)
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing
Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng
2017-05-01
Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.
Analysis and Design Methods for Nonlinear Control Systems
1990-03-01
entitled "Design of Nonlinear PID Controllers ." In this paper it is demonstrated that the extended linearization approach can be applied to standard...Sciences and Systems, Baltimore, Maryland, pp. 675-680, 1987. [3] WJ. Rugh, "Design of Nonlinear PID Controllers ," AIChE Journa Vol. 33, No. 10, pp. 1738
Zia, Haider
2017-06-01
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a notable example being the generalized derivative non-linear Schrödinger equation that arises in non-linear optics with self-steepening terms. These differential equations feature terms that were previously inaccessible to model accurately with low computational resources. The new method maintains a 3rd order error even with these additional terms and models the equation in all three spatial dimensions and time. The class of non-linear differential equations that this method applies to is shown. The method is fully derived and implementation of the method in the split-step architecture is shown. This paper lays the mathematical ground work for an upcoming paper employing this method in white-light generation simulations in bulk material.
Schroeter, Jens; Wunsch, Carl
1986-01-01
The paper studies with finite difference nonlinear circulation models the uncertainties in interesting flow properties, such as western boundary current transport, potential and kinetic energy, owing to the uncertainty in the driving surface boundary condition. The procedure is based upon nonlinear optimization methods. The same calculations permit quantitative study of the importance of new information as a function of type, region of measurement and accuracy, providing a method to study various observing strategies. Uncertainty in a model parameter, the bottom friction coefficient, is studied in conjunction with uncertain measurements. The model is free to adjust the bottom friction coefficient such that an objective function is minimized while fitting a set of data to within prescribed bounds. The relative importance of the accuracy of the knowledge about the friction coefficient with respect to various kinds of observations is then quantified, and the possible range of the friction coefficients is calculated.
Analysis of efficient preconditioned defect correction methods for nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2014-01-01
prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow......Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... models. Our study is particularly relevant for fast and efficient simulation of non-breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization...
An operator expansion method for computing nonlinear surface waves on a ferrofluid jet
Guyenne, Philippe; Părău, Emilian I.
2016-09-01
We present a new numerical method to simulate the time evolution of axisymmetric nonlinear waves on the surface of a ferrofluid jet. It is based on the reduction of this problem to a lower-dimensional computation involving surface variables alone. To do so, we describe the associated Dirichlet-Neumann operator in terms of a Taylor series expansion where each term can be efficiently computed by a pseudo-spectral scheme using the fast Fourier transform. We show detailed numerical tests on the convergence of this operator and, to illustrate the performance of our method, we simulate the long-time propagation and pairwise collisions of axisymmetric solitary waves. Both depression and elevation waves are examined by varying the magnetic field. Comparisons with weakly nonlinear predictions are also provided.
A method for regulating strong nonlinear vibration energy of the flexible arm
Directory of Open Access Journals (Sweden)
Yushu Bian
2015-07-01
Full Text Available For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration absorber. Through examples and analyses, it is verified that this control method is effective in regulating strong vibration energy and can be used to suppress strong nonlinear vibration of the flexible arm undergoing rigid motion.
Energy Technology Data Exchange (ETDEWEB)
Potemki, Valeri G. [Moscow State Engineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Automatics and Electronics; Borisevich, Valentine D.; Yupatov, Sergei V. [Moscow State Enineering Physics Institute (Technical University), Moscow (Russian Federation). Dept. of Technical Physics
1996-12-31
This paper describes the the next evolution step in development of the direct method for solving systems of Nonlinear Algebraic Equations (SNAE). These equations arise from the finite difference approximation of original nonlinear partial differential equations (PDE). This method has been extended on the SNAE with three variables. The solving SNAE bases on Reiterating General Singular Value Decomposition of rectangular matrix pencils (RGSVD-algorithm). In contrast to the computer algebra algorithm in integer arithmetic based on the reduction to the Groebner`s basis that algorithm is working in floating point arithmetic and realizes the reduction to the Kronecker`s form. The possibilities of the method are illustrated on the example of solving the one-dimensional diffusion equation for 3-component model isotope mixture in a ga centrifuge. The implicit scheme for the finite difference equations without simplifying the nonlinear properties of the original equations is realized. The technique offered provides convergence to the solution for the single run. The Toolbox SNAE is developed in the framework of the high performance numeric computation and visualization software MATLAB. It includes more than 30 modules in MATLAB language for solving SNAE with two and three variables. (author) 7 refs., 10 figs.
Nonlinear ultrasonic measurements based on cross-correlation filtering techniques
Yee, Andrew; Stewart, Dylan; Bunget, Gheorghe; Kramer, Patrick; Farinholt, Kevin; Friedersdorf, Fritz; Pepi, Marc; Ghoshal, Anindya
2017-02-01
Cyclic loading of mechanical components promotes the formation of dislocation dipoles in metals, which can serve as precursors to crack nucleation and ultimately lead to failure. In the laboratory setting, an acoustic nonlinearity parameter has been assessed as an effective indicator for characterizing the progression of fatigue damage precursors. However, the need to use monochromatic waves of medium-to-high acoustic energy has presented a constraint, making it problematic for use in field applications. This paper presents a potential approach for field measurement of acoustic nonlinearity by using general purpose ultrasonic pulser-receivers. Nonlinear ultrasonic measurements during fatigue testing were analyzed by the using contact and immersion pulse-through method. A novel cross-correlation filtering technique was developed to extract the fundamental and higher harmonic waves from the signals. As in the case of the classic harmonic generation, the nonlinearity parameters of the second and third harmonics indicate a strong correlation with fatigue cycles. Consideration was given to potential nonlinearities in the measurement system, and tests have confirmed that measured second harmonic signals exhibit a linear dependence on the input signal strength, further affirming the conclusion that this parameter relates to damage precursor formation from cyclic loading.
Photoconductive and nonlinear optical properties of composites based on metallophthalocyanines
Vannikov, A. V.; Grishina, A. D.; Gorbunova, Yu. G.; Tsivadze, A. Yu.
2015-08-01
The photoconductive, photorefractive and nonlinear optical properties of composites from polyvinylcarbazole or aromatic polyimide containing supramolecular ensembles of (tetra-15-crown-5) - phthalocyaninato gallium, indium, - phthalocyaninateacetato yttrium, - phthalocyaninato ruthenium with axially coordinated pyrazine molecules were investigated at 633, 1030 and 1064nmusing continuous and pulsed lasers. Supramolecular ensembles (SE) were prepared through dissolution of molecular metallophthalocyanines in tetrachloroethane (TCE) and subsequent treatment via three cycles of heating to 90∘C and slow cooling to room temperature. The zscan method in femtosecond and nanosecond regimeswas used for measuring nonlinear optical properties phthalocyaninato indium and yttrium in TCE solutions and polymer films. It was established that effect of heavy metallic atom is basic factor which determines the quantum yield, photorefractive amplification of laser object beam, dielectric susceptibility of third order and nonlinear optical properties of metallophthalocyanines.
Nonlinear system identification based on internal recurrent neural networks.
Puscasu, Gheorghe; Codres, Bogdan; Stancu, Alexandru; Murariu, Gabriel
2009-04-01
A novel approach for nonlinear complex system identification based on internal recurrent neural networks (IRNN) is proposed in this paper. The computational complexity of neural identification can be greatly reduced if the whole system is decomposed into several subsystems. This approach employs internal state estimation when no measurements coming from the sensors are available for the system states. A modified backpropagation algorithm is introduced in order to train the IRNN for nonlinear system identification. The performance of the proposed design approach is proven on a car simulator case study.
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...
Phased-array sources based on nonlinear metamaterial nanocavities.
Wolf, Omri; Campione, Salvatore; Benz, Alexander; Ravikumar, Arvind P; Liu, Sheng; Luk, Ting S; Kadlec, Emil A; Shaner, Eric A; Klem, John F; Sinclair, Michael B; Brener, Igal
2015-07-01
Coherent superposition of light from subwavelength sources is an attractive prospect for the manipulation of the direction, shape and polarization of optical beams. This phenomenon constitutes the basis of phased arrays, commonly used at microwave and radio frequencies. Here we propose a new concept for phased-array sources at infrared frequencies based on metamaterial nanocavities coupled to a highly nonlinear semiconductor heterostructure. Optical pumping of the nanocavity induces a localized, phase-locked, nonlinear resonant polarization that acts as a source feed for a higher-order resonance of the nanocavity. Varying the nanocavity design enables the production of beams with arbitrary shape and polarization. As an example, we demonstrate two second harmonic phased-array sources that perform two optical functions at the second harmonic wavelength (∼5 μm): a beam splitter and a polarizing beam splitter. Proper design of the nanocavity and nonlinear heterostructure will enable such phased arrays to span most of the infrared spectrum.
Nonlinear dynamics of nanoelectromechanical cantilevers based on nanowire piezoresistive detection
Directory of Open Access Journals (Sweden)
Baguet S.
2012-07-01
Full Text Available The nonlinear dynamics of in-plane nanoelectromechanical cantilevers based on silicon nanowire piezoresistive detection is investigated using a comprehensive analytical model that remains valid up to large displacements in the case of electrostatic actuation. This multiphysics model takes into account geometric, inertial and electrostatic nonlinearities as well as the fringing field effects which are significant for thin resonators. The bistability as well as multistability limits are considered in order to provide close-form expressions of the critical amplitudes. Third order nonlinearity cancellation is analytically inspected and set via an optimal DC drive voltage which permits the actuation of the NEMS beyond its critical amplitude. It may result on a large enhancement of the sensor performances by driving optimally the nanocantilever at very large amplitude, while suppressing the hysteresis.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
Controlling chaos based on an adaptive nonlinear compensator mechanism
Institute of Scientific and Technical Information of China (English)
Tian Ling-Ling; Li Dong-Hai; Sun Xian-Fang
2008-01-01
The control problems of chaotic systems are investigated in the presence of parametric uncertainty and persistent external disturbances based on nonlinear control theory.By using a designed nonlinear compensator mechanism,the system deterministic nonlinearity,parametric uncertainty and disturbance effect can be compensated effectively.The renowned chaotic Lorenz system subjected to parametric variations and external disturbances is studied as an illustrative example.From the Lyapunov stability theory,sufficient conditions for choosing control parameters to guarantee chaos control are derived.Several experiments are carried out,including parameter change experiments,set-point change experiments and disturbance experiments.Simulation results indicate that the chaotic motion can be regulated not only to steady states but also to any desired periodic orbits with great immunity to parametric variations and external disturbances.
Phase Structure of the Non-Linear σ-MODEL with Oscillator Representation Method
Mishchenko, Yuriy; Ji, Chueng-R.
2004-03-01
Non-Linear σ-model plays an important role in many areas of theoretical physics. Been initially uintended as a simple model for chiral symmetry breaking, this model exhibits such nontrivial effects as spontaneous symmetry breaking, asymptotic freedom and sometimes is considered as an effective field theory for QCD. Besides, non-linear σ-model can be related to the strong-coupling limit of O(N) ϕ4-theory, continuous limit of N-dim. system of quantum spins, fermion gas and many others and takes important place in undertanding of how symmetries are realized in quantum field theories. Because of this variety of connections, theoretical study of the critical properties of σ-model is interesting and important. Oscillator representation method is a theoretical tool for studying the phase structure of simple QFT models. It is formulated in the framework of the canonical quantization and is based on the view of the unitary non-equivalent representations as possible phases of a QFT model. Successfull application of the ORM to ϕ4 and ϕ6 theories in 1+1 and 2+1 dimensions motivates its study in more complicated models such as non-linear σ-model. In our talk we introduce ORM, establish its connections with variational approach in QFT. We then present results of ORM in non-linear σ-model and try to interprete them from the variational point of view. Finally, we point out possible directions for further research in this area.
ISS method for coordination control of nonlinear dynamical agents under directed topology.
Wang, Xiangke; Qin, Jiahu; Yu, Changbin
2014-10-01
The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.
Adhesive nonlinearity in Lamb-wave-based structural health monitoring systems
Shan, Shengbo; Cheng, Li; Li, Peng
2017-02-01
Structural health monitoring (SHM) techniques with nonlinear Lamb waves have gained wide popularity due to their high sensitivity to microstructural changes for the detection of damage precursors. Despite the significant progress made, various unavoidable nonlinear sources in a practical SHM system, as well as their impact on the detection, have not been fully assessed and understood. For the real-time and online monitoring, transducers are usually permanently bonded on the structure under inspection. In this case, the inherent material nonlinear properties of the bonding layer, referred to as adhesive nonlinearity (AN), may create undesired interference to the SHM system, or even jeopardize the damage diagnosis if they become serious. In this paper, a nonlinear theoretical framework is developed, covering the process of wave generation, propagation and sensing, with the aim of investigating the mechanism and characteristics of AN-induced Lamb waves in plates, which potentially allows for further system optimization to minimize the influence of AN. The model shows that an equivalent nonlinear normal stress is generated in the bonding layer due to its nonlinear material behavior, which, through its coupling with the system, is responsible for the generation of second harmonic Lamb waves in the plate, subsequently resulting in the nonlinear responses in the captured signals. With the aid of the finite element (FE) modeling and a superposition method for nonlinear feature extraction, the theoretical model is validated in terms of generation mechanism of the AN-induced wave components as well as their propagating characteristics. Meanwhile, the influence of the AN is evaluated by comparing the AN-induced nonlinear responses with those caused by the material nonlinearity of the plate, showing that AN should be considered as a non-negligible nonlinear source in a typical nonlinear Lamb-wave-based SHM system. In addition, the theoretical model is also experimentally
Observer Based Compensators for Nonlinear Systems
1989-03-31
coordinate change that achieves exact linearization could as well be calculated using the Hunt-Su linearization method. However, in our approach, we...the above, we obtain the exact linearization (implying that the development by the authors. system (52) satisfies the Hunt--Su condition): The multi
Application of homotopy-perturbation method to nonlinear population dynamics models
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, M.S.H. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia); Hashim, I. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)], E-mail: ishak_h@ukm.my; Abdulaziz, O. [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)
2007-08-20
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)
A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics
Energy Technology Data Exchange (ETDEWEB)
Jay R. Johnson; Simon Wing
2004-01-28
Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.
Directory of Open Access Journals (Sweden)
Sharifi Somayeh
2016-01-01
Full Text Available In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to 814≈1.682${8^{{\\textstyle{1 \\over 4}}}} \\approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including comparison with the existing methods. Moreover, the attraction basins of the proposed methods are shown with some comparisons to the other existing methods.
Implementation of a strain energy-based nonlinear finite element in the object-oriented environment
Wegner, Tadeusz; Pęczak, Andrzej
2010-03-01
The objective of the paper is to describe a novel finite element computational method based on a strain energy density function and to implement it in the object-oriented environment. The original energy-based finite element was put into the known standard framework of classes and handled in a different manner. The nonlinear properties of material are defined with a modified strain energy density function. The local relaxation procedure proposed as a method used to resolve a nonlinear problem is implemented in C++ language. The hexahedral element with eight nodes as well as the adaptation of the nonlinear finite element is introduced. The chosen numerical model is made of nearly incompressible hyperelastic material. The application of the proposed element is shown on the example of a rectangular parallelepiped with a hollow port.
Liu, Jingwei
2011-01-01
A function based nonlinear least squares estimation (FNLSE) method is proposed and investigated in parameter estimation of Jelinski-Moranda software reliability model. FNLSE extends the potential fitting functions of traditional least squares estimation (LSE), and takes the logarithm transformed nonlinear least squares estimation (LogLSE) as a special case. A novel power transformation function based nonlinear least squares estimation (powLSE) is proposed and applied to the parameter estimation of Jelinski-Moranda model. Solved with Newton-Raphson method, Both LogLSE and powLSE of Jelinski-Moranda models are applied to the mean time between failures (MTBF) predications on six standard software failure time data sets. The experimental results demonstrate the effectiveness of powLSE with optimal power index compared to the classical least--squares estimation (LSE), maximum likelihood estimation (MLE) and LogLSE in terms of recursively relative error (RE) index and Braun statistic index.
Wideband nonlinear time reversal seismo-acoustic method for landmine detection.
Sutin, Alexander; Libbey, Brad; Fillinger, Laurent; Sarvazyan, Armen
2009-04-01
Acoustic and seismic waves provide a method to localize compliant mines by vibrating the top plate and a thin soil layer above the mine. This vibration is mostly linear, but also includes a small nonlinear deviation. The main goal of this paper is to introduce a method of processing that uses phase-inversion to observe nonlinear effects in a wide frequency band. The method extracts a nonlinear part of surface velocity from two similar broadcast signals of opposite sign by summing and cancelling the linear components and leaving the nonlinear components. This phase-inversion method is combined with time reversal focusing to provide increased seismic vibration and enhance the nonlinear effect. The experiments used six loudspeakers in a wood box placed over sand in which inert landmines were buried. The nonlinear surface velocity of the sand with a mine compared to the sand without a mine was greater as compared to a linear technique.
Energy Technology Data Exchange (ETDEWEB)
Jin Chen
2009-12-07
Efficient and robust Variable Relaxation Solver, based on pseudo-transient continuation, is developed to solve nonlinear anisotropic thermal conduction arising from fusion plasma simulations. By adding first and/or second order artificial time derivatives to the system, this type of method advances the resulting time-dependent nonlinear PDEs to steady state, which is the solution to be sought. In this process, only the stiffness matrix itself is involved so that the numerical complexity and errors can be greatly reduced. In fact, this work is an extension of integrating efficient linear elliptic solvers for fusion simulation on Cray XIE. Two schemes are derived in this work, first and second order Variable Relaxations. Four factors are observed to be critical for efficiency and preservation of solution's symmetric structure arising from periodic boundary condition: refining meshes in different coordinate directions, initializing nonlinear process, varying time steps in both temporal and spatial directions, and accurately generating nonlinear stiffness matrix. First finer mesh scale should be taken in strong transport direction; Next the system is carefully initialized by the solution with linear conductivity; Third, time step and relaxation factor are vertex-based varied and optimized at each time step; Finally, the nonlinear stiffness matrix is updated by just scaling corresponding linear one with the vector generated from nonlinear thermal conductivity.
Nonlinear model predictive control with guaraneed stability based on pesudolinear neural networks
Institute of Scientific and Technical Information of China (English)
WANG Yongji; WANG Hong
2004-01-01
A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is investigated. The stability of the closed loop model predictive control system is analyzed based on Lyapunov theory to obtain the sufficient condition for the asymptotical stability of the neural predictive control system. A simulation was carried out for an exothermic first-order reaction in a continuous stirred tank reactor. It is demonstrated that the proposed control strategy is applicable to some of nonlinear systems.
Wang, Sijia; Peterson, Daniel J.; Gatenby, J. C.; Li, Wenbin; Grabowski, Thomas J.; Madhyastha, Tara M.
2017-01-01
Correction of echo planar imaging (EPI)-induced distortions (called “unwarping”) improves anatomical fidelity for diffusion magnetic resonance imaging (MRI) and functional imaging investigations. Commonly used unwarping methods require the acquisition of supplementary images during the scanning session. Alternatively, distortions can be corrected by nonlinear registration to a non-EPI acquired structural image. In this study, we compared reliability using two methods of unwarping: (1) nonlinear registration to a structural image using symmetric normalization (SyN) implemented in Advanced Normalization Tools (ANTs); and (2) unwarping using an acquired field map. We performed this comparison in two different test-retest data sets acquired at differing sites (N = 39 and N = 32). In both data sets, nonlinear registration provided higher test-retest reliability of the output fractional anisotropy (FA) maps than field map-based unwarping, even when accounting for the effect of interpolation on the smoothness of the images. In general, field map-based unwarping was preferable if and only if the field maps were acquired optimally.
Adaptive Predistortion Using Cubic Spline Nonlinearity Based Hammerstein Modeling
Wu, Xiaofang; Shi, Jianghong
In this paper, a new Hammerstein predistorter modeling for power amplifier (PA) linearization is proposed. The key feature of the model is that the cubic splines, instead of conventional high-order polynomials, are utilized as the static nonlinearities due to the fact that the splines are able to represent hard nonlinearities accurately and circumvent the numerical instability problem simultaneously. Furthermore, according to the amplifier's AM/AM and AM/PM characteristics, real-valued cubic spline functions are utilized to compensate the nonlinear distortion of the amplifier and the following finite impulse response (FIR) filters are utilized to eliminate the memory effects of the amplifier. In addition, the identification algorithm of the Hammerstein predistorter is discussed. The predistorter is implemented on the indirect learning architecture, and the separable nonlinear least squares (SNLS) Levenberg-Marquardt algorithm is adopted for the sake that the separation method reduces the dimension of the nonlinear search space and thus greatly simplifies the identification procedure. However, the convergence performance of the iterative SNLS algorithm is sensitive to the initial estimation. Therefore an effective normalization strategy is presented to solve this problem. Simulation experiments were carried out on a single-carrier WCDMA signal. Results show that compared to the conventional polynomial predistorters, the proposed Hammerstein predistorter has a higher linearization performance when the PA is near saturation and has a comparable linearization performance when the PA is mildly nonlinear. Furthermore, the proposed predistorter is numerically more stable in all input back-off cases. The results also demonstrate the validity of the convergence scheme.
Geometric methods for nonlinear many-body quantum systems
Lewin, Mathieu
2010-01-01
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\\'nski and G\\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and ...
Kireeva, Natalia V; Ovchinnikova, Svetlana I; Tetko, Igor V; Asiri, Abdullah M; Balakin, Konstantin V; Tsivadze, Aslan Yu
2014-05-01
Over the years, a number of dimensionality reduction techniques have been proposed and used in chemoinformatics to perform nonlinear mappings. In this study, four representatives of nonlinear dimensionality reduction methods related to two different families were analyzed: distance-based approaches (Isomap and Diffusion Maps) and topology-based approaches (Generative Topographic Mapping (GTM) and Laplacian Eigenmaps). The considered methods were applied for the visualization of three toxicity datasets by using four sets of descriptors. Two methods, GTM and Diffusion Maps, were identified as the best approaches, which thus made it impossible to prioritize a single family of the considered dimensionality reduction methods. The intrinsic dimensionality assessment of data was performed by using the Maximum Likelihood Estimation. It was observed that descriptor sets with a higher intrinsic dimensionality contributed maps of lower quality. A new statistical coefficient, which combines two previously known ones, was proposed to automatically rank the maps. Instead of relying on one of the best methods, we propose to automatically generate maps with different parameter values for different descriptor sets. By following this procedure, the maps with the highest values of the introduced statistical coefficient can be automatically selected and used as a starting point for visual inspection by the user.
On Newton-Like Methods for Solving Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we present a family of general Newton-like methods with a parametric function for finding a zero of a univariate function, permitting f′(x)=0 in some points. The case of multiple roots is not treated. The methods are proved to be quadratically convergent provided the weak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative methods with a variable parameter are developed.
Nonlinear vibrations of shallow shells with complex boundary: R-functions method and experiments
Kurpa, Lidia; Pilgun, Galina; Amabili, Marco
2007-10-01
Geometrically nonlinear vibrations of shallow circular cylindrical panels with complex shape of the boundary are considered. The R-functions theory and variational methods are used to study the problem. The R-functions method (RFM) allows constructing in analytical form the sequence of basis functions satisfying the given boundary conditions in case of complex shape of the boundary. The problem is reduced to a single second-order differential equation with quadratic and cubic nonlinear terms. The method developed has been initially applied to study free vibrations of shallow circular cylindrical panels with rectangular base for different boundary conditions: (i) clamped edges, (ii) in-plane immovable simply supported edges, (iii) classically simply supported edges, and (iv) in-plane free simply supported edges. Then, the same approach is applied to a shell with complex shape of the boundary. Experiments have been conducted on an aluminum panel with complex shape of the boundary in order to identify the nonlinear response of the fundamental mode; these experimental results have been compared to numerical results.
An improved method for nonlinear parameter estimation: a case study of the Rössler model
He, Wen-Ping; Wang, Liu; Jiang, Yun-Di; Wan, Shi-Quan
2016-08-01
Parameter estimation is an important research topic in nonlinear dynamics. Based on the evolutionary algorithm (EA), Wang et al. (2014) present a new scheme for nonlinear parameter estimation and numerical tests indicate that the estimation precision is satisfactory. However, the convergence rate of the EA is relatively slow when multiple unknown parameters in a multidimensional dynamical system are estimated simultaneously. To solve this problem, an improved method for parameter estimation of nonlinear dynamical equations is provided in the present paper. The main idea of the improved scheme is to use all of the known time series for all of the components in some dynamical equations to estimate the parameters in single component one by one, instead of estimating all of the parameters in all of the components simultaneously. Thus, we can estimate all of the parameters stage by stage. The performance of the improved method was tested using a classic chaotic system—Rössler model. The numerical tests show that the amended parameter estimation scheme can greatly improve the searching efficiency and that there is a significant increase in the convergence rate of the EA, particularly for multiparameter estimation in multidimensional dynamical equations. Moreover, the results indicate that the accuracy of parameter estimation and the CPU time consumed by the presented method have no obvious dependence on the sample size.
Scene matching based on non-linear pre-processing on reference image and sensed image
Institute of Scientific and Technical Information of China (English)
Zhong Sheng; Zhang Tianxu; Sang Nong
2005-01-01
To solve the heterogeneous image scene matching problem, a non-linear pre-processing method for the original images before intensity-based correlation is proposed. The result shows that the proper matching probability is raised greatly. Especially for the low S/N image pairs, the effect is more remarkable.
Nonlinear mode decomposition: A noise-robust, adaptive decomposition method
Iatsenko, Dmytro; McClintock, Peter V. E.; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool—nonlinear mode decomposition (NMD)—which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques—which, together with the adaptive choice of their parameters, make it extremely noise robust—and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
Nonlinear mode decomposition: a noise-robust, adaptive decomposition method.
Iatsenko, Dmytro; McClintock, Peter V E; Stefanovska, Aneta
2015-09-01
The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.
On the use of nonlinear regularization in inverse method for the tachocline profile determination
Corbard, T; Provost, J P; Blanc-Féraud, L
1998-01-01
Inversions of rotational splittings have shown that the surface layers and the so-called solar tachocline at the base of the convection zone are regions in which high radial gradients of the rotation rate occur. The usual regularization methods tend to smooth out every high gradients in the solution and may not be appropriate for the study of a zone like the tachocline. In this paper we use nonlinear regularization methods that are developed for edge-preserving regularization in computed imaging (e.g. Blanc-Féraud et al. 1995) and we apply them in the helioseismic context of rotational inversions.
LOCAL DISCONTINUOUS GALERKIN METHODS FOR THREE CLASSES OF NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Yan Xu; Chi-wang Shu
2004-01-01
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear K(n, n, n)equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions.The numerical experiments also include the compacton solutions of a generalized fifthorder KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear K(n, n, n) equations.
Directory of Open Access Journals (Sweden)
U. Filobello-Nino
2015-01-01
Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.
Nonlinear generalized source method for modeling second-harmonic generation in diffraction gratings
Weismann, Martin; Panoiu, Nicolae C
2015-01-01
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source method to nonlinear optical interactions by incorporating the contribution of nonlinear polarization sources to the diffracted field in the algorithm. We derive the mathematical formalism underlying the numerical method and introduce the Fourier-factorization suitable for nonlinear calculations. The numerical efficiency and runtime characteristics of the method are investigated in a set of benchmark calculations: the results corresponding to the fundamental frequency are compared to those obtained from a reference method and the beneficial effects of the modified Fourier-factorization rule on the accuracy of the nonlinear computations is demonstrated. In order to illustrate the capabilities of our method, we employ it to demonstrate strong enhancement of second-harmonic genera...
Directory of Open Access Journals (Sweden)
Md. Nur Alam
2016-06-01
Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.
Institute of Scientific and Technical Information of China (English)
Long Shuyao; Zhang Qin
2000-01-01
In this paper the dual reciprocity boundary element method is employed to solve nonlinear differential equation 2 u + u + εu3 = b. Results obtained in an example have a good agreement with those by FEM and show the applicability and simplicity of dual reciprocity method(DRM) in solving nonlinear dif ferential equations.
Variational iteration method for solving non-linear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Hemeda, A.A. [Department of Mathematics, Faculty of Science, University of Tanta, Tanta (Egypt)], E-mail: aahemeda@yahoo.com
2009-02-15
In this paper, we shall use the variational iteration method to solve some problems of non-linear partial differential equations (PDEs) such as the combined KdV-MKdV equation and Camassa-Holm equation. The variational iteration method is superior than the other non-linear methods, such as the perturbation methods where this method does not depend on small parameters, such that it can fined wide application in non-linear problems without linearization or small perturbation. In this method, the problems are initially approximated with possible unknowns, then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory.
Kannan, Rohit; Tangirala, Arun K.
2014-06-01
Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.
A nonlinear regression model-based predictive control algorithm.
Dubay, R; Abu-Ayyad, M; Hernandez, J M
2009-04-01
This paper presents a unique approach for designing a nonlinear regression model-based predictive controller (NRPC) for single-input-single-output (SISO) and multi-input-multi-output (MIMO) processes that are common in industrial applications. The innovation of this strategy is that the controller structure allows nonlinear open-loop modeling to be conducted while closed-loop control is executed every sampling instant. Consequently, the system matrix is regenerated every sampling instant using a continuous function providing a more accurate prediction of the plant. Computer simulations are carried out on nonlinear plants, demonstrating that the new approach is easily implemented and provides tight control. Also, the proposed algorithm is implemented on two real time SISO applications; a DC motor, a plastic injection molding machine and a nonlinear MIMO thermal system comprising three temperature zones to be controlled with interacting effects. The experimental closed-loop responses of the proposed algorithm were compared to a multi-model dynamic matrix controller (MPC) with improved results for various set point trajectories. Good disturbance rejection was attained, resulting in improved tracking of multi-set point profiles in comparison to multi-model MPC.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A novel nonlinear combination process monitoring method was proposed based on techniques with memory effect (multivariate exponentially weighted moving average (MEWMA)) and kernel independent component analysis (KICA). The method was developed for dealing with nonlinear issues and detecting small or moderate drifts in one or more process variables with autocorrelation. MEWMA charts use additional information from the past history of the process for keeping the memory effect of the process behavior trend. KICA is a recently developed statistical technique for revealing hidden, nonlinear statistically independent factors that underlie sets of measurements and it is a two-phase algorithm: whitened kernel principal component analysis (KPCA) plus independent component analysis (ICA). The application to the fluid catalytic cracking unit (FCCU) simulated process indicates that the proposed combined method based on MEWMA and KICA can effectively capture the nonlinear relationship and detect small drifts in process variables. Its performance significantly outperforms monitoring method based on ICA, MEWMA-ICA and KICA, especially for long-term performance deterioration.
Kanjilal, Oindrila; Manohar, C. S.
2017-07-01
The study considers the problem of simulation based time variant reliability analysis of nonlinear randomly excited dynamical systems. Attention is focused on importance sampling strategies based on the application of Girsanov's transformation method. Controls which minimize the distance function, as in the first order reliability method (FORM), are shown to minimize a bound on the sampling variance of the estimator for the probability of failure. Two schemes based on the application of calculus of variations for selecting control signals are proposed: the first obtains the control force as the solution of a two-point nonlinear boundary value problem, and, the second explores the application of the Volterra series in characterizing the controls. The relative merits of these schemes, vis-à-vis the method based on ideas from the FORM, are discussed. Illustrative examples, involving archetypal single degree of freedom (dof) nonlinear oscillators, and a multi-degree of freedom nonlinear dynamical system, are presented. The credentials of the proposed procedures are established by comparing the solutions with pertinent results from direct Monte Carlo simulations.
Conformal structure-preserving method for damped nonlinear Schrödinger equation
Fu, Hao; Zhou, Wei-En; Qian, Xu; Song, Song-He; Zhang, Li-Ying
2016-11-01
In this paper, we propose a conformal momentum-preserving method to solve a damped nonlinear Schrödinger (DNLS) equation. Based on its damped multi-symplectic formulation, the DNLS system can be split into a Hamiltonian part and a dissipative part. For the Hamiltonian part, the average vector field (AVF) method and implicit midpoint method are employed in spatial and temporal discretizations, respectively. For the dissipative part, we can solve it exactly. The proposed method conserves the conformal momentum conservation law in any local time-space region. With periodic boundary conditions, this method also preserves the total conformal momentum and the dissipation rate of momentum exactly. Numerical experiments are presented to demonstrate the conservative properties of the proposed method. Project supported by the National Natural Science Foundation of China (Grant Nos. 11571366, 11501570, and 11601514) and the Open Foundation of State Key Laboratory of High Performance Computing of China (Grant No. JC15-02-02).
Adaptive sampling for nonlinear dimensionality reduction based on manifold learning
DEFF Research Database (Denmark)
Franz, Thomas; Zimmermann, Ralf; Goertz, Stefan
2017-01-01
We make use of the non-intrusive dimensionality reduction method Isomap in order to emulate nonlinear parametric flow problems that are governed by the Reynolds-averaged Navier-Stokes equations. Isomap is a manifold learning approach that provides a low-dimensional embedding space...... that is approximately isometric to the manifold that is assumed to be formed by the high-fidelity Navier-Stokes flow solutions under smooth variations of the inflow conditions. The focus of the work at hand is the adaptive construction and refinement of the Isomap emulator: We exploit the non-Euclidean Isomap metric...... to detect and fill up gaps in the sampling in the embedding space. The performance of the proposed manifold filling method will be illustrated by numerical experiments, where we consider nonlinear parameter-dependent steady-state Navier-Stokes flows in the transonic regime....
Institute of Scientific and Technical Information of China (English)
Wang Jun-Song; Yuan Jing; Li Qiang; Yuan Rui-Xi
2011-01-01
This paper uses a correlation dimension based nonlinear analysis approach to analyse the dynamics of network traffics with three different application protocols-HTTP, FTP and SMTP. First, the phase space is reconstructed and the embedding parameters are obtained by the mutual information method. Secondly, the correlation dimensions of three different traffics are calculated and the results of analysis have demonstrated that the dynamics of the three different application protocol traffics is different from each other in nature, i.e. HTTP and FTP traffics are chaotic,furthermore, the former is more complex than the later; on the other hand, SMTP traffic is stochastic. It is shown that correlation dimension approach is an efficient method to understand and to characterize the nonlinear dynamics of HTTP, FTP and SMTP protocol network traffics. This analysis provided insight into and a more accurate understanding of nonlinear dynamics of internet traffics which have a complex mixture of chaotic and stochastic components.
A SIMPLIFIED CALCULATING METHOD OF NONLINEAR FREQUENCY OF CABLE NET UNDER MEAN WIND LOAD
Institute of Scientific and Technical Information of China (English)
Feng Ruoqiang; Wu Yue; Shen Shizhao
2006-01-01
The cable net supported glass curtain wallas the most advanced technique in dot point supported glass curtain wall, is widely used in China. Because of its large deflection and high nonlinearity under wind load, the dynamic performance of the cable net is greatly different from that of the conventional linear structures. The continuous membrane theory is used to construct the nonlinear vibration differential equation of the cable net, and the harmonic balance method is used to solve the analytic formula of the nonlinear frequency. In order to verify the accuracy of the above analytic formula, the results of the formula and the nonlinear FEM time-history method are compared and found to be in good agreement. Furthermore, the nonlinear vibration differential equation and the nonlinear frequency obtained in this paper are the basis for the wind-induced response analysis of a cable net under fluctuating wind load.
Concrete damage diagnosed using the non-classical nonlinear acoustic method
Institute of Scientific and Technical Information of China (English)
Zhou Dao; Liu Xiao-Zhou; Gong Xiu-Fen; Nazarov V E; Ma Li
2009-01-01
It is known that the strength of concrete is seriously affected by damage and cracking. In this paper, six concrete samples under different damage levels are studied. The experimental results show a linear dependence of the resonance frequency shift on strain amplitude at the fundamental frequency, and approximate quadratic dependence of the am-plitudes of the second and third harmonics on strain amplitude at the fundamental frequency as well. In addition, the amplitude of the third harmonics is shown to increase with the increase of damage level, which is even higher than that of the second harmonics in samples with higher damage levels. These are three properties of non-classical nonlinear acoustics. The nonlinear parameters increase from 106 to 108 with damage level, and are more sensitive to the damage level of the concrete than the linear parameters obtained by using traditional acoustics methods. So, this method based on non-classical nonlinear acoustics may provide a better means of non-destructive testing (NDT) of concrete and other porous materials.
Improved Accuracy of Nonlinear Parameter Estimation with LAV and Interval Arithmetic Methods
Directory of Open Access Journals (Sweden)
Humberto Muñoz
2009-06-01
Full Text Available The reliable solution of nonlinear parameter es- timation problems is an important computational problem in many areas of science and engineering, including such applications as real time optimization. Its goal is to estimate accurate model parameters that provide the best ﬁt to measured data, despite small- scale noise in the data or occasional large-scale mea- surement errors (outliers. In general, the estimation techniques are based on some kind of least squares or maximum likelihood criterion, and these require the solution of a nonlinear and non-convex optimiza- tion problem. Classical solution methods for these problems are local methods, and may not be reliable for ﬁnding the global optimum, with no guarantee the best model parameters have been found. Interval arithmetic can be used to compute completely and reliably the global optimum for the nonlinear para- meter estimation problem. Finally, experimental re- sults will compare the least squares, l2, and the least absolute value, l1, estimates using interval arithmetic in a chemical engineering application.
Analysis of Nonlinear Vibration of Hard Coating Thin Plate by Finite Element Iteration Method
Directory of Open Access Journals (Sweden)
Hui Li
2014-01-01
Full Text Available This paper studies nonlinear vibration mechanism of hard coating thin plate based on macroscopic vibration theory and proposes finite element iteration method (FEIM to theoretically calculate its nature frequency and vibration response. First of all, strain dependent mechanical property of hard coating is briefly introduced and polynomial method is adopted to characterize the storage and loss modulus of coating material. Then, the principle formulas of inherent and dynamic response characteristics of the hard coating composite plate are derived. And consequently specific analysis procedure is proposed by combining ANSYS APDL and self-designed MATLAB program. Finally, a composite plate coated with MgO + Al2O3 is taken as a study object and both nonlinear vibration test and analysis are conducted on the plate specimen with considering strain dependent mechanical parameters of hard coating. Through comparing the resulting frequency and response results, the practicability and reliability of FEIM have been verified and the corresponding analysis results can provide an important reference for further study on nonlinear vibration mechanism of hard coating composite structure.
Nonlinear Diffusion Filtering of the GOCE-Based Satellite-Only Mean Dynamic Topography
Cunderlik, Robert; Mikula, Karol
2015-03-01
The paper presents nonlinear diffusion filtering of the GOCE-based satellite-only mean dynamic topography (MDT). Our approach is based on a numerical solution to the nonlinear diffusion equation defined on the discretized Earth’s surface using the regularized surface Perona-Malik Model. For its numerical discretization we use a surface finite volume method. A key idea is that the diffusivity coefficient depends on the edge detector. It allows effectively reduce the stripping noise while preserve important gradients in filtered data. Numerical experiments present nonlinear filtering of the geopotential evaluated from the GO_CONS_GCF_2_ DIR_R5 model on the DTU13 mean sea surface. After filtering the geopotential is transformed into the MDT.
Commutator-based linearization of $N = 1$ nonlinear supersymmetry
Tsuda, Motomu
2016-01-01
We consider the linearization of $N = 1$ nonlinear supersymmetry (NLSUSY) based on a commutator algebra in Volkov-Akulov NLSUSY theory. We show explicitly that $U(1)$ gauge and scalar supermultiplets in addition to a vector supermultiplet with general auxiliary fields in linear SUSY theories are obtained from a same set of bosonic and fermionic functionals (composites) which are expressed as simple products of the powers of a Nambu-Goldstone fermion and a fundamental determinant in the NLSUSY theory.
Beam-Based Nonlinear Optics Corrections in Colliders
Pilat, Fulvia Caterina; Malitsky, Nikolay; Ptitsyn, Vadim
2005-01-01
A method has been developed to measure and correct operationally the non-linear effects of the final focusing magnets in colliders, which gives access to the effects of multi-pole errors by applying closed orbit bumps, and analyzing the resulting tune and orbit shifts. This technique has been tested and used during 3 years of RHIC (the Relativistic Heavy Ion Collider at BNL) operations. I will discuss here the theoretical basis of the method, the experimental set-up, the correction results, the present understanding of the machine model, the potential and limitations of the method itself as compared with other non linear correction techniques.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
Nonlinear system identification with global and local soft computing methods
Energy Technology Data Exchange (ETDEWEB)
Runkler, T.A. [Siemens AG, Muenchen (Germany). Zentralabt. Technik Information und Kommunikation
2000-10-01
An important step in the design of control systems is system identification. Data driven system identification finds functional models for the system's input output behavior. Regression methods are simple and effective, but may cause overshoots for complicated characteristics. Neural network approaches such as the multilayer perceptron yield very accurate models, but are black box approaches which leads to problems in system and stability analysis. In contrast to these global modeling methods crisp and fuzzy rule bases represent local models that can be extracted from data by clustering methods. Depending on the type and number of models different degrees of model accuracy can be achieved. (orig.)
[Non-linear rectification of sensor based on immune genetic algorithm].
Lu, Lirong; Zhou, Jinyang; Niu, Xiaodong
2014-08-01
A non-linear rectification based on immune genetic algorithm (IGA) is proposed in this paper, for the shortcoming of the non-linearity rectification. This algorithm introducing the biologic immune mechanism into the genetic algorithm can restrain the disadvantages that the poor precision, slow convergence speed and early maturity of the genetic algorithm. Computer simulations indicated that the algorithm not only keeps population diversity, but also increases the convergent speed, precision and the stability greatly. The results have shown the correctness and effectiveness of the method.