New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi...
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...
New developments in state estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgård, Peter Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
2000-01-01
Based on an interpolation formula, accurate state estimators for nonlinear systems can be derived. The estimators do not require derivative information which makes them simple to implement.; State estimators for nonlinear systems are derived based on polynomial approximations obtained with a multi......-dimensional interpolation formula. It is shown that under certain assumptions the estimators perform better than estimators based on Taylor approximations. Nevertheless, the implementation is significantly simpler as no derivatives are required. Thus, it is believed that the new state estimators can replace well...
Advances in Derivative-Free State Estimation for Nonlinear Systems
DEFF Research Database (Denmark)
Nørgaard, Magnus; Poulsen, Niels Kjølstad; Ravn, Ole
In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet the implemen......In this paper we show that it involves considerable advantages to use polynomial approximations obtained with an interpolation formula for derivation of state estimators for nonlinear systems. The estimators become more accurate than estimators based on Taylor approximations, and yet...... the implementation is significantly simpler as no derivatives are required. Thus, it is believed that estimators derived in this way can replace well-known filters, such as the extended Kalman filter (EKF) and its higher order relatives, in most practical applications. In addition to proposing a new set of state...
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...
Progressive Bayes: a new framework for nonlinear state estimation
Hanebeck, Uwe D.; Briechle, Kai; Rauh, Andreas
2003-04-01
This paper is concerned with recursively estimating the internal state of a nonlinear dynamic system by processing noisy measurements and the known system input. In the case of continuous states, an exact analytic representation of the probability density characterizing the estimate is generally too complex for recursive estimation or even impossible to obtain. Hence, it is replaced by a convenient type of approximate density characterized by a finite set of parameters. Of course, parameters are desired that systematically minimize a given measure of deviation between the (often unknown) exact density and its approximation, which in general leads to a complicated optimization problem. Here, a new framework for state estimation based on progressive processing is proposed. Rather than trying to solve the original problem, it is exactly converted into a corresponding system of explicit ordinary first-order differential equations. Solving this system over a finite "time" interval yields the desired optimal density parameters.
Nonlinear Filtering Techniques Comparison for Battery State Estimation
Directory of Open Access Journals (Sweden)
Aspasia Papazoglou
2014-09-01
Full Text Available The performance of estimation algorithms is vital for the correct functioning of batteries in electric vehicles, as poor estimates will inevitably jeopardize the operations that rely on un-measurable quantities, such as State of Charge and State of Health. This paper compares the performance of three nonlinear estimation algorithms: the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter, where a lithium-ion cell model is considered. The effectiveness of these algorithms is measured by their ability to produce accurate estimates against their computational complexity in terms of number of operations and execution time required. The trade-offs between estimators' performance and their computational complexity are analyzed.
State estimation of connected vehicles using a nonlinear ensemble filter
Institute of Scientific and Technical Information of China (English)
刘江; 陈华展; 蔡伯根; 王剑
2015-01-01
The concept of connected vehicles is with great potentials for enhancing the road transportation systems in the future. To support the functions and applications under the connected vehicles frame, the estimation of dynamic states of the vehicles under the cooperative environments is a fundamental issue. By integrating multiple sensors, localization modules in OBUs (on-board units) require effective estimation solutions to cope with various operation conditions. Based on the filtering estimation framework for sensor fusion, an ensemble Kalman filter (EnKF) is introduced to estimate the vehicle’s state with observations from navigation satellites and neighborhood vehicles, and the original EnKF solution is improved by using the cubature transformation to fulfill the requirements of the nonlinearity approximation capability, where the conventional ensemble analysis operation in EnKF is modified to enhance the estimation performance without increasing the computational burden significantly. Simulation results from a nonlinear case and the cooperative vehicle localization scenario illustrate the capability of the proposed filter, which is crucial to realize the active safety of connected vehicles in future intelligent transportation.
A bias identification and state estimation methodology for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
An analysis of a new nonlinear estimation technique: The state-dependent Ricatti equation method
Ewing, Craig Michael
1999-10-01
Research into nonlinear estimation techniques for terminal homing missiles has been conducted for many decades. The terminal state estimator, also called the guidance filter, is responsible for providing accurate estimates of target motion for use in guiding the missile to a collision course with the target. Some form of the extended-Kalman filter (EKF) has become the standard estimation technique employed in most modern weapon guidance systems. EKF linearization of nonlinear dynamics and/or measurements can cause problems of divergence when confronted by highly nonlinear conditions. The objective of this dissertation is to analyze a new nonlinear estimation technique that is based on the parameterization of the nonlinearities. This parameterization converts the nonlinear estimation problem into the form of a steady-state continuous Kalman filtering problem with state-dependent coefficients. This new technique, called the state-dependent Ricatti equation filter (SDREF), allows the nonlinearities of the system to be fully incorporated into the filter design, before stochastic uncertainties are imposed, without the need for linearization. The SDREF was investigated in three problems: an exoatmospheric, terminal homing, ballistic-missile intercept problem; a highly nonlinear pendulum example; and an algorithmic loss of observability problem. The exoatmospheric guidance problem examined nonlinear measurements with linear dynamics. To investigate the SDREF when used with a combination of nonlinear dynamics and nonlinear measurements, a highly nonlinear, two-state pendulum problem was also examined. While these problems were useful in gaining insight into the performance characteristics of the SDREF, no formal proof of stability could be determined for the original formulation of the estimator. The original SDREF solved an algebraic SDRE that arose from an infinite-time horizon formulation of the nonlinear filtering problem. A modification to the SDREF formulation was
ESTIMATE ACCURACY OF NONLINEAR COEFFICIENTS OF SQUEEZEFILM DAMPER USING STATE VARIABLE FILTER METHOD
Institute of Scientific and Technical Information of China (English)
1998-01-01
The estimate model for a nonlinear system of squeeze-film damper (SFD) is described.The method of state variable filter (SVF) is used to estimate the coefficients of SFD.The factors which are critical to the estimate accuracy are discussed.
Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters
Sun, Tao; Xin, Ming
2017-05-01
Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.
Sun, Xiaodian; Jin, Li; Xiong, Momiao
2008-01-01
It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.
Becis-Aubry, Yasmina; Boutayeb, Mohamed; Darouach, Mohamed
2006-01-01
International audience; This contribution proposes a recursive and easily implementable online algorithm for state estimation of multi-output discrete-time systems with nonlinear dynamics and linear measurements in presence of unknown but bounded disturbances corrupting both the state and measurement equations. The proposed algorithm is based on state bounding techniques and is decomposed into two steps : time update and observation update that uses a switching estimation Kalman-like gain mat...
Directory of Open Access Journals (Sweden)
Houda Salhi
2016-01-01
Full Text Available This paper deals with the parameter estimation problem for multivariable nonlinear systems described by MIMO state-space Wiener models. Recursive parameters and state estimation algorithms are presented using the least squares technique, the adjustable model, and the Kalman filter theory. The basic idea is to estimate jointly the parameters, the state vector, and the internal variables of MIMO Wiener models based on a specific decomposition technique to extract the internal vector and avoid problems related to invertibility assumption. The effectiveness of the proposed algorithms is shown by an illustrative simulation example.
Directory of Open Access Journals (Sweden)
Il Young Song
2015-01-01
Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.
Recursive prediction error methods for online estimation in nonlinear state-space models
Directory of Open Access Journals (Sweden)
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.
Nonlinear Adaptive Descriptor Observer for the Joint States and Parameters Estimation
2016-08-29
In this note, the joint state and parameters estimation problem for nonlinear multi-input multi-output descriptor systems is considered. Asymptotic convergence of the adaptive descriptor observer is established by a sufficient set of linear matrix inequalities for the noise-free systems. The noise corrupted systems are also considered and it is shown that the state and parameters estimation errors are bounded for bounded noises. In addition, if the noises are bounded and have zero mean, then the estimation errors asymptotically converge to zero in the mean. The performance of the proposed adaptive observer is illustrated by a numerical example.
Lin, Tai-Chia; Petrovic, Milan S; Hajaiej, Hichem; Chen, Goong
2016-01-01
The virial theorem is a nice property for the linear Schrodinger equation in atomic and molecular physics as it gives an elegant ratio between the kinetic and potential energies and is useful in assessing the quality of numerically computed eigenvalues. If the governing equation is a nonlinear Schrodinger equation with power-law nonlinearity, then a similar ratio can be obtained but there seems no way of getting any eigenvalue estimate. It is surprising as far as we are concerned that when the nonlinearity is either square-root or saturable nonlinearity (not a power-law), one can develop a virial theorem and eigenvalue estimate of nonlinear Schrodinger (NLS) equations in R2 with square-root and saturable nonlinearity, respectively. Furthermore, we show here that the eigenvalue estimate can be used to obtain the 2nd order term (which is of order $ln\\Gamma$) of the lower bound of the ground state energy as the coefficient $\\Gamma$ of the nonlinear term tends to infinity.
Fenili, André
2012-11-01
In this paper the author investigates the angular position and vibration control of a nonlinear rigid-flexible two link robotic manipulator considering fast angular maneuvers. The nonlinear control technique named State-Dependent Riccati Equation (SDRE) is used here to achieve these aims. In a more realistic approach, it is considered that some states can be measured and some states cannot be measured. The states not measured are estimated in order to be used for the SDRE control. These states are all the angular velocities and the velocity of deformation of the flexible link. A state-dependent Riccati equation-based estimator is used here. Not only different initial conditions between the system to be controlled (here named "real" system) and the estimator but also a different mathematical model is considered as the estimation model in order to verify the limitations of the proposed estimation and control techniques. The mathematical model that emulates the real system to be controlled considers two modes expansion and the estimation model considers only one mode expansion. The results for the different approaches are compared and discussed.
Elenchezhiyan, M; Prakash, J
2015-09-01
In this work, state estimation schemes for non-linear hybrid dynamic systems subjected to stochastic state disturbances and random errors in measurements using interacting multiple-model (IMM) algorithms are formulated. In order to compute both discrete modes and continuous state estimates of a hybrid dynamic system either an IMM extended Kalman filter (IMM-EKF) or an IMM based derivative-free Kalman filters is proposed in this study. The efficacy of the proposed IMM based state estimation schemes is demonstrated by conducting Monte-Carlo simulation studies on the two-tank hybrid system and switched non-isothermal continuous stirred tank reactor system. Extensive simulation studies reveal that the proposed IMM based state estimation schemes are able to generate fairly accurate continuous state estimates and discrete modes. In the presence and absence of sensor bias, the simulation studies reveal that the proposed IMM unscented Kalman filter (IMM-UKF) based simultaneous state and parameter estimation scheme outperforms multiple-model UKF (MM-UKF) based simultaneous state and parameter estimation scheme.
Nonlinear neural network for hemodynamic model state and input estimation using fMRI data
Karam, Ayman M.
2014-11-01
Originally inspired by biological neural networks, artificial neural networks (ANNs) are powerful mathematical tools that can solve complex nonlinear problems such as filtering, classification, prediction and more. This paper demonstrates the first successful implementation of ANN, specifically nonlinear autoregressive with exogenous input (NARX) networks, to estimate the hemodynamic states and neural activity from simulated and measured real blood oxygenation level dependent (BOLD) signals. Blocked and event-related BOLD data are used to test the algorithm on real experiments. The proposed method is accurate and robust even in the presence of signal noise and it does not depend on sampling interval. Moreover, the structure of the NARX networks is optimized to yield the best estimate with minimal network architecture. The results of the estimated neural activity are also discussed in terms of their potential use.
Pre-Trained Neural Networks used for Non-Linear State Estimation
DEFF Research Database (Denmark)
Bayramoglu, Enis; Andersen, Nils Axel; Ravn, Ole
2011-01-01
The paper focuses on nonlinear state estimation assuming non-Gaussian distributions of the states and the disturbances. The posterior distribution and the aposteriori distribution is described by a chosen family of paramtric distributions. The state transformation then results in a transformation...... of the paramters in the distribution. This transformation is approximated by a neural network using offline training, which is based on monte carlo sampling. In the paper, there will also be presented a method to construct a flexible distributions well suited for covering the effect of the non...
Miao, Zhiyong; Shi, Hongyang; Zhang, Yi; Xu, Fan
2017-10-01
In this paper, a new variational Bayesian adaptive cubature Kalman filter (VBACKF) is proposed for nonlinear state estimation. Although the conventional VBACKF performs better than cubature Kalman filtering (CKF) in solving nonlinear systems with time-varying measurement noise, its performance may degrade due to the uncertainty of the system model. To overcome this drawback, a multilayer feed-forward neural network (MFNN) is used to aid the conventional VBACKF, generalizing it to attain higher estimation accuracy and robustness. In the proposed neural-network-aided variational Bayesian adaptive cubature Kalman filter (NN-VBACKF), the MFNN is used to turn the state estimation of the VBACKF adaptively, and it is used for both state estimation and in the online training paradigm simultaneously. To evaluate the performance of the proposed method, it is compared with CKF and VBACKF via target tracking problems. The simulation results demonstrate that the estimation accuracy and robustness of the proposed method are better than those of the CKF and VBACKF.
DEFF Research Database (Denmark)
Petersen, Lars Norbert; Jørgensen, John Bagterp; Rawlings, James B.
2015-01-01
In this paper, we develop an economically optimizing Nonlinear Model Predictive Controller (E-NMPC) for a complete spray drying plant with multiple stages. In the E-NMPC the initial state is estimated by an extended Kalman Filter (EKF) with noise covariances estimated by an autocovariance least...... squares method (ALS). We present a model for the spray drying plant and use this model for simulation as well as for prediction in the E-NMPC. The open-loop optimal control problem in the E-NMPC is solved using the single-shooting method combined with a quasi-Newton Sequential Quadratic programming (SQP...
Luo, Xiaodong
2014-10-01
The ensemble Kalman filter (EnKF) is an efficient algorithm for many data assimilation problems. In certain circumstances, however, divergence of the EnKF might be spotted. In previous studies, the authors proposed an observation-space-based strategy, called residual nudging, to improve the stability of the EnKF when dealing with linear observation operators. The main idea behind residual nudging is to monitor and, if necessary, adjust the distances (misfits) between the real observations and the simulated ones of the state estimates, in the hope that by doing so one may be able to obtain better estimation accuracy. In the present study, residual nudging is extended and modified in order to handle nonlinear observation operators. Such extension and modification result in an iterative filtering framework that, under suitable conditions, is able to achieve the objective of residual nudging for data assimilation problems with nonlinear observation operators. The 40-dimensional Lorenz-96 model is used to illustrate the performance of the iterative filter. Numerical results show that, while a normal EnKF may diverge with nonlinear observation operators, the proposed iterative filter remains stable and leads to reasonable estimation accuracy under various experimental settings.
Rosenblatt, Marcus; Timmer, Jens; Kaschek, Daniel
2016-01-01
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.
Electric vehicle state of charge estimation: Nonlinear correlation and fuzzy support vector machine
Sheng, Hanmin; Xiao, Jian
2015-05-01
The aim of this study is to estimate the state of charge (SOC) of the lithium iron phosphate (LiFePO4) battery pack by applying machine learning strategy. To reduce the noise sensitive issue of common machine learning strategies, a kind of SOC estimation method based on fuzzy least square support vector machine is proposed. By applying fuzzy inference and nonlinear correlation measurement, the effects of the samples with low confidence can be reduced. Further, a new approach for determining the error interval of regression results is proposed to avoid the control system malfunction. Tests are carried out on modified COMS electric vehicles, with two battery packs each consists of 24 50 Ah LiFePO4 batteries. The effectiveness of the method is proven by the test and the comparison with other popular methods.
Billings, S. A.
1988-03-01
Time and frequency domain identification methods for nonlinear systems are reviewed. Parametric methods, prediction error methods, structure detection, model validation, and experiment design are discussed. Identification of a liquid level system, a heat exchanger, and a turbocharge automotive diesel engine are illustrated. Rational models are introduced. Spectral analysis for nonlinear systems is treated. Recursive estimation is mentioned.
Directory of Open Access Journals (Sweden)
Hongjian Wang
2014-01-01
Full Text Available We present a support vector regression-based adaptive divided difference filter (SVRADDF algorithm for improving the low state estimation accuracy of nonlinear systems, which are typically affected by large initial estimation errors and imprecise prior knowledge of process and measurement noises. The derivative-free SVRADDF algorithm is significantly simpler to compute than other methods and is implemented using only functional evaluations. The SVRADDF algorithm involves the use of the theoretical and actual covariance of the innovation sequence. Support vector regression (SVR is employed to generate the adaptive factor to tune the noise covariance at each sampling instant when the measurement update step executes, which improves the algorithm’s robustness. The performance of the proposed algorithm is evaluated by estimating states for (i an underwater nonmaneuvering target bearing-only tracking system and (ii maneuvering target bearing-only tracking in an air-traffic control system. The simulation results show that the proposed SVRADDF algorithm exhibits better performance when compared with a traditional DDF algorithm.
Directory of Open Access Journals (Sweden)
Dalei Song
2012-10-01
Full Text Available The adaptive extended set‐membership filter (AESMF for nonlinear ellipsoidal estimation suffers a mismatch between real process noise and its set boundaries, which may result in unstable estimation. In this paper, a MIT method‐based adaptive set‐membership filter, for the optimization of the set boundaries of process noise, is developed and applied to the nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed MIT‐AESMF, the estimation effectiveness and boundary accuracy of traditional AESMF are substantially improved. Simulation results have shown the efficiency and robustness of the proposed method.
A separated bias identification and state estimation algorithm for nonlinear systems
Caglayan, A. K.; Lancraft, R. E.
1983-01-01
A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
State estimation of nonlinear stochastic systems using a novel meta-heuristic particle filter
DEFF Research Database (Denmark)
Ahmadi, Mohamadreza; Mojallali, Hamed; Izadi-Zamanabadi, Roozbeh
2012-01-01
This paper proposes a new version of the particle filtering (PF) algorithm based on the invasive weed optimization (IWO) method. The sub-optimality of the sampling step in the PF algorithm is prone to estimation errors. In order to avert such approximation errors, this paper suggests applying...... the IWO algorithm by translating the sampling step into a nonlinear optimization problem. By introducing an appropriate fitness function, the optimization problem is properly treated. The validity of the proposed method is evaluated against three distinct examples: the stochastic volatility estimation...... problem in finance, the severely nonlinear waste water sludge treatment plant, and the benchmark target tracking on re-entry problem. By simulation analysis and evaluation, it is verified that applying the suggested IWO enhanced PF algorithm (PFIWO) would contribute to significant estimation performance...
Directory of Open Access Journals (Sweden)
Peng Guo
2012-12-01
Full Text Available With appropriate vibration modeling and analysis the incipient failure of key components such as the tower, drive train and rotor of a large wind turbine can be detected. In this paper, the Nonlinear State Estimation Technique (NSET has been applied to model turbine tower vibration to good effect, providing an understanding of the tower vibration dynamic characteristics and the main factors influencing these. The developed tower vibration model comprises two different parts: a sub-model used for below rated wind speed; and another for above rated wind speed. Supervisory control and data acquisition system (SCADA data from a single wind turbine collected from March to April 2006 is used in the modeling. Model validation has been subsequently undertaken and is presented. This research has demonstrated the effectiveness of the NSET approach to tower vibration; in particular its conceptual simplicity, clear physical interpretation and high accuracy. The developed and validated tower vibration model was then used to successfully detect blade angle asymmetry that is a common fault that should be remedied promptly to improve turbine performance and limit fatigue damage. The work also shows that condition monitoring is improved significantly if the information from the vibration signals is complemented by analysis of other relevant SCADA data such as power performance, wind speed, and rotor loads.
Zitelli, Gregory; Djouadi, Seddik M; Day, Judy D
2015-10-01
The inflammatory response aims to restore homeostasis by means of removing a biological stress, such as an invading bacterial pathogen. In cases of acute systemic inflammation, the possibility of collateral tissue damage arises, which leads to a necessary down-regulation of the response. A reduced ordinary differential equations (ODE) model of acute inflammation was presented and investigated in [10]. That system contains multiple positive and negative feedback loops and is a highly coupled and nonlinear ODE. The implementation of nonlinear model predictive control (NMPC) as a methodology for determining proper therapeutic intervention for in silico patients displaying complex inflammatory states was initially explored in [5]. Since direct measurements of the bacterial population and the magnitude of tissue damage/dysfunction are not readily available or biologically feasible, the need for robust state estimation was evident. In this present work, we present results on the nonlinear reachability of the underlying model, and then focus our attention on improving the predictability of the underlying model by coupling the NMPC with a particle filter. The results, though comparable to the initial exploratory study, show that robust state estimation of this highly nonlinear model can provide an alternative to prior updating strategies used when only partial access to the unmeasurable states of the system are available.
Quach, Minh; Brunel, Nicolas; d'Alché-Buc, Florence
2007-12-01
Statistical inference of biological networks such as gene regulatory networks, signaling pathways and metabolic networks can contribute to build a picture of complex interactions that take place in the cell. However, biological systems considered as dynamical, non-linear and generally partially observed processes may be difficult to estimate even if the structure of interactions is given. Using the same approach as Sitz et al. proposed in another context, we derive non-linear state-space models from ODEs describing biological networks. In this framework, we apply Unscented Kalman Filtering (UKF) to the estimation of both parameters and hidden variables of non-linear state-space models. We instantiate the method on a transcriptional regulatory model based on Hill kinetics and a signaling pathway model based on mass action kinetics. We successfully use synthetic data and experimental data to test our approach. This approach covers a large set of biological networks models and gives rise to simple and fast estimation algorithms. Moreover, the Bayesian tool used here directly provides uncertainty estimates on parameters and hidden states. Let us also emphasize that it can be coupled with structure inference methods used in Graphical Probabilistic Models. Matlab code available on demand.
Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems
Mahdi Alavi, S. M.; Saif, Mehrdad
2013-12-01
This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.
An FEM-Based State Estimation Approach to Nonlinear Hybrid Positioning Systems
Directory of Open Access Journals (Sweden)
Yu-Xin Zhao
2013-01-01
Full Text Available For hybrid positioning systems (HPSs, the estimator design is a crucial and important problem. In this paper, a finite-element-method- (FEM- based state estimation approach is proposed to HPS. As the weak solution of hybrid stochastic differential model is denoted by the Kolmogorov's forward equation, this paper constructs its interpolating point through the classical fourth-order Runge-Kutta method. Then, it approaches the solution with biquadratic interpolation function to obtain a prior probability density function of the state. A posterior probability density function is gained through Bayesian formula finally. In theory, the proposed scheme has more advantages in the performance of complexity and convergence for low-dimensional systems. By taking an illustrative example, numerical experiment results show that the new state estimator is feasible and has good performance than PF and UKF.
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Yin Hua
2015-04-01
Full Text Available Estimation of state of charge (SOC is of great importance for lithium-ion (Li-ion batteries used in electric vehicles. This paper presents a state of charge estimation method using nonlinear predictive filter (NPF and evaluates the proposed method on the lithium-ion batteries with different chemistries. Contrary to most conventional filters which usually assume a zero mean white Gaussian process noise, the advantage of NPF is that the process noise in NPF is treated as an unknown model error and determined as a part of the solution without any prior assumption, and it can take any statistical distribution form, which improves the estimation accuracy. In consideration of the model accuracy and computational complexity, a first-order equivalent circuit model is applied to characterize the battery behavior. The experimental test is conducted on the LiCoO2 and LiFePO4 battery cells to validate the proposed method. The results show that the NPF method is able to accurately estimate the battery SOC and has good robust performance to the different initial states for both cells. Furthermore, the comparison study between NPF and well-established extended Kalman filter for battery SOC estimation indicates that the proposed NPF method has better estimation accuracy and converges faster.
Palatella, Luigi; Trevisan, Anna; Rambaldi, Sandro
2013-08-01
Valuable information for estimating the traffic flow is obtained with current GPS technology by monitoring position and velocity of vehicles. In this paper, we present a proof of concept study that shows how the traffic state can be estimated using only partial and noisy data by assimilating them in a dynamical model. Our approach is based on a data assimilation algorithm, developed by the authors for chaotic geophysical models, designed to be equivalent but computationally much less demanding than the traditional extended Kalman filter. Here we show that the algorithm is even more efficient if the system is not chaotic and demonstrate by numerical experiments that an accurate reconstruction of the complete traffic state can be obtained at a very low computational cost by monitoring only a small percentage of vehicles.
Estimation of LISS(local input-to-state stability) properties for nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Compared with input-to-state stability(ISS) in global version,the concept of local input-to-state stability(LISS) is more relevant and meaningful in practice.The key of assessing LISS properties lies in investigating three main ingredients,the local region of initial states,the local region of external inputs and the asymptotic gain.It is the objective of this paper to propose a numerical algorithm for estimating LISS properties on the theoretical foundation of quadratic form LISS-Lyapunov function.Given developments of linear matrix inequality(LMI) methods,this algorithm is effective and powerful.A typical power electronics based system with common DC bus is served as a demonstration for quantitative results.
Directory of Open Access Journals (Sweden)
G. Forget
2015-10-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Nonlinear estimation and control of automotive drivetrains
Chen, Hong
2014-01-01
Nonlinear Estimation and Control of Automotive Drivetrains discusses the control problems involved in automotive drivetrains, particularly in hydraulic Automatic Transmission (AT), Dual Clutch Transmission (DCT) and Automated Manual Transmission (AMT). Challenging estimation and control problems, such as driveline torque estimation and gear shift control, are addressed by applying the latest nonlinear control theories, including constructive nonlinear control (Backstepping, Input-to-State Stable) and Model Predictive Control (MPC). The estimation and control performance is improved while the calibration effort is reduced significantly. The book presents many detailed examples of design processes and thus enables the readers to understand how to successfully combine purely theoretical methodologies with actual applications in vehicles. The book is intended for researchers, PhD students, control engineers and automotive engineers. Hong Chen is a professor at the State Key Laboratory of Automotive Simulation and...
Nonlinear estimation and classification
Hansen, Mark; Holmes, Christopher; Mallick, Bani; Yu, Bin
2003-01-01
Researchers in many disciplines face the formidable task of analyzing massive amounts of high-dimensional and highly-structured data This is due in part to recent advances in data collection and computing technologies As a result, fundamental statistical research is being undertaken in a variety of different fields Driven by the complexity of these new problems, and fueled by the explosion of available computer power, highly adaptive, non-linear procedures are now essential components of modern "data analysis," a term that we liberally interpret to include speech and pattern recognition, classification, data compression and signal processing The development of new, flexible methods combines advances from many sources, including approximation theory, numerical analysis, machine learning, signal processing and statistics The proposed workshop intends to bring together eminent experts from these fields in order to exchange ideas and forge directions for the future
Directory of Open Access Journals (Sweden)
G. Forget
2015-05-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and highly integrated with the MITgcm. They are both subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of model-data constraints and adjustable control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The reference ECCO v4 solution is a dynamically consistent ocean state estimate (ECCO-Production, release 1 without un-identified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model-data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Fliess, Michel; Sira-Ramirez, Hebertt
2007-01-01
Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint.
Directory of Open Access Journals (Sweden)
Yulong Ying
2015-01-01
Full Text Available In the lifespan of a gas turbine engine, abrupt faults and performance degradation of its gas-path components may happen; however the performance degradation is not easily foreseeable when the level of degradation is small. Gas path analysis (GPA method has been widely applied to monitor gas turbine engine health status as it can easily obtain the magnitudes of the detected component faults. However, when the number of components within engine is large or/and the measurement noise level is high, the smearing effect may be strong and the degraded components may not be recognized. In order to improve diagnostic effect, a nonlinear steady-state model based gas turbine health status estimation approach with improved particle swarm optimization algorithm (PSO-GPA has been proposed in this study. The proposed approach has been tested in ten test cases where the degradation of a model three-shaft marine engine has been analyzed. These case studies have shown that the approach can accurately search and isolate the degraded components and further quantify the degradation for major gas-path components. Compared with the typical GPA method, the approach has shown better measurement noise immunity and diagnostic accuracy.
Fliess, Michel; Join, Cédric; Sira-Ramirez, Hebertt
2008-01-01
International audience; Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line ...
Space vehicle pose estimation via optical correlation and nonlinear estimation
Rakoczy, John M.; Herren, Kenneth A.
2008-03-01
A technique for 6-degree-of-freedom (6DOF) pose estimation of space vehicles is being developed. This technique draws upon recent developments in implementing optical correlation measurements in a nonlinear estimator, which relates the optical correlation measurements to the pose states (orientation and position). For the optical correlator, the use of both conjugate filters and binary, phase-only filters in the design of synthetic discriminant function (SDF) filters is explored. A static neural network is trained a priori and used as the nonlinear estimator. New commercial animation and image rendering software is exploited to design the SDF filters and to generate a large filter set with which to train the neural network. The technique is applied to pose estimation for rendezvous and docking of free-flying spacecraft and to terrestrial surface mobility systems for NASA's Vision for Space Exploration. Quantitative pose estimation performance will be reported. Advantages and disadvantages of the implementation of this technique are discussed.
Dreano, D.
2017-04-05
Specification and tuning of errors from dynamical models are important issues in data assimilation. In this work, we propose an iterative expectation-maximisation (EM) algorithm to estimate the model error covariances using classical extended and ensemble versions of the Kalman smoother. We show that, for additive model errors, the estimate of the error covariance converges. We also investigate other forms of model error, such as parametric or multiplicative errors. We show that additive Gaussian model error is able to compensate for non additive sources of error in the algorithms we propose. We also demonstrate the limitations of the extended version of the algorithm and recommend the use of the more robust and flexible ensemble version. This article is a proof of concept of the methodology with the Lorenz-63 attractor. We developed an open-source Python library to enable future users to apply the algorithm to their own nonlinear dynamical models.
Zimmer, Christoph
2016-01-01
Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models.
Zimmer, Christoph
2016-01-01
Background Computational modeling is a key technique for analyzing models in systems biology. There are well established methods for the estimation of the kinetic parameters in models of ordinary differential equations (ODE). Experimental design techniques aim at devising experiments that maximize the information encoded in the data. For ODE models there are well established approaches for experimental design and even software tools. However, data from single cell experiments on signaling pathways in systems biology often shows intrinsic stochastic effects prompting the development of specialized methods. While simulation methods have been developed for decades and parameter estimation has been targeted for the last years, only very few articles focus on experimental design for stochastic models. Methods The Fisher information matrix is the central measure for experimental design as it evaluates the information an experiment provides for parameter estimation. This article suggest an approach to calculate a Fisher information matrix for models containing intrinsic stochasticity and high nonlinearity. The approach makes use of a recently suggested multiple shooting for stochastic systems (MSS) objective function. The Fisher information matrix is calculated by evaluating pseudo data with the MSS technique. Results The performance of the approach is evaluated with simulation studies on an Immigration-Death, a Lotka-Volterra, and a Calcium oscillation model. The Calcium oscillation model is a particularly appropriate case study as it contains the challenges inherent to signaling pathways: high nonlinearity, intrinsic stochasticity, a qualitatively different behavior from an ODE solution, and partial observability. The computational speed of the MSS approach for the Fisher information matrix allows for an application in realistic size models. PMID:27583802
Energy Technology Data Exchange (ETDEWEB)
Tunc Aldemir; Don W. Miller; Brian k. Hajek; Peng Wang
2002-04-01
The DSD (Dynamic System Doctor) is a system-independent, interactive software under development for on-line state/parameter estimation in dynamic systems (1), partially supported through a Nuclear Engineering Education (NEER) grant during 1998-2001. This paper summarizes the recent accomplishments in improving the user-friendliness and computational capability of DSD
Directory of Open Access Journals (Sweden)
Meleiro L.A.C.
2000-01-01
Full Text Available Most advanced computer-aided control applications rely on good dynamics process models. The performance of the control system depends on the accuracy of the model used. Typically, such models are developed by conducting off-line identification experiments on the process. These experiments for identification often result in input-output data with small output signal-to-noise ratio, and using these data results in inaccurate model parameter estimates [1]. In this work, a multivariable adaptive self-tuning controller (STC was developed for a biotechnological process application. Due to the difficulties involving the measurements or the excessive amount of variables normally found in industrial process, it is proposed to develop "soft-sensors" which are based fundamentally on artificial neural networks (ANN. A second approach proposed was set in hybrid models, results of the association of deterministic models (which incorporates the available prior knowledge about the process being modeled with artificial neural networks. In this case, kinetic parameters - which are very hard to be accurately determined in real time industrial plants operation - were obtained using ANN predictions. These methods are especially suitable for the identification of time-varying and nonlinear models. This advanced control strategy was applied to a fermentation process to produce ethyl alcohol (ethanol in industrial scale. The reaction rate considered for substratum consumption, cells and ethanol productions are validated with industrial data for typical operating conditions. The results obtained show that the proposed procedure in this work has a great potential for application.
DEFF Research Database (Denmark)
Knudsen, Torben
2014-01-01
Dynamic inflow is an effect which is normally not included in the models used for wind turbine control design. Therefore, potential improvement from including this effect exists. The objective in this project is to improve the methods previously developed for this and especially to verify...... the results using full-scale wind turbine data. The previously developed methods were based on extended Kalman filtering. This method has several drawback compared to unscented Kalman filtering which has therefore been developed. The unscented Kalman filter was first tested on linear and non-linear test cases...... which was successful. Then the estimation of a wind turbine state including dynamic inflow was tested on a simulated NREL 5MW turbine was performed. This worked perfectly with wind speeds from low to nominal wind speed as the output prediction errors where white. In high wind where the pitch actuator...
Nonlinear Estimation with Applications to Drilling
Stamnes, Øyvind Nistad
2011-01-01
This thesis addresses the topic of nonlinear estimation and its applications. Particular emphasis is given to downhole pressure estimation for Managed Pressure Drilling (MPD), but due to the mathematical similarities of the two problems, velocity estimation for mechanical systems is also considered. The thesis consists of the following three parts:Part I of this thesis addresses the problem of pressure estimation for MPD systems. Over the last decade MPD has emerged as a tool for drilling of...
An extended nonlinear state predictor for a class of nonlinear time delay systems
Institute of Scientific and Technical Information of China (English)
WANG Dong; ZHOU Donghua; JIN Yihui
2004-01-01
An extended nonlinear state predictor (ENSP) for a class of nonlinear systems with input time delay is proposed. Based on the extended Kalman filter (EKF), the ENSP first estimates the current states according to the previous estimations and estimation errors, next calculates the future state values via the system model, and then adjusts the values based on the current errors. After a state predictive algorithm for a class of linear systems is presented, it is extended to a class of nonlinear time delay systems and the detailed ENSP algorithm is further proposed. Finally, computer simulations with the nonlinear example are presented, which demonstrates that the proposed ENSP can effectively and accurately predict the future states for a class of nonlinear time-delay systems no matter whether the state variables change quickly or slowly.
Optimized spectral estimation for nonlinear synchronizing systems.
Sommerlade, Linda; Mader, Malenka; Mader, Wolfgang; Timmer, Jens; Thiel, Marco; Grebogi, Celso; Schelter, Björn
2014-03-01
In many fields of research nonlinear dynamical systems are investigated. When more than one process is measured, besides the distinct properties of the individual processes, their interactions are of interest. Often linear methods such as coherence are used for the analysis. The estimation of coherence can lead to false conclusions when applied without fulfilling several key assumptions. We introduce a data driven method to optimize the choice of the parameters for spectral estimation. Its applicability is demonstrated based on analytical calculations and exemplified in a simulation study. We complete our investigation with an application to nonlinear tremor signals in Parkinson's disease. In particular, we analyze electroencephalogram and electromyogram data.
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.
Spin squeezing in nonlinear spin coherent states
Wang, Xiaoguang
2001-01-01
We introduce the nonlinear spin coherent state via its ladder operator formalism and propose a type of nonlinear spin coherent state by the nonlinear time evolution of spin coherent states. By a new version of spectroscopic squeezing criteria we study the spin squeezing in both the spin coherent state and nonlinear spin coherent state. The results show that the spin coherent state is not squeezed in the x, y, and z directions, and the nonlinear spin coherent state may be squeezed in the x and...
Estimating the uncertainty in underresolved nonlinear dynamics
Energy Technology Data Exchange (ETDEWEB)
Chorin, Alelxandre; Hald, Ole
2013-06-12
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Bayesian parameter estimation for nonlinear modelling of biological pathways
Directory of Open Access Journals (Sweden)
Ghasemi Omid
2011-12-01
Full Text Available Abstract Background The availability of temporal measurements on biological experiments has significantly promoted research areas in systems biology. To gain insight into the interaction and regulation of biological systems, mathematical frameworks such as ordinary differential equations have been widely applied to model biological pathways and interpret the temporal data. Hill equations are the preferred formats to represent the reaction rate in differential equation frameworks, due to their simple structures and their capabilities for easy fitting to saturated experimental measurements. However, Hill equations are highly nonlinearly parameterized functions, and parameters in these functions cannot be measured easily. Additionally, because of its high nonlinearity, adaptive parameter estimation algorithms developed for linear parameterized differential equations cannot be applied. Therefore, parameter estimation in nonlinearly parameterized differential equation models for biological pathways is both challenging and rewarding. In this study, we propose a Bayesian parameter estimation algorithm to estimate parameters in nonlinear mathematical models for biological pathways using time series data. Results We used the Runge-Kutta method to transform differential equations to difference equations assuming a known structure of the differential equations. This transformation allowed us to generate predictions dependent on previous states and to apply a Bayesian approach, namely, the Markov chain Monte Carlo (MCMC method. We applied this approach to the biological pathways involved in the left ventricle (LV response to myocardial infarction (MI and verified our algorithm by estimating two parameters in a Hill equation embedded in the nonlinear model. We further evaluated our estimation performance with different parameter settings and signal to noise ratios. Our results demonstrated the effectiveness of the algorithm for both linearly and nonlinearly
Kyung-Tae Nam; Seung-Joon Lee; Tae-Yong Kuc; Hyungjong Kim
2015-01-01
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 co...
Ahmad, Mukhtar
2012-01-01
State estimation is one of the most important functions in power system operation and control. This area is concerned with the overall monitoring, control, and contingency evaluation of power systems. It is mainly aimed at providing a reliable estimate of system voltages. State estimator information flows to control centers, where critical decisions are made concerning power system design and operations. This valuable resource provides thorough coverage of this area, helping professionals overcome challenges involving system quality, reliability, security, stability, and economy.Engineers are
Hybrid fault diagnosis of nonlinear systems using neural parameter estimators.
Sobhani-Tehrani, E; Talebi, H A; Khorasani, K
2014-02-01
This paper presents a novel integrated hybrid approach for fault diagnosis (FD) of nonlinear systems taking advantage of both the system's mathematical model and the adaptive nonlinear approximation capability of computational intelligence techniques. Unlike most FD techniques, the proposed solution simultaneously accomplishes fault detection, isolation, and identification (FDII) within a unified diagnostic module. At the core of this solution is a bank of adaptive neural parameter estimators (NPEs) associated with a set of single-parameter fault models. The NPEs continuously estimate unknown fault parameters (FPs) that are indicators of faults in the system. Two NPE structures, series-parallel and parallel, are developed with their exclusive set of desirable attributes. The parallel scheme is extremely robust to measurement noise and possesses a simpler, yet more solid, fault isolation logic. In contrast, the series-parallel scheme displays short FD delays and is robust to closed-loop system transients due to changes in control commands. Finally, a fault tolerant observer (FTO) is designed to extend the capability of the two NPEs that originally assumes full state measurements for systems that have only partial state measurements. The proposed FTO is a neural state estimator that can estimate unmeasured states even in the presence of faults. The estimated and the measured states then comprise the inputs to the two proposed FDII schemes. Simulation results for FDII of reaction wheels of a three-axis stabilized satellite in the presence of disturbances and noise demonstrate the effectiveness of the proposed FDII solutions under partial state measurements.
Ground motion estimation and nonlinear seismic analysis
Energy Technology Data Exchange (ETDEWEB)
McCallen, D.B.; Hutchings, L.J.
1995-08-14
Site specific predictions of the dynamic response of structures to extreme earthquake ground motions are a critical component of seismic design for important structures. With the rapid development of computationally based methodologies and powerful computers over the past few years, engineers and scientists now have the capability to perform numerical simulations of many of the physical processes associated with the generation of earthquake ground motions and dynamic structural response. This paper describes application of a physics based, deterministic, computational approach for estimation of earthquake ground motions which relies on site measurements of frequently occurring small (i.e. M < 3 ) earthquakes. Case studies are presented which illustrate application of this methodology for two different sites, and nonlinear analyses of a typical six story steel frame office building are performed to illustrate the potential sensitivity of nonlinear response to site conditions and proximity to the causative fault.
Nonlinear regime-switching state-space (RSSS) models.
Chow, Sy-Miin; Zhang, Guangjian
2013-10-01
Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.
Estimating dynamic equilibrium economies: linear versus nonlinear likelihood
2004-01-01
This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a sequential Monte Carlo filter proposed by Fernández-Villaverde and Rubio-Ramírez (2004) and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. The authors report two main results...
Nonlinear wavelet estimation of regression function with random desigm
Institute of Scientific and Technical Information of China (English)
张双林; 郑忠国
1999-01-01
The nonlinear wavelet estimator of regression function with random design is constructed. The optimal uniform convergence rate of the estimator in a ball of Besov space Bp,q? is proved under quite genera] assumpations. The adaptive nonlinear wavelet estimator with near-optimal convergence rate in a wide range of smoothness function classes is also constructed. The properties of the nonlinear wavelet estimator given for random design regression and only with bounded third order moment of the error can be compared with those of nonlinear wavelet estimator given in literature for equal-spaced fixed design regression with i.i.d. Gauss error.
Nonlinear Estimation With Sparse Temporal Measurements
2016-09-01
technology. Measurements have inherent precision and accuracy uncertainty preventing perfect knowledge of the system state. Additionally, each system state...xi)µTg(x) + µg(x)g(xi) T ) + 1 N − 1 N∑ i=1 µg(x)µ T g(x) (1.18) This method rapidly succumbs to Bellman’s " curse of dimensionality," the exponential... knowledge of each state when estimation commences. A fixed step, Runge-Kutta fourth-order solver is used to propagate the process model be- tween
Directory of Open Access Journals (Sweden)
Jianping Gao
2015-01-01
Full Text Available Accurate state of charge (SoC estimation is of great significance for the lithium-ion battery to ensure its safety operation and to prevent it from overcharging or overdischarging. To achieve reliable SoC estimation for Li4Ti5O12 lithium-ion battery cell, three filtering methods have been compared and evaluated. A main contribution of this study is that a general three-step model-based battery SoC estimation scheme has been proposed. It includes the processes of battery data measurement, parametric modeling, and model-based SoC estimation. With the proposed general scheme, multiple types of model-based SoC estimators have been developed and evaluated for battery management system application. The detailed comparisons on three advanced adaptive filter techniques, which include extend Kalman filter, unscented Kalman filter, and adaptive extend Kalman filter (AEKF, have been implemented with a Li4Ti5O12 lithium-ion battery. The experimental results indicate that the proposed model-based SoC estimation approach with AEKF algorithm, which uses the covariance matching technique, performs well with good accuracy and robustness; the mean absolute error of the SoC estimation is within 1% especially with big SoC initial error.
A Genetic Algorithm Approach to Nonlinear Least Squares Estimation
Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.
2004-01-01
A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…
A Nonlinear Attitude Estimator for Attitude and Heading Reference Systems Based on MEMS Sensors
DEFF Research Database (Denmark)
Wang, Yunlong; Soltani, Mohsen; Hussain, Dil muhammed Akbar
2016-01-01
the problems in previous research works. Moreover, the estimation of MEMS gyroscope bias is also inclueded in this estimator. The designed nonlinear attitude estimator is firstly tested in simulation environment and then implemented in an AHRS hardware for further experiments. Finally, the attitude estimation......In this paper, a nonlinear attitude estimator is designed for an Attitude Heading and Reference System (AHRS) based on Micro Electro-Mechanical Systems (MEMS) sensors. The design process of the attitude estimator is stated with detail, and the equilibrium point of the estimator error model...
NONLINEAR ESTIMATION METHODS FOR AUTONOMOUS TRACKED VEHICLE WITH SLIP
Institute of Scientific and Technical Information of China (English)
ZHOU Bo; HAN Jianda
2007-01-01
In order to achieve precise, robust autonomous guidance and control of a tracked vehicle, a kinematic model with longitudinal and lateral slip is established. Four different nonlinear filters are used to estimate both state vector and time-varying parameter vector of the created model jointly. The first filter is the well-known extended Kalman filter. The second filter is an unscented version of the Kalman filter. The third one is a particle filter using the unscented Kalman filter to generate the importance proposal distribution. The last one is a novel and guaranteed filter that uses a linear set-membership estimator and can give an ellipsoid set in which the true state lies. The four different approaches have different complexities, behavior and advantages that are surveyed and compared.
Nonlinear speed estimation of a GPS-free UAV
Santosuosso, Giovanni L.; Benzemrane, Khadidja; Damm, Gilney
2011-11-01
In this article, the problem of robust state observer design for a class of unmanned aerial vehicles (UAVs) is addressed. A prototype four-rotors helicopter robot for indoors and outdoors applications is considered: the drone is not equipped with GPS related devices, so we describe a strategy to estimate its translational velocity vector based on acceleration, angles and angular speeds measurements only. Since the linearised system is non-observable at the equilibrium point, a nonlinear observability verification is performed for persistently exciting trajectories. A global exponential solution to this open problem is provided in the framework of adaptive observation theory when exact measurements are available. A modified observer is presented to enhance velocity estimation robustness in the realistic case of noisy measurements. The results are compared with a classical estimation strategy based on the extended Kalman filter to test the algorithm's performance.
Institute of Scientific and Technical Information of China (English)
刘济; 高丽君
2014-01-01
It is significant to estimate the important process variables when process models are unknown. Therefore, the method of combining unscented Kalman filter(UKF) with neural network is used to solve the state estimation problems for a class of nonlinear systems whose models are unknown. The dynamic neural network is used to model for the nonlinear system, and the state and weights are updated at the same time by using UKF, which can achieve the purposes that the neural network approximate the real model, and the estimated values follow the real values. Two simulation examples are given to verify that the proposed approach gets good effects of estimation, and the greater the proportion of state in the output, the higher the estimation precision.%在模型未知的情况下，估计过程的重要变量尤为重要。鉴于此，采用不敏卡尔曼滤波(UKF)与神经网络相结合的方法，解决一类未知模型非线性系统的状态估计问题。采用动态神经网络对非线性系统进行建模，利用UKF对状态和权值进行同时更新，从而达到神经网络逼近真实模型，估计值跟随真实值的目的。通过两个仿真实例表明了所提出的方法具有良好的估计效果，并且状态在输出中的比重越大，其估计精度越高。
Highway traffic estimation of improved precision using the derivative-free nonlinear Kalman Filter
Rigatos, Gerasimos; Siano, Pierluigi; Zervos, Nikolaos; Melkikh, Alexey
2015-12-01
The paper proves that the PDE dynamic model of the highway traffic is a differentially flat one and by applying spatial discretization its shows that the model's transformation into an equivalent linear canonical state-space form is possible. For the latter representation of the traffic's dynamics, state estimation is performed with the use of the Derivative-free nonlinear Kalman Filter. The proposed filter consists of the Kalman Filter recursion applied on the transformed state-space model of the highway traffic. Moreover, it makes use of an inverse transformation, based again on differential flatness theory which enables to obtain estimates of the state variables of the initial nonlinear PDE model. By avoiding approximate linearizations and the truncation of nonlinear terms from the PDE model of the traffic's dynamics the proposed filtering methods outperforms, in terms of accuracy, other nonlinear estimators such as the Extended Kalman Filter. The article's theoretical findings are confirmed through simulation experiments.
Identification of a Class of Non-linear State Space Models using RPE Techniques
DEFF Research Database (Denmark)
Zhou, Wei-Wu; Blanke, Mogens
1989-01-01
The RPE (recursive prediction error) method in state-space form is developed in the nonlinear systems and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions...... of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows a quite convincing performance of the filter as combined parameter and state estimator...
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.
Estimating nonlinear dynamic equilibrium economies: a likelihood approach
2004-01-01
This paper presents a framework to undertake likelihood-based inference in nonlinear dynamic equilibrium economies. The authors develop a sequential Monte Carlo algorithm that delivers an estimate of the likelihood function of the model using simulation methods. This likelihood can be used for parameter estimation and for model comparison. The algorithm can deal both with nonlinearities of the economy and with the presence of non-normal shocks. The authors show consistency of the estimate and...
Nonlinear State Space Modeling and System Identification for Electrohydraulic Control
Directory of Open Access Journals (Sweden)
Jun Yan
2013-01-01
Full Text Available The paper deals with nonlinear modeling and identification of an electrohydraulic control system for improving its tracking performance. We build the nonlinear state space model for analyzing the highly nonlinear system and then develop a Hammerstein-Wiener (H-W model which consists of a static input nonlinear block with two-segment polynomial nonlinearities, a linear time-invariant dynamic block, and a static output nonlinear block with single polynomial nonlinearity to describe it. We simplify the H-W model into a linear-in-parameters structure by using the key term separation principle and then use a modified recursive least square method with iterative estimation of internal variables to identify all the unknown parameters simultaneously. It is found that the proposed H-W model approximates the actual system better than the independent Hammerstein, Wiener, and ARX models. The prediction error of the H-W model is about 13%, 54%, and 58% less than the Hammerstein, Wiener, and ARX models, respectively.
Institute of Scientific and Technical Information of China (English)
陈思忠; 卢凡; 吴志成; 杨林; 赵玉壮
2015-01-01
针对悬架系统非线性特性提出反馈线性化卡尔曼滤波算法。基于微分几何理论，通过求解坐标变换，将车辆非线性振动模型变换成可观测标准型，实现系统精确反馈线性化；采用线性卡尔曼滤波算法，针对变换的线性系统设计观测器，通过坐标逆变换获得原非线性系统的状态观测值。仿真结果表明，该算法能提高车辆振动状态观测精度、降低运算量。%Aiming at the nonlinearity of suspension system,a feedback linearization Kalman filter algorithm was proposed.Based on the differential geometry theory,the nonlinear vehicle vibration model was transformed into a certain observable normal form via the change of state coordinates.Based on the obtained linearized system,an observer was designed by using Kalman filter algorithm.Finally the estimated states of the nonlinear system were obtained through inverse transformation.The simulation results show that compared with the extended Kalman observer,the proposed algorithm can improve the observation accuracy of vehicle vibration states and reduce computational complexity.
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.
Multiple nonlinear parameter estimation using PI feedback control
Lith, van P. F.; Witteveen, H.; Betlem, B.H.L.; Roffel, B.
2001-01-01
Nonlinear parameters often need to be estimated during the building of chemical process models. To accomplish this, many techniques are available. This paper discusses an alternative view to parameter estimation, where the concept of PI feedback control is used to estimate model parameters. The appr
On state estimation in electric drives
Energy Technology Data Exchange (ETDEWEB)
Leon, A.E., E-mail: aleon@ymail.co [Instituto de Investigaciones en Ingenieria Electrica (IIIE) ' Alfredo Desages' (UNS-CONICET), Departamento de Ingenieria Electrica y de Computadoras, Universidad Nacional del Sur - UNS, 1253 Alem Avenue, P.O. 8000, Bahia Blanca (Argentina); Solsona, J.A., E-mail: jsolsona@uns.edu.a [Instituto de Investigaciones en Ingenieria Electrica (IIIE) ' Alfredo Desages' (UNS-CONICET), Departamento de Ingenieria Electrica y de Computadoras, Universidad Nacional del Sur - UNS, 1253 Alem Avenue, P.O. 8000, Bahia Blanca (Argentina)
2010-03-15
This paper deals with state estimation in electric drives. On one hand a nonlinear observer is designed, whereas on the other hand the speed state is estimated by using the dirty derivative from the position measured. The dirty derivative is an approximate version of the perfect derivative which introduces an estimation error few times analyzed in drive applications. For this reason, our proposal in this work consists in illustrating several aspects on the performance of the dirty derivator in presence of both model uncertainties and noisy measurements. To this end, a case study is introduced. The case study considers rotor speed estimation in a permanent magnet stepper motor, by assuming that rotor position and electrical variables are measured. In addition, this paper presents comments about the connection between dirty derivators and observers, and advantages and disadvantages of both techniques are also remarked.
A nonlinear state-space approach to hysteresis identification
Noël, J. P.; Esfahani, A. F.; Kerschen, G.; Schoukens, J.
2017-02-01
Most studies tackling hysteresis identification in the technical literature follow white-box approaches, i.e. they rely on the assumption that measured data obey a specific hysteretic model. Such an assumption may be a hard requirement to handle in real applications, since hysteresis is a highly individualistic nonlinear behaviour. The present paper adopts a black-box approach based on nonlinear state-space models to identify hysteresis dynamics. This approach is shown to provide a general framework to hysteresis identification, featuring flexibility and parsimony of representation. Nonlinear model terms are constructed as a multivariate polynomial in the state variables, and parameter estimation is performed by minimising weighted least-squares cost functions. Technical issues, including the selection of the model order and the polynomial degree, are discussed, and model validation is achieved in both broadband and sine conditions. The study is carried out numerically by exploiting synthetic data generated via the Bouc-Wen equations.
ASYMPTOTIC EFFICIENT ESTIMATION IN SEMIPARAMETRIC NONLINEAR REGRESSION MODELS
Institute of Scientific and Technical Information of China (English)
ZhuZhongyi; WeiBocheng
1999-01-01
In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extendedto fixed design semiparametrie nonlinear regression models. For these semiparametrie nonlinear regression models,the resulting estimator of parametric component of the model is shown to beasymptotically efficient and the strong convergence rate of nonparametric component is investigated. Many results (for example Chen (1988) ,Gao & Zhao (1993), Rice (1986) et al. ) are extended to fixed design semiparametric nonlinear regression models.
Artificial Neural Network Based State Estimators Integrated into Kalmtool
DEFF Research Database (Denmark)
Bayramoglu, Enis; Ravn, Ole; Poulsen, Niels Kjølstad
2012-01-01
In this paper we present a toolbox enabling easy evaluation and comparison of dierent ltering algorithms. The toolbox is called Kalmtool and is a set of MATLAB tools for state estimation of nonlinear systems. The toolbox now contains functions for Articial Neural Network Based State Estimation...
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Sequential MCMC Estimation of Nonlinear Instantaneous Frequency
2007-04-01
the WD for multicomponent sig- nals, the smoothing may smear the estimated IF values. IF estimation of seismic data was used in conjunction with the...Ws(t, f)df. (3) For multicomponent signals, ∑ l Al(t)e j2πcϕl(t), with nonlin- ear phase ϕl(t), the IF in (2) no longer provides the signal’s matched...collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources
Algorithms for non-linear M-estimation
DEFF Research Database (Denmark)
Madsen, Kaj; Edlund, O; Ekblom, H
1997-01-01
a sequence of estimation problems for linearized models is solved. In the testing we apply four estimators to ten non-linear data fitting problems. The test problems are also solved by the Generalized Levenberg-Marquardt method and standard optimization BFGS method. It turns out that the new method...
PARAMETER ESTIMATION METHODOLOGY FOR NONLINEAR SYSTEMS: APPLICATION TO INDUCTION MOTOR
Institute of Scientific and Technical Information of China (English)
G.KENNE; F.FLORET; H.NKWAWO; F.LAMNABHI-LAGARRIGUE
2005-01-01
This paper deals with on-line state and parameter estimation of a reasonably large class of nonlinear continuous-time systems using a step-by-step sliding mode observer approach. The method proposed can also be used for adaptation to parameters that vary with time. The other interesting feature of the method is that it is easily implementable in real-time. The efficiency of this technique is demonstrated via the on-line estimation of the electrical parameters and rotor flux of an induction motor. This application is based on the standard model of the induction motor expressed in rotor coordinates with the stator current and voltage as well as the rotor speed assumed to be measurable.Real-time implementation results are then reported and the ability of the algorithm to rapidly estimate the motor parameters is demonstrated. These results show the robustness of this approach with respect to measurement noise, discretization effects, parameter uncertainties and modeling inaccuracies.Comparisons between the results obtained and those of the classical recursive least square algorithm are also presented. The real-time implementation results show that the proposed algorithm gives better performance than the recursive least square method in terms of the convergence rate and the robustness with respect to measurement noise.
Modelling and Estimation of Hammerstein System with Preload Nonlinearity
Directory of Open Access Journals (Sweden)
Khaled ELLEUCH
2010-12-01
Full Text Available This paper deals with modelling and parameter identification of nonlinear systems described by Hammerstein model having asymmetric static nonlinearities known as preload nonlinearity characteristic. The simultaneous use of both an easy decomposition technique and the generalized orthonormal bases leads to a particular form of Hammerstein model containing a minimal parameters number. The employ of orthonormal bases for the description of the linear dynamic block conducts to a linear regressor model, so that least squares techniques can be used for the parameter estimation. Singular Values Decomposition (SVD technique has been applied to separate the coupled parameters. To demonstrate the feasibility of the identification method, an illustrative example is included.
ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL'S EQUATIONS
Institute of Scientific and Technical Information of China (English)
Marián Slodi(c)ka; Ján Bu(s)a Jr.
2008-01-01
This paper is devoted to the study of a nonlinear evolution eddy current model of the type (б)tB(H) +▽×(▽×H) = 0 subject to homogeneous Dirichlet boundary conditions H×v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B(H). We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B(H).
Nonlinear approximation with dictionaries I. Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2004-01-01
We study various approximation classes associated with m-term approximation by elements from a (possibly) redundant dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation...... with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove...
Nonlinear approximation with dictionaries, I: Direct estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
We study various approximation classes associated with $m$-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best $m$-term approximation is compared to new classes defined by considering $m......$-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space...
Nonlinear Interferometry via Fock State Projection
Khoury, G; Eisenberg, H S; Fonseca, E J S
2006-01-01
We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.
Nonlinear Interferometry via Fock-State Projection
Khoury, G.; Eisenberg, H. S.; Fonseca, E. J. S.; Bouwmeester, D.
2006-05-01
We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).OPEXFF1094-408710.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.
A process fault estimation strategy for non-linear dynamic systems
Pazera, Marcin; Korbicz, Józef
2017-01-01
The paper deals with the problem of simultaneous state and process fault estimation for non-linear dynamic systems. Instead of estimating the fault directly, its product with state and the state itself are estimated. To derive the fault from the product, a simple algebraic approach is proposed. The estimation strategy is based on the quadratic boundedness approach. The final part of the paper presents an illustrative example concerning a laboratory multi-tank system. The real data experiments clearly exhibit the performance of the proposed approach.
A generalization error estimate for nonlinear systems
DEFF Research Database (Denmark)
Larsen, Jan
1992-01-01
models of linear and simple neural network systems. Within the linear system GEN is compared to the final prediction error criterion and the leave-one-out cross-validation technique. It was found that the GEN estimate of the true generalization error is less biased on the average. It is concluded...
Chemical Nonlinearities and Radical Pair Lifetime Estimation
Robinson, Gregory
2013-03-01
Much attention has recently developed around chemical reactions that depend on applied static magnetic fields as weak as earth's. This interest is largely motivated by experiments that implicate the role of spin-selective radical pair recombination in biological magnetic sensing. Existing literature uses a straightforward calculation to approximate the expected lifetime of coherent radical pairs as a function of the minimum RF amplitude that is observed to disrupt magnetic navigation, apparently by decohering the radical pair via electronic Zeeman excitations. But we show that chemical nonlinearities can preclude direct computation of coherent pair lifetime without considering the cellular signalling mechanisms involved, and discuss whether it can explain the surprising fragility of some animals' compass sense. In particular, we demonstrate that an autocatalytic cycle can introduce threshold effects on the disruption sensitivity to applied oscillatory magnetic fields. We will show examples in the mean-field limit and consider the consequences of noise and fluctuations in the Freidlin-Wentzell picture of perturbed dynamical systems.
Discrete state space modeling and control of nonlinear unknown systems.
Savran, Aydogan
2013-11-01
A novel procedure for integrating neural networks (NNs) with conventional techniques is proposed to design industrial modeling and control systems for nonlinear unknown systems. In the proposed approach, a new recurrent NN with a special architecture is constructed to obtain discrete-time state-space representations of nonlinear dynamical systems. It is referred as the discrete state-space neural network (DSSNN). In the DSSNN, the outputs of the hidden layer neurons of the DSSNN represent the system's (pseudo) state. The inputs are fed to output neurons and the delayed outputs of the hidden layer neurons are fed to their inputs via adjustable weights. The discrete state space model of the actual system is directly obtained by training the DSSNN with the input-output data. A training procedure based on the back-propagation through time (BPTT) algorithm is developed. The Levenberg-Marquardt (LM) method with a trust region approach is used to update the DSSNN weights. Linear state space models enable to use well developed conventional analysis and design techniques. Thus, building a linear model of a system has primary importance in industrial applications. Thus, a suitable linearization procedure is proposed to derive the linear state space model from the nonlinear DSSNN representation. The controllability, observability and stability properties are examined. The state feedback controllers are designed with both the linear quadratic regulator (LQR) and the pole placement techniques. The regulator and servo control problems are both addressed. A full order observer is also designed to estimate the state variables. The performance of the proposed procedure is demonstrated by applying for both single-input single-output (SISO) and multiple-input multiple-output (MIMO) nonlinear control problems. © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Reduced Noise Effect in Nonlinear Model Estimation Using Multiscale Representation
Directory of Open Access Journals (Sweden)
Mohamed N. Nounou
2010-01-01
Full Text Available Nonlinear process models are widely used in various applications. In the absence of fundamental models, it is usually relied on empirical models, which are estimated from measurements of the process variables. Unfortunately, measured data are usually corrupted with measurement noise that degrades the accuracy of the estimated models. Multiscale wavelet-based representation of data has been shown to be a powerful data analysis and feature extraction tool. In this paper, these characteristics of multiscale representation are utilized to improve the estimation accuracy of the linear-in-the-parameters nonlinear model by developing a multiscale nonlinear (MSNL modeling algorithm. The main idea in this MSNL modeling algorithm is to decompose the data at multiple scales, construct multiple nonlinear models at multiple scales, and then select among all scales the model which best describes the process. The main advantage of the developed algorithm is that it integrates modeling and feature extraction to improve the robustness of the estimated model to the presence of measurement noise in the data. This advantage of MSNL modeling is demonstrated using a nonlinear reactor model.
Identification of a class of nonlinear state-space models using RPE techniques
DEFF Research Database (Denmark)
Zhou, W. W.; Blanke, Mogens
1986-01-01
The recursive prediction error methods in state-space form have been efficiently used as parameter identifiers for linear systems, and especially Ljung's innovations filter using a Newton search direction has proved to be quite ideal. In this paper, the RPE method in state-space form is developed...... to the nonlinear case and extended to include the exact form of a nonlinearity, thus enabling structure preservation for certain classes of nonlinear systems. Both the discrete and the continuous-discrete versions of the algorithm in an innovations model are investigated, and a nonlinear simulation example shows...... a quite convincing performance of the filter as combined parameter and state estimator....
Directory of Open Access Journals (Sweden)
Yin Dawei
2010-12-01
Full Text Available The estimation of aeroengine component deviation parameters (CDP is an important portion of aeronautical propulsion system performance-seeking control (PSC, which employs linear Kalman filter based on piecewise state variable model (SVM traditionally. But it’s not easy to get SVM, and the process of linearizing the nonlinear model to get the SVM will introduce errors. So parameters nonlinear estimation was introduced based on the nonlinear aeroengine model directly. The nonlinear estimation model is established according to aeroengine operation balance and the measured and calculated values matching of measurable parameters. The nonlinear estimation was changed to a problem of solving complex nonlinear equations, which is equal to an optimization problem. Time-varying inertia weight particle swarm optimization (PSO with constriction factor was employed to solve the problem in order to satisfy the requirement of precision and calculation speed. The simulation results of a given turbofan engine show that utilizing the improved PSO algorithm can estimate the CPD precisely with satisfied converging speed.
On State Estimation with Bad Data Detection
Xu, Weiyu; Tang, Ao
2011-01-01
In this paper, we consider the problem of state estimation through observations possibly corrupted with both bad data and additive observation noises. A mixed $\\ell_1$ and $\\ell_2$ convex programming is used to separate both sparse bad data and additive noises from the observations. Through using the almost Euclidean property for a linear subspace, we derive a new performance bound for the state estimation error under sparse bad data and additive observation noises. Our main contribution is to provide sharp bounds on the almost Euclidean property of a linear subspace, using the "escape-through-a-mesh" theorem from geometric functional analysis. We also propose and numerically evaluate an iterative convex programming approach to performing bad data detections in nonlinear electrical power networks problems.
Nonlinear observer to estimate polarization phenomenon in membrane distillation
Directory of Open Access Journals (Sweden)
Khoukhi Billal
2015-01-01
Full Text Available This paper presents a bi-dimensional dynamic model of Direct Contact Membrane Desalination (DCMD process. Most of the MD configuration processes have been modeled as steady-state one-dimensional systems. Stationary two-dimensional MD models have been considered only in very few studies. In this work, a dynamic model of a DCMD process is developed. The model is implemented using Matlab/Simulink environment. Numerical simulations are conducted for different operational parameters at the module inlets such as the feed and permeate temperature or feed and permeate flow rate. The results are compared with experimental data published in the literature. The work presents also a feed forward control that compensates the possible decrease of the temperature gradient by increasing the flow rate. This work also deals with a development of nonlinear observer to estimate temperature polarization inside the membrane. The observer gives a good profile and longitudinal temperature estimations and shows a good prediction of pure water flux production.
Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint
Martínez-Guerra, Rafael
2017-01-01
This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.
A Concept of Approximated Densities for Efficient Nonlinear Estimation
Directory of Open Access Journals (Sweden)
Virginie F. Ruiz
2002-10-01
Full Text Available This paper presents the theoretical development of a nonlinear adaptive filter based on a concept of filtering by approximated densities (FAD. The most common procedures for nonlinear estimation apply the extended Kalman filter. As opposed to conventional techniques, the proposed recursive algorithm does not require any linearisation. The prediction uses a maximum entropy principle subject to constraints. Thus, the densities created are of an exponential type and depend on a finite number of parameters. The filtering yields recursive equations involving these parameters. The update applies the Bayes theorem. Through simulation on a generic exponential model, the proposed nonlinear filter is implemented and the results prove to be superior to that of the extended Kalman filter and a class of nonlinear filters based on partitioning algorithms.
Maximum Likelihood Estimation of Nonlinear Structural Equation Models.
Lee, Sik-Yum; Zhu, Hong-Tu
2002-01-01
Developed an EM type algorithm for maximum likelihood estimation of a general nonlinear structural equation model in which the E-step is completed by a Metropolis-Hastings algorithm. Illustrated the methodology with results from a simulation study and two real examples using data from previous studies. (SLD)
Nonlinear system identification and control using state transition algorithm
Yang, Chunhua; Gui, Weihua
2012-01-01
This paper presents a novel optimization method named state transition algorithm (STA) to solve the problem of identification and control for nonlinear system. In the proposed algorithm, a solution to optimization problem is considered as a state, and the updating of a solution equates to the process of state transition, which makes the STA easy to understand and convenient to be implemented. First, the STA is applied to identify the optimal parameters of the estimated system with previously known structure. With the accurate estimated model, an off-line PID controller is then designed optimally by using the STA as well. Experimental results demonstrate the validity of the methodology, and comparison to STA with other optimization algorithms confirms that STA is a promising alternative method for system identification and control due to its stronger search ability, faster convergence speed and more stable performance.
CONSERVATIVE ESTIMATING FUNCTIONIN THE NONLINEAR REGRESSION MODEL WITHAGGREGATED DATA
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.
On space enrichment estimator for nonlinear Poisson-Boltzmann
Randrianarivony, Maharavo
2013-10-01
We consider the mathematical aspect of the nonlinear Poisson-Boltzmann equation which physically governs the ionic interaction between solute and solvent media. The presented a-posteriori estimates can be computed locally in a very efficient manner. The a-posteriori error is based upon hierarchical space enrichment which ensures its efficiency and reliability. A brief survey of the solving of the nonlinear system resulting from the FEM discretization is reported. To corroborate the analysis, we report on a few numerical results for illustrations. We numerically examine some values of the constants encountered in the theoretical study.
Robust Nonlinear Regression in Enzyme Kinetic Parameters Estimation
Directory of Open Access Journals (Sweden)
Maja Marasović
2017-01-01
Full Text Available Accurate estimation of essential enzyme kinetic parameters, such as Km and Vmax, is very important in modern biology. To this date, linearization of kinetic equations is still widely established practice for determining these parameters in chemical and enzyme catalysis. Although simplicity of linear optimization is alluring, these methods have certain pitfalls due to which they more often then not result in misleading estimation of enzyme parameters. In order to obtain more accurate predictions of parameter values, the use of nonlinear least-squares fitting techniques is recommended. However, when there are outliers present in the data, these techniques become unreliable. This paper proposes the use of a robust nonlinear regression estimator based on modified Tukey’s biweight function that can provide more resilient results in the presence of outliers and/or influential observations. Real and synthetic kinetic data have been used to test our approach. Monte Carlo simulations are performed to illustrate the efficacy and the robustness of the biweight estimator in comparison with the standard linearization methods and the ordinary least-squares nonlinear regression. We then apply this method to experimental data for the tyrosinase enzyme (EC 1.14.18.1 extracted from Solanum tuberosum, Agaricus bisporus, and Pleurotus ostreatus. The results on both artificial and experimental data clearly show that the proposed robust estimator can be successfully employed to determine accurate values of Km and Vmax.
State Estimation for Tensegrity Robots
Caluwaerts, Ken; Bruce, Jonathan; Friesen, Jeffrey M.; Sunspiral, Vytas
2016-01-01
Tensegrity robots are a class of compliant robots that have many desirable traits when designing mass efficient systems that must interact with uncertain environments. Various promising control approaches have been proposed for tensegrity systems in simulation. Unfortunately, state estimation methods for tensegrity robots have not yet been thoroughly studied. In this paper, we present the design and evaluation of a state estimator for tensegrity robots. This state estimator will enable existing and future control algorithms to transfer from simulation to hardware. Our approach is based on the unscented Kalman filter (UKF) and combines inertial measurements, ultra wideband time-of-flight ranging measurements, and actuator state information. We evaluate the effectiveness of our method on the SUPERball, a tensegrity based planetary exploration robotic prototype. In particular, we conduct tests for evaluating both the robot's success in estimating global position in relation to fixed ranging base stations during rolling maneuvers as well as local behavior due to small-amplitude deformations induced by cable actuation.
Fault Diagnosis of Nonlinear Systems Using Structured Augmented State Models
Institute of Scientific and Technical Information of China (English)
Jochen Aβfalg; Frank Allg(o)wer
2007-01-01
This paper presents an internal model approach for modeling and diagnostic functionality design for nonlinear systems operating subject to single- and multiple-faults. We therefore provide the framework of structured augmented state models. Fault characteristics are considered to be generated by dynamical exosystems that are switched via equality constraints to overcome the augmented state observability limiting the number of diagnosable faults. Based on the proposed model, the fault diagnosis problem is specified as an optimal hybrid augmented state estimation problem. Sub-optimal solutions are motivated and exemplified for the fault diagnosis of the well-known three-tank benchmark. As the considered class of fault diagnosis problems is large, the suggested approach is not only of theoretical interest but also of high practical relevance.
Nonlinear Memory and Risk Estimation in Financial Records
Bunde, Armin; Bogachev, Mikhail I.
It is well known that financial data sets are multifractal and governed by nonlinear correlations. Here we are interested in the daily returns of a financial asset and in the way the occurrence of large gains or losses is triggered by the nonlinear memory. To this end, we study the statistics of the return intervals between gains (or losses) above a certain threshold Q. In the case of i.i.d. random numbers the probability density function (pdf) of the return intervals decays exponentially and the return intervals are uncorrelated. Here we show that the nonlinear correlations lead to a power law decay of the pdf and linear long-term correlations between the return intervals that are described by a power-law decay of the corresponding autocorrelation function. From the pdf of the return intervals one obtains the risk function W Q (t; Δt), which is the probability that within the next Δt units of time at least one event above Q occurs, if the last event occurred t time units ago. We propose an analytical estimate of W Q and show explicitly that the proposed method is superior to the conventional precursory pattern recognition technique widely used in signal analysis, which requires considerable fine-tuning and is difficult to implement. We also show that the estimation of the Value at Risk, which is a standard tool in finances, can be improved considerably compared with previous estimates.
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation.
Liu, Xi; Qu, Hua; Zhao, Jihong; Yue, Pengcheng; Wang, Meng
2016-09-20
A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.
Estimation of Nonlinear Dynamic Panel Data Models with Individual Effects
Directory of Open Access Journals (Sweden)
Yi Hu
2014-01-01
Full Text Available This paper suggests a generalized method of moments (GMM based estimation for dynamic panel data models with individual specific fixed effects and threshold effects simultaneously. We extend Hansen’s (Hansen, 1999 original setup to models including endogenous regressors, specifically, lagged dependent variables. To address the problem of endogeneity of these nonlinear dynamic panel data models, we prove that the orthogonality conditions proposed by Arellano and Bond (1991 are valid. The threshold and slope parameters are estimated by GMM, and asymptotic distribution of the slope parameters is derived. Finite sample performance of the estimation is investigated through Monte Carlo simulations. It shows that the threshold and slope parameter can be estimated accurately and also the finite sample distribution of slope parameters is well approximated by the asymptotic distribution.
Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.
Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello
2007-01-01
A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.
State dependent matrices and balanced energy functions for nonlinear systems
Scherpen, Jacquelien M.A.; Gray, W. Steven
2000-01-01
The nonlinear extension of the balancing procedure requires the case of state dependent quadratic forms for the energy functions, i.e., the nonlinear extensions of the linear Gramians are state dependent matrices. These extensions have some interesting ambiguities that do not occur in the linear cas
Nonlinear ionic transport through microstructured solid electrolytes: homogenization estimates
Curto Sillamoni, Ignacio J.; Idiart, Martín I.
2016-10-01
We consider the transport of multiple ionic species by diffusion and migration through microstructured solid electrolytes in the presence of strong electric fields. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is heuristically deduced from a multi-scale convergence analysis of the relevant field equations. The resulting homogenized response involves an effective dissipation potential per species. Each potential is mathematically akin to that of a standard nonlinear heterogeneous conductor. A ‘linear-comparison’ homogenization technique is then used to generate estimates for these nonlinear potentials in terms of available estimates for corresponding linear conductors. By way of example, use is made of the Maxwell-Garnett and effective-medium linear approximations to generate estimates for two-phase systems with power-law dissipation. Explicit formulas are given for some limiting cases. In the case of threshold-type behavior, the estimates exhibit non-analytical dilute limits and seem to be consistent with fields localized in low energy paths.
Coupled Ito equations of continuous quantum state measurement, and estimation
Diósi, L; Konrad, T; Scherer, A; Audretsch, Juergen; Diosi, Lajos; Konrad, Thomas; Scherer, Artur
2006-01-01
We discuss a non-linear stochastic master equation that governs the time-evolution of the estimated quantum state. Its differential evolution corresponds to the infinitesimal updates that depend on the time-continuous measurement of the true quantum state. The new stochastic master equation couples to the two standard stochastic differential equations of time-continuous quantum measurement. For the first time, we can prove that the calculated estimate almost always converges to the true state, also at low-efficiency measurements. We show that our single-state theory can be adapted to weak continuous ensemble measurements as well.
Linear vs. nonlinear porosity estimation of NMR oil reservoir data
Directory of Open Access Journals (Sweden)
Mohsen Abdou Abou Mandour
2010-09-01
Full Text Available Nuclear magnetic resonance is widely used to assess oil reservoir properties especially those that can not be evaluated using conventional techniques. In this regard, porosity determination and the related estimation of the oil present play a very important role in assessing the eco1nomic value of the oil wells. Nuclear Magnetic Resonance data is usually fit to the sum of decaying exponentials. The resulting distribution; i.e. T2 distribution; is directly related to porosity determination. In this work, three reservoir core samples (Tight Sandstone and two Carbonate samples were analyzed. Linear Least Square method (LLS and non-linear least square fitting using Levenberg-Marquardt method were used to calculate the T2 distribution and the resulting incremental porosity. Parametric analysis for the two methods was performed to evaluate the impact of number of exponentials, and effect of the regularization parameter (? on the smoothing of the solution. Effect of the type of solution on porosity determination was carried out. It was found that 12 exponentials is the optimum number of exponentials for both the linear and nonlinear solutions. In the mean time, it was shown that the linear solution begins to be smooth at α = 0.5 which corresponds to the standard industrial value for the regularization parameter. The order of magnitude of time needed for the linear solution is in the range of few minutes while it is in the range of few hours for the nonlinear solution. Regardless of the fact that small differences exist between the linear and nonlinear solutions, these small values make an appreciable difference in porosity. The nonlinear solution predicts 12% less porosity for the tight sandstone sample and 4.5 % and 13 % more porosity in the two carbonate samples respectively.
Murphy, Patrick Charles
1985-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.
Sensorless position estimator applied to nonlinear IPMC model
Bernat, Jakub; Kolota, Jakub
2016-11-01
This paper addresses the issue of estimating position for an ionic polymer metal composite (IPMC) known as electro active polymer (EAP). The key step is the construction of a sensorless mode considering only current feedback. This work takes into account nonlinearities caused by electrochemical effects in the material. Owing to the recent observer design technique, the authors obtained both Lyapunov function based estimation law as well as sliding mode observer. To accomplish the observer design, the IPMC model was identified through a series of experiments. The research comprises time domain measurements. The identification process was completed by means of geometric scaling of three test samples. In the proposed design, the estimated position accurately tracks the polymer position, which is illustrated by the experiments.
Prediction and simulation errors in parameter estimation for nonlinear systems
Aguirre, Luis A.; Barbosa, Bruno H. G.; Braga, Antônio P.
2010-11-01
This article compares the pros and cons of using prediction error and simulation error to define cost functions for parameter estimation in the context of nonlinear system identification. To avoid being influenced by estimators of the least squares family (e.g. prediction error methods), and in order to be able to solve non-convex optimisation problems (e.g. minimisation of some norm of the free-run simulation error), evolutionary algorithms were used. Simulated examples which include polynomial, rational and neural network models are discussed. Our results—obtained using different model classes—show that, in general the use of simulation error is preferable to prediction error. An interesting exception to this rule seems to be the equation error case when the model structure includes the true model. In the case of error-in-variables, although parameter estimation is biased in both cases, the algorithm based on simulation error is more robust.
Multivariable adaptive control and estimation of a nonlinear wastewater treatment process
Energy Technology Data Exchange (ETDEWEB)
Ben Youssef, C.; Dahhou, B. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France)]|[Institut National des Sciences Appliquees (INSA), 31 - Toulouse (France)
1995-12-31
In this paper, an approach for estimating biological state and parameter variables and for controlling a non linear wastewater treatment process is developed. Combination of a nonlinear estimation procedure and a multivariable reference model control law provides favourable performances for tracking a given model-based reference model despite disturbances and system parameter uncertainties. Convergence of both estimation and control scheme are demonstrated via Lyapunov`s method. Simulation study with additive measurements noises and parameter jumps shows the efficiency and significant robustness of the control methodology developed for this non linear process. (author) 13 refs.
Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems
N'Doye, Ibrahima
2015-07-01
This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.
Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems
Directory of Open Access Journals (Sweden)
Banga Julio R
2006-11-01
Full Text Available Abstract Background We consider the problem of parameter estimation (model calibration in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector. In order to surmount these difficulties, global optimization (GO methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness. Results We have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown structure (i.e. black-box models. In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned successful methods. Conclusion Robust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously
Campbell, D A; Chkrebtii, O
2013-12-01
Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories.
Noise and nonlinear estimation with optimal schemes in DTI.
Özcan, Alpay
2010-11-01
In general, the estimation of the diffusion properties for diffusion tensor experiments (DTI) is accomplished via least squares estimation (LSE). The technique requires applying the logarithm to the measurements, which causes bad propagation of errors. Moreover, the way noise is injected to the equations invalidates the least squares estimate as the best linear unbiased estimate. Nonlinear estimation (NE), despite its longer computation time, does not possess any of these problems. However, all of the conditions and optimization methods developed in the past are based on the coefficient matrix obtained in a LSE setup. In this article, NE for DTI is analyzed to demonstrate that any result obtained relatively easily in a linear algebra setup about the coefficient matrix can be applied to the more complicated NE framework. The data, obtained using non-optimal and optimized diffusion gradient schemes, are processed with NE. In comparison with LSE, the results show significant improvements, especially for the optimization criterion. However, NE does not resolve the existing conflicts and ambiguities displayed with LSE methods.
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.
Cao, Jiguo
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
Cao, Jiguo; Huang, Jianhua Z; Wu, Hulin
2012-01-01
Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online.
New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics
Institute of Scientific and Technical Information of China (English)
KUANG Mai-Hua; MA Shan-Jun; LIU Dong-Mei
2008-01-01
Based on the technique of integral within an ordered product of nonlinear bosonic operators, we construct a new kind of tripartite nonlinear entangled state |α,γ>λ in 3-mode Fock space, which can make up a complete set. We also simply discuss its properties and application.
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
State of charge estimation in Ni-MH rechargeable batteries
Energy Technology Data Exchange (ETDEWEB)
Milocco, R.H. [Grupo Control Automatico y Sistemas (GCAyS), Depto. Electrotecnia, Facultad de Ingenieria, Universidad Nacional del Comahue, Buenos Aires 1400, 8300 Neuquen (Argentina); Castro, B.E. [Instituto de Investigaciones Fisicoquimicas Teoricas y Aplicadas (INIFTA), Universidad Nacional de La Plata, Suc 4, CC16 (1900), La Plata (Argentina)
2009-10-20
In this work we estimate the state of charge (SOC) of Ni-MH rechargeable batteries using the Kalman filter based on a simplified electrochemical model. First, we derive the complete electrochemical model of the battery which includes diffusional processes and kinetic reactions in both Ni and MH electrodes. The full model is further reduced in a cascade of two parts, a linear time invariant dynamical sub-model followed by a static nonlinearity. Both parts are identified using the current and potential measured at the terminals of the battery with a simple 1-D minimization procedure. The inverse of the static nonlinearity together with a Kalman filter provide the SOC estimation as a linear estimation problem. Experimental results with commercial batteries are provided to illustrate the estimation procedure and to show the performance. (author)
Passive Control and ε-Bound Estimation of Singularly Perturbed Systems with Nonlinear Nonlinearities
Directory of Open Access Journals (Sweden)
Linna Zhou
2013-01-01
Full Text Available This paper considers the problems of passivity analysis and synthesis of singularly perturbed systems with nonlinear uncertainties. By a novel storage function depending on the singular perturbation parameter ε, a new method is proposed to estimate the ε-bound, such that the system is passive when the singular perturbation parameter is lower than the ε-bound. Furthermore, a controller design method is proposed to achieve a predefined ε-bound. The proposed results are shown to be less conservative than the existing ones because the adopted storage function is more general. Finally, an RLC circuit is presented to illustrate the advantages and effectiveness of the proposed methods.
Superposition of nonlinear coherent states on a sphere
Directory of Open Access Journals (Sweden)
T Hosseinzadeh
2013-09-01
Full Text Available In this paper, by using the nonlinear coherent states on a sphere, we introduce superposition of the aforementioned coherent states. Then, we consider quantum optical properties of these new superposed states and compare these properties with the corresponding properties of the nonlinear coherent states on the sphere. Specifically, we investigate their characteristics function, photon-number distribution, Mandel parameter, quadrature squeezing, anti-bunching effect and Wigner function, and obtain the curvature effect on the properties of the superposed states. Finally, by using the trapped atom system, we introduce a theoretical scheme to generate superposition of the coherent states on the sphere.
Parameter Estimation Technique of Nonlinear Prosthetic Hand System
Directory of Open Access Journals (Sweden)
M.H.Jali
2016-10-01
Full Text Available This paper illustrated the parameter estimation technique of motorized prosthetic hand system. Prosthetic hands have become importance device to help amputee to gain a normal functional hand. By integrating various types of actuators such as DC motor, hydraulic and pneumatic as well as mechanical part, a highly useful and functional prosthetic device can be produced. One of the first steps to develop a prosthetic device is to design a control system. Mathematical modeling is derived to ease the control design process later on. This paper explained the parameter estimation technique of a nonlinear dynamic modeling of the system using Lagrangian equation. The model of the system is derived by considering the energies of the finger when it is actuated by the DC motor. The parameter estimation technique is implemented using Simulink Design Optimization toolbox in MATLAB. All the parameters are optimized until it achieves a satisfactory output response. The results show that the output response of the system with parameter estimation value produces a better response compare to the default value
Recent advances in estimating nonlinear models with applications in economics and finance
Ma, Jun
2013-01-01
Featuring current research in economics, finance and management, this book surveys nonlinear estimation techniques and offers new methods and insights into nonlinear time series analysis. Covers Markov Switching Models for analyzing economics series and more.
De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.
2017-09-01
The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.
Directory of Open Access Journals (Sweden)
Bahita Mohamed
2011-01-01
Full Text Available In this work, we introduce an adaptive neural network controller for a class of nonlinear systems. The approach uses two Radial Basis Functions, RBF networks. The first RBF network is used to approximate the ideal control law which cannot be implemented since the dynamics of the system are unknown. The second RBF network is used for on-line estimating the control gain which is a nonlinear and unknown function of the states. The updating laws for the combined estimator and controller are derived through Lyapunov analysis. Asymptotic stability is established with the tracking errors converging to a neighborhood of the origin. Finally, the proposed method is applied to control and stabilize the inverted pendulum system.
Realization of non-linear coherent states by photonic lattices
Directory of Open Access Journals (Sweden)
Shahram Dehdashti
2015-06-01
Full Text Available In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2 and su(1, 1 coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Realization of non-linear coherent states by photonic lattices
Energy Technology Data Exchange (ETDEWEB)
Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn [State Key Laboratory of Modern Optical Instrumentations, Zhejiang University, Hangzhou 310027 (China); The Electromagnetics Academy at Zhejiang University, Zhejiang University, Hangzhou 310027 (China); Liu, Jiarui, E-mail: jrliu@zju.edu.cn; Yu, Faxin [School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027 (China)
2015-06-15
In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.
Controllability, not chaos, key criterion for ocean state estimation
Gebbie, Geoffrey; Hsieh, Tsung-Lin
2017-07-01
The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or 4D-VAR) has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient-descent algorithms is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task - a solution of the time-dependent surface boundary conditions that result from atmosphere-ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that nonlinearity should not be a fundamental obstacle to ocean state estimation with eddy-resolving models, especially when using an improved first-guess trajectory.
Controllability, not chaos, key criterion for ocean state estimation
Directory of Open Access Journals (Sweden)
G. Gebbie
2017-07-01
Full Text Available The Lagrange multiplier method for combining observations and models (i.e., the adjoint method or 4D-VAR has been avoided or approximated when the numerical model is highly nonlinear or chaotic. This approach has been adopted primarily due to difficulties in the initialization of low-dimensional chaotic models, where the search for optimal initial conditions by gradient-descent algorithms is hampered by multiple local minima. Although initialization is an important task for numerical weather prediction, ocean state estimation usually demands an additional task – a solution of the time-dependent surface boundary conditions that result from atmosphere–ocean interaction. Here, we apply the Lagrange multiplier method to an analogous boundary control problem, tracking the trajectory of the forced chaotic pendulum. Contrary to previous assertions, it is demonstrated that the Lagrange multiplier method can track multiple chaotic transitions through time, so long as the boundary conditions render the system controllable. Thus, the nonlinear timescale poses no limit to the time interval for successful Lagrange multiplier-based estimation. That the key criterion is controllability, not a pure measure of dynamical stability or chaos, illustrates the similarities between the Lagrange multiplier method and other state estimation methods. The results with the chaotic pendulum suggest that nonlinearity should not be a fundamental obstacle to ocean state estimation with eddy-resolving models, especially when using an improved first-guess trajectory.
Robust Homography Estimation Based on Nonlinear Least Squares Optimization
Directory of Open Access Journals (Sweden)
Wei Mou
2014-01-01
Full Text Available The homography between image pairs is normally estimated by minimizing a suitable cost function given 2D keypoint correspondences. The correspondences are typically established using descriptor distance of keypoints. However, the correspondences are often incorrect due to ambiguous descriptors which can introduce errors into following homography computing step. There have been numerous attempts to filter out these erroneous correspondences, but it is unlikely to always achieve perfect matching. To deal with this problem, we propose a nonlinear least squares optimization approach to compute homography such that false matches have no or little effect on computed homography. Unlike normal homography computation algorithms, our method formulates not only the keypoints’ geometric relationship but also their descriptor similarity into cost function. Moreover, the cost function is parametrized in such a way that incorrect correspondences can be simultaneously identified while the homography is computed. Experiments show that the proposed approach can perform well even with the presence of a large number of outliers.
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...
State energy data report 1994: Consumption estimates
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-10-01
This document provides annual time series estimates of State-level energy consumption by major economic sector. The estimates are developed in the State Energy Data System (SEDS), operated by EIA. SEDS provides State energy consumption estimates to members of Congress, Federal and State agencies, and the general public, and provides the historical series needed for EIA`s energy models. Division is made for each energy type and end use sector. Nuclear electric power is included.
Optimal state discrimination and unstructured search in nonlinear quantum mechanics
Childs, Andrew M.; Young, Joshua
2016-02-01
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit using the Gross-Pitaevskii equation, a model of nonlinear quantum mechanics that arises as an effective description of Bose-Einstein condensates. Using this protocol, we present an algorithm for unstructured search in the Gross-Pitaevskii model, obtaining an exponential improvement over a previous algorithm of Meyer and Wong. This result establishes a limitation on the effectiveness of the Gross-Pitaevskii approximation. More generally, we demonstrate similar behavior under a family of related nonlinearities, giving evidence that the ability to quickly discriminate nonorthogonal states and thereby solve unstructured search is a generic feature of nonlinear quantum mechanics.
Energy Technology Data Exchange (ETDEWEB)
Harlim, John, E-mail: jharlim@psu.edu [Department of Mathematics and Department of Meteorology, the Pennsylvania State University, University Park, PA 16802, Unites States (United States); Mahdi, Adam, E-mail: amahdi@ncsu.edu [Department of Mathematics, North Carolina State University, Raleigh, NC 27695 (United States); Majda, Andrew J., E-mail: jonjon@cims.nyu.edu [Department of Mathematics and Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012 (United States)
2014-01-15
A central issue in contemporary science is the development of nonlinear data driven statistical–dynamical models for time series of noisy partial observations from nature or a complex model. It has been established recently that ad-hoc quadratic multi-level regression models can have finite-time blow-up of statistical solutions and/or pathological behavior of their invariant measure. Recently, a new class of physics constrained nonlinear regression models were developed to ameliorate this pathological behavior. Here a new finite ensemble Kalman filtering algorithm is developed for estimating the state, the linear and nonlinear model coefficients, the model and the observation noise covariances from available partial noisy observations of the state. Several stringent tests and applications of the method are developed here. In the most complex application, the perfect model has 57 degrees of freedom involving a zonal (east–west) jet, two topographic Rossby waves, and 54 nonlinearly interacting Rossby waves; the perfect model has significant non-Gaussian statistics in the zonal jet with blocked and unblocked regimes and a non-Gaussian skewed distribution due to interaction with the other 56 modes. We only observe the zonal jet contaminated by noise and apply the ensemble filter algorithm for estimation. Numerically, we find that a three dimensional nonlinear stochastic model with one level of memory mimics the statistical effect of the other 56 modes on the zonal jet in an accurate fashion, including the skew non-Gaussian distribution and autocorrelation decay. On the other hand, a similar stochastic model with zero memory levels fails to capture the crucial non-Gaussian behavior of the zonal jet from the perfect 57-mode model.
DEFF Research Database (Denmark)
Sommer, Helle Mølgaard; Holst, Helle; Spliid, Henrik;
1995-01-01
and the growth of the biomass are described by the Monod model consisting of two nonlinear coupled first-order differential equations. The objective of this study was to estimate the kinetic parameters in the Monod model and to test whether the parameters from the three identical experiments have the same values....... Estimation of the parameters was obtained using an iterative maximum likelihood method and the test used was an approximative likelihood ratio test. The test showed that the three sets of parameters were identical only on a 4% alpha level....
DEFF Research Database (Denmark)
Belleter, Dennis J.W.; Galeazzi, Roberto; Fossen, Thor Inge
2015-01-01
This paper presents a global exponential stability (GES) proof for a signalbased nonlinear wave encounter frequency estimator. The estimator under consideration is a second-order nonlinear observer designed to estimate the frequency of a sinusoid with unknown frequency, amplitude and phase. The G...
Institute of Scientific and Technical Information of China (English)
田行伟; 石莹; 高阳; 蒋函彤; 王子宁
2016-01-01
利用Taylor级数展开法将非线性非方广义系统线性化，再利用奇异值分解方法将线性化后的非方广义系统降阶为等价正常系统；基于Kalman滤波理论，得到非线性非方广义系统Kal-man状态预报器和滤波器。并给出了数值Matlab仿真算例，验证了所提方法的有效性。%Taylor series expansion is used to making the nonlinear non-square descriptor systems to be linearized , then using singular value decomposition method to reduced a normal system .Basing on Kalman filtering theory , the state Kalman filter and predictor for the nonlinear non-square descriptor systems are presented .The simulation example is given to show the correctness and effectiveness of the proposed algorithm .
State Alcohol-Impaired-Driving Estimates
... estimates presented, and for 2012 range from a low of 10-percent known BACs to a high of 91-percent known BACs. States with higher rates of known BACs yield estimates of fatal crash alcohol involvement with greater accuracy and precision. State-by-State ...
State energy data report 1993: Consumption estimates
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-07-01
The State Energy Data Report (SEDR) provides annual time series estimates of State-level energy consumption by major economic sector. The estimates are developed in the State Energy Data System (SEDS), which is maintained and operated by the Energy Information Administration (EIA). The goal in maintaining SEDS is to create historical time series of energy consumption by State that are defined as consistently as possible over time and across sectors. SEDS exists for two principal reasons: (1) to provide State energy consumption estimates to Members of Congress, Federal and State agencies, and the general public; and (2) to provide the historical series necessary for EIA`s energy models.
Power system operations: State estimation distributed processing
Ebrahimian, Mohammad Reza
We present an application of a robust and fast parallel algorithm to power system state estimation with minimal amount of modifications to existing state estimators presently in place using the Auxiliary Problem Principle. We demonstrate its effectiveness on IEEE test systems, the Electric Reliability Counsel of Texas (ERCOT), and the Southwest Power Pool (SPP) systems. Since state estimation formulation may lead to an ill-conditioned system, we provide analytical explanations of the effects of mixtures of measurements on the condition of the state estimation information matrix. We demonstrate the closeness of the analytical equations to condition of several test case systems including IEEE RTS-96 and IEEE 118 bus systems. The research on the condition of the state estimation problem covers the centralized as well as distributed state estimation.
Nonlinear self-flipping of polarization states in asymmetric waveguides
Zhang, Wen Qi; Monro, Tanya M; Afshar, V Shahraam
2012-01-01
Waveguides of subwavelength dimensions with asymmetric geometries, such as rib waveguides, can display nonlinear polarization effects in which the nonlinear phase difference dominates the linear contribution, provided the birefringence is sufficiently small. We demonstrate that self-flipping polarization states can appear in such rib waveguides at low (mW) power levels. We describe an optical power limiting device with optimized rib waveguide parameters that can operate at low powers with switching properties.
On a state space approach to nonlinear H∞ control
Schaft, van der A.J.
1991-01-01
We study the standard H∞ optimal control problem using state feedback for smooth nonlinear control systems. The main theorem obtained roughly states that the L2-induced norm (from disturbances to inputs and outputs) can be made smaller than a constant γ > 0 if the corresponding H∞ norm for the syste
Solid-State Thermionic Power Generators: An Analytical Analysis in the Nonlinear Regime
Zebarjadi, M.
2017-07-01
Solid-state thermionic power generators are an alternative to thermoelectric modules. In this paper, we develop an analytical model to investigate the performance of these generators in the nonlinear regime. We identify dimensionless parameters determining their performance and provide measures to estimate an acceptable range of thermal and electrical resistances of thermionic generators. We find the relation between the optimum load resistance and the internal resistance and suggest guidelines for the design of thermionic power generators. Finally, we show that in the nonlinear regime, thermionic power generators can have efficiency values higher than the state-of-the-art thermoelectric modules.
State Energy Data Report, 1991: Consumption estimates
Energy Technology Data Exchange (ETDEWEB)
1993-05-01
The State Energy Data Report (SEDR) provides annual time series estimates of State-level energy consumption by major economic sector. The estimates are developed in the State Energy Data System (SEDS), which is maintained and operated by the Energy Information Administration (EIA). The goal in maintaining SEDS is to create historical time series of energy consumption by State that are defined as consistently as possible over time and across sectors. SEDS exists for two principal reasons: (1) to provide State energy consumption estimates to the Government, policy makers, and the public; and (2) to provide the historical series necessary for EIA`s energy models.
Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.
Estimation of Nonlinear Three-dimensional Constitutive Law for DNA Molecules
Palanthandalam-Madapusi, Harish J
2010-01-01
Long length-scale structural deformations of DNA play a central role in many biological processes including gene expression. The elastic rod model, which uses a continuum approximation, has emerged as a viable tool to model deformations of DNA molecules. The elastic rod model predictions are however very sensitive to the constitutive law (material properties) of the molecule, which in turn, vary along the molecules length according to its base-pair sequence. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we develop techniques to use elastic rod model equations in combination with limited experimental measurements or high-fidelity molecular dynamics simulation data to estimate the nonlinear constitutive law governing DNA molecules. We first cast the elastic rod model equations in state-space form and express the effect of the unknown constitutive law as an unknown input to the...
On event based state estimation
Sijs, J.; Lazar, M.
2009-01-01
To reduce the amount of data transfer in networked control systems and wireless sensor networks, measurements are usually taken only when an event occurs, rather than at each synchronous sampling instant. However, this complicates estimation and control problems considerably. The goal of this paper
On event based state estimation
Sijs, J.; Lazar, M.
2009-01-01
To reduce the amount of data transfer in networked control systems and wireless sensor networks, measurements are usually taken only when an event occurs, rather than at each synchronous sampling instant. However, this complicates estimation and control problems considerably. The goal of this paper
Nonlinear H-ininity state feedback controllers:
DEFF Research Database (Denmark)
Cromme, Marc; Møller-Pedersen, Jens; Pagh Petersen, Martin
1997-01-01
From a general point of view the state feedback H∞ suboptimal control problem is reasonably well understood. Important problems remain with regard to a priori information of the size of the neighbourhood where the local state feedback H∞ problem is solvable. This problem is solved regionally (sem...
Noninvasive tissue temperature estimation using nonlinear ultrasound harmonics
Maraghechi, Borna; Kolios, Michael C.; Tavakkoli, Jahan
2017-03-01
Non-invasive tissue temperature estimation is important in thermal therapies for having an efficient treatment. A noninvasive ultrasonic technique for monitoring tissue temperature changes is proposed based on the changes in the harmonics of ultrasound backscatter as a function of temperature. The backscattered pressure amplitudes of the fundamental frequency (p1), the second (p2) and the third (p3) harmonics generated by nonlinear ultrasound propagation and the ratios of the second and the third harmonics over the fundamental frequency (p2/p1 and p3/p1) were investigated as a function of temperature. The acoustic harmonics were generated and detected with a commercial high frequency ultrasound imaging system in pulse-echo mode. The experiments were performed on tissue-mimicking gel phantoms and ex vivo bovine muscle tissues. The temperature was increased from 26°C to 46°C in increments of 2°C. The average values of p1, p2, p3, p2/p1, p3/p1 increased by 14%, 50%, 117%, 37% and 92% for the gel phantoms, and for the tissue samples increased by 29%, 50%, 170%, 10% and 109%, respectively. The results indicate that the harmonic amplitudes and their ratios are highly sensitive to propagation medium's temperature and could potentially be used for noninvasive ultrasound thermometry.
Parameter Estimation of Nonlinear Systems by Dynamic Cuckoo Search.
Liao, Qixiang; Zhou, Shudao; Shi, Hanqing; Shi, Weilai
2017-04-01
In order to address with the problem of the traditional or improved cuckoo search (CS) algorithm, we propose a dynamic adaptive cuckoo search with crossover operator (DACS-CO) algorithm. Normally, the parameters of the CS algorithm are kept constant or adapted by empirical equation that may result in decreasing the efficiency of the algorithm. In order to solve the problem, a feedback control scheme of algorithm parameters is adopted in cuckoo search; Rechenberg's 1/5 criterion, combined with a learning strategy, is used to evaluate the evolution process. In addition, there are no information exchanges between individuals for cuckoo search algorithm. To promote the search progress and overcome premature convergence, the multiple-point random crossover operator is merged into the CS algorithm to exchange information between individuals and improve the diversification and intensification of the population. The performance of the proposed hybrid algorithm is investigated through different nonlinear systems, with the numerical results demonstrating that the method can estimate parameters accurately and efficiently. Finally, we compare the results with the standard CS algorithm, orthogonal learning cuckoo search algorithm (OLCS), an adaptive and simulated annealing operation with the cuckoo search algorithm (ACS-SA), a genetic algorithm (GA), a particle swarm optimization algorithm (PSO), and a genetic simulated annealing algorithm (GA-SA). Our simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
Xu, Ru-Gang; Koga, Dennis (Technical Monitor)
2001-01-01
The goal of 'Estimate' is to take advantage of attitude information to produce better pose while staying flexible and robust. Currently there are several instruments that are used for attitude: gyros, inclinometers, and compasses. However, precise and useful attitude information cannot come from one instrument. Integration of rotational rates, from gyro data for example, would result in drift. Therefore, although gyros are accurate in the short-term, accuracy in the long term is unlikely. Using absolute instruments such as compasses and inclinometers can result in an accurate measurement of attitude in the long term. However, in the short term, the physical nature of compasses and inclinometers, and the dynamic nature of a mobile platform result in highly volatile and therefore useless data. The solution then is to use both absolute and relative data. Kalman Filtering is known to be able to combine gyro and compass/inclinometer data to produce stable and accurate attitude information. Since the model of motion is linear and the data comes in as discrete samples, a Discrete Kalman Filter was selected as the core of the new estimator. Therefore, 'Estimate' can be divided into two parts: the Discrete Kalman Filter and the code framework.
On the estimation of the attainability set of nonlinear control systems
Energy Technology Data Exchange (ETDEWEB)
Ekimov, A.V.; Balykina, Yu.E.; Svirkin, M.V. [Saint Petersburg State University, 198504, Universitetskii pr., 35, Saint Petersburg (Russian Federation)
2015-03-10
Analysis of the attainability set and construction of its estimates greatly facilitates the solution of a variety of problems in mathematical control theory. In the paper, the problem of boundedness of the integral funnel of nonlinear controlled system is considered. Some estimates of the attainability sets for a nonlinear controlled system are presented. Theorems on the boundedness of considered integral funnels are proved.
An Unscented Kalman Filter Approach to the Estimation of Nonlinear Dynamical Systems Models
Chow, Sy-Miin; Ferrer, Emilio; Nesselroade, John R.
2007-01-01
In the past several decades, methodologies used to estimate nonlinear relationships among latent variables have been developed almost exclusively to fit cross-sectional models. We present a relatively new estimation approach, the unscented Kalman filter (UKF), and illustrate its potential as a tool for fitting nonlinear dynamic models in two ways:…
Estimating Nonlinear Structural Models: EMM and the Kenny-Judd Model
Lyhagen, Johan
2007-01-01
The estimation of nonlinear structural models is not trivial. One reason for this is that a closed form solution of the likelihood may not be feasible or does not exist. We propose to estimate nonlinear structural models using the efficient method of moments, as generating data according to the models is often very easy. A simulation study of the…
Estimation and filtering of nonlinear systems application to a waste-water treatment process
Energy Technology Data Exchange (ETDEWEB)
Ben Youssef, C.; Dahhou, B. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France). Lab. d`Automatique et d`Analyse des Systemes]|[Institut National des Sciences Appliquees (INSA), 31 - Toulouse (France); Zeng, F.Y.; Rols, J.L. [Institut National des Sciences Appliquees (INSA), 31 - Toulouse (France)
1994-04-01
A fundamental task in design and control of biotechnological processes is system modelling. This task is made difficult by the scarceness of on-line direct sensors for some key variables and by the fact that identifiability of models including Michaelis-Menten type of nonlinearities is not straightforward. The use of adaptive estimation approaches constitutes an interesting alternative to circumvent these kind of problems. This paper discusses an identification technique derived to solve the problem of estimating simultaneously inaccessible state variables and time-varying parameters of a nonlinear wastewater treatment process. An extended linearization technique using Kronecker`s calculation provides the error model of the joint observer-estimator procedure which convergence is proved via Lyapunov`s method. Sufficient conditions for stability of this joint identification scheme are given and discussed according to the persistence excitation conditions of the signals. A simulation study with measurement noises and abrupt jumps of the process parameters shows the feasibility and significant robustness of the proposed adaptive estimation methodologies. (author). (author). 10 refs., 3 figs.
Parameter and State Estimator for State Space Models
Directory of Open Access Journals (Sweden)
Ruifeng Ding
2014-01-01
Full Text Available This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.
Parameter and state estimator for state space models.
Ding, Ruifeng; Zhuang, Linfan
2014-01-01
This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.
Stability properties of nonlinear dynamical systems and evolutionary stable states
Energy Technology Data Exchange (ETDEWEB)
Gleria, Iram, E-mail: iram@fis.ufal.br [Instituto de Física, Universidade Federal de Alagoas, 57072-970 Maceió-AL (Brazil); Brenig, Leon [Faculté des Sciences, Université Libre de Bruxelles, 1050 Brussels (Belgium); Rocha Filho, Tarcísio M.; Figueiredo, Annibal [Instituto de Física and International Center for Condensed Matter Physics, Universidade de Brasília, 70919-970 Brasília-DF (Brazil)
2017-03-18
Highlights: • We address the problem of equilibrium stability in a general class of non-linear systems. • We link Evolutionary Stable States (ESS) to stable fixed points of square quasi-polynomial (QP) systems. • We show that an interior ES point may be related to stable interior fixed points of QP systems. - Abstract: In this paper we address the problem of stability in a general class of non-linear systems. We establish a link between the concepts of asymptotic stable interior fixed points of square Quasi-Polynomial systems and evolutionary stable states, a property of some payoff matrices arising from evolutionary games.
Target Tracking in 3-D Using Estimation Based Nonlinear Control Laws for UAVs
Directory of Open Access Journals (Sweden)
Mousumi Ahmed
2016-02-01
Full Text Available This paper presents an estimation based backstepping like control law design for an Unmanned Aerial Vehicle (UAV to track a moving target in 3-D space. A ground-based sensor or an onboard seeker antenna provides range, azimuth angle, and elevation angle measurements to a chaser UAV that implements an extended Kalman filter (EKF to estimate the full state of the target. A nonlinear controller then utilizes this estimated target state and the chaser’s state to provide speed, flight path, and course/heading angle commands to the chaser UAV. Tracking performance with respect to measurement uncertainty is evaluated for three cases: (1 stationary white noise; (2 stationary colored noise and (3 non-stationary (range correlated white noise. Furthermore, in an effort to improve tracking performance, the measurement model is made more realistic by taking into consideration range-dependent uncertainties in the measurements, i.e., as the chaser closes in on the target, measurement uncertainties are reduced in the EKF, thus providing the UAV with more accurate control commands. Simulation results for these cases are shown to illustrate target state estimation and trajectory tracking performance.
Ebrahimian, Hamed; Astroza, Rodrigo; Conte, Joel P.; de Callafon, Raymond A.
2017-02-01
This paper presents a framework for structural health monitoring (SHM) and damage identification of civil structures. This framework integrates advanced mechanics-based nonlinear finite element (FE) modeling and analysis techniques with a batch Bayesian estimation approach to estimate time-invariant model parameters used in the FE model of the structure of interest. The framework uses input excitation and dynamic response of the structure and updates a nonlinear FE model of the structure to minimize the discrepancies between predicted and measured response time histories. The updated FE model can then be interrogated to detect, localize, classify, and quantify the state of damage and predict the remaining useful life of the structure. As opposed to recursive estimation methods, in the batch Bayesian estimation approach, the entire time history of the input excitation and output response of the structure are used as a batch of data to estimate the FE model parameters through a number of iterations. In the case of non-informative prior, the batch Bayesian method leads to an extended maximum likelihood (ML) estimation method to estimate jointly time-invariant model parameters and the measurement noise amplitude. The extended ML estimation problem is solved efficiently using a gradient-based interior-point optimization algorithm. Gradient-based optimization algorithms require the FE response sensitivities with respect to the model parameters to be identified. The FE response sensitivities are computed accurately and efficiently using the direct differentiation method (DDM). The estimation uncertainties are evaluated based on the Cramer-Rao lower bound (CRLB) theorem by computing the exact Fisher Information matrix using the FE response sensitivities with respect to the model parameters. The accuracy of the proposed uncertainty quantification approach is verified using a sampling approach based on the unscented transformation. Two validation studies, based on realistic
Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation
Directory of Open Access Journals (Sweden)
Xi Liu
2016-09-01
Full Text Available A new algorithm called maximum correntropy unscented Kalman filter (MCUKF is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC, the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.
Algorithm of the managing systems state estimation
Directory of Open Access Journals (Sweden)
Skubilin M. D.
2010-02-01
Full Text Available The possibility of an electronic estimation of automatic and automated managing systems state is analyzed. An estimation of a current state (functional readiness of technical equipment and person-operator as integrated system allows to take operatively adequate measures on an exception and-or minimisation of consequences of system’s transition in a supernumerary state. The offered method is universal enough and can be recommended for normalisation of situations on transport, mainly in aircraft.
ESTIMATE OF DISCRETE NONLINEARITIES IN A MAINLY LINEAR DYNAMIC SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The class of system considered is a single degree of freedom undamped vibrating system with a clearance in which the dynamical behavior is described by a state-space representation in real time. The direct identification technique for the estimate of a clearance and other parameters in the system is presented in terms of least squares method and stepby-step iteration approach. For numerical simulation purpose, the simulated data are achieved by corrupting the modeled responses. The mathematical algorithm, which is put forward, has proven to be effective through a practical numerical example.
State and parameter estimation in bio processes
Energy Technology Data Exchange (ETDEWEB)
Maher, M.; Roux, G.; Dahhou, B. [Centre National de la Recherche Scientifique (CNRS), 31 - Toulouse (France)]|[Institut National des Sciences Appliquees (INSA), 31 - Toulouse (France)
1994-12-31
A major difficulty in monitoring and control of bio-processes is the lack of reliable and simple sensors for following the evolution of the main state variables and parameters such as biomass, substrate, product, growth rate, etc... In this article, an adaptive estimation algorithm is proposed to recover the state and parameters in bio-processes. This estimator utilizes the physical process model and the reference model approach. Experimentations concerning estimation of biomass and product concentrations and specific growth rate, during batch, fed-batch and continuous fermentation processes are presented. The results show the performance of this adaptive estimation approach. (authors) 12 refs.
Outlier Rejecting Multirate Model for State Estimation
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Wavelet transform was introduced to detect and eliminate outliers in time-frequency domain. The outlier rejection and multirate information extraction were initially incorporated by wavelet transform, a new outlier rejecting multirate model for state estimation was proposed. The model is applied to state estimation with interacting multiple model, as the outlier is eliminated and more reasonable multirate information is extracted, the estimation accuracy is greatly enhanced. The simulation results prove that the new model is robust to outliers and the estimation performance is significantly improved.
Development of a nonlinear estimator-based model of pilot performance during brownout conditions
Schultz, Karl Ulrich
During conditions of visual occlusion, pilots are forced to rapidly adapt their scan to accommodate the new observable states via instruments rather than the visual environment. During this transition, the provision of aircraft state information via other than visual modalities improves pilot performance presumably through the increase in situational awareness provided immediately following the visual occlusion event. The Tactile Situational Awareness System (TSAS) was developed to provide continuous position information to the pilot via tactile rather than visual means. However, as a low-resolution display, significant preprocessing of information is required to maximize utility of this new technology. Development of a nonlinear time varying estimator based multivariable model enables more accurate reproduction of pilot performance than previous models and provides explanations of many observed phenomena. The use of LQR feedback and an optimal estimator is heuristically consistent with reported strategies and was able to match pilot incorporation of multi-modal displays. Development of a nonlinear stochastic map of pilot "move-and-hold" control performance was able to accurately match increased pilot control noise at higher frequencies, a phenomenon formerly attributed to closed loop neuromuscular effects. The continued improvement of this model could eventually result in the early stage mathematical prediction of the effectiveness of emerging cockpit technology and preprocessing algorithms, prior to costly hardware development and flight evaluation.
State energy data report 1996: Consumption estimates
Energy Technology Data Exchange (ETDEWEB)
NONE
1999-02-01
The State Energy Data Report (SEDR) provides annual time series estimates of State-level energy consumption by major economic sectors. The estimates are developed in the Combined State Energy Data System (CSEDS), which is maintained and operated by the Energy Information Administration (EIA). The goal in maintaining CSEDS is to create historical time series of energy consumption by State that are defined as consistently as possible over time and across sectors. CSEDS exists for two principal reasons: (1) to provide State energy consumption estimates to Members of Congress, Federal and State agencies, and the general public and (2) to provide the historical series necessary for EIA`s energy models. To the degree possible, energy consumption has been assigned to five sectors: residential, commercial, industrial, transportation, and electric utility sectors. Fuels covered are coal, natural gas, petroleum, nuclear electric power, hydroelectric power, biomass, and other, defined as electric power generated from geothermal, wind, photovoltaic, and solar thermal energy. 322 tabs.
Analysis and design for the second order nonlinear continuous extended states observer
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The extended state observer (ESO) is a novel observer for a class of uncertain systems. Since ESO adopts the continuous non-smooth structure, the classical observer design theory is hard to use for ESO analysis. In this note, the self-stable region (SSR) approach, which is a nonlinear synthesis method for nonlinear uncertain systems, will be used for ESO design and its stability analysis. The advantages of the non-smooth structure in ESO for improving the convergence properties and the estimation precision will be shown.
Introduction to quantum-state estimation
Teo, Yong Siah
2016-01-01
Quantum-state estimation is an important field in quantum information theory that deals with the characterization of states of affairs for quantum sources. This book begins with background formalism in estimation theory to establish the necessary prerequisites. This basic understanding allows us to explore popular likelihood- and entropy-related estimation schemes that are suitable for an introductory survey on the subject. Discussions on practical aspects of quantum-state estimation ensue, with emphasis on the evaluation of tomographic performances for estimation schemes, experimental realizations of quantum measurements and detection of single-mode multi-photon sources. Finally, the concepts of phase-space distribution functions, which compatibly describe these multi-photon sources, are introduced to bridge the gap between discrete and continuous quantum degrees of freedom. This book is intended to serve as an instructive and self-contained medium for advanced undergraduate and postgraduate students to gra...
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A new robust on-line fault diagnosis method based on least squares estimate for nonlinear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of the DAS, this method firstly constructs an auxiliary system consisting of a difference equation and an algebraic equation, then, based on the relationship between the state deviation and the faults in the difference equation and the relationship between the algebraic variable deviation and the faults in algebraic equation, it identifies the faults on-line through least squares estimate. This method can not only detect, isolate and identify faults for DAS, but also give the upper bound of the error of fault identification. The simulation results indicate that it can give satisfactory diagnostic results for both abrupt and incipient faults.
Estimating state-contingent production functions
DEFF Research Database (Denmark)
Rasmussen, Svend; Karantininis, Kostas
The paper reviews the empirical problem of estimating state-contingent production functions. The major problem is that states of nature may not be registered and/or that the number of observation per state is low. Monte Carlo simulation is used to generate an artificial, uncertain production...... environment based on Cobb Douglas production functions with state-contingent parameters. The pa-rameters are subsequently estimated based on different sizes of samples using Generalized Least Squares and Generalized Maximum Entropy and the results are compared. It is concluded that Maximum Entropy may...
Two-state filtering for joint state-parameter estimation
Santitissadeekorn, Naratip
2014-01-01
This paper presents an approach for simultaneous estimation of the state and unknown parameters in a sequential data assimilation framework. The state augmentation technique, in which the state vector is augmented by the model parameters, has been investigated in many previous studies and some success with this technique has been reported in the case where model parameters are additive. However, many geophysical or climate models contains non-additive parameters such as those arising from physical parametrization of sub-grid scale processes, in which case the state augmentation technique may become ineffective since its inference about parameters from partially observed states based on the cross covariance between states and parameters is inadequate if states and parameters are not linearly correlated. In this paper, we propose a two-stages filtering technique that runs particle filtering (PF) to estimate parameters while updating the state estimate using Ensemble Kalman filter (ENKF; these two "sub-filters" ...
Localized States in Discrete Nonlinear Schrödinger Equations
Cai, D; Grønbech-Jensen, N; Cai, David; Grønbech-Jensen, Niels
1993-01-01
A new 1-D discrete nonlinear Schrödinger (NLS) Hamiltonian is introduced which includes the integrable Ablowitz-Ladik system as a limit. The symmetry properties of the system are studied. The relationship between intrinsic localized states and the soliton of the Ablowitz-Ladik NLS is discussed. It is pointed out that a staggered localized state can be viewed as a particle of a {\\em negative} effective mass. It is shown that staggered localized states can exist in the discrete dark NLS. The motion of localized states and Peierls-Nabarro pinning are studied.
State estimation for wave energy converters
Energy Technology Data Exchange (ETDEWEB)
Bacelli, Giorgio; Coe, Ryan Geoffrey
2017-04-01
This report gives a brief discussion and examples on the topic of state estimation for wave energy converters (WECs). These methods are intended for use to enable real-time closed loop control of WECs.
State estimation for anaerobic digesters using the ADM1.
Gaida, D; Wolf, C; Meyer, C; Stuhlsatz, A; Lippel, J; Bäck, T; Bongards, M; McLoone, S
2012-01-01
The optimization of full-scale biogas plant operation is of great importance to make biomass a competitive source of renewable energy. The implementation of innovative control and optimization algorithms, such as Nonlinear Model Predictive Control, requires an online estimation of operating states of biogas plants. This state estimation allows for optimal control and operating decisions according to the actual state of a plant. In this paper such a state estimator is developed using a calibrated simulation model of a full-scale biogas plant, which is based on the Anaerobic Digestion Model No.1. The use of advanced pattern recognition methods shows that model states can be predicted from basic online measurements such as biogas production, CH4 and CO2 content in the biogas, pH value and substrate feed volume of known substrates. The machine learning methods used are trained and evaluated using synthetic data created with the biogas plant model simulating over a wide range of possible plant operating regions. Results show that the operating state vector of the modelled anaerobic digestion process can be predicted with an overall accuracy of about 90%. This facilitates the application of state-based optimization and control algorithms on full-scale biogas plants and therefore fosters the production of eco-friendly energy from biomass.
The light filament as a new nonlinear polarization state
Kovachev, Lubomir M
2015-01-01
We present an analytical approach to the theory of nonlinear propagation in gases of femtosecond optical pulses with broad-band spectrum . The vector character of the nonlinear third-order polarization of the electrical field in air is investigated in details. A new polarization state is presented by using left-hand and right-hand circular components of the electrical field . The corresponding system of vector amplitude equations is derived in the rotating basis. We found that this system of nonlinear equations has $3D+1$ vector soliton solutions with Lorentz shape. The solution presents a relatively stable propagation and rotation with GHz frequency of the vector of the electrical field in a plane orthogonal to the direction of propagation. The evolution of the intensity profile demonstrates a weak self-compression and a week spherical wave in the first milliseconds of propagation.
New Concepts for Shipboard Sea State Estimation
DEFF Research Database (Denmark)
Nielsen, Ulrik D.; Bjerregård, Mikkel; Galeazzi, Roberto
2015-01-01
The wave buoy analogy is a tested means for shipboard sea state estimation. Basically, the estimation principle resembles that of a traditional wave rider buoy which relies, fundamentally, on transfer functions used to relate measured wave-induced responses and the unknown wave excitation. This p...
State estimation for random closed sets
Lieshout, van M.N.M.; Stein, Alfred; Allard, Denis
2015-01-01
State estimation entails the estimation of an unobserved random closed set from (partial) observation of an associated random set. Examples include edge effect correction, cluster detection, filtering and prediction. We focus on inference for random sets based on points sampled on its boundary. Such
State Estimation for the VASIMR Plasma Engine
2008-01-01
This paper presents work on the application of virtual metrology techniques to the VAriable Specific Impulse Magnetoplasma Rocket (VASMIR) engine. The work concentrates on the estimation of internal temperatures of the rocket using state space models and Optical Emission Spectroscopy (OES). These estimations are useful as direct thermal measurements will not be available in the final system design.
Directory of Open Access Journals (Sweden)
Yan Che
2012-01-01
Full Text Available The estimation problem is investigated for a class of stochastic nonlinear systems with distributed time-varying delays and missing measurements. The considered distributed time-varying delays, stochastic nonlinearities, and missing measurements are modeled in random ways governed by Bernoulli stochastic variables. The discussed nonlinearities are expressed by the statistical means. By using the linear matrix inequality method, a sufficient condition is established to guarantee the mean-square stability of the estimation error, and then the estimator parameters are characterized by the solution to a set of LMIs. Finally, a simulation example is exploited to show the effectiveness of the proposed design procedures.
Efficient Estimation of first Passage Probability of high-Dimensional Nonlinear Systems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
An efficient method for estimating low first passage probabilities of high-dimensional nonlinear systems based on asymptotic estimation of low probabilities is presented. The method does not require any a priori knowledge of the system, i.e. it is a black-box method, and has very low requirements......, the failure probabilities of three well-known nonlinear systems are estimated. Next, a reduced degree-of-freedom model of a wind turbine is developed and is exposed to a turbulent wind field. The model incorporates very high dimensions and strong nonlinearities simultaneously. The failure probability...
Minimization and error estimates for a class of the nonlinear Schrodinger eigenvalue problems
Institute of Scientific and Technical Information of China (English)
MurongJIANG; JiachangSUN
2000-01-01
It is shown that the nonlinear eigenvaiue problem can be transformed into a constrained functional problem. The corresponding minimal function is a weak solution of this nonlinear problem. In this paper, one type of the energy functional for a class of the nonlinear SchrSdinger eigenvalue problems is proposed, the existence of the minimizing solution is proved and the error estimate is given out.
Monitoring composite curing using nonlinear model-free estimators with infrared spectroscopy data
Tung, Sanhuang
Composite materials (e.g., fiber-reinforced epoxy resin) have many advantages over conventional materials. However, costs associated with product scraps and post-process inspections make them too expensive to be widely used. The key to lowering the cost is the knowledge of online product information, which is very difficult to estimate by mathematical models due to the complexity of simultaneous competing curing reactions. Realtime process monitoring techniques using nondestructive evaluation (NDE) sensors offer a more feasible approach to obtain this information. This dissertation is a study of methods for predicting mix ratio and degree-of-cure in epoxy/amine curing processes. In situ IR spectroscopy was the NDE technique used and all data were collected from small-scale experiments simulating the resin transfer molding (RTM) process at three levels of curing temperatures and four levels of mix ratios. The RTM process could be described as two major phases, i.e., mixing/injection and curing. These two phases lead to the two problems we studied. The first problem studied is to predict compositions of epoxy/amine mixtures. The second problem, which is more important, is to predict degree-of-cure during epoxy curing. In situ IR spectroscopy data were used as the predicting variables to predict quality properties of interest. We studied the issues of dealing with complex IR spectra, which, in our case, have 1751 wavenumbers. and developed new nonlinear estimators that make more accurate predictions than current estimators. Dimension reduction and nonlinear mapping are two important steps to make accurate predictions from complex IR spectroscopy data. We evaluated current techniques of reducing dimensionality by extracting features from correlated data and removing irrelevant data. We also evaluated linear and nonlinear mapping techniques from both projection-based and kernel-based methods. Our research came up with better estimators with respect to prediction
Robust control of a class of non-affine nonlinear systems by state and output feedback
Institute of Scientific and Technical Information of China (English)
陈贞丰; 章云
2014-01-01
Robust control design is presented for a general class of uncertain non-affine nonlinear systems. The design employs feedback linearization, coupled with two high-gain observers:the first to estimate the feedback linearization error based on the full state information and the second to estimate the unmeasured states of the system when only the system output is available for feedback. All the signals in the closed loop are guaranteed to be uniformly ultimately bounded (UUB) and the output of the system is proven to converge to a small neighborhood of the origin. The proposed approach not only handles the difficulty in controlling non-affine nonlinear systems but also simplifies the stability analysis of the closed loop due to its linear control structure. Simulation results show the effectiveness of the approach.
Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable
du Toit, Stephen H. C.; Cudeck, Robert
2009-01-01
A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…
State estimation of chemical engineering systems tending to multiple solutions
Directory of Open Access Journals (Sweden)
N. P. G. Salau
2014-09-01
Full Text Available A well-evaluated state covariance matrix avoids error propagation due to divergence issues and, thereby, it is crucial for a successful state estimator design. In this paper we investigate the performance of the state covariance matrices used in three unconstrained Extended Kalman Filter (EKF formulations and one constrained EKF formulation (CEKF. As benchmark case studies we have chosen: a a batch chemical reactor with reversible reactions whose system model and measurement are such that multiple states satisfy the equilibrium condition and b a CSTR with exothermic irreversible reactions and cooling jacket energy balance whose nonlinear behavior includes multiple steady-states and limit cycles. The results have shown that CEKF is in general the best choice of EKF formulations (even if they are constrained with an ad hoc clipping strategy which avoids undesired states for such case studies. Contrary to a clipped EKF formulation, CEKF incorporates constraints into an optimization problem, which minimizes the noise in a least square sense preventing a bad noise distribution. It is also shown that, although the Moving Horizon Estimation (MHE provides greater robustness to a poor guess of the initial state, converging in less steps to the actual states, it is not justified for our examples due to the high additional computational effort.
Adaptive steady-state stabilization for nonlinear dynamical systems
Braun, David J.
2008-07-01
By means of LaSalle’s invariance principle, we propose an adaptive controller with the aim of stabilizing an unstable steady state for a wide class of nonlinear dynamical systems. The control technique does not require analytical knowledge of the system dynamics and operates without any explicit knowledge of the desired steady-state position. The control input is achieved using only system states with no computer analysis of the dynamics. The proposed strategy is tested on Lorentz, van der Pol, and pendulum equations.
Miranowicz, A; Miranowicz, Adam; Leonski, Wieslaw
2006-01-01
Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically-induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
Interconnected delay and state observer for nonlinear systems with time-varying input delay
Léchappé, V; Moulay, Emmanuel; Plestan, F; Glumineau, A.
2016-01-01
International audience; This work presents a general framework to estimate both state and delay thanks to two interconnected observers. This scheme can be applied to a large class of nonlinear systems with time-varying input delay. In order to illustrate this approach, a new delay observer based on an optimization technique is proposed. Theoretical results are illustrated and compared with existing works in simulation.
Nonlinear Least Squares Methods for Joint DOA and Pitch Estimation
DEFF Research Database (Denmark)
Jensen, Jesper Rindom; Christensen, Mads Græsbøll; Jensen, Søren Holdt
2013-01-01
In this paper, we consider the problem of joint direction-of-arrival (DOA) and fundamental frequency estimation. Joint estimation enables robust estimation of these parameters in multi-source scenarios where separate estimators may fail. First, we derive the exact and asymptotic Cram\\'{e}r-Rao...... estimation. Moreover, simulations on real-life data indicate that the NLS and aNLS methods are applicable even when reverberation is present and the noise is not white Gaussian....
Joint state and parameter estimation in particle filtering and stochastic optimization
Institute of Scientific and Technical Information of China (English)
Xiaojun YANG; Keyi XING; Kunlin SHI; Quan PAN
2008-01-01
In this paper,an adaptive estimation algorithm is proposed for non-linear dynamic systems with unknown static parameters based on combination of particle filtering and Simultaneous Perturbation Stochastic Approximation(SPSA)technique.The estimations of parameters are obtained by maximum-likelihood estimation and sampling within particle filtering framework,and the SPSA is used for stochastic optimization and to approximate the gradient of the cost function.The proposed algorithm achieves combined estimation of dynamic state and static parameters of nonlinear systerns.Simulation result demonstrates the feasibility and efficiency of the proposed algorithm.
Decay estimate of viscosity solutions of nonlinear parabolic PDEs and applications
Directory of Open Access Journals (Sweden)
Silvana Marchi
2014-05-01
Full Text Available The aim of this paper is to establish a decay estimate for viscosity solutions of nonlinear PDEs. As an application we prove existence and uniqueness for time almost periodic viscosity solutions.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backfitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Inferring gene regulatory networks via nonlinear state-space models and exploiting sparsity.
Noor, Amina; Serpedin, Erchin; Nounou, Mohamed; Nounou, Hazem N
2012-01-01
This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.
Soft Sensor for Inputs and Parameters Using Nonlinear Singular State Observer in Chemical Processes
Institute of Scientific and Technical Information of China (English)
许锋; 汪晔晔; 罗雄麟
2013-01-01
Chemical processes are usually nonlinear singular systems. In this study, a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes, which are augmented as state variables. Based on the observability of the singular system, this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters. When the observability is satisfied, the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer. The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation. With the catalyst circulation rate as the only unknown input without model error, one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst cir-culation rate. However, when uncertain model parameters also exist, additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.
A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites (Preprint)
2011-07-01
AFRL-RX-WP-TP-2011-4232 A MODEL FOR ESTIMATING NONLINEAR DEFORMATION AND DAMAGE IN CERAMIC MATRIX COMPOSITES (PREPRINT) Unni Santhosh and...5a. CONTRACT NUMBER In-house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 62102F 6. AUTHOR(S) Unni Santhosh and Jalees Ahmad 5d. PROJECT...Composite Materials, 2010 A Model for Estimating Nonlinear Deformation and Damage in Ceramic Matrix Composites Unni Santhosh and Jalees Ahmad Research
Estimation in continuous-time stochastic| volatility models using nonlinear filters
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Vestergaard, M.; Madsen, Henrik
2000-01-01
Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308.......Presents a correction to the authorship of the article 'Estimation in Continuous-Time Stochastic Volatility Models Using Nonlinear Filters,' published in the periodical 'International Journal of Theoretical and Applied Finance,' Vol. 3, No. 2., pp. 279-308....
Ramachandran, S.; Wells, W. R.
1974-01-01
This paper is concerned with the estimation of stability and control parameters of a high performance fighter aircraft from data obtained from high angle of attack flight. The estimation process utilizes a maximum likelihood algorithm derived for the case of a nonlinear aerodynamic force and moment model. The aircraft used was a high speed variable sweep heavy weight fighter with twin vertical tails. Comparisons of results from the nonlinear analysis are made with linear theory and wind tunnel results when available.
Efficent Estimation of the Non-linear Volatility and Growth Model
2009-01-01
Ramey and Ramey (1995) introduced a non-linear model relating volatility to growth. The solution of this model by generalised computer algorithms for non-linear maximum likelihood estimation encounters the usual difficulties and is, at best, tedious. We propose an algebraic solution for the model that provides fully efficient estimators and is elementary to implement as a standard ordinary least squares procedure. This eliminates issues such as the ‘guesstimation’ of initial values and mul...
On global attraction to stationary states for wave equations with concentrated nonlinearities
Kopylova, E.
2016-01-01
The global attraction to stationary states is established for solutions to 3D wave equations with concentrated nonlinearities: each finite energy solution converges as $t\\to\\pm\\infty$ to stationary states. The attraction is caused by nonlinear energy radiation.
Nonlinear Optical Spectroscopy of Excited States in Polyfluorene
Tong, M; Vardeny, Z V
2006-01-01
We used a variety of nonlinear optical (NLO) spectroscopies to study the singlet excited states order, and primary photoexcitations in polyfluorene; an important blue emitting p-conjugated polymer. The polarized NLO spectroscopies include ultrafast pump-probe photomodulation, two-photon absorption, and electroabsorption. For completeness we also measured the linear absorption and photoluminescence spectra. We found that the primary photoexcitations in polyfluorene are singlet excitons.
Estimating the Energy State of Liquids
Directory of Open Access Journals (Sweden)
Lianwen Wang
2014-12-01
Full Text Available In contrast to the gaseous and the solid states, the liquid state does not have a simple model that could be developed into a quantitative theory. A central issue in the understanding of liquids is to estimate the energy state of liquids. Here, on the basis of our recent studies on crystal melting, we show that the energy sate of liquids may be reasonably approximated by the energy and volume of a vacancy. Consequently, estimation of the liquid state energy is significantly simplified comparing with previous methods that inevitably invoke many-body interactions. Accordingly, a possible equation for the state for liquids is proposed. On this basis, it seems that a simple model for liquids is in sight.
Sub-Second Parallel State Estimation
Energy Technology Data Exchange (ETDEWEB)
Chen, Yousu [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Rice, Mark J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Glaesemann, Kurt R. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Wang, Shaobu [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Huang, Zhenyu [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2014-10-31
This report describes the performance of Pacific Northwest National Laboratory (PNNL) sub-second parallel state estimation (PSE) tool using the utility data from the Bonneville Power Administrative (BPA) and discusses the benefits of the fast computational speed for power system applications. The test data were provided by BPA. They are two-days’ worth of hourly snapshots that include power system data and measurement sets in a commercial tool format. These data are extracted out from the commercial tool box and fed into the PSE tool. With the help of advanced solvers, the PSE tool is able to solve each BPA hourly state estimation problem within one second, which is more than 10 times faster than today’s commercial tool. This improved computational performance can help increase the reliability value of state estimation in many aspects: (1) the shorter the time required for execution of state estimation, the more time remains for operators to take appropriate actions, and/or to apply automatic or manual corrective control actions. This increases the chances of arresting or mitigating the impact of cascading failures; (2) the SE can be executed multiple times within time allowance. Therefore, the robustness of SE can be enhanced by repeating the execution of the SE with adaptive adjustments, including removing bad data and/or adjusting different initial conditions to compute a better estimate within the same time as a traditional state estimator’s single estimate. There are other benefits with the sub-second SE, such as that the PSE results can potentially be used in local and/or wide-area automatic corrective control actions that are currently dependent on raw measurements to minimize the impact of bad measurements, and provides opportunities to enhance the power grid reliability and efficiency. PSE also can enable other advanced tools that rely on SE outputs and could be used to further improve operators’ actions and automated controls to mitigate effects
Distributed Robust Power System State Estimation
Kekatos, Vassilis
2012-01-01
Deregulation of energy markets, penetration of renewables, advanced metering capabilities, and the urge for situational awareness, all call for system-wide power system state estimation (PSSE). Implementing a centralized estimator though is practically infeasible due to the complexity scale of an interconnection, the communication bottleneck in real-time monitoring, regional disclosure policies, and reliability issues. In this context, distributed PSSE methods are treated here under a unified and systematic framework. A novel algorithm is developed based on the alternating direction method of multipliers. It leverages existing PSSE solvers, respects privacy policies, exhibits low communication load, and its convergence to the centralized estimates is guaranteed even in the absence of local observability. Beyond the conventional least-squares based PSSE, the decentralized framework accommodates a robust state estimator. By exploiting interesting links to the compressive sampling advances, the latter jointly es...
Estimation on nonlinear damping in second order distributed parameter systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1989-01-01
An approximation and convergence theory for the identification of nonlinear damping in abstract wave equations is developed. It is assumed that the unknown dissipation mechanism to be identified can be described by a maximal monotone operator acting on the generalized velocity. The stiffness is assumed to be linear and symmetric. Functional analytic techniques are used to establish that solutions to a sequence of finite dimensional (Galerkin) approximating identification problems in some sense approximate a solution to the original infinite dimensional inverse problem.
Parameter estimation of a nonlinear magnetic universe from observations
Montiel, Ariadna; Salzano, Vincenzo
2014-01-01
The cosmological model consisting of a nonlinear magnetic field obeying the Lagrangian L= \\gamma F^{\\alpha}, F being the electromagnetic invariant, coupled to a Robertson-Walker geometry is tested with observational data of Type Ia Supernovae, Long Gamma-Ray Bursts and Hubble parameter measurements. The statistical analysis show that the inclusion of nonlinear electromagnetic matter is enough to produce the observed accelerated expansion, with not need of including a dark energy component. The electromagnetic matter with abundance $\\Omega_B$, gives as best fit from the combination of all observational data sets \\Omega_B=0.562^{+0.037}_{-0.038} for the scenario in which \\alpha=-1, \\Omega_B=0.654^{+0.040}_{-0.040} for the scenario with \\alpha=-1/4 and \\Omega_B=0.683^{+0.039}_{-0.043} for the one with \\alpha=-1/8. These results indicate that nonlinear electromagnetic matter could play the role of dark energy, with the theoretical advantage of being a mensurable field.
Error estimation in the direct state tomography
Sainz, I.; Klimov, A. B.
2016-10-01
We show that reformulating the Direct State Tomography (DST) protocol in terms of projections into a set of non-orthogonal bases one can perform an accuracy analysis of DST in a similar way as in the standard projection-based reconstruction schemes, i.e., in terms of the Hilbert-Schmidt distance between estimated and true states. This allows us to determine the estimation error for any measurement strength, including the weak measurement case, and to obtain an explicit analytic form for the average minimum square errors.
DEFF Research Database (Denmark)
Vich, Catalina; Berg, Rune W.; Guillamon, Antoni
2017-01-01
Subthreshold fluctuations in neuronal membrane potential traces contain nonlinear components, and employing nonlinear models might improve the statistical inference. We propose a new strategy to estimate synaptic conductances, which has been tested using in silico data and applied to in vivo...... recordings. The model is constructed to capture the nonlinearities caused by subthreshold activated currents, and the estimation procedure can discern between excitatory and inhibitory conductances using only one membrane potential trace. More precisely, we perform second order approximations of biophysical...... models to capture the subthreshold nonlinearities, resulting in quadratic integrate-and-fire models, and apply approximate maximum likelihood estimation where we only suppose that conductances are stationary in a 50–100 ms time window. The results show an improvement compared to existent procedures...
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.
State energy data report 1992: Consumption estimates
Energy Technology Data Exchange (ETDEWEB)
1994-05-01
This is a report of energy consumption by state for the years 1960 to 1992. The report contains summaries of energy consumption for the US and by state, consumption by source, comparisons to other energy use reports, consumption by energy use sector, and describes the estimation methodologies used in the preparation of the report. Some years are not listed specifically although they are included in the summary of data.
Induction Motor Flux Estimation using Nonlinear Sliding Observers
Directory of Open Access Journals (Sweden)
Hakiki Khalid
2007-01-01
Full Text Available A nonlinear sliding flux was proposed for an induction motor. Its dynamic observation errors converge asymptotically to zero, independently from the inputs. The aim of this work was to study the robustness of this observer with respect to the variation of the rotor resistance known to be a crucial parameter for the control. The dynamic performance of this sliding observer was compared to that of Verghese observer via a simulation of an IM driven by U/F control in open loop.
Optimization-based particle filter for state and parameter estimation
Institute of Scientific and Technical Information of China (English)
Li Fu; Qi Fei; Shi Guangming; Zhang Li
2009-01-01
In recent years, the theory of particle filter has been developed and widely used for state and parameter estimation in nonlinear/non-Gaussian systems. Choosing good importance density is a critical issue in particle filter design. In order to improve the approximation of posterior distribution, this paper provides an optimization-based algorithm (the steepest descent method) to generate the proposal distribution and then sample particles from the distribution. This algorithm is applied in 1-D case, and the simulation results show that the proposed particle filter performs better than the extended Kalman filter (EKF), the standard particle filter (PF), the extended Kalman particle filter (PF-EKF) and the unscented particle filter (UPF) both in efficiency and in estimation precision.
Steady-state negative Wigner functions of nonlinear nanomechanical oscillators
Rips, Simon; Wilson-Rae, Ignacio; Hartmann, Michael J
2011-01-01
We propose a scheme to prepare nanomechanical oscillators in non-classical steady states, characterized by a pronounced negative Wigner function. In our optomechanical approach, the mechanical oscillator couples to multiple laser driven resonances of an optical cavity. By lowering the resonant frequency of the oscillator via an inhomogeneous electrostatic field, we significantly enhance its intrinsic geometric nonlinearity per phonon. This causes the motional sidebands to split into separate spectral lines for each phonon number and transitions between individual phonon Fock states can be selectively addressed. We show that this enables preparation of the nanomechanical oscillator in a single phonon Fock state. Our scheme can for example be implemented with a carbon nanotube dispersively coupled to the evanescent field of a state of the art whispering gallery mode microcavity.
Ouali, D.; Chebana, F.; Ouarda, T. B. M. J.
2017-06-01
The high complexity of hydrological systems has long been recognized. Despite the increasing number of statistical techniques that aim to estimate hydrological quantiles at ungauged sites, few approaches were designed to account for the possible nonlinear connections between hydrological variables and catchments characteristics. Recently, a number of nonlinear machine-learning tools have received attention in regional frequency analysis (RFA) applications especially for estimation purposes. In this paper, the aim is to study nonlinearity-related aspects in the RFA of hydrological variables using statistical and machine-learning approaches. To this end, a variety of combinations of linear and nonlinear approaches are considered in the main RFA steps (delineation and estimation). Artificial neural networks (ANNs) and generalized additive models (GAMs) are combined to a nonlinear ANN-based canonical correlation analysis (NLCCA) procedure to ensure an appropriate nonlinear modeling of the complex processes involved. A comparison is carried out between classical linear combinations (CCAs combined with linear regression (LR) model), semilinear combinations (e.g., NLCCA with LR) and fully nonlinear combinations (e.g., NLCCA with GAM). The considered models are applied to three different data sets located in North America. Results indicate that fully nonlinear models (in both RFA steps) are the most appropriate since they provide best performances and a more realistic description of the physical processes involved, even though they are relatively more complex than linear ones. On the other hand, semilinear models which consider nonlinearity either in the delineation or estimation steps showed little improvement over linear models. The linear approaches provided the lowest performances.
Estimation of Physical Parameters in Linear and Nonlinear Dynamic Systems
DEFF Research Database (Denmark)
Knudsen, Morten
and estimation of physical parameters in particular. 2. To apply the new methods for modelling of specific objects, such as loudspeakers, ac- and dc-motors wind turbines and beat exchangers. A reliable quality measure of an obtained parameter estimate is a prerequisite for any reasonable use of the result...
Zayane, Chadia
2014-06-01
In this paper, we address a special case of state and parameter estimation, where the system can be put on a cascade form allowing to estimate the state components and the set of unknown parameters separately. Inspired by the nonlinear Balloon hemodynamic model for functional Magnetic Resonance Imaging problem, we propose a hierarchical approach. The system is divided into two subsystems in cascade. The state and input are first estimated from a noisy measured signal using an adaptive observer. The obtained input is then used to estimate the parameters of a linear system using the modulating functions method. Some numerical results are presented to illustrate the efficiency of the proposed method.
State estimation for integrated vehicle dynamics control
Zuurbier, J.; Bremmer, P.
2002-01-01
This paper discusses a vehicle controller and a state estimator that was implemented and tested in a vehicle equipped with a combined braking and chassis control system to improve handling. The vehicle dynamics controller consists of a feed forward body roll compensation and a feedback stability con
State Estimation for the Automotive SCR Process
DEFF Research Database (Denmark)
Zhou, Guofeng; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp
2012-01-01
Selective catalytic reduction (SCR) of NOx is a widely applied diesel engine exhaust gas aftertreatment technology. For advanced SCR process control, like model predictive control, full state information of the process is required. The ammonia coverage ratio inside the catalyst is difficult...... present for SCR in engine applications, we recommend to estimating the ammonia coverage using the extended Kalman filter....
Equations of States in Singular Statistical Estimation
Watanabe, Sumio
2007-01-01
Learning machines which have hierarchical structures or hidden variables are singular statistical models because they are nonidentifiable and their Fisher information matrices are singular. In singular statistical models, neither the Bayes a posteriori distribution converges to the normal distribution nor the maximum likelihood estimator satisfies asymptotic normality. This is the main reason why it has been difficult to predict their generalization performances from trained states. In this paper, we study four errors, (1) Bayes generalization error, (2) Bayes training error, (3) Gibbs generalization error, and (4) Gibbs training error, and prove that there are mathematical relations among these errors. The formulas proved in this paper are equations of states in statistical estimation because they hold for any true distribution, any parametric model, and any a priori distribution. Also we show that Bayes and Gibbs generalization errors are estimated by Bayes and Gibbs training errors, and propose widely appl...
Motorcycle state estimation for lateral dynamics
Teerhuis, A. P.; Jansen, S. T. H.
2012-08-01
The motorcycle lean (or roll) angle development is one of the main characteristics of motorcycle lateral dynamics. Control of motorcycle motions requires an accurate assessment of this quantity and for safety applications also the risk of sliding needs to be considered. Direct measurement of the roll angle and tyre slip is not available; therefore, a method of model-based estimation is developed to estimate the state of a motorcycle. This paper investigates the feasibility of such a motorcycle state estimator (MCSE). A simplified analytic model of a motorcycle is developed by comparison to an extended multi-body model of the motorcycle, designed in Matlab/SimMechanics. The analytic model is used inside an extended Kalman filter. Experimental results of an instrumented Yamaha FJR1300 motorcycle show that the MCSE is a feasible concept for obtaining signals related to the lateral dynamics of the motorcycle.
Nonlinear system modeling with random matrices: echo state networks revisited.
Zhang, Bai; Miller, David J; Wang, Yue
2012-01-01
Echo state networks (ESNs) are a novel form of recurrent neural networks (RNNs) that provide an efficient and powerful computational model approximating nonlinear dynamical systems. A unique feature of an ESN is that a large number of neurons (the "reservoir") are used, whose synaptic connections are generated randomly, with only the connections from the reservoir to the output modified by learning. Why a large randomly generated fixed RNN gives such excellent performance in approximating nonlinear systems is still not well understood. In this brief, we apply random matrix theory to examine the properties of random reservoirs in ESNs under different topologies (sparse or fully connected) and connection weights (Bernoulli or Gaussian). We quantify the asymptotic gap between the scaling factor bounds for the necessary and sufficient conditions previously proposed for the echo state property. We then show that the state transition mapping is contractive with high probability when only the necessary condition is satisfied, which corroborates and thus analytically explains the observation that in practice one obtains echo states when the spectral radius of the reservoir weight matrix is smaller than 1.
Directory of Open Access Journals (Sweden)
Guowei Cai
2014-01-01
Full Text Available As to strong nonlinearity of doubly fed induction generators (DFIG and uncertainty of its model, a novel rotor current controller with nonlinearity and robustness is proposed to enhance fault ride-though (FRT capacities of grid-connected DFIG. Firstly, the model error, external disturbances, and the uncertain factors were estimated by constructing extended state observer (ESO so as to achieve linearization model, which is compensated dynamically from nonlinear model. And then rotor current controller of DFIG is designed by using terminal sliding mode variable structure control theory (TSMC. The controller has superior dynamic performance and strong robustness. The simulation results show that the proposed control approach is effective.
Nonlinear Bayesian Estimation of BOLD Signal under Non-Gaussian Noise
Directory of Open Access Journals (Sweden)
Ali Fahim Khan
2015-01-01
Full Text Available Modeling the blood oxygenation level dependent (BOLD signal has been a subject of study for over a decade in the neuroimaging community. Inspired from fluid dynamics, the hemodynamic model provides a plausible yet convincing interpretation of the BOLD signal by amalgamating effects of dynamic physiological changes in blood oxygenation, cerebral blood flow and volume. The nonautonomous, nonlinear set of differential equations of the hemodynamic model constitutes the process model while the weighted nonlinear sum of the physiological variables forms the measurement model. Plagued by various noise sources, the time series fMRI measurement data is mostly assumed to be affected by additive Gaussian noise. Though more feasible, the assumption may cause the designed filter to perform poorly if made to work under non-Gaussian environment. In this paper, we present a data assimilation scheme that assumes additive non-Gaussian noise, namely, the e-mixture noise, affecting the measurements. The proposed filter MAGSF and the celebrated EKF are put to test by performing joint optimal Bayesian filtering to estimate both the states and parameters governing the hemodynamic model under non-Gaussian environment. Analyses using both the synthetic and real data reveal superior performance of the MAGSF as compared to EKF.
Nonlinear Random Effects Mixture Models: Maximum Likelihood Estimation via the EM Algorithm.
Wang, Xiaoning; Schumitzky, Alan; D'Argenio, David Z
2007-08-15
Nonlinear random effects models with finite mixture structures are used to identify polymorphism in pharmacokinetic/pharmacodynamic phenotypes. An EM algorithm for maximum likelihood estimation approach is developed and uses sampling-based methods to implement the expectation step, that results in an analytically tractable maximization step. A benefit of the approach is that no model linearization is performed and the estimation precision can be arbitrarily controlled by the sampling process. A detailed simulation study illustrates the feasibility of the estimation approach and evaluates its performance. Applications of the proposed nonlinear random effects mixture model approach to other population pharmacokinetic/pharmacodynamic problems will be of interest for future investigation.
Comparisons of Estimation Procedures for Nonlinear Multilevel Models
Directory of Open Access Journals (Sweden)
Ali Reza Fotouhi
2003-05-01
Full Text Available We introduce General Multilevel Models and discuss the estimation procedures that may be used to fit multilevel models. We apply the proposed procedures to three-level binary data generated in a simulation study. We compare the procedures by two criteria, Bias and efficiency. We find that the estimates of the fixed effects and variance components are substantially and significantly biased using Longford's Approximation and Goldstein's Generalized Least Squares approaches by two software packages VARCL and ML3. These estimates are not significantly biased and are very close to real values when we use Markov Chain Monte Carlo (MCMC using Gibbs sampling or Nonparametric Maximum Likelihood (NPML approach. The Gaussian Quadrature (GQ approach, even with small number of mass points results in consistent estimates but computationally problematic. We conclude that the MCMC and the NPML approaches are the recommended procedures to fit multilevel models.
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.
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.
Efficient Estimation of first Passage Probability of high-Dimensional Nonlinear Systems
DEFF Research Database (Denmark)
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Bucher, Christian
2011-01-01
on the system memory. Consequently, high-dimensional problems can be handled, and nonlinearities in the model neither bring any difficulty in applying it nor lead to considerable reduction of its efficiency. These characteristics suggest that the method is a powerful candidate for complicated problems. First......, the failure probabilities of three well-known nonlinear systems are estimated. Next, a reduced degree-of-freedom model of a wind turbine is developed and is exposed to a turbulent wind field. The model incorporates very high dimensions and strong nonlinearities simultaneously. The failure probability...
Directory of Open Access Journals (Sweden)
Espen R. Jakobsen
2002-05-01
Full Text Available Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations. Furthermore, we provide existence, uniqueness, and Holder continuity results for bounded viscosity solutions of such equations. Our results are general enough to encompass Hamilton-Jacobi-Bellman-Isaacs's equations of zero-sum, two-player stochastic differential games. An immediate consequence of the results obtained herein is a rate of convergence for the vanishing viscosity method for fully nonlinear degenerate elliptic equations.
Smoothing and Decay Estimates for Nonlinear Diffusion Equations Equations of Porous Medium Type
Vázquez, Juan Luis
2006-01-01
This text is concerned with the quantitative aspects of the theory of nonlinear diffusion equations; equations which can be seen as nonlinear variations of the classical heat equation. They appear as mathematical models in different branches of Physics, Chemistry, Biology, and Engineering, and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on estimates and functional analysis.Concentrating on a class of equations with nonlinearities of power type that lead to degenerate or singular parabolicity ("equations of porou
Measurement-Induced Strong Kerr Nonlinearity for Weak Quantum States of Light
Costanzo, Luca S.; Coelho, Antonio S.; Biagi, Nicola; Fiurášek, Jaromír; Bellini, Marco; Zavatta, Alessandro
2017-07-01
Strong nonlinearity at the single photon level represents a crucial enabling tool for optical quantum technologies. Here we report on experimental implementation of a strong Kerr nonlinearity by measurement-induced quantum operations on weak quantum states of light. Our scheme coherently combines two sequences of single photon addition and subtraction to induce a nonlinear phase shift at the single photon level. We probe the induced nonlinearity with weak coherent states and characterize the output non-Gaussian states with quantum state tomography. The strong nonlinearity is clearly witnessed as a change of sign of specific off-diagonal density matrix elements in the Fock basis.
Estimated Water Flows in 2005: United States
Energy Technology Data Exchange (ETDEWEB)
Smith, C A; Belles, R D; Simon, A J
2011-03-16
Flow charts depicting water use in the United States have been constructed from publicly available data and estimates of water use patterns. Approximately 410,500 million gallons per day of water are managed throughout the United States for use in farming, power production, residential, commercial, and industrial applications. Water is obtained from four major resource classes: fresh surface-water, saline (ocean) surface-water, fresh groundwater and saline (brackish) groundwater. Water that is not consumed or evaporated during its use is returned to surface bodies of water. The flow patterns are represented in a compact 'visual atlas' of 52 state-level (all 50 states in addition to Puerto Rico and the Virgin Islands) and one national water flow chart representing a comprehensive systems view of national water resources, use, and disposition.
An Empirical State Error Covariance Matrix for Batch State Estimation
Frisbee, Joseph H., Jr.
2011-01-01
State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the
Robust state estimation for uncertain linear systems with deterministic input signals
Institute of Scientific and Technical Information of China (English)
Huabo LIU; Tong ZHOU
2014-01-01
In this paper, we investigate state estimations of a dynamical system in which not only process and measurement noise, but also parameter uncertainties and deterministic input signals are involved. The sensitivity penalization based robust state estimation is extended to uncertain linear systems with deterministic input signals and parametric uncertainties which may nonlinearly affect a state-space plant model. The form of the derived robust estimator is similar to that of the well-known Kalman filter with a comparable computational complexity. Under a few weak assumptions, it is proved that though the derived state estimator is biased, the bound of estimation errors is finite and the covariance matrix of estimation errors is bounded. Numerical simulations show that the obtained robust filter has relatively nice estimation performances.
Estimated United States Transportation Energy Use 2005
Energy Technology Data Exchange (ETDEWEB)
Smith, C A; Simon, A J; Belles, R D
2011-11-09
A flow chart depicting energy flow in the transportation sector of the United States economy in 2005 has been constructed from publicly available data and estimates of national energy use patterns. Approximately 31,000 trillion British Thermal Units (trBTUs) of energy were used throughout the United States in transportation activities. Vehicles used in these activities include automobiles, motorcycles, trucks, buses, airplanes, rail, and ships. The transportation sector is powered primarily by petroleum-derived fuels (gasoline, diesel and jet fuel). Biomass-derived fuels, electricity and natural gas-derived fuels are also used. The flow patterns represent a comprehensive systems view of energy used within the transportation sector.
Energy Technology Data Exchange (ETDEWEB)
Obeid, Jamila; Magnin, Jean-Pierre [Grenoble University, LEPMI, UMR 5631 (CNRS-INPG-UJF), Laboratoire d' Electrochimie et de Physico chimie des Materiaux et Interfaces, BP 75, 38402 St. Martin d' Heres (France); Flaus, Jean-Marie; Adrot, Olivier [Grenoble University, G-SCOP UMR 272 (CNRS-INPG-UJF), Laboratoire des Sciences pour la Conception, l' Optimisation et la Production, 46, avenue Felix Viallet, 38031 Grenoble (France); Willison, John C. [Laboratoire de Chimie et Biologie des Metaux (UMR 5249 CEA-CNRS-UJF), iRTSV/LCBM, CEA-Grenoble, 38054 Grenoble (France)
2010-10-15
This paper addresses the problem of estimating the states of an anaerobic photosynthetic process used for biohydrogen production by the photosynthetic bacterium Rhodobacter capsulatus. The process is described by a non-linear, time-discrete model and the state estimation is solved using an observer based on the Moving-Horizon State Estimation Method (MHSE). This approach is based on the minimization of a criterion (a non-linear function), in this case, the difference between the estimated output and the measured output of the system over a considered time horizon, where the solution is computed by using a numerical interval method. The observer was successfully applied to hydrogen production by R. capsulatus strain B10 in a batch process. (author)
Estimation of Aircraft Nonlinear Unsteady Parameters From Wind Tunnel Data
Klein, Vladislav; Murphy, Patrick C.
1998-01-01
Aerodynamic equations were formulated for an aircraft in one-degree-of-freedom large amplitude motion about each of its body axes. The model formulation based on indicial functions separated the resulting aerodynamic forces and moments into static terms, purely rotary terms and unsteady terms. Model identification from experimental data combined stepwise regression and maximum likelihood estimation in a two-stage optimization algorithm that can identify the unsteady term and rotary term if necessary. The identification scheme was applied to oscillatory data in two examples. The model identified from experimental data fit the data well, however, some parameters were estimated with limited accuracy. The resulting model was a good predictor for oscillatory and ramp input data.
Estimation of growth parameters using a nonlinear mixed Gompertz model.
Wang, Z; Zuidhof, M J
2004-06-01
In order to maximize the utility of simulation models for decision making, accurate estimation of growth parameters and associated variances is crucial. A mixed Gompertz growth model was used to account for between-bird variation and heterogeneous variance. The mixed model had several advantages over the fixed effects model. The mixed model partitioned BW variation into between- and within-bird variation, and the covariance structure assumed with the random effect accounted for part of the BW correlation across ages in the same individual. The amount of residual variance decreased by over 55% with the mixed model. The mixed model reduced estimation biases that resulted from selective sampling. For analysis of longitudinal growth data, the mixed effects growth model is recommended.
Multivariable Control and Online State Estimation of an FCC Unit
Directory of Open Access Journals (Sweden)
A. T. Boum
2015-10-01
Full Text Available The purpose of this paper is to realize multivariable control , tuning and online state estimation of some parameters of the FCC unit . We implemented two control structures with the manipulated variables being the air inlet flow rate in the regenerator, the regenerated catalyst flow rate and the feed flow rate and, the controlled variable being the temperatures in the riser and in the densed bed of the regenerator. A novel four transfer function is built and used for controllability studies. Hard constraints are imposed with respect to the manipulated variables. Simulation results show that the configuration made of two inputs and two outputs is more easy to tune for control purposes. Althought there are important dynamic interactions between the components of the FCC and important nonlinearities, linear model predictive control is able to maintain a smooth multivariable control of the plant, while taking into account the different constraints. Tuning strategy is implemented to improve the tracking of the set point. Online state estimation is carried out with the use of the extended Kalman filter. The estimation gives results that can be used for monitoring purposes even in the presence of model mismatch.
Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects
2017-02-22
AFRL-AFOSR-UK-TR-2017-0023 Linear and Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects Marco Martorella... UNIVERSITY DI PISA, DEPARTMENT DI INGEGNERIA Final Report 02/22/2017 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research...Nonlinear Time-Frequency Analysis for Parameter Estimation of Resident Space Objects 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-14-1-0183 5c. PROGRAM
Bootstrapping Nonlinear Least Squares Estimates in the Kalman Filter Model.
1986-01-01
Bias Bootstrapa 3.933 x 103 0.651 x 103 -0.166 x 10-- b b Newton - Rapshon 1.380 x 10- 0.479 x 10- 10_c 0_ c , e -.., Emperical 3.605 x 10 -0.026 x 10...most cases, parameter estimation for the KF model has been accomplished by maximum likelihood techniques involving the use of scoring or Newton ...is well behaved, the Newton -Raphson and scoring procedures enjoy quadratic convergence in the neighborhood of the maximum and one has a ready-made
Optimal and Suboptimal Estimation of Nonlinear Stochastic Systems.
1984-01-09
IEEE TRANSACTIONS ON AUTOMATIC CONTROL , vol. AC-25, April 1980, pp. 299-302. 2. J.L. Speyer, S.I. Marcus, and J...Krainak, "A Decentralized Team Decision Problem with an Exponential Cost Criterion," IEEE TRANSACTIONS ON AUTOMATIC CONTROL , vol. AC-25, October 1980...223-245. 4. K. Hsu and S.I. Marcus, "Decentralized Control of Finite State Markov Processes," IEEE TRANSACTIONS ON AUTOMATIC CONTROL , vol.
Estimations of non-linearities in structural vibrations of string musical instruments
Ege, Kerem; Boutillon, Xavier
2012-01-01
Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies, we characterise weak non-linearities by a signal-model approach based on cascade of Hammerstein models. In this approach, in a chain of two non-linear systems, two measurements are sufficient to estimate the non-linear contribution of the second (sub-)system which cannot be directly linearly driven, as a function of the exciting frequency. The experiment consists in exciting the instrument acoustically. The linear and non-linear contributions to the response of (a) the loudspeaker coupled to the room, (b) the instrument can be separated. Some methodological issues will be discussed. Findings pertaining to several instruments - one piano, two guitars, one violin - will be presented.
Capacity estimates for optical transmission based on the nonlinear Fourier transform
Derevyanko, Stanislav A.; Prilepsky, Jaroslaw E.; Turitsyn, Sergei K.
2016-09-01
What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km.
Explicit Integration of Friedmann's Equation with Nonlinear Equations of State
Chen, Shouxin; Yang, Yisong
2015-01-01
This paper is a continuation of our earlier study on the integrability of the Friedmann equations in the light of the Chebyshev theorem. Our main focus will be on a series of important, yet not previously touched, problems when the equation of state for the perfect-fluid universe is nonlinear. These include the generalized Chaplygin gas, two-term energy density, trinomial Friedmann, Born--Infeld, and two-fluid models. We show that some of these may be integrated using Chebyshev's result while other are out of reach by the theorem but may be integrated explicitly by other methods. With the explicit integration, we are able to understand exactly the roles of the physical parameters in various models play in the cosmological evolution. For example, in the Chaplygin gas universe, it is seen that, as far as there is a tiny presence of nonlinear matter, linear matter makes contribution to the dark matter, which becomes significant near the phantom divide line. The Friedmann equations also arise in areas of physics ...
Directory of Open Access Journals (Sweden)
Haorui Liu
2016-01-01
Full Text Available In the car control systems, it is hard to measure some key vehicle states directly and accurately when running on the road and the cost of the measurement is high as well. To address these problems, a vehicle state estimation method based on the kernel principal component analysis and the improved Elman neural network is proposed. Combining with nonlinear vehicle model of three degrees of freedom (3 DOF, longitudinal, lateral, and yaw motion, this paper applies the method to the soft sensor of the vehicle states. The simulation results of the double lane change tested by Matlab/SIMULINK cosimulation prove the KPCA-IENN algorithm (kernel principal component algorithm and improved Elman neural network to be quick and precise when tracking the vehicle states within the nonlinear area. This algorithm method can meet the software performance requirements of the vehicle states estimation in precision, tracking speed, noise suppression, and other aspects.
Energy Technology Data Exchange (ETDEWEB)
Han, Dong Ki; Chang, Pyung Hun [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2010-08-15
We propose an enhanced controller to improve the robustness of Time Delay Control (TDC) for a robot manipulator in the presence of nonlinear friction, such as Coulomb friction. The problem of TDC is first analyzed with TDC as a trajectory control for a robot manipulator in the presence of nonlinear friction. Gradient estimation is used to solve this problem. The proposed controller is called TDC with Gradient Estimator (TDCGE). Comparing with a prior research to improve the robustness of TDC, named TDCSA, the TDCGE is much simpler to design. Through 1 DOF linear motor experiment, it is verified that the TDCGE is more robust against nonlinear friction than TDC and the TDCGE has a similar robustness to the TDCSA. In addition, it is confirmed that the TDCGE is easily implemented in the multi degree-of-freedom robot manipulator through a 3 DOF spatial robot manipulator experiment
DEFF Research Database (Denmark)
Chon, K H; Cohen, R J; Holstein-Rathlou, N H
1997-01-01
A linear and nonlinear autoregressive moving average (ARMA) identification algorithm is developed for modeling time series data. The algorithm uses Laguerre expansion of kernals (LEK) to estimate Volterra-Wiener kernals. However, instead of estimating linear and nonlinear system dynamics via moving...... average models, as is the case for the Volterra-Wiener analysis, we propose an ARMA model-based approach. The proposed algorithm is essentially the same as LEK, but this algorithm is extended to include past values of the output as well. Thus, all of the advantages associated with using the Laguerre...... function remain with our algorithm; but, by extending the algorithm to the linear and nonlinear ARMA model, a significant reduction in the number of Laguerre functions can be made, compared with the Volterra-Wiener approach. This translates into a more compact system representation and makes...
Tkachova, P.; Krot, A.; Minervina, H.
It is well known that there is chaos in convective process in atmosphere and ocean. In particular,dynamic model of Lorenz [1] describes the Rayleigh-Benard convection phenomenon. Phase trajectories of Lorenz equation system are characterized by strange alternative properties: on the one hand, they diverge (because of positive Lyapunov exponents), on the second hand, they attract to the limited domain of phase space called an attractor [1]. The Lorenz attractor has specific geometrical structure and can be characterized by means of fractal dimension. In this connection the aim of this work is development of analysis of Lorenz attractor based on the proposed nonlinear decomposition into matrix series [2]. This analysis permits to estimate the values of characteristic parameters (including control one) of Lorenz attractors and predict their evolution in time. Using results of matrix decomposition [2], it is not difficult to see that the change of vector function (describing the Lorenz attractor) can be approximated by only linear and quadratic terms [3]. Because values of the first and second order derivatives can be calculated by means of numerical methods we can estimate the change of the vector function from computational experiment. In result, the values of parameters of the Lorenz's attractor can be estimated. This permits us to solve the identification task of the current dynamical state of a convective aerodynamic flows. Moreover, using the results of matrix decomposition we can estimate the minimal embedding dimension [4] for the Lorenz attractor based on experimental data. References: [1] P.Berge,Y.Pomeau and C.Vidal. L'ordre dans le chaos: Vers une approche deterministe de la turbulence. Hermann:Paris,1988. [2] A.M.Krot, "Matrix decompositions of vector functions and shift operators on the trajectories of a nonlinear dynamical system", Nonlinear Phenomena in Complex Systems,vol.4, N2, pp.106- 115, 2001. [3] A.M.Krot and P
Nonlinear analysis of gravity signals based on estimating attractor topological characteristics
Minervina, H.
2003-04-01
The nonlinear dynamical systems (NDSs) and processes with self-organization named as complex systems[1] are investi- gated with great activity in last decades.The gravity phe- nomenon can be also interpreted from the point of view of the self-organization theory first of all as primary irre- versible process [1].The NDS behavior are described on the basis of reconstruction of its attractor in m-dimensional Euclidean state-space and estimation of attractor topolo- gical characteristics(including minimal embedding dimension, scaling factors etc). With this aim it is necessary to select the state-space with the minimal dimension m* as the value m* is an upper limit of the degrees of freedom for a system. The determing m* on the basis of various correlative topological methods requires large computer expenditures [2]. Such methods have essential computational complexity and demand long time series (N is approximatly equal to 10000 - 100000 points) for their implementation. The method proposed in [3]-[5] allows to reduce the compu- tational complexity. However,the proposed locally topolo- gical method has especially heuristic character.This paper gives the theoretical ground of a local-topological method for defining minimal attractor embedding dimension on the basis of proposed matrix series into the state-space [6]. This method requires much less experimental data and is stable to changing m* [3],[5].The investigation of digital gravity signals using local-topological analysis of chaotic attractor trajectories is carried out. For this case we use the geodynamic ground of monotoring for observing variations of gravity field of the Earth on the base of quartz gravi- meters as GNU-KS. The computer confirmation of the theore- tical results is presented. References [1] G.Nicolis and I.Prigogine. Exploring Complexity. W.H.Freeman and Co., New York, 1989. [2] P.Grassberger and I. Procaccia,Characterization of strange attractors, Phys. Rev.Lett. vol.50, 346-349,1983. [3] V
Vuori, Kaarina; Strandén, Ismo; Sevón-Aimonen, Marja-Liisa; Mäntysaari, Esa A
2006-01-01
A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.
Estimation and Analysis of Nonlinear Stochastic Systems. Ph.D. Thesis
Marcus, S. I.
1975-01-01
The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.
State-variable analysis of non-linear circuits with a desk computer
Cohen, E.
1981-01-01
State variable analysis was used to analyze the transient performance of non-linear circuits on a desk top computer. The non-linearities considered were not restricted to any circuit element. All that is required for analysis is the relationship defining each non-linearity be known in terms of points on a curve.
Sunbuloglu, Emin; Bozdag, Ergun; Toprak, Tuncer; Islak, Civan
2013-01-01
This study is aimed at setting a method of experimental parameter estimation for large-deforming nonlinear viscoelastic continuous fibre-reinforced composite material model. Specifically, arterial tissue was investigated during experimental research and parameter estimation studies, due to medical, scientific and socio-economic importance of soft tissue research. Using analytical formulations for specimens under combined inflation/extension/torsion on thick-walled cylindrical tubes, in vitro experiments were carried out with fresh sheep arterial segments, and parameter estimation procedures were carried out on experimental data. Model restrictions were pointed out using outcomes from parameter estimation. Needs for further studies that can be developed are discussed.
Charged anisotropic matter with linear or nonlinear equation of state
Varela, Victor; Ray, Saibal; Chakraborty, Kaushik; Kalam, Mehedi
2010-01-01
Ivanov pointed out substantial analytical difficulties associated with self-gravitating, static, isotropic fluid spheres when pressure explicitly depends on matter density. Simplification achieved with the introduction of electric charge were noticed as well. We deal with self-gravitating, charged, anisotropic fluids and get even more flexibility in solving the Einstein-Maxwell equations. In order to discuss analytical solutions we extend Krori and Barua's method to include pressure anisotropy and linear or non-linear equations of state. The field equations are reduced to a system of three algebraic equations for the anisotropic pressures as well as matter and electrostatic energy densities. Attention is paid to compact sources characterized by positive matter density and positive radial pressure. Arising solutions satisfy the energy conditions of general relativity. Spheres with vanishing net charge contain fluid elements with unbounded proper charge density located at the fluid-vacuum interface. Notably the...
Directory of Open Access Journals (Sweden)
Wu Chong
2015-03-01
Full Text Available Simultaneous state and parameter estimation based actuator fault detection and diagnosis (FDD for single-rotor unmanned helicopters (UHs is investigated in this paper. A literature review of actuator FDD for UHs is given firstly. Based on actuator healthy coefficients (AHCs, which are introduced to represent actuator faults, a combined dynamic model is established with the augmented state containing both the flight state and AHCs. Then the actuator fault detection and diagnosis problem is transformed into a general nonlinear estimation one: given control inputs and the measured flight state contaminated by measurement noises, estimate both the flight state and AHCs recursively in each time-step, which is also known as the simultaneous state and parameter estimation problem. The estimated AHCs can further be used for fault tolerant control (FTC. Based on the existing widely used nonlinear estimation methods such as the unscented Kalman filter (UKF and the extended set-membership filter (ESMF, three kinds of adaptive schemes (KF-UKF, MIT-UKF and MIT-ESMF are proposed by our team to improve the actuator FDD performance. A comprehensive comparative study on these different estimation methods is given in detail to illustrate their advantages and disadvantages when applied to unmanned helicopter actuator FDD.
Age and Creative Productivity: Nonlinear Estimation of an Information-Processing Model.
Simonton, Dean Keith
1989-01-01
Applied two-step cognitive model to relationship between age and creative productivity. Selected ideation and elaboration rates as information-processing parameters that define mathematical function which describes age curves and specifies their variance across disciplines. Applied non-linear estimation program to further validate model. Despite…
Estimating marginal properties of quantitative real-time PCR data using nonlinear mixed models
DEFF Research Database (Denmark)
Gerhard, Daniel; Bremer, Melanie; Ritz, Christian
2014-01-01
A unified modeling framework based on a set of nonlinear mixed models is proposed for flexible modeling of gene expression in real-time PCR experiments. Focus is on estimating the marginal or population-based derived parameters: cycle thresholds and ΔΔc(t), but retaining the conditional mixed mod...
Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain
Zhang, B.; Billings, S. A.
2017-02-01
The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.
A Nonlinear Observer for Estimating Transverse Stability Parameters of Marine Surface Vessels
DEFF Research Database (Denmark)
Galeazzi, Roberto; Perez, Tristan
2011-01-01
This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel’s centre of gravity due...
Parity Relation Based Fault Estimation for Nonlinear Systems: An LMI Approach
Institute of Scientific and Technical Information of China (English)
Sing Kiong Nguang; Ping Zhang; Steven X. Ding
2007-01-01
This paper proposes a parity relation based fault estimation for a class of nonlinear systems which can be modelled by Takagi-Sugeno (TS) fuzzy models. The design of a parity relation based residual generator is formulated in terms of a family of linear matrix inequalities (LMIs). A numerical example is provided to illustrate the effectiveness of the proposed design techniques.
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2002-01-01
Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.
Roozegar, Mehdi; Mahjoob, Mohammad J.; Ayati, Moosa
2017-05-01
This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton-Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.
Uniform Approximate Estimation for Nonlinear Nonhomogenous Stochastic System with Unknown Parameter
2012-01-01
The error bound in probability between the approximate maximum likelihood estimator (AMLE) and the continuous maximum likelihood estimator (MLE) is investigated for nonlinear nonhomogenous stochastic system with unknown parameter. The rates of convergence of the approximations for Itô and ordinary integral are introduced under some regular assumptions. Based on these results, the in probability rate of convergence of the approximate log-likelihood function to the true continuous log-likelihoo...
The effect of compression on tuning estimates in a simple nonlinear auditory filter model
DEFF Research Database (Denmark)
Marschall, Marton; MacDonald, Ewen; Dau, Torsten
2013-01-01
, there is evidence that human frequency-selectivity estimates depend on whether an iso-input or an iso-response measurement paradigm is used (Eustaquio-Martin et al., 2011). This study presents simulated tuning estimates using a simple compressive auditory filter model, the bandpass nonlinearity (BPNL), which......, then compression alone may explain a large part of the behaviorally observed differences in tuning between simultaneous and forward-masking conditions....
Almaraz, Pablo; Green, Andy J; Aguilera, Eduardo; Rendón, Miguel A; Bustamante, Javier
2012-09-01
1. Understanding the impact of environmental variability on migrating species requires the estimation of sequential abiotic effects in different geographic areas across the life cycle. For instance, waterfowl (ducks, geese and swans) usually breed widely dispersed throughout their breeding range and gather in large numbers in their wintering headquarters, but there is a lack of knowledge on the effects of the sequential environmental conditions experienced by migrating birds on the long-term community dynamics at their wintering sites. 2. Here, we analyse multidecadal time-series data of 10 waterfowl species wintering in the Guadalquivir Marshes (SW Spain), the single most important wintering site for waterfowl breeding in Europe. We use a multivariate state-space approach to estimate the effects of biotic interactions, local environmental forcing during winter and large-scale climate during breeding and migration on wintering multispecies abundance fluctuations, while accounting for partial observability (observation error and missing data) in both population and environmental data. 3. The joint effect of local weather and large-scale climate explained 31·6% of variance at the community level, while the variability explained by interspecific interactions was negligible (observations through data augmentation increased the estimated magnitude of environmental forcing by an average 30·1% and reduced the impact of stochasticity by 39·3% when accounting for observation error. Interestingly however, the impact of environmental forcing on community dynamics was underestimated by an average 15·3% and environmental stochasticity overestimated by 14·1% when ignoring both observation error and data augmentation. 5. These results provide a salient example of sequential multiscale environmental forcing in a major migratory bird community, which suggests a demographic link between the breeding and wintering grounds operating through nonlinear environmental effects
Ponte Castañeda, Pedro
2016-11-01
This paper presents a variational method for estimating the effective constitutive response of composite materials with nonlinear constitutive behavior. The method is based on a stationary variational principle for the macroscopic potential in terms of the corresponding potential of a linear comparison composite (LCC) whose properties are the trial fields in the variational principle. When used in combination with estimates for the LCC that are exact to second order in the heterogeneity contrast, the resulting estimates for the nonlinear composite are also guaranteed to be exact to second-order in the contrast. In addition, the new method allows full optimization with respect to the properties of the LCC, leading to estimates that are fully stationary and exhibit no duality gaps. As a result, the effective response and field statistics of the nonlinear composite can be estimated directly from the appropriately optimized linear comparison composite. By way of illustration, the method is applied to a porous, isotropic, power-law material, and the results are found to compare favorably with earlier bounds and estimates. However, the basic ideas of the method are expected to work for broad classes of composites materials, whose effective response can be given appropriate variational representations, including more general elasto-plastic and soft hyperelastic composites and polycrystals.
Liquid-state acoustically-nonlinear nanoplasmonic source of optical frequency combs
Maksymov, Ivan S
2016-01-01
Nonlinear acoustic interactions in liquids are effectively stronger than nonlinear optical interactions in solids. Thus, harnessing these interactions will offer new possibilities in the design of ultra-compact nonlinear photonic devices. We theoretically demonstrate a hybrid, liquid-state and nanoplasmonic, source of optical frequency combs compatible with fibre-optic technology. This source relies on a nanoantenna to harness the strength of nonlinear acoustic effects and synthesise optical spectra from ultrasound.
Directory of Open Access Journals (Sweden)
Xia Liu
2017-02-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. In this article, we consider a class of discrete nonlinear Schrodinger equations with unbounded potentials. We obtain some new sufficient conditions on the multiplicity results of ground state solutions for the equations by using the symmetric mountain pass lemma. Recent results in the literature are greatly improved.
Constrained State Estimation for Individual Localization in Wireless Body Sensor Networks
Directory of Open Access Journals (Sweden)
Xiaoxue Feng
2014-11-01
Full Text Available Wireless body sensor networks based on ultra-wideband radio have recently received much research attention due to its wide applications in health-care, security, sports and entertainment. Accurate localization is a fundamental problem to realize the development of effective location-aware applications above. In this paper the problem of constrained state estimation for individual localization in wireless body sensor networks is addressed. Priori knowledge about geometry among the on-body nodes as additional constraint is incorporated into the traditional filtering system. The analytical expression of state estimation with linear constraint to exploit the additional information is derived. Furthermore, for nonlinear constraint, first-order and second-order linearizations via Taylor series expansion are proposed to transform the nonlinear constraint to the linear case. Examples between the first-order and second-order nonlinear constrained filters based on interacting multiple model extended kalman filter (IMM-EKF show that the second-order solution for higher order nonlinearity as present in this paper outperforms the first-order solution, and constrained IMM-EKF obtains superior estimation than IMM-EKF without constraint. Another brownian motion individual localization example also illustrates the effectiveness of constrained nonlinear iterative least square (NILS, which gets better filtering performance than NILS without constraint.
Energy Technology Data Exchange (ETDEWEB)
Belmonte-Beitia, Juan [Departamento de Matematicas, E. T. S. de Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la IngenierIa (IMACI), E. T. S. I. Industriales, Avda. Camilo Jose Cela, s/n Universidad de Castilla-La Mancha 13071 Ciudad Real (Spain)
2009-01-23
We introduce a model of a Bose-Einstein condensate based on the one-dimensional nonlinear Schroedinger equation, in which the nonlinear term depends on the domain. The nonlinear term changes a cubic term into a quintic term, according to the domain considered. We study the existence, stability and bifurcation of solutions, and use the qualitative theory of dynamical systems to study certain properties of such solutions.
Word, Daniel P; Cummings, Derek A T; Burke, Donald S; Iamsirithaworn, Sopon; Laird, Carl D
2012-08-07
Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.
Khairuzzaman, Md; Zhang, Chao; Igarashi, Koji; Katoh, Kazuhiro; Kikuchi, Kazuro
2010-03-01
We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.
Energy Technology Data Exchange (ETDEWEB)
Cloutier, J.R.; D`Souza, C.N.; Mracek, C.P. [Air Force Armament Directorate, Eglin, FL (United States)
1994-12-31
A little known technique for systematically designing nonlinear regulators is analyzed. The technique consists of first using direct parameterization to bring the nonlinear system to a linear structure having state-dependent coefficients (SDC). A state-dependent Riccati equation (SDRE) is then solved at each point x along the trajectory to obtain a nonlinear feedback controller of the form u = -R{sup -1}(x)B{sup T}(x)P(x)x, where P(x) is the solution of the SDRE. In the case of scalar x, it is shown that the SDRE approach yields a control solution which satisfies all of the necessary conditions for optimality even when the state and control weightings are functions of the state. It is also shown that the solution is globally asymptotically stable. In the multivariable case, the optimality, suboptimality and stability properties of the SDRE method are investigated. Under various mild assumptions of controllability and observability, the following is shown: (a) concerning the necessary conditions for optimality, where H is the Hamiltonian of the system, H{sub u} = 0 is always satisfied and, under stability, {lambda} = -H{sub x} is asymptotically satisfied at a quadratic rate as the states are driven toward the origin, (b) if it exists, a parameter-dependent SDC parameterization can be computed such that the multivariable SDRE closed loop solution satisfies all of the necessary conditions for optimality for a given initial condition, and (c) the method is locally asymptotically stable. A general nonlinear minimum-energy (nonlinear H{sub {infinity}}) problem is then posed. For this problem, the SDRF, method involves the solution of two coupled state-dependent Riccati equations at each point x along the trajectory. In the case of full state information, again under mild assumptions of controllability and observability, it is shown that the SDRE non-linear H{sub {infinity}} controller is internally locally asymptotically stable.
Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models
Directory of Open Access Journals (Sweden)
Yi Hu
2014-01-01
Full Text Available Generalized method of moments (GMM has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.
A framework for interpreting regularized state estimation
Sugiura, Nozomi; Fujii, Yosuke; Kamachi, Masafumi; Ishikawa, Yoichi; Awaji, Toshiyuki
2015-01-01
Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled by adjusting initial conditions to bring all stable modes closer to observations and by using a continuous guide to direct unstable modes toward a reference time series. This interpretation provides a consistent and effective procedure for solving problems of long-term state estimation. By applying this approach to an ocean general circulation model with a parameterized vertical diffusion procedure, it is demonstrated that tangent linear and adjoint models in this framework should have no unstable modes and hence be suitable for tracking persistent signals. This methodology is widely applicable to extend the assimilation period in 4D-Var.
DEFF Research Database (Denmark)
Gørgens, Tue; Skeels, Christopher L.; Wurtz, Allan
This paper explores estimation of a class of non-linear dynamic panel data models with additive unobserved individual-specific effects. The models are specified by moment restrictions. The class includes the panel data AR(p) model and panel smooth transition models. We derive an efficient set of ...... Carlo experiment. We find that estimation of the parameters in the transition function can be problematic but that there may be significant benefits in terms of forecast performance....... of moment restrictions for estimation and apply the results to estimation of panel smooth transition models with fixed effects, where the transition may be determined endogenously. The performance of the GMM estimator, both in terms of estimation precision and forecasting performance, is examined in a Monte...
Directory of Open Access Journals (Sweden)
Wameedh Riyadh Abdul-Adheem
2016-12-01
Full Text Available This paper presents a new strategy for the active disturbance rejection control (ADRC of a general uncertain system with unknown bounded disturbance based on a nonlinear sliding mode extended state observer (SMESO. Firstly, a nonlinear extended state observer is synthesized using sliding mode technique for a general uncertain system assuming asymptotic stability. Then the convergence characteristics of the estimation error are analyzed by Lyapunov strategy. It revealed that the proposed SMESO is asymptotically stable and accurately estimates the states of the system in addition to estimating the total disturbance. Then, an ADRC is implemented by using a nonlinear state error feedback (NLSEF controller; that is suggested by J. Han and the proposed SMESO to control and actively reject the total disturbance of a permanent magnet DC (PMDC motor. These disturbances caused by the unknown exogenous disturbances and the matched uncertainties of the controlled model. The proposed SMESO is compared with the linear extended state observer (LESO. Through digital simulations using MATLAB / SIMULINK, the chattering phenomenon has been reduced dramatically on the control input channel compared to LESO. Finally, the closed-loop system exhibits a high immunity to torque disturbance and quite robustness to matched uncertainties in the system.
Directory of Open Access Journals (Sweden)
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.
Larsen, Jon S.; Santos, Ilmar F.
2015-06-01
The demand for oil-free turbo compressors is increasing. Current trends are divided between active magnetic bearings and air foil bearings (AFB), the latter being important due to mechanical simplicity. AFB supported rotors are sensitive to unbalance due to low damping and nonlinear characteristics, hence accurate prediction of their response is important. This paper gives theoretical and experimental contributions by implementing and validating a new method to simulate the nonlinear steady-state response of a rotor supported by three pads segmented AFBs. The fluid film pressures, foil deflections and rotor movements are simultaneously solved, considering foil stiffness and damping coefficients estimated using a structural model, previously described and validated against experiments.
Application of radial basis neural network for state estimation of ...
African Journals Online (AJOL)
user
conventional Weighted Least Squares (WLS) State Estimator on basis of time, ... The conventional state estimation is based on algorithmic method of solving a large ... The RBF unit or transfer function is similar to Gaussian density function, ...
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.
Nonlinear State and Parameter Estimation for Hopper Dredgers
Stano, P.M.
2013-01-01
A Trailing Suction Hopper Dredger (TSHD) is a ship that excavates sediments from the sea bottom while sailing. In situ material is excavated with a special tool called the Drag-Head, then it is hydraulically transported through a pipe to the hopper where it is temporarily stored. After the dredging
Ground state solutions for nonlinear fractional Schrodinger equations involving critical growth
Directory of Open Access Journals (Sweden)
Hua Jin
2017-03-01
Full Text Available This article concerns the ground state solutions of nonlinear fractional Schrodinger equations involving critical growth. We obtain the existence of ground state solutions when the potential is not a constant and not radial. We do not use the Ambrosetti-Rabinowitz condition, or the monotonicity condition on the nonlinearity.
Integral input-to-state stability of nonlinear control systems with delays
Energy Technology Data Exchange (ETDEWEB)
Zhu Wenli [Department of Economics Mathematics, South Western University of Finance and Economics, Chengdu 610074 (China)]. E-mail: zhuwl@swufe.edu.cn; Yi Zhang [Computational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054 (China)]. E-mail: zhangyi@uestc.edu.cn
2007-10-15
Integral input-to-state stability is an interesting concept that has been recently introduced to nonlinear control systems. This paper generalizes this concept to nonlinear control systems with delays. These delays can be bounded, unbounded, and even infinite. Theorems for integral input-to-state stability are derived by developing the method of Razumikhin technique in the theory of functional differential equations.
Vision Aided State Estimation for Helicopter Slung Load System
DEFF Research Database (Denmark)
Bisgaard, Morten; Bendtsen, Jan Dimon; la Cour-Harbo, Anders
2007-01-01
This paper presents the design and verification of a state estimator for a helicopter based slung load system. The estimator is designed to augment the IMU driven estimator found in many helicopter UAV s and uses vision based updates only. The process model used for the estimator is a simple 4 st...... the estimator is verified using flight data and it is shown that it is capable of reliably estimating the slung load states....
INTERVAL STATE ESTIMATION FOR SINGULAR DIFFERENTIAL EQUATION SYSTEMS WITH DELAYS
Directory of Open Access Journals (Sweden)
T. A. Kharkovskaia
2016-07-01
Full Text Available The paper deals with linear differential equation systems with algebraic restrictions (singular systems and a method of interval observer design for this kind of systems. The systems contain constant time delay, measurement noise and disturbances. Interval observer synthesis is based on monotone and cooperative systems technique, linear matrix inequations, Lyapunov function theory and interval arithmetic. The set of conditions that gives the possibility for interval observer synthesis is proposed. Results of synthesized observer operation are shown on the example of dynamical interindustry balance model. The advantages of proposed method are that it is adapted to observer design for uncertain systems, if the intervals of admissible values for uncertain parameters are given. The designed observer is capable to provide asymptotically definite limits on the estimation accuracy, since the interval of admissible values for the object state is defined at every instant. The obtained result provides an opportunity to develop the interval estimation theory for complex systems that contain parametric uncertainty, varying delay and nonlinear elements. Interval observers increasingly find applications in economics, electrical engineering, mechanical systems with constraints and optimal flow control.
Phase sensitivity in deformed-state superposition considering nonlinear phase shifts
Berrada, K.
2016-07-01
We study the problem of the phase estimation for the deformation-state superposition (DSS) under perfect and lossy (due to a dissipative interaction of DSS with their environment) regimes. The study is also devoted to the phase enhancement of the quantum states resulting from a generalized non-linearity of the phase shifts, both without and with losses. We find that such a kind of superposition can give the smallest variance in the phase parameter in comparison with usual Schrödinger cat states in different order of non-linearity even if for a larger average number of photons. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement between the DSS and its environment is investigated during the dissipation. We show that partial entanglement trapping occurs during the dynamics depending on the kind of deformation and mean photon number. These features make the DSS with a larger average number of photons a good candidate for implementation of schemes of quantum optics and information with high precision.
Characterizaticr of Solid State Laser and Nonlinear Optical Materials.
1995-02-02
materials useful in the different methods for obtaining frequency agility: narrow line emitters with multiple lasing channels and nonlinear optical materials . In...codoped with two or more rare earth ions were studied and computers models developed to explain their spectral dynamics. The nonlinear optical materials investigated
Nonlinear functional response parameter estimation in a stochastic predator-prey model.
Gilioli, Gianni; Pasquali, Sara; Ruggeri, Fabrizio
2012-01-01
Parameter estimation for the functional response of predator-prey systems is a critical methodological problem in population ecology. In this paper we consider a stochastic predator-prey system with non-linear Ivlev functional response and propose a method for model parameter estimation based on time series of field data. We tackle the problem of parameter estimation using a Bayesian approach relying on a Markov Chain Monte Carlo algorithm. The efficiency of the method is tested on a set of simulated data. Then, the method is applied to a predator-prey system of importance for Integrated Pest Management and biological control, the pest mite Tetranychus urticae and the predatory mite Phytoseiulus persimilis. The model is estimated on a dataset obtained from a field survey. Finally, the estimated model is used to forecast predator-prey dynamics in similar fields, with slightly different initial conditions.
MOHAMMED, M. A. SI; BOUSSADIA, H.; BELLAR, A.; ADNANE, A.
2017-01-01
This paper presents a brief synthesis and useful performance analysis of different attitude filtering algorithms (attitude determination algorithms, attitude estimation algorithms, and nonlinear observers) applied to Low Earth Orbit Satellite in terms of accuracy, convergence time, amount of memory, and computation time. This latter is calculated in two ways, using a personal computer and also using On-board computer 750 (OBC 750) that is being used in many SSTL Earth observation missions. The use of this comparative study could be an aided design tool to the designer to choose from an attitude determination or attitude estimation or attitude observer algorithms. The simulation results clearly indicate that the nonlinear Observer is the more logical choice.
Energy Technology Data Exchange (ETDEWEB)
Heasler, Patrick G.; Posse, Christian; Hylden, Jeff L.; Anderson, Kevin K.
2007-06-13
This paper presents a nonlinear Bayesian regression algorithm for the purpose of detecting and estimating gas plume content from hyper-spectral data. Remote sensing data, by its very nature, is collected under less controlled conditions than laboratory data. As a result, the physics-based model that is used to describe the relationship between the observed remotesensing spectra, and the terrestrial (or atmospheric) parameters that we desire to estimate, is typically littered with many unknown "nuisance" parameters (parameters that we are not interested in estimating, but also appear in the model). Bayesian methods are well-suited for this context as they automatically incorporate the uncertainties associated with all nuisance parameters into the error estimates of the parameters of interest. The nonlinear Bayesian regression methodology is illustrated on realistic simulated data from a three-layer model for longwave infrared (LWIR) measurements from a passive instrument. This shows that this approach should permit more accurate estimation as well as a more reasonable description of estimate uncertainty.
Exponential H∞ synchronization and state estimation for chaotic systems via a unified model.
Liu, Meiqin; Zhang, Senlin; Fan, Zhen; Zheng, Shiyou; Sheng, Weihua
2013-07-01
In this paper, H∞ synchronization and state estimation problems are considered for different types of chaotic systems. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems, such as Hopfield neural networks, cellular neural networks, Chua's circuits, unified chaotic systems, Qi systems, chaotic recurrent multilayer perceptrons, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal H∞ norm constraint. The state estimation problem is then studied for the same unified model, where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level. The parameters of these controllers and filters are obtained by solving the eigenvalue problem. Most chaotic systems can be transformed into this unified model, and H∞ synchronization controllers and state estimators for these systems are designed in a unified way. Three numerical examples are provided to show the usefulness of the proposed H∞ synchronization and state estimation conditions.
Directory of Open Access Journals (Sweden)
Lee HyunYoung
2010-01-01
Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.
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.
Estimates for solutions to a class of nonlinear time-delay systems of neutral type
Directory of Open Access Journals (Sweden)
Gennadii V. Demidenko
2015-02-01
Full Text Available We consider nonlinear time-delay systems of neutral type with constant coefficients in the linear terms, $$ \\frac{d}{dt}\\big(y(t + D y(t-\\tau\\big = A y(t + B y(t-\\tau + F(t, y(t, y(t-\\tau. $$ We obtain estimates characterizing the exponential decay of solutions at infinity, and dependending on the norms of the powers of D.
Minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems
Liu, Chungen
2009-01-01
In this paper, we consider the minimal period estimates for brake orbits of nonlinear symmetric Hamiltonian systems. We prove that if the Hamiltonian function $H\\in C^2(\\Bbb R^{2n}, \\Bbb R)$ is super-quadratic and convex, for every number $\\tau>0$, there exists at least one $\\tau$-periodic brake orbit $(\\tau,x)$ with minimal period $\\tau$ or $\\tau/2$ provided $H(Nx)=H(x)$.
THE ESTIMATION OF ORDERING DEGREE OF CORONA-POLED NONLINEAR OPTICAL POLYMER FILMS
Institute of Scientific and Technical Information of China (English)
YE Cheng; DONG Haiou; WANG Jiafu
1992-01-01
The investigation of electrochromic effect of corona-poled nonlinear optical polymer films is an effective method for the estimation of poling level and the selection of poling conditions. The poling electric field Ep and orientational order parameter φ, which are the important parameters to predict d33 of poled tilms, can be calculated by a simple operation from the number of red shift of charge transfer absorption band. The calculated results are in good agreement with the experimental data.
Aguirre, Luis Antonio; Teixeira, Bruno Otávio S.; Tôrres, Leonardo Antônio B.
2005-08-01
This paper addresses the problem of state estimation for nonlinear systems by means of the unscented Kalman filter (UKF). Compared to the traditional extended Kalman filter, the UKF does not require the local linearization of the system equations used in the propagation stage. Important results using the UKF have been reported recently but in every case the system equations used by the filter were considered known. Not only that, such models are usually considered to be differential equations, which requires that numerical integration be performed during the propagation phase of the filter. In this paper the dynamical equations of the system are taken to be difference equations—thus avoiding numerical integration—and are built from data without prior knowledge. The identified models are subsequently implemented in the filter in order to accomplish state estimation. The paper discusses the impact of not knowing the exact equations and using data-driven models in the context of state and joint state-and-parameter estimation. The procedure is illustrated by means of examples that use simulated and measured data.
Optical nonlinearities of excitonic states in atomically thin 2D transition metal dichalcogenides.
Energy Technology Data Exchange (ETDEWEB)
Soh, Daniel Beom Soo
2017-09-01
We calculated the optical nonlinearities of the atomically thin monolayer transition metal dichalcogenide material (particularly MoS 2 ), particularly for those linear and nonlinear tran- sition processes that utilize the bound exciton states. We adopted the bound and the unbound exciton states as the basis for the Hilbert space, and derived all the dynamical density matri- ces that provides the induced current density, from which the nonlinear susceptibilities can be drawn order-by-order via perturbative calculations. We provide the nonlinear susceptibil- ities for the linear, the second-harmonic, the third-harmonic, and the kerr-type two-photon processes.
Linear and nonlinear ARMA model parameter estimation using an artificial neural network
Chon, K. H.; Cohen, R. J.
1997-01-01
This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.
Carroll, Raymond J.
2010-05-01
This paper considers identification and estimation of a general nonlinear Errors-in-Variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values; and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest - the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates - is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterized, we propose sieve Quasi Maximum Likelihood Estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.
Parameter estimation of cutting tool temperature nonlinear model using PSO algorithm
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In cutting tool temperature experiment, a large number of related data could be available. In order to define the relationship among the experiment data, the nonlinear regressive curve of cutting tool temperature must be constructed based on the data. This paper proposes the Particle Swarm Optimization (PSO) algorithm for estimating the parameters such a curve. The PSO algorithm is an evolutional method based on a very simple concept. Comparison of PSO results with those of GA and LS methods showed that the PSO algorithm is more effective for estimating the parameters of the above curve.
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2011-06-01
Full Text Available The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich. The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well.
State Estimation of the Electric Drive Articulated Dump Truck Based on UKF
Institute of Scientific and Technical Information of China (English)
Chun Jin; Tong Liu; Yanhua Shen
2015-01-01
The requirements of vehicle dynamic stability control are higher than ever as the significant increase of electric drive articulated vehicle speed. According to the construction features of articulated dumping truck and nonlinear characteristics of moving vehicles, nonlinear observer of vehicle status is designed to strength robustness of dynamic control system in this paper. A 4⁃degree⁃of⁃freedom nonlinear dynamic model of articulated electric drive vehicle is built as reference model to estimate the state of the articulated vehicle. And by adopting Unscented Kalman Filter ( UKF ) algorithm, a series of state parameters such as longitudinal velocities of front and rear frames, yaw rate and side⁃slip angle are estimated. During the test of 60 t articulated electric drive vehicle, 2 inertial navigation modules are installed in the front frame and rear frame respectively and the speed of each electric drive wheel is obtained simultaneously. As the test results suggest, in various working conditions, the algorithm based on UKF is able to accurately estimate the state parameters of articulated vehicle with the estimated error less than 5%. The proposed method is justified to be the theoretical basis and application guidance for articulated vehicle stability control.
Institute of Scientific and Technical Information of China (English)
ZHANG Jia-zhong; LIU Yan; CHEN Dang-min
2005-01-01
From viewpoint of nonlinear dynamics, the model reduction and its influence on the long-term behaviours of a class of nonlinear dissipative autonomous dynamical system with higher dimension are investigated theoretically under some assumptions. The system is analyzed in the state space with an introduction of a distance definition which can be used to describe the distance between the full system and the reduced system, and the solution of the full system is then projected onto the complete space spanned by the eigenvectors of the linear operator of the governing equations. As a result, the influence of mode series tnncation on the long-term behaviours and the error estimate are derived, showing that the error is dependent on the first products of frequencies and damping ratios in the subspace spanned by the eigenvectors with higher modal damping. Furthermore, the fundamental understanding for the topological change of the solution due to the application of different model reduction is interpreted in a mathematically precise way, using the qualitative theory of nonlinear dynamics.
Tampere, C.M.J.; Immers, L.H.
2007-01-01
Abstract— This paper presents a traffic state estimation and prediction model based on the cell transmission model (CTM). The nonlinear CTM is transcribed in a closed analytical statespace form for use within a general extended Kalman filtering framework. The state-space CTM switches implicitly betw
Eppenhof, Koen A. J.; Pluim, Josien P. W.
2017-02-01
Error estimation in medical image registration is valuable when validating, comparing, or combining registration methods. To validate a nonlinear image registration method, ideally the registration error should be known for the entire image domain. We propose a supervised method for the estimation of a registration error map for nonlinear image registration. The method is based on a convolutional neural network that estimates the norm of the residual deformation from patches around each pixel in two registered images. This norm is interpreted as the registration error, and is defined for every pixel in the image domain. The network is trained using a set of artificially deformed images. Each training example is a pair of images: the original image, and a random deformation of that image. No manually labeled ground truth error is required. At test time, only the two registered images are required as input. We train and validate the network on registrations in a set of 2D digital subtraction angiography sequences, such that errors up to eight pixels can be estimated. We show that for this range of errors the convolutional network is able to learn the registration error in pairs of 2D registered images at subpixel precision. Finally, we present a proof of principle for the extension to 3D registration problems in chest CTs, showing that the method has the potential to estimate errors in 3D registration problems.
DEFF Research Database (Denmark)
Sommer, Helle Mølgaard; Holst, Helle; Spliid, Henrik
1995-01-01
Three identical microbiological experiments were carried out and analysed in order to examine the variability of the parameter estimates. The microbiological system consisted of a substrate (toluene) and a biomass (pure culture) mixed together in an aquifer medium. The degradation of the substrate...
Nonlinear Channel Estimation for OFDM System by Complex LS-SVM under High Mobility Conditions
Charrada, Anis; 10.5121/ijwmn.2011.3412
2011-01-01
A nonlinear channel estimator using complex Least Square Support Vector Machines (LS-SVM) is proposed for pilot-aided OFDM system and applied to Long Term Evolution (LTE) downlink under high mobility conditions. The estimation algorithm makes use of the reference signals to estimate the total frequency response of the highly selective multipath channel in the presence of non-Gaussian impulse noise interfering with pilot signals. Thus, the algorithm maps trained data into a high dimensional feature space and uses the structural risk minimization (SRM) principle to carry out the regression estimation for the frequency response function of the highly selective channel. The simulations show the effectiveness of the proposed method which has good performance and high precision to track the variations of the fading channels compared to the conventional LS method and it is robust at high speed mobility.
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.
Deng, Linhua
2015-07-01
Three nonlinear analysis techniques, including cross-recurrence plot, line of synchronization, and cross-wavelet transform, are proposed to estimate the coherent phase vibrations of nonlinear and non-stationary time series. The case study utilizes the monthly averages of sunspot areas during the time interval from May 1874 to August 2014. The following prominent results are found: (1) the phase-leading hemisphere of long-term sunspot areas has changed twice in the past 140 years, indicating that the hemispheric imbalances and apparent phase differences on both hemispheres are a prevalent behavior and are not anomalous; (2) the alternating regularity of hemispheric asynchronism exhibits a cyclical pattern of 4.5+3.5 cycles, and the magnetic flux excess in a certain hemisphere during the ascending branch of a cycle can be taken as an indication of the phase-leading hemisphere in this cycle. We firmly believe that powerful nonlinear approaches are more advanced than classical linear methods when they are combined to determine the dynamic complexity of nonlinear physical systems.
Optimal State Estimation of Pure Qubits on Circles
Institute of Scientific and Technical Information of China (English)
A. Ugulava; ZHANG Li-Hua; L. Chotorlishvili; SONG Wei; V. Skrinnikov; CAO Zhuo-Liang; G. Mchedlishvili
2008-01-01
We consider the problem of state estimation of qubits chosen from circles. It is shown that any qubit encoded in pairs chosen from a fixed circle parallel to the x-y equator with different phases contains the same information. We also investigate the problem of state estimation of qubits from three circles. The optimal estimation fidelity is derived.
Full-Order Sliding Mode Control for High-Order Nonlinear System Based on Extended State Observer
Institute of Scientific and Technical Information of China (English)
CHEN Qiang; TAO Liang; NAN Yurong
2016-01-01
In this paper,a full-order sliding mode control based on extended state observer (FSMC+ESO) is proposed for high-order nonlinear system with unknown system states and uncertainties.The extended state observer (ESO) is employed to estimate both the unknown system states and uncertainties so that the restriction that the system states should be completely measurable is relaxed,and a full-order sliding mode controller is designed based on the ESO estimation to overcome the chattering problem existing in ordinary reduced-order sliding mode control.Simulation results show that the proposed method facilitates the practical application with respect to good tracking performance and chattering elimination.
Development of an on-line state estimator for fed-batch filamentous fungal fermentations
DEFF Research Database (Denmark)
Mears, Lisa; Stocks, Stuart M.; Albæk, Mads O.
Bioprocesses can be challenging to model due to complex and non-linear process dynamics [1]. In addition there is a lack of robust, on-line sensors for key parameters of interest in the field, such as substrate, product and biomass concentration [2]. These factors lead to limitations in the ability...... to monitor and control bioprocess systems. There is therefore an interest in state estimation, in order to model these key process states based on available on-line measurements [1]. This work discusses the application of a first principle model to pilot scale filamentous fungal fermentation systems operated...... pressure [4], [5]. This stoichiometric-based coupled process model is successfully applied on-line as a state estimator in order to predict the biomass and product concentration, from robust, available on-line measurements. Such state estimators will be valuable as part of control strategy development...
Decentralized estimation of sensor systematic error andtarget state vector
Institute of Scientific and Technical Information of China (English)
贺明科; 王正明; 朱炬波
2003-01-01
An accurate estimation of the sensor systematic error is significant for improving the performance of target tracking system. The existing methods usually append the bias states directly to the variable states to form augmented state vectors and utilize the conventional Kalman estimator to achieve state vectors estimate. So doing is expensive in computation, and much work is devoted to decoupling variable states and systematic error. But the decentralied estimation of systematic errors and reduction of the amount of computation as well as decentralied track fusion are far from being realized. This paper addresses distributed track fusion problem in multi-sensor tracking system in the presence of sensor bias. By this method, variable states and systematic error is decoupled. Decentralized systematic error estimation and track fusion are achieved. Simulation results verify that this method can get accurate estimation of systematic error and state vector.
Directory of Open Access Journals (Sweden)
Mäntysaari Esa A
2006-06-01
Full Text Available Abstract A method based on Taylor series expansion for estimation of location parameters and variance components of non-linear mixed effects models was considered. An attractive property of the method is the opportunity for an easily implemented algorithm. Estimation of non-linear mixed effects models can be done by common methods for linear mixed effects models, and thus existing programs can be used after small modifications. The applicability of this algorithm in animal breeding was studied with simulation using a Gompertz function growth model in pigs. Two growth data sets were analyzed: a full set containing observations from the entire growing period, and a truncated time trajectory set containing animals slaughtered prematurely, which is common in pig breeding. The results from the 50 simulation replicates with full data set indicate that the linearization approach was capable of estimating the original parameters satisfactorily. However, estimation of the parameters related to adult weight becomes unstable in the case of a truncated data set.
Identification of Nonlinear Nonautonomous State Space Systems from Input-Output Measurements
Verdult, Vincent; Verhaegen, Michel; Scherpen, Jacquelien
2000-01-01
This paper presents a method to determine a nonlinear state space model from a finite number of measurements of the inputs and outputs. The method is based on embedding theory for nonlinear systems, and can be viewed as an extension of the subspace identification method for linear systems. The paper
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
Vision Aided State Estimation for Helicopter Slung Load System
DEFF Research Database (Denmark)
Bisgaard, Morten; Bendtsen, Jan Dimon; la Cour-Harbo, Anders
2007-01-01
This paper presents the design and verification of a state estimator for a helicopter based slung load system. The estimator is designed to augment the IMU driven estimator found in many helicopter UAV s and uses vision based updates only. The process model used for the estimator is a simple 4 st...
Boland, J. S., III
1975-01-01
A general simulation program is presented (GSP) involving nonlinear state estimation for space vehicle flight navigation systems. A complete explanation of the iterative guidance mode guidance law, derivation of the dynamics, coordinate frames, and state estimation routines are given so as to fully clarify the assumptions and approximations involved so that simulation results can be placed in their proper perspective. A complete set of computer acronyms and their definitions as well as explanations of the subroutines used in the GSP simulator are included. To facilitate input/output, a complete set of compatable numbers, with units, are included to aid in data development. Format specifications, output data phrase meanings and purposes, and computer card data input are clearly spelled out. A large number of simulation and analytical studies were used to determine the validity of the simulator itself as well as various data runs.
Indian Academy of Sciences (India)
Hari Prakash; Devendra K Singh
2010-03-01
It is shown that all optical polarization states of light except plane and circular polarization states undergo an intensity-dependent change in normal incidence of light in an isotropic nonlinear Kerr medium. This effect should be detectable and we propose an experiment for detecting nonlinear susceptibility involved in that part of nonlinear polarization, which depends on the polarization state of light also.
Institute of Scientific and Technical Information of China (English)
TANG NianSheng; CHEN XueDong; WANG XueRen
2009-01-01
Semiparametric reproductive dispersion nonlinear model (SRDNM) is an extension of nonlinear reproductive dispersion models and semiparametric nonlinear regression models, and includes semiparametric nonlinear model and semiparametric generalized linear model as its special cases. Based on the local kernel estimate of nonparametric component, profile-kernel and backfitting estimators of parameters of interest are proposed in SRDNM, and theoretical comparison of both estimators is also investigated in this paper. Under some regularity conditions, strong consistency and asymptotic normality of two estimators are proved. It is shown that the backtitting method produces a larger asymptotic variance than that for the profile-kernel method. A simulation study and a real example are used to illustrate the proposed methodologies.
Optimal state estimation for d-dimensional quantum systems
Bruss, D
1999-01-01
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and, furthermore, for generalized inputs supported on the symmetric subspace.
Yang, Ji Seung; Cai, Li
2014-01-01
The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…
Yang, Ji Seung; Cai, Li
2014-01-01
The main purpose of this study is to improve estimation efficiency in obtaining maximum marginal likelihood estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM). Results indicate that the MH-RM algorithm can produce estimates and standard…
Lewis, Robert Michael
1997-01-01
This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.
Estimation of region of attraction for polynomial nonlinear systems: a numerical method.
Khodadadi, Larissa; Samadi, Behzad; Khaloozadeh, Hamid
2014-01-01
This paper introduces a numerical method to estimate the region of attraction for polynomial nonlinear systems using sum of squares programming. This method computes a local Lyapunov function and an invariant set around a locally asymptotically stable equilibrium point. The invariant set is an estimation of the region of attraction for the equilibrium point. In order to enlarge the estimation, a subset of the invariant set defined by a shape factor is enlarged by solving a sum of squares optimization problem. In this paper, a new algorithm is proposed to select the shape factor based on the linearized dynamic model of the system. The shape factor is updated in each iteration using the computed local Lyapunov function from the previous iteration. The efficiency of the proposed method is shown by a few numerical examples.
Nonlinear Least-Squares Time-Difference Estimation from Sub-Nyquist-Rate Samples
Harada, Koji; Sakai, Hideaki
In this paper, time-difference estimation of filtered random signals passed through multipath channels is discussed. First, we reformulate the approach based on innovation-rate sampling (IRS) to fit our random signal model, then use the IRS results to drive the nonlinear least-squares (NLS) minimization algorithm. This hybrid approach (referred to as the IRS-NLS method) provides consistent estimates even for cases with sub-Nyquist sampling assuming the use of compactly-supported sampling kernels that satisfies the recently-developed nonaliasing condition in the frequency domain. Numerical simulations show that the proposed NLS-IRS method can improve performance over the straight-forward IRS method, and provides approximately the same performance as the NLS method with reduced sampling rate, even for closely-spaced time delays. This enables, given a fixed observation time, significant reduction in the required number of samples, while maintaining the same level of estimation performance.
Hu, Chaofang; Gao, Zhifei; Ren, Yanli; Liu, Yunbing
2016-11-01
In this paper, a reusable launch vehicle (RLV) attitude control problem with actuator faults is addressed via the robust adaptive nonlinear fault-tolerant control (FTC) with norm estimation. Firstly, the accurate tracking task of attitude angles in the presence of parameter uncertainties and external disturbances is considered. A fault-free controller is proposed using dynamic surface control (DSC) combined with fuzzy adaptive approach. Furthermore, the minimal learning parameter strategy via norm estimation technique is introduced to reduce the multi-parameter adaptive computation burden of fuzzy approximation of the lump uncertainties. Secondly, a compensation controller is designed to handle the partial loss fault of actuator effectiveness. The unknown maximum eigenvalue of actuator efficiency loss factors is estimated online. Moreover, stability analysis guarantees that all signals of the closed-loop control system are semi-global uniformly ultimately bounded. Finally, illustrative simulations show the effectiveness of the proposed method.
A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains
Bonforte, Matteo; Vázquez, Juan Luis
2015-10-01
We investigate quantitative properties of the nonnegative solutions to the nonlinear fractional diffusion equation, , posed in a bounded domain, , with m > 1 for t > 0. As we use one of the most common definitions of the fractional Laplacian , 0 zero Dirichlet boundary conditions. We consider a general class of very weak solutions of the equation, and obtain a priori estimates in the form of smoothing effects, absolute upper bounds, lower bounds, and Harnack inequalities. We also investigate the boundary behaviour and we obtain sharp estimates from above and below. In addition, we obtain similar estimates for fractional semilinear elliptic equations. Either the standard Laplacian case s = 1 or the linear case m = 1 are recovered as limits. The method is quite general, suitable to be applied to a number of similar problems.
Non-linear shrinkage estimation of large-scale structure covariance
Joachimi, Benjamin
2017-03-01
In many astrophysical settings, covariance matrices of large data sets have to be determined empirically from a finite number of mock realizations. The resulting noise degrades inference and precludes it completely if there are fewer realizations than data points. This work applies a recently proposed non-linear shrinkage estimator of covariance to a realistic example from large-scale structure cosmology. After optimizing its performance for the usage in likelihood expressions, the shrinkage estimator yields subdominant bias and variance comparable to that of the standard estimator with a factor of ∼50 less realizations. This is achieved without any prior information on the properties of the data or the structure of the covariance matrix, at a negligible computational cost.
Accurate quantum state estimation via "Keeping the experimentalist honest"
Blume-Kohout, R; Blume-Kohout, Robin; Hayden, Patrick
2006-01-01
In this article, we derive a unique procedure for quantum state estimation from a simple, self-evident principle: an experimentalist's estimate of the quantum state generated by an apparatus should be constrained by honesty. A skeptical observer should subject the estimate to a test that guarantees that a self-interested experimentalist will report the true state as accurately as possible. We also find a non-asymptotic, operational interpretation of the quantum relative entropy function.
Mathematical model of transmission network static state estimation
Directory of Open Access Journals (Sweden)
Ivanov Aleksandar
2012-01-01
Full Text Available In this paper the characteristics and capabilities of the power transmission network static state estimator are presented. The solving process of the mathematical model containing the measurement errors and their processing is developed. To evaluate difference between the general model of state estimation and the fast decoupled state estimation model, the both models are applied to an example, and so derived results are compared.
Advanced topics in control and estimation of state-multiplicative noisy systems
Gershon, Eli
2013-01-01
Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems begins with an introduction and extensive literature survey. The text proceeds to cover solutions of measurement-feedback control and state problems and the formulation of the Bounded Real Lemma for both continuous- and discrete-time systems. The continuous-time reduced-order and stochastic-tracking control problems for delayed systems are then treated. Ideas of nonlinear stability are introduced for infinite-horizon systems, again, in both the continuous- and discrete-time cases. The reader is introduced to six practical examples of noisy state-multiplicative control and filtering associated with various fields of control engineering. The book is rounded out by a three-part appendix containing stochastic tools necessary for a proper appreciation of the text: a basic introduction to nonlinear stochastic differential equations and aspects of switched systems and peak to peak optimal control and filtering. Advanced Topics in Contr...
Modeling, State Estimation and Control of Unmanned Helicopters
Lau, Tak Kit
error modeling and the filtering method for the sensor noise compensation. Moreover, we provide a fully automatic algorithm to tune our method. Finally, we evaluate our method on an instrumented gasoline helicopter. Experiments show that the technique enables the robust positioning of flying helicopters when no GNSS measurement is available. The design of an autopilot for an unmanned helicopter is made difficult by its nonlinear, coupled and non-minimum phase dynamics. Here, we consider a reinforcement learning approach to transfer motion skills from human to machine, and hence to achieve autonomous flight control. By making efficient use of a series of state-and-action pairs given by a human pilot, our algorithm bootstraps a parameterized control policy and learns to hover and follow trajectories after one manual flight. One key observation our algorithm is based on is that, although it is often difficult to retrieve the human pilots' hidden desiderata that formulate their state-feedback mechanisms in controlling the helicopters, it is possible to intercept the states of a helicopter and the actions by a human pilot and then to fit both into a model. We demonstrate the performance of our learning controller in experiments. The results described in this dissertation shed new and important light on the technology necessary to advance the current state of the unmanned helicopters. From a comprehensive dynamics modeling that addresses perplexing cross-couplings on the unmanned helicopters, to a robust state estimation against GNSS outage and a learn-from-scarce-sample control for an unmanned helicopter, we provide a starting point for the cultivation of the next-generation unmanned helicopters that can operate with the least possible human intervention.
Enhancement of Kerr nonlinearity and its application to entangled state discrimination
Institute of Scientific and Technical Information of China (English)
NIU Yue-ping; QIAN Jun; FENG Xun-li; GONG Shang-qing
2007-01-01
In this paper, the recent research on the enhan-ced Kerr nonlinearity and its application in entangled state discrimination is reported. Two kinds of dynamics, including interacting double dark resonances and spontaneously gen-erated coherence, are presented to enhance the Kerr nonlin-earity. The application of Kerr nonlinearity in quantum state discrimination is also discussed. An arbitrary Greenberger-Horne-Zeilinger state can be discriminated using two-photon polarization parity detection which resorts to cross-Kerr no-nlinearity between a single-photon qubit and probe field. In addition, a scheme for Greenberger-Home-Zeilinger state discrimination of matter qubits is also proposed using the dipole induced transparency in a cavity-dipole system.
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
A Robust Nonlinear Observer for Real-Time Attitude Estimation Using Low-Cost MEMS Inertial Sensors
Guerrero-Castellanos, José Fermi; Madrigal-Sastre, Heberto; Durand, Sylvain; Torres, Lizeth; Muñoz-Hernández, German Ardul
2013-01-01
This paper deals with the attitude estimation of a rigid body equipped with angular velocity sensors and reference vector sensors. A quaternion-based nonlinear observer is proposed in order to fuse all information sources and to obtain an accurate estimation of the attitude. It is shown that the observer error dynamics can be separated into two passive subsystems connected in “feedback”. Then, this property is used to show that the error dynamics is input-to-state stable when the measurement disturbance is seen as an input and the error as the state. These results allow one to affirm that the observer is “robustly stable”. The proposed observer is evaluated in real-time with the design and implementation of an Attitude and Heading Reference System (AHRS) based on low-cost MEMS (Micro-Electro-Mechanical Systems) Inertial Measure Unit (IMU) and magnetic sensors and a 16-bit microcontroller. The resulting estimates are compared with a high precision motion system to demonstrate its performance. PMID:24201316
Nonlinear effect of elastic vortexlike motion on the dynamic stress state of solids
Shilko, Evgeny V.; Grinyaev, Yurii V.; Popov, Mikhail V.; Popov, Valentin L.; Psakhie, Sergey G.
2016-05-01
We present a theoretical analysis of the dynamic stress-strain state of regions in a solid body that are involved in a collective elastic vortexlike motion. It is shown that the initiation of elastic vortexlike motion in the material is accompanied by the appearance of dilatancy and equivalent strain, the magnitudes of which are proportional to the square of the ratio of linear velocity on the periphery of the elastic vortex to the velocity of longitudinal elastic waves (P wave). Under conditions of dynamic loading the described dynamic effects are able to initiate inelastic deformation or destruction of the material at loading speeds of a few percent of the P -wave speed. The obtained analytical estimates suggest that dynamic nonlinear strains can make a significant contribution in a number of widely studied nonlinear dynamic phenomena in solids. Among them are the effect of acoustic (dynamic) dilatancy in solids and granular media, which leads to the generation of longitudinal elastic waves by transverse waves [V. Tournat et al., Phys. Rev. Lett. 92, 085502 (2004), 10.1103/PhysRevLett.92.085502] and the formation of an array of intense "hot spots" (reminiscent of shear-induced hydrodynamic instabilities in fluids) in adiabatic shear bands [P. R. Guduru et al., Phys. Rev. E 64, 036128 (2001), 10.1103/PhysRevE.64.036128].
Institute of Scientific and Technical Information of China (English)
Yan-ping Chen; Yun-qing Huang
2001-01-01
Improved L2-error estimates are computed for mixed finite element methods for second order nonlinear hyperbolic equations. Results are given for the continuous-time case. The convergence of the values for both the scalar function and the flux is demonstrated. The technique used here covers the lowest-order Raviart-Thomas spaces, as well as the higherorder spaces. A second paper will present the analysis of a fully discrete scheme (Numer.Math. J. Chinese Univ. vol.9, no.2, 2000, 181-192).
Teaca, Bogdan; Told, Daniel
2016-01-01
Using large resolution numerical simulations of GK turbulence, spanning an interval ranging from the end of the fluid scales to the electron gyroradius, we study the energy transfers in the perpendicular direction for a proton-electron plasma in a slab magnetic geometry. In addition, to aid our understanding of the nonlinear cascade, we use an idealized test representation for the energy transfers between two scales, mimicking the dynamics of turbulence in an infinite inertial range. For GK turbulence, a detailed analysis of nonlinear energy transfers that account for the separation of energy exchanging scales is performed. We show that locality functions associated with the energy cascade across dyadic (i.e. multiple of two) separated scales achieve an asymptotic state, recovering clear values for the locality exponents. We relate these exponents to the energy exchange between two scales, diagnostics that are less computationally intensive than the locality functions. It is the first time asymptotic locality...
DEFF Research Database (Denmark)
Fossen, T.I.; Blanke, M.
2000-01-01
Accurate propeller shaft speed controllers can be designed by using nonlinear control theory and feedback from the axial water velocity in the propeller disc. In this paper, an output feedback controller is derived, reconstructing the axial flow velocity from vehicle speed measurements, using...... a three-state model of propeller shaft speed, forward (surge) speed of the vehicle, and the axial flow velocity. Lyapunov stability theory is used to prove that a nonlinear observer combined with an output feedback integral controller provide exponential stability. The output feedback controller...... compensates for variations in thrust due to time variations in advance speed. This is a major problem when applying conventional vehicle-propeller control systems, The proposed controller is simulated for an underwater vehicle equipped with a single propeller. The simulations demonstrate that the axial water...
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-03-01
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects’ affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain’s motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
Higher-order Multivariable Polynomial Regression to Estimate Human Affective States.
Wei, Jie; Chen, Tong; Liu, Guangyuan; Yang, Jiemin
2016-03-21
From direct observations, facial, vocal, gestural, physiological, and central nervous signals, estimating human affective states through computational models such as multivariate linear-regression analysis, support vector regression, and artificial neural network, have been proposed in the past decade. In these models, linear models are generally lack of precision because of ignoring intrinsic nonlinearities of complex psychophysiological processes; and nonlinear models commonly adopt complicated algorithms. To improve accuracy and simplify model, we introduce a new computational modeling method named as higher-order multivariable polynomial regression to estimate human affective states. The study employs standardized pictures in the International Affective Picture System to induce thirty subjects' affective states, and obtains pure affective patterns of skin conductance as input variables to the higher-order multivariable polynomial model for predicting affective valence and arousal. Experimental results show that our method is able to obtain efficient correlation coefficients of 0.98 and 0.96 for estimation of affective valence and arousal, respectively. Moreover, the method may provide certain indirect evidences that valence and arousal have their brain's motivational circuit origins. Thus, the proposed method can serve as a novel one for efficiently estimating human affective states.
A supervised machine learning estimator for the non-linear matter power spectrum - SEMPS
Mohammed, Irshad
2015-01-01
In this article, we argue that models based on machine learning (ML) can be very effective in estimating the non-linear matter power spectrum ($P(k)$). We employ the prediction ability of the supervised ML algorithms to build an estimator for the $P(k)$. The estimator is trained on a set of cosmological models, and redshifts for which the $P(k)$ is known, and it learns to predict $P(k)$ for any other set. We review three ML algorithms -- Random Forest, Gradient Boosting Machines, and K-Nearest Neighbours -- and investigate their prime parameters to optimize the prediction accuracy of the estimator. We also compute an optimal size of the training set, which is realistic enough, and still yields high accuracy. We find that, employing the optimal values of the internal parameters, a set of $50-100$ cosmological models is enough to train the estimator that can predict the $P(k)$ for a wide range of cosmological models, and redshifts. Using this configuration, we build a blackbox -- Supervised Estimator for Matter...
Nonlinear systems time-varying parameter estimation: Application to induction motors
Energy Technology Data Exchange (ETDEWEB)
Kenne, Godpromesse [Laboratoire d' Automatique et d' Informatique Appliquee (LAIA), Departement de Genie Electrique, IUT FOTSO Victor, Universite de Dschang, B.P. 134 Bandjoun (Cameroon); Ahmed-Ali, Tarek [Ecole Nationale Superieure des Ingenieurs des Etudes et Techniques d' Armement (ENSIETA), 2 Rue Francois Verny, 29806 Brest Cedex 9 (France); Lamnabhi-Lagarrigue, F. [Laboratoire des Signaux et Systemes (L2S), C.N.R.S-SUPELEC, Universite Paris XI, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette (France); Arzande, Amir [Departement Energie, Ecole Superieure d' Electricite-SUPELEC, 3 Rue Joliot Curie, 91192 Gif-sur-Yvette (France)
2008-11-15
In this paper, an algorithm for time-varying parameter estimation for a large class of nonlinear systems is presented. The proof of the convergence of the estimates to their true values is achieved using Lyapunov theories and does not require that the classical persistent excitation condition be satisfied by the input signal. Since the induction motor (IM) is widely used in several industrial sectors, the algorithm developed is potentially useful for adjusting the controller parameters of variable speed drives. The method proposed is simple and easily implementable in real-time. The application of this approach to on-line estimation of the rotor resistance of IM shows a rapidly converging estimate in spite of measurement noise, discretization effects, parameter uncertainties (e.g. inaccuracies on motor inductance values) and modeling inaccuracies. The robustness analysis for this IM application also revealed that the proposed scheme is insensitive to the stator resistance variations within a wide range. The merits of the proposed algorithm in the case of on-line time-varying rotor resistance estimation are demonstrated via experimental results in various operating conditions of the induction motor. The experimental results obtained demonstrate that the application of the proposed algorithm to update on-line the parameters of an adaptive controller (e.g. IM and synchronous machines adaptive control) can improve the efficiency of the industrial process. The other interesting features of the proposed method include fault detection/estimation and adaptive control of IM and synchronous machines. (author)
MCMC for non-linear state space models using ensembles of latent sequences
2013-01-01
Non-linear state space models are a widely-used class of models for biological, economic, and physical processes. Fitting these models to observed data is a difficult inference problem that has no straightforward solution. We take a Bayesian approach to the inference of unknown parameters of a non-linear state model; this, in turn, requires the availability of efficient Markov Chain Monte Carlo (MCMC) sampling methods for the latent (hidden) variables and model parameters. Using the ensemble ...
State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation
Directory of Open Access Journals (Sweden)
Junhai Luo
2014-01-01
Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.
Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass
Amir, Naila; Iqbal, Shahid
2016-07-01
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
Liu, Xiaomang; Liu, Changming; Brutsaert, Wilfried
2016-12-01
The performance of a nonlinear formulation of the complementary principle for evaporation estimation was investigated in 241 catchments with different climate conditions in the eastern monsoon region of China. Evaporation (Ea) calculated by the water balance equation was used as the reference. Ea estimated by the calibrated nonlinear formulation was generally in good agreement with the water balance results, especially in relatively dry catchments. The single parameter in the nonlinear formulation, namely αe as a weak analog of the alpha parameter of Priestley and Taylor (), tended to exhibit larger values in warmer and humid near-coastal areas, but smaller values in colder, drier environments inland, with a significant dependency on the aridity index (AI). The nonlinear formulation combined with the equation relating the one parameter and AI provides a promising method to estimate regional Ea with standard and routinely measured meteorological data.
State estimation for a hexapod robot
CSIR Research Space (South Africa)
Lubbe, Estelle
2015-09-01
Full Text Available on a quadruped. The EKF fuses the kinematic model with on-board IMU measurements to estimate the pose of the robot. The methodology was tested with experiments using a physical hexapod robot and validated with independent ground truth measurements....
DEFF Research Database (Denmark)
Khazraj, Hesam; Silva, Filipe Miguel Faria da; Bak, Claus Leth
2016-01-01
Dynamic State Estimation (DSE) is a critical tool for analysis, monitoring and planning of a power system. The concept of DSE involves designing state estimation with Extended Kalman Filter (EKF) or Unscented Kalman Filter (UKF) methods, which can be used by wide area monitoring to improve...... the stability of power system. State estimation with EKF and UKF methods can be used for monitoring and estimating the dynamic state variables of multi-machine power systems, which are generator rotor speed and rotor angle. This paper uses Powerfactory to solve power flow analysis of simulations, then a non......-linear state estimator is developed in MatLab to solve states by applying the unscented Kalman filter (UKF) and Extended Kalman Filter (EKF) algorithm. Finally, a DSE model is built for a 14 bus power system network to evaluate the proposed algorithm for the networks.This article will focus on comparing...
Numerical estimation of 3D mechanical forces exerted by cells on non-linear materials.
Palacio, J; Jorge-Peñas, A; Muñoz-Barrutia, A; Ortiz-de-Solorzano, C; de Juan-Pardo, E; García-Aznar, J M
2013-01-04
The exchange of physical forces in both cell-cell and cell-matrix interactions play a significant role in a variety of physiological and pathological processes, such as cell migration, cancer metastasis, inflammation and wound healing. Therefore, great interest exists in accurately quantifying the forces that cells exert on their substrate during migration. Traction Force Microscopy (TFM) is the most widely used method for measuring cell traction forces. Several mathematical techniques have been developed to estimate forces from TFM experiments. However, certain simplifications are commonly assumed, such as linear elasticity of the materials and/or free geometries, which in some cases may lead to inaccurate results. Here, cellular forces are numerically estimated by solving a minimization problem that combines multiple non-linear FEM solutions. Our simulations, free from constraints on the geometrical and the mechanical conditions, show that forces are predicted with higher accuracy than when using the standard approaches.
Nonlinear morphoelastic plates II: Exodus to buckled states
McMahon, J.
2011-05-11
Morphoelasticity is the theory of growing elastic materials. The theory is based on the multiplicative decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing non-linear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed. © SAGE Publications 2011.
Improving quantum state estimation with mutually unbiased bases.
Adamson, R B A; Steinberg, A M
2010-07-16
When used in quantum state estimation, projections onto mutually unbiased bases have the ability to maximize information extraction per measurement and to minimize redundancy. We present the first experimental demonstration of quantum state tomography of two-qubit polarization states to take advantage of mutually unbiased bases. We demonstrate improved state estimation as compared to standard measurement strategies and discuss how this can be understood from the structure of the measurements we use. We experimentally compared our method to the standard state estimation method for three different states and observe that the infidelity was up to 1.84 ± 0.06 times lower by using our technique than it was by using standard state estimation methods.
Estimation of land surface evaporation using a generalized nonlinear complementary relationship
Zhang, Lu; Cheng, Lei; Brutsaert, Wilfried
2017-02-01
Evaporation is a key component of the hydrological cycle and affects regional water resources. Although the physics of evaporation is well understood, its estimation in practice remains a challenge. Among available methods for estimating it, the complementary principle of Bouchet has the potential to provide a practical tool for regional water resources assessment. In this study, the generalized nonlinear formulation of this principle by Brutsaert (2015) was tested against evaporation measurements from four flux stations in Australia under different climatic and vegetation conditions. The method was implemented using meteorological data and Class A pan evaporation measurements. After calibration the estimated daily evaporation values were in good agreement with flux station measurements with a mean correlation coefficient of 0.83 and a bias of 4% on average. More accurate estimates of daily evaporation were obtained when the evaporative demand or apparent potential evaporation was determined from the Penman equation instead of from pan evaporation. The obtained parameter values were found to lie well within the ranges of reported values in the literature. Advantages of the method are that only routine meteorological data are required and that it can be used to estimate long-term evaporation trends.
Estimating equations for biomarker based exposure estimation under non-steady-state conditions.
Bartell, Scott M; Johnson, Wesley O
2011-06-13
Unrealistic steady-state assumptions are often used to estimate toxicant exposure rates from biomarkers. A biomarker may instead be modeled as a weighted sum of historical time-varying exposures. Estimating equations are derived for a zero-inflated gamma distribution for daily exposures with a known exposure frequency. Simulation studies suggest that the estimating equations can provide accurate estimates of exposure magnitude at any reasonable sample size, and reasonable estimates of the exposure variance at larger sample sizes.
Lagrangian Multi-Class Traffic State Estimation
Yuan, Y.
2013-01-01
Road traffic is important to everybody in the world. People travel and commute everyday. For those who travel by cars (or other types of road vehicles), traffic congestion is a daily experience. One essential goal of traffic researchers is to reduce traffic congestion and to improve the whole traffic system operation and the environment. To achieve this goal, we have to first understand prevailing traffic situations, then perform pro-active traffic control and management. The estimation of tr...
A novel approach to power system state estimation and controller design
Energy Technology Data Exchange (ETDEWEB)
Mohammadi, A. [Ferdowsi Univ. of Mashhad, Mashhad (Iran, Islamic Republic of). Dept. of Electrical Engineering]|[Islamic Azad Univ. of Iran, Tehran (Iran, Islamic Republic of). Dept. of Electrical Engineering; Pariz, N.; Shanechi, H.M. [Ferdowsi Univ. of Mashhad, Mashhad (Iran, Islamic Republic of). Dept. of Electrical Engineering; Hesamzadeh, M.; Seifi, H. [Tarbiat Modarres Univ., Tehran (Iran, Islamic Republic of). Dept. of Electrical Engineering; Keivani, H. [Islamic Azad Univ. of Iran, Tehran (Iran, Islamic Republic of). Dept. of Electrical Engineering
2005-07-01
A novel state estimating and controller design for nonlinear power systems was presented. The linear quadratic Gaussian (LQG) design used a Kalman filter and was based on a modal series model in order to introduce dynamics typically lost when using linear models. The single inertia model of a turbine generator connected to an infinite busbar was represented by an eleventh order nonlinear state space set of equations. The parameters of a micro-machine model of a 660 MW generator were studied. The voltage regulator model was a simplified representation of an Institute of Electrical and Electronics Engineers (IEEE) type AC4 model. The governor model was a 2-time constant approximation which represented main and interceptor values governed in parallel to reduce computational time. Simulations were conducted using MATLAB/SIMULINK software in order to validate the controller design, in which a fault was assumed to be at the high voltage terminals of the generator transformer. An eleventh order linear model of a nonlinear power system was then compared with the controller design. Results of the study suggested that the damping swings were controlled by the LQC modal series-based controller. It was concluded that further research is needed to investigate modal series models for state estimation in adaptive and robust control of power systems. 16 refs., 5 figs.
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
Coherent states for nonlinear harmonic oscillator and some of its properties
Energy Technology Data Exchange (ETDEWEB)
Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@sns.nust.edu.pk; Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)
2015-06-15
A one-dimensional nonlinear harmonic oscillator is studied in the context of generalized coherent states. We develop a perturbative framework to compute the eigenvalues and eigenstates for the quantum nonlinear oscillator and construct the generalized coherent states based on Gazeau-Klauder formalism. We analyze their statistical properties by means of Mandel parameter and second order correlation function. Our analysis reveals that the constructed coherent states exhibit super-Poissonian statistics. Moreover, it is shown that the coherent states mimic the phenomena of quantum revivals and fractional revivals during their time evolution. The validity of our results has been discussed in terms of various parametric bounds imposed by our computational scheme.
Efficient Quantum State Estimation with Over-complete Tomography
Zhang, Chi; Xiang, Guo-Yong; Zhang, Yong-Sheng; Li, Chuan-Feng; Guo, Guang-Can
2011-01-01
It is widely accepted that the selection of measurement bases can affect the efficiency of quantum state estimation methods, precision of estimating an unknown state can be improved significantly by simply introduce a set of symmetrical measurement bases. Here we compare the efficiencies of estimations with different numbers of measurement bases by numerical simulation and experiment in optical system. The advantages of using a complete set of symmetrical measurement bases are illustrated mor...
Parameter and State Estimation of Large-Scale Complex Systems Using Python Tools
Directory of Open Access Journals (Sweden)
M. Anushka S. Perera
2015-07-01
Full Text Available This paper discusses the topics related to automating parameter, disturbance and state estimation analysis of large-scale complex nonlinear dynamic systems using free programming tools. For large-scale complex systems, before implementing any state estimator, the system should be analyzed for structural observability and the structural observability analysis can be automated using Modelica and Python. As a result of structural observability analysis, the system may be decomposed into subsystems where some of them may be observable --- with respect to parameter, disturbances, and states --- while some may not. The state estimation process is carried out for those observable subsystems and the optimum number of additional measurements are prescribed for unobservable subsystems to make them observable. In this paper, an industrial case study is considered: the copper production process at Glencore Nikkelverk, Kristiansand, Norway. The copper production process is a large-scale complex system. It is shown how to implement various state estimators, in Python, to estimate parameters and disturbances, in addition to states, based on available measurements.
Simultaneous state and actuator fault estimation for satellite attitude control systems
Institute of Scientific and Technical Information of China (English)
Cheng Yao; Wang Rixin; Xu Minqiang; Li Yuqing
2016-01-01
In this paper, a new nonlinear augmented observer is proposed and applied to satellite attitude control systems. The observer can estimate system state and actuator fault simultaneously. It can enhance the performances of rapidly-varying faults estimation. Only original system matrices are adopted in the parameter design. The considered faults can be unbounded, and the proposed augmented observer can estimate a large class of faults. Systems without disturbances and the fault whose finite times derivatives are zero piecewise are initially considered, followed by a discussion of a general situation where the system is subject to disturbances and the finite times derivatives of the faults are not null but bounded. For the considered nonlinear system, convergence conditions of the observer are provided and the stability analysis is performed using Lyapunov direct method. Then a feasible algorithm is explored to compute the observer parameters using linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is illustrated by considering an example of a closed-loop satellite attitude control system. The simulation results show satisfactory perfor-mance in estimating states and actuator faults. It also shows that multiple faults can be estimated successfully.
State-of-charge estimation in lithium-ion batteries: A particle filter approach
Tulsyan, Aditya; Tsai, Yiting; Gopaluni, R. Bhushan; Braatz, Richard D.
2016-11-01
The dynamics of lithium-ion batteries are complex and are often approximated by models consisting of partial differential equations (PDEs) relating the internal ionic concentrations and potentials. The Pseudo two-dimensional model (P2D) is one model that performs sufficiently accurately under various operating conditions and battery chemistries. Despite its widespread use for prediction, this model is too complex for standard estimation and control applications. This article presents an original algorithm for state-of-charge estimation using the P2D model. Partial differential equations are discretized using implicit stable algorithms and reformulated into a nonlinear state-space model. This discrete, high-dimensional model (consisting of tens to hundreds of states) contains implicit, nonlinear algebraic equations. The uncertainty in the model is characterized by additive Gaussian noise. By exploiting the special structure of the pseudo two-dimensional model, a novel particle filter algorithm that sweeps in time and spatial coordinates independently is developed. This algorithm circumvents the degeneracy problems associated with high-dimensional state estimation and avoids the repetitive solution of implicit equations by defining a 'tether' particle. The approach is illustrated through extensive simulations.
Kukush, Alexander; Schneeweiss, Hans
2004-01-01
We compare the asymptotic covariance matrix of the ML estimator in a nonlinear measurement error model to the asymptotic covariance matrices of the CS and SQS estimators studied in Kukush et al (2002). For small measurement error variances they are equal up to the order of the measurement error variance and thus nearly equally efficient.
A fast nonlinear regression method for estimating permeability in CT perfusion imaging.
Bennink, Edwin; Riordan, Alan J; Horsch, Alexander D; Dankbaar, Jan Willem; Velthuis, Birgitta K; de Jong, Hugo W
2013-11-01
Blood-brain barrier damage, which can be quantified by measuring vascular permeability, is a potential predictor for hemorrhagic transformation in acute ischemic stroke. Permeability is commonly estimated by applying Patlak analysis to computed tomography (CT) perfusion data, but this method lacks precision. Applying more elaborate kinetic models by means of nonlinear regression (NLR) may improve precision, but is more time consuming and therefore less appropriate in an acute stroke setting. We propose a simplified NLR method that may be faster and still precise enough for clinical use. The aim of this study is to evaluate the reliability of in total 12 variations of Patlak analysis and NLR methods, including the simplified NLR method. Confidence intervals for the permeability estimates were evaluated using simulated CT attenuation-time curves with realistic noise, and clinical data from 20 patients. Although fixating the blood volume improved Patlak analysis, the NLR methods yielded significantly more reliable estimates, but took up to 12 × longer to calculate. The simplified NLR method was ∼4 × faster than other NLR methods, while maintaining the same confidence intervals (CIs). In conclusion, the simplified NLR method is a new, reliable way to estimate permeability in stroke, fast enough for clinical application in an acute stroke setting.
Nonlinear robust control of proton exchange membrane fuel cell by state feedback exact linearization
Energy Technology Data Exchange (ETDEWEB)
Li, Q.; Chen, W. [School of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan Province (China); Wang, Y.; Jia, J. [School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue 639798, Singapore (Singapore); Han, M. [School of Engineering, Temasek Polytechnic, Tampines 529757, Singapore (Singapore)
2009-10-20
By utilizing the state feedback exact linearization approach, a nonlinear robust control strategy is designed based on a multiple-input multiple-output (MIMO) dynamic nonlinear model of proton exchange membrane fuel cell (PEMFC). The state feedback exact linearization approach can achieve the global exact linearization via the nonlinear coordinate transformation and the dynamic extension algorithm such that H{sub {infinity}} robust control strategy can be directly utilized to guarantee the robustness of the system. The proposed dynamic nonlinear model is tested by comparing the simulation results with the experimental data in Fuel Cell Application Centre in Temasek Polytechnic. The comprehensive results of simulation manifest that the dynamic nonlinear model with nonlinear robust control law has better transient and robust stability when the vehicle running process is simulated. The proposed nonlinear robust controller will be very useful to protect the membrane damage by keeping the pressure deviations as small as possible during large disturbances and prolong the stack life of PEMFC. (author)
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.
Discrete Localized States and Localization Dynamics in Discrete Nonlinear Schrödinger Equations
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yu.B.; Mezentsev, V.K.
1996-01-01
Dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity is taken into account. Stability properties of the stationary solutions...... are examined. The importance of the existence of stable immobile solitons in the two-dimensional dynamics of the travelling pulses is demonstrated. The process of forming narrow states from initially broad standing or moving excitations through the quasi-collapse mechanism is analyzed. The typical scenario...
Localized excitations in nonlinear complex systems current state of the art and future perspectives
Cuevas-Maraver, Jesús; Frantzeskakis, Dimitri; Karachalios, Nikos; Kevrekidis, Panayotis; Palmero-Acebedo, Faustino
2014-01-01
The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.
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.
Linear and nonlinear photonic Jackiw-Rebbi states in interfaced binary waveguide arrays
Tran, Truong X.; Biancalana, Fabio
2017-07-01
We study analytically and numerically the optical analog of the Jackiw-Rebbi states in quantum-field theory. These solutions exist at the interface of two binary waveguide arrays, which are described by two Dirac equations with masses of opposite sign. We show that these special states are topologically robust not only in the linear regime, but also in the nonlinear one (with both focusing and defocusing nonlinearities). We also reveal that one can effectively generate Jackiw-Rebbi states starting from Dirac solitons.
Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application
MA,LI; Lin ZHAO
2007-01-01
We establish the uniqueness of ground states of some coupled nonlinear Schrodinger systems in the whole space. We firstly use Schwartz symmetrization to obtain the existence of ground states for a more general case. To prove the uniqueness of ground states, we use the radial symmetry of the ground states to transform the systems into an ordinary differential system, and then we use the integral forms of the system. More interestingly, as an application of our uniqueness results, we derive a s...
Chaotic and steady state behaviour of a nonlinear controlled gyro subjected to harmonic disturbances
Energy Technology Data Exchange (ETDEWEB)
Perez Polo, Manuel F. [Department of Fisica, Ingenieria de Sistemas y Teoria de la Senal, Universidad de Alicante, Escuela Politecnica Superior, Campus de San Vicente, 03071 Alicante (Spain)]. E-mail: manolo@dfists.ua.es; Perez Molina, Manuel [Facultad de Ciencias Matematicas, Universidad Nacional de Educacion a Distancia, UNED, C/Boyero 12-1A, Alicante 03007 (Spain)]. E-mail: ma_perez_m@hotmail.com
2007-07-15
Chaotic and steady state motions of a nonlinear controlled gimbals suspension gyro used to stabilize an external body are studied in this paper. The equations of the gyro without nonlinear control are deduced from the Euler-Lagrange equations by using the nutation theory. The equations of the system show that a cyclic variable appears. Its elimination allows us to find an auxiliary nonlinear system from which it is possible to deduce a nonlinear control law in order to obtain a desired equilibrium point. From the analysis of the nonlinear control law it is possible to show that due to both harmonic disturbances in the platform of the gyro and in the body to stabilize, regular and chaotic motions can appear. The chaotic motion is researched by means of chaos maps, bifurcation diagrams, sensitivity to initial conditions, Lyapunov exponents and Fourier spectrum density. The transition from chaotic to steady state motion by eliminating the harmonic disturbances from the modification of the initial nonlinear control law is also researched. Next, the paper shows how to use the chaotic motion in order to obtain small input signals so that the desired equilibrium state of the gyro can be reached. The developed methodology and its compared performance are evaluated through analytical methods and numerical simulations.
Stable estimation of two coefficients in a nonlinear Fisher-KPP equation
Cristofol, Michel; Roques, Lionel
2013-09-01
We consider the inverse problem of determining two non-constant coefficients in a nonlinear parabolic equation of the Fisher-Kolmogorov-Petrovsky-Piskunov type. For the equation ut = DΔu + μ(x) u - γ(x)u2 in (0, T) × Ω, which corresponds to a classical model of population dynamics in a bounded heterogeneous environment, our results give a stability inequality between the couple of coefficients (μ, γ) and some observations of the solution u. These observations consist in measurements of u: in the whole domain Ω at two fixed times, in a subset ω⊂⊂Ω during a finite time interval and on the boundary of Ω at all times t ∈ (0, T). The proof relies on parabolic estimates together with the parabolic maximum principle and Hopf’s lemma which enable us to use a Carleman inequality. This work extends previous studies on the stable determination of non-constant coefficients in parabolic equations, as it deals with two coefficients and with a nonlinear term. A consequence of our results is the uniqueness of the couple of coefficients (μ, γ), given the observation of u. This uniqueness result was obtained in a previous paper but in the one-dimensional case only.
TBA equations for excited states in the O(3) and O(4) nonlinear $\\sigma$-model
Balog, J.; Hegedus, A
2003-01-01
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Application of the Characteristic Time Expansion Method for Estimating Nonlinear Restoring Forces
Directory of Open Access Journals (Sweden)
Yung-Wei Chen
2013-01-01
Full Text Available This paper proposes a characteristic time expansion method (CTEM for estimating nonlinear restoring forces. Because noisy data and numerical instability are the main causes of numerical developing problems in an inverse field, a polynomial to identify restoring forces is usually adopted to eliminate these problems. However, results of the way doing are undesirable for a high order of polynomial. To overcome this difficulty, the characteristic length (CL is introduced into the power series, and a natural regularization technique is applied to ensure numerical stability and determine the existence of a solution. As compared to previous solutions presented in other researches, the proposed method is a desirable and accurate solver for the problem of restoring the force in the inverse vibration problems.
Semrau, Daniel; Xu, Tianhua; Shevchenko, Nikita A; Paskov, Milen; Alvarado, Alex; Killey, Robert I; Bayvel, Polina
2017-01-01
Achievable information rates (AIRs) of wideband optical communication systems using a ∼40 nm (∼5 THz) erbium-doped fiber amplifier and ∼100 nm (∼12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It has been found that a probabilistically shaped DP-1024QAM constellation, combined with FF-NLC, yields achievable information rates of ∼75 Tbit/s for the EDFA scheme and ∼223 Tbit/s for the Raman amplification scheme over a 2000 km standard single-mode fiber transmission.
On the Aleksandrov-Bakel'man-Pucci Estimate for Some Elliptic and Parabolic Nonlinear Operators
Argiolas, Roberto; Charro, Fernando; Peral, Ireneo
2011-12-01
In this work we prove the Aleksandrov-Bakel'man-Pucci estimate for (possibly degenerate) nonlinear elliptic and parabolic equations of the form -div left( Fleft( nabla u(x)right) right) =fleft(xright) quad in Ω subset mathbb{R}n and ut(x,t)-div left( Fleft( nabla u(x,t)right) right) =fleft( x,tright) quad in Qsubset mathbb{R}^{n+1} for F a {fancyscript{C}^1} monotone field under some suitable conditions. Examples of applications such as the p-Laplacian and the Mean Curvature Flow are considered, as well as extensions of the general results to equations that are not in divergence form, such as the m-curvature flow.
MEG and fMRI fusion for nonlinear estimation of neural and BOLD signal changes
Directory of Open Access Journals (Sweden)
Sergey M Plis
2010-11-01
Full Text Available The combined analysis of MEG/EEG and functional MRI measurements can lead to improvement in the description of the dynamical and spatial properties of brain activity. In this paper we empirically demonstrate this improvement using simulated and recorded task related MEG and fMRI activity. Neural activity estimates were derived using a dynamic Bayesian network with continuous real valued parameters by means of a sequential Monte Carlo technique. In synthetic data, we show that MEG and fMRI fusion improves estimation of the indirectly observed neural activity and smooths tracking of the BOLD response. In recordings of task related neural activity the combination of MEG and fMRI produces a result with greater SNR, that confirms the expectation arising from the nature of the experiment. The highly nonlinear model of the BOLD response poses a difficult inference problem for neural activity estimation; computational requirements are also high due to the time and space complexity. We show that joint analysis of the data improves the system's behavior by stabilizing the differential equations system and by requiring fewer computational resources.
Simulating the Effect of Non-Linear Mode-Coupling in Cosmological Parameter Estimation
Kiessling, A; Heavens, A F
2011-01-01
Fisher Information Matrix methods are commonly used in cosmology to estimate the accuracy that cosmological parameters can be measured with a given experiment, and to optimise the design of experiments. However, the standard approach usually assumes both data and parameter estimates are Gaussian-distributed. Further, for survey forecasts and optimisation it is usually assumed the power-spectra covariance matrix is diagonal in Fourier-space. But in the low-redshift Universe, non-linear mode-coupling will tend to correlate small-scale power, moving information from lower to higher-order moments of the field. This movement of information will change the predictions of cosmological parameter accuracy. In this paper we quantify this loss of information by comparing naive Gaussian Fisher matrix forecasts with a Maximum Likelihood parameter estimation analysis of a suite of mock weak lensing catalogues derived from N-body simulations, based on the SUNGLASS pipeline, for a 2-D and tomographic shear analysis of a Eucl...
Variance-Constrained State Estimation for Complex Networks With Randomly Varying Topologies.
Dong, Hongli; Hou, Nan; Wang, Zidong; Ren, Weijian
2017-05-23
This paper investigates the variance-constrained H∞ state estimation problem for a class of nonlinear time-varying complex networks with randomly varying topologies, stochastic inner coupling, and measurement quantization. A Kronecker delta function and Markovian jumping parameters are utilized to describe the random changes of network topologies. A Gaussian random variable is introduced to model the stochastic disturbances in the inner coupling of complex networks. As a kind of incomplete measurements, measurement quantization is taken into consideration so as to account for the signal distortion phenomenon in the transmission process. Stochastic nonlinearities with known statistical characteristics are utilized to describe the stochastic evolution of the complex networks. We aim to design a finite-horizon estimator, such that in the simultaneous presence of quantized measurements and stochastic inner coupling, the prescribed variance constraints on the estimation error and the desired H∞ performance requirements are guaranteed over a finite horizon. Sufficient conditions are established by means of a series of recursive linear matrix inequalities, and subsequently, the estimator gain parameters are derived. A simulation example is presented to illustrate the effectiveness and applicability of the proposed estimator design algorithm.
On Perceptual Distortion Minimization and Nonlinear Least-Squares Frequency Estimation
DEFF Research Database (Denmark)
Christensen, Mads Græsbøll; Jensen, Søren Holdt
2006-01-01
In this paper, we present a framework for perceptual error minimization and sinusoidal frequency estimation based on a new perceptual distortion measure, and we state its optimal solution. Using this framework, we relate a number of well-known practical methods for perceptual sinusoidal parameter...
Direct measurement of non-linear properties of bipartite quantum states
Bovino, F A; Castagnoli, G C; Ekert, A; Horodecki, P; Sergienko, A V; Alves, Carolina Moura; Bovino, Fabio Antonio; Castagnoli, Giuseppe; Ekert, Artur; Horodecki, Pawel; Sergienko, Alexander Vladimir
2005-01-01
Non-linear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number parameters that specify the state. Here we extract a non-local and a non-linear quantity, namely the Renyi entropy, from local measurements on two pairs of polarization entangled photons. We also introduce a "phase marking" technique which allows to select uncorrupted outcomes even with non-deterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of a non-linear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-CHSH inequalities.
A nonlinear plasmonic resonator for three-state all-optical switching
Amin, Muhammad
2014-01-01
A nonlinear plasmonic resonator design is proposed for three-state all-optical switching at frequencies including near infrared and lower red parts of the spectrum. The tri-stable response required for three-state operation is obtained by enhancing nonlinearities of a Kerr medium through multiple (higher order) plasmons excited on resonator\\'s metallic surfaces. Indeed, simulations demonstrate that exploitation of multiple plasmons equips the proposed resonator with a multi-band tri-stable response, which cannot be obtained using existing nonlinear plasmonic devices that make use of single mode Lorentzian resonances. Multi-band three-state optical switching that can be realized using the proposed resonator has potential applications in optical communications and computing. © 2014 Optical Society of America.
DEFF Research Database (Denmark)
Jouffroy, Jerome; Lottin, Jacques
2002-01-01
For original paper see T.I.Fossen and M.Blanke, ibid., vol.25, pp.241-55 (2000). In the work presented by Fossen and Blanke, a nonlinear observer for estimation of propeller axial flow velocity for UUVs was introduced. The proof of the convergence behavior of the observer was carried out with a L......For original paper see T.I.Fossen and M.Blanke, ibid., vol.25, pp.241-55 (2000). In the work presented by Fossen and Blanke, a nonlinear observer for estimation of propeller axial flow velocity for UUVs was introduced. The proof of the convergence behavior of the observer was carried out...
DEFF Research Database (Denmark)
Jouffroy, Jerome; Lottin, Jacques
2002-01-01
For original paper see T.I.Fossen and M.Blanke, ibid., vol.25, pp.241-55 (2000). In the work presented by Fossen and Blanke, a nonlinear observer for estimation of propeller axial flow velocity for UUVs was introduced. The proof of the convergence behavior of the observer was carried out with a L......For original paper see T.I.Fossen and M.Blanke, ibid., vol.25, pp.241-55 (2000). In the work presented by Fossen and Blanke, a nonlinear observer for estimation of propeller axial flow velocity for UUVs was introduced. The proof of the convergence behavior of the observer was carried out...
Traditional and alternative nonlinear models for estimating the growth of Morada Nova sheep
Directory of Open Access Journals (Sweden)
Laaina de Andrade Souza
2013-09-01
Full Text Available In the present study, alternative and traditional nonlinear models to describe growth curves of Morada Nova sheep reared in the state of Bahia, Brazil, were applied. The nonlinear models were: Schnute, Mitscherlich, Gompertz, Logistic, Meloun I Meloun II, III Meloun, Gamito and Meloun IV. The model adjustment was evaluated by using: Adjusted Coefficient of Determination (R²aj, Akaike Information Criterion (AIC, Bayesian Information Criterion (BIC, Mean Squared Error of Prediction (MEP and Coefficient of Determination of Prediction (R²p. The selection of the best model was based on cluster analysis, using the evaluators as variables. Six out of the nine tested models converged, while Meloun I and Meloun IV were equally effective in explaining animal growth, without significant influence of sex or type of parturition over the curve parameters. The models Meloun I and IV have the best adjustment and reveal a remarkable reduction of weight gain after 150 days of age, which indicates special attention should be given to feeding at this stage.
Statistical estimation of the efficiency of quantum state tomography protocols.
Bogdanov, Yu I; Brida, G; Genovese, M; Kulik, S P; Moreva, E V; Shurupov, A P
2010-07-02
A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography.
Robust control of robots via linear estimated state feedback
Berghuis, Harry; Nijmeijer, Henk
1994-01-01
In this note we propose a robust tracking controller for robots that requires only position measurements. The controller consists of two parts: a linear observer part that generates an estimated error state from the error on the joint position and a linear feedback part that utilizes this estimated
Non-linear ultimate strength and stability limit state analysis of a wind turbine blade
DEFF Research Database (Denmark)
Rosemeier, Malo; Berring, Peter; Branner, Kim
2016-01-01
flap-wise loading has been compared with a linear response to determine the blade's resistance in the ultimate strength and stability limit states. The linear analysis revealed an unrealistic failure mechanism and failure mode. Further, it did not capture the highly non-linear response of the blade...... of an imperfection. The more realistic non-linear approaches yielded more optimistic results than the mandatory linear bifurcation analysis. Consequently, the investigated blade designed after the lesser requirements was sufficient. Using the non-linear approaches, considering inter-fibre failure as the critical...... failure mode, yielded still a significant safety margin for the designer (7–28%). The non-linear response was significantly dependent on the scaling of the imperfection. Eurocode's method of applying an imperfection appeared more realistic than the GL method. Since the considered blade withstood 135...
Duan, Zhaoxia; Xiang, Zhengrong; Karimi, Hamid Reza
2014-07-01
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality-based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired controller gains is derived. An illustrative example is provided to show the usefulness and effectiveness of the proposed method.
Inexact Picard iterative scheme for steady-state nonlinear diffusion in random heterogeneous media.
Mohan, P Surya; Nair, Prasanth B; Keane, Andy J
2009-04-01
In this paper, we present a numerical scheme for the analysis of steady-state nonlinear diffusion in random heterogeneous media. The key idea is to iteratively solve the nonlinear stochastic governing equations via an inexact Picard iteration scheme, wherein the nonlinear constitutive law is linearized using the current guess of the solution. The linearized stochastic governing equations are then spatially discretized and approximately solved using stochastic reduced basis projection schemes. The approximation to the solution process thus obtained is used as the guess for the next iteration. This iterative procedure is repeated until an appropriate convergence criterion is met. Detailed numerical studies are presented for diffusion in a square domain for varying degrees of nonlinearity. The numerical results are compared against benchmark Monte Carlo simulations, and it is shown that the proposed approach provides good approximations for the response statistics at modest computational effort.
Estimation of Nonlinear DC-Motor Models Using a Sensitivity Approach
DEFF Research Database (Denmark)
Knudsen, Morten; Jensen, J.G.
1995-01-01
A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed.......A nonlinear model structure for a permanent magnet DC-motor, appropriate for simulation and controller design, is developed....
On the evaluation of uncertainties for state estimation with the Kalman filter
Eichstädt, S.; Makarava, N.; Elster, C.
2016-12-01
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous areas. It provides sequentially calculated estimates of the system states along with a corresponding covariance matrix. For nonlinear systems, the extended Kalman filter is often used. This is derived from the Kalman filter by linearization around the current estimate. A key issue in metrology is the evaluation of the uncertainty associated with the Kalman filter state estimates. The ‘Guide to the Expression of Uncertainty in Measurement’ (GUM) and its supplements serve as the de facto standard for uncertainty evaluation in metrology. We explore the relationship between the covariance matrix produced by the Kalman filter and a GUM-compliant uncertainty analysis. In addition, the results of a Bayesian analysis are considered. For the case of linear systems with known system matrices, we show that all three approaches are compatible. When the system matrices are not precisely known, however, or when the system is nonlinear, this equivalence breaks down and different results can then be reached. For precisely known nonlinear systems, though, the result of the extended Kalman filter still corresponds to the linearized uncertainty propagation of the GUM. The extended Kalman filter can suffer from linearization and convergence errors. These disadvantages can be avoided to some extent by applying Monte Carlo procedures, and we propose such a method which is GUM-compliant and can also be applied online during the estimation. We illustrate all procedures in terms of a 2D dynamic system and compare the results with those obtained by particle filtering, which has been proposed for the approximate calculation of a Bayesian solution. Finally, we give some recommendations based on our findings.
Onboard sea state estimation based on measured ship motions
DEFF Research Database (Denmark)
Nielsen, Ulrik Dam; Stredulinsky, David C.
2011-01-01
It is possible to obtain estimates of the sea state at the specific position of an advancing vessel by processing measurements of the vessel’s wave-induced responses. The analogy to a wave rider buoy is clear, although the situation of an advancing ship is more complex due to forward speed....... The paper studies the ‘wave buoy analogy’, and a large set of full-scale motion measurements is considered. It is shown that the wave buoy analogy gives fairly accurate estimates of sea state parameters when compared to estimates from real wave rider buoys....
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.
A method to estimate the absolute ultrasonic nonlinearity parameter from relative measurements.
Kim, Jongbeom; Song, Dong-Gi; Jhang, Kyung-Young
2017-02-17
The ultrasonic nonlinearity parameter, β, is determined from the displacement amplitude of the second-order harmonic frequency component generated during the propagation of ultrasonic waves through a material. This parameter is generally referred to as the absolute parameter. Meanwhile, it is difficult to measure the small displacement amplitude of the second-order harmonic component; therefore, most studies measure the relative parameter determined from the detected signal amplitude. However, for quantitative assessment of material degradation, the absolute parameter is still required. This study proposes a method to estimate the absolute parameter for damaged material by measuring the relative parameter. This method is based on the fact that the fractional ratio of the relative parameters between different materials is identical to that of the absolute parameters after compensation for material dependent differences such as the wavenumber and detection-sensitivity. In order to experimentally verify the method, the relative parameters of heat-treated Al6061-T6 alloy specimens with different aging times were measured to compare with absolute parameters directly measured by piezo-electric detection. The results show that the fluctuations of both parameters with respect to aging time were very similar to each other, and that the absolute parameters estimated by the proposed method were in good agreement with those measured directly.
Murphy, P. C.
1986-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.
A Simplified Estimation of Latent State--Trait Parameters
Hagemann, Dirk; Meyerhoff, David
2008-01-01
The latent state-trait (LST) theory is an extension of the classical test theory that allows one to decompose a test score into a true trait, a true state residual, and an error component. For practical applications, the variances of these latent variables may be estimated with standard methods of structural equation modeling (SEM). These…
Virtual speed sensors based algorithm for expressway traffic state estimation
Institute of Scientific and Technical Information of China (English)
XU DongWei; DONG HongHui; JIA LiMin; QIN Yong
2012-01-01
The accurate estimation of expressway traffic state can provide decision-making for both travelers and traffic managers.The speed is one of the most representative parameter of the traffic state.So the expressway speed spatial distribution can be taken as the expressway traffic state equivalent.In this paper,an algorithm based on virtual speed sensors (VSS) is presented to estimate the expressway traffic state (the speed spatial distribution).To gain the spatial distribution of expressway traffic state,virtual speed sensors are defined between adjacent traffic flow sensors.Then,the speed data extracted from traffic flow sensors in time series are mapped to space series to design virtual speed sensors.Then the speed of virtual speed sensors can be calculated with the weight matrix which is related with the speed of virtual speed sensors and the speed data extracted from traffic flow sensors and the speed data extracted from traffic flow sensors in time series.Finally,the expressway traffic state (the speed spatial distribution) can be gained.The acquisition of average travel speed of the expressway is taken for application of this traffic state estimation algorithm.One typical expressway in Beijing is adopted for the experiment analysis.The results prove that this traffic state estimation approach based on VSS is feasible and can achieve a high accuracy.
Power system static state estimation using Kalman filter algorithm
Directory of Open Access Journals (Sweden)
Saikia Anupam
2016-01-01
Full Text Available State estimation of power system is an important tool for operation, analysis and forecasting of electric power system. In this paper, a Kalman filter algorithm is presented for static estimation of power system state variables. IEEE 14 bus system is employed to check the accuracy of this method. Newton Raphson load flow study is first carried out on our test system and a set of data from the output of load flow program is taken as measurement input. Measurement inputs are simulated by adding Gaussian noise of zero mean. The results of Kalman estimation are compared with traditional Weight Least Square (WLS method and it is observed that Kalman filter algorithm is numerically more efficient than traditional WLS method. Estimation accuracy is also tested for presence of parametric error in the system. In addition, numerical stability of Kalman filter algorithm is tested by considering inclusion of zero mean errors in the initial estimates.
Shen, Bo; Wang, Zidong; Liu, Xiaohui
2011-01-01
In this paper, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. A novel concept of bounded H(∞) synchronization is proposed to handle the time-varying nature of the complex networks. Such a concept captures the transient behavior of the time-varying complex network over a finite horizon, where the degree of bounded synchronization is quantified in terms of the H(∞)-norm. A general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. By utilizing a time-varying real-valued function and the Kronecker product, criteria are established that ensure the bounded H(∞) synchronization in terms of a set of recursive linear matrix inequalities (RLMIs), where the RLMIs can be computed recursively by employing available MATLAB toolboxes. The bounded H(∞) state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that, over a finite horizon, the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level. Again, an RLMI approach is developed for the state estimation problem. Finally, two simulation examples are exploited to show the effectiveness of the results derived in this paper.
Triangular and Trapezoidal Fuzzy State Estimation with Uncertainty on Measurements
Directory of Open Access Journals (Sweden)
Mohammad Sadeghi Sarcheshmah
2012-01-01
Full Text Available In this paper, a new method for uncertainty analysis in fuzzy state estimation is proposed. The uncertainty is expressed in measurements. Uncertainties in measurements are modelled with different fuzzy membership functions (triangular and trapezoidal. To find the fuzzy distribution of any state variable, the problem is formulated as a constrained linear programming (LP optimization. The viability of the proposed method would be verified with the ones obtained from the weighted least squares (WLS and the fuzzy state estimation (FSE in the 6-bus system and in the IEEE-14 and 30 bus system.
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Estimating the Burden of Chagas Disease in the United States.
Directory of Open Access Journals (Sweden)
Jennifer Manne-Goehler
2016-11-01
Full Text Available In recent years, there has been growing awareness of the significant burden of Chagas disease in the United States (US. However, epidemiological data on both prevalence and access to care for this disease are limited. The objective of this study is to provide an updated national estimate of Chagas disease prevalence, the first state-level estimates of cases of T. cruzi infection in the US and to analyze these estimates in the context of data on confirmed cases of infection in the US blood supply.In this study, we calculated estimates of the state and national prevalence of Chagas disease. The number of residents originally from Chagas disease endemic countries were computed using data on Foreign-Born Hispanic populations from the American Community Survey, along with recent prevalence estimates for Chagas disease in Latin America from the World Health Organization that were published in 2006 and updated in 2015. We then describe the distribution of estimated cases in each state in relation to the number of infections identified in the donated blood supply per data from the AABB (formerly American Association of Blood Banks.The results of this analysis offer an updated national estimate of 238,091 cases of T. cruzi infection in the United States as of 2012, using the same method as was used by Bern and Montgomery to estimate cases in 2005. This estimate indicates that there are 62,070 cases less than the most recent prior estimate, though it does not include undocumented immigrants who may account for as many as 109,000 additional cases. The state level results show that four states (California, Texas, Florida and New York have over 10,000 cases and an additional seven states have over 5,000 cases. Moreover, since 2007, the AABB has reported 1,908 confirmed cases of T. cruzi infection identified through screening of blood donations.This study demonstrates a substantial burden of Chagas disease in the US, with state variation that reflects the
Estimating the Burden of Chagas Disease in the United States.
Manne-Goehler, Jennifer; Umeh, Chukwuemeka A; Montgomery, Susan P; Wirtz, Veronika J
2016-11-01
In recent years, there has been growing awareness of the significant burden of Chagas disease in the United States (US). However, epidemiological data on both prevalence and access to care for this disease are limited. The objective of this study is to provide an updated national estimate of Chagas disease prevalence, the first state-level estimates of cases of T. cruzi infection in the US and to analyze these estimates in the context of data on confirmed cases of infection in the US blood supply. In this study, we calculated estimates of the state and national prevalence of Chagas disease. The number of residents originally from Chagas disease endemic countries were computed using data on Foreign-Born Hispanic populations from the American Community Survey, along with recent prevalence estimates for Chagas disease in Latin America from the World Health Organization that were published in 2006 and updated in 2015. We then describe the distribution of estimated cases in each state in relation to the number of infections identified in the donated blood supply per data from the AABB (formerly American Association of Blood Banks). The results of this analysis offer an updated national estimate of 238,091 cases of T. cruzi infection in the United States as of 2012, using the same method as was used by Bern and Montgomery to estimate cases in 2005. This estimate indicates that there are 62,070 cases less than the most recent prior estimate, though it does not include undocumented immigrants who may account for as many as 109,000 additional cases. The state level results show that four states (California, Texas, Florida and New York) have over 10,000 cases and an additional seven states have over 5,000 cases. Moreover, since 2007, the AABB has reported 1,908 confirmed cases of T. cruzi infection identified through screening of blood donations. This study demonstrates a substantial burden of Chagas disease in the US, with state variation that reflects the distribution of
Energy Technology Data Exchange (ETDEWEB)
Shen, W.X. [School of Engineering, Monash University Malaysia, 2 Jalan Kolej, Bandar Sunway, 46150 Petaling Jaya, Selangor Darul Ehsan (Malaysia)
2007-02-15
This paper reviews recent definitions of the state of charge (SOC) that are often used to estimate the battery residual available capacity (BRAC) for lead-acid batteries in electric vehicles (EVs) and identifies their shortcomings. Then, the state of available capacity (SOAC), instead of the SOC, is defined to denote the BRAC in EVs, which refers to the percentage of the battery available capacity (BAC) of the discharge current profile for the EV battery at the fully charged state. Based on the experimentation of different discharge current profiles, including theoretical current profiles and practical current profiles under EV driving cycles, the discharged and regenerative capacity distribution is proposed to describe discharge current profiles for the SOAC estimation. Because of the complexity and nonlinearity of the relationship between the SOAC and the capacity distribution at different temperatures, a neural network (NN) is applied to this SOAC estimation. Comparisons between the estimated SOACs by the NN and the calculated SOACs from the experimental data are used for verification. The results confirm that the proposed approach can provide an accurate and effective estimation of the BRAC for lead-acid batteries in EVs. (author)
Björk, Marcus; Ingle, R Reeve; Gudmundson, Erik; Stoica, Petre; Nishimura, Dwight G; Barral, Joëlle K
2014-09-01
The balanced steady-state free precession (bSSFP) pulse sequence has shown to be of great interest due to its high signal-to-noise ratio efficiency. However, bSSFP images often suffer from banding artifacts due to off-resonance effects, which we aim to minimize in this article. We present a general and fast two-step algorithm for 1) estimating the unknowns in the bSSFP signal model from multiple phase-cycled acquisitions, and 2) reconstructing band-free images. The first step, linearization for off-resonance estimation (LORE), solves the nonlinear problem approximately by a robust linear approach. The second step applies a Gauss-Newton algorithm, initialized by LORE, to minimize the nonlinear least squares criterion. We name the full algorithm LORE-GN. We derive the Cramér-Rao bound, a theoretical lower bound of the variance for any unbiased estimator, and show that LORE-GN is statistically efficient. Furthermore, we show that simultaneous estimation of T1 and T2 from phase-cycled bSSFP is difficult, since the Cramér-Rao bound is high at common signal-to-noise ratio. Using simulated, phantom, and in vivo data, we illustrate the band-reduction capabilities of LORE-GN compared to other techniques, such as sum-of-squares. Using LORE-GN we can successfully minimize banding artifacts in bSSFP. Copyright © 2013 Wiley Periodicals, Inc.
Nonlinear closed loop optimal control: a modified state-dependent Riccati equation.
Rafee Nekoo, S
2013-03-01
The state-dependent Riccati equation (SDRE), as a controller, has been introduced and implemented since the 90s. In this article, the other aspects of this controller are declared which shows the capability of this technique. First, a general case which has control nonlinearities and time varying weighting matrix Q is solved with three approaches: exact solution (ES), online control update (OCU) and power series approximation (PSA). The proposed PSA in this paper is able to deal with time varying or state-dependent Q in nonlinear systems. As a result of having the solution of nonlinear systems with complex Q containing constraints, using OCU and proposed PSA, a method is introduced to prevent the collision of an end-effector of a robot and an obstacle which shows the adaptability of the SDRE controller. Two examples to support the idea are presented and conferred. Supplementing constraints to the SDRE via matrix Q, this approach is named a modified SDRE.
Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M; Derocher, Andrew E; Lewis, Mark A; Jonsen, Ian D; Mills Flemming, Joanna
2016-05-25
State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
De Siena, S; Illuminati, F; Siena, Silvio De; Lisi, Antonio Di; Illuminati, Fabrizio
2002-01-01
We introduce nonlinear canonical transformations that yield effective Hamiltonians of multiphoton down conversion processes, and we define the associated non-Gaussian multiphoton squeezed states as the coherent states of the multiphoton Hamiltonians. We study in detail the four-photon processes and the associated non-Gaussian four-photon squeezed states. The realization of squeezing, the behavior of the field statistics, and the structure of the phase space distributions show that these states realize a natural four-photon generalization of the two-photon squeezed states.
DEFF Research Database (Denmark)
Andreasen, Martin Møller; Christensen, Bent Jesper
This paper suggests a new and easy approach to estimate linear and non-linear dynamic term structure models with latent factors. We impose no distributional assumptions on the factors and they may therefore be non-Gaussian. The novelty of our approach is to use many observables (yields or bonds p...
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.
DEFF Research Database (Denmark)
Jimenez, M.J.; Madsen, Henrik; Bloem, J.J.
2008-01-01
(MAP) estimation is presented along with a software implementation. As a case study, the modelling of the thermal characteristics of a building integrated PV component is considered. The EC-JRC Ispra has made experimental data available. Both linear and non-linear models are identified. It is shown...
Estimating Deaths Attributable to Obesity in the United States
Flegal, Katherine. M.; Williamson, David F.; Pamuk, Elsie R.; Rosenberg, Harry M.
2004-01-01
Estimates of deaths attributable to obesity in the United States rely on estimates from epidemiological cohorts of the relative risk of mortality associated with obesity. However, these relative risk estimates are not necessarily appropriate for the total US population, in part because of exclusions to control for baseline health status and exclusion or underrepresentation of older adults. Most deaths occur among older adults; estimates of deaths attributable to obesity can vary widely depending on the assumptions about the relative risks of mortality associated with obesity among the elderly. Thus, it may be difficult to estimate deaths attributable to obesity with adequate accuracy and precision. We urge efforts to improve the data and methods for estimating this statistic. PMID:15333299
DEFF Research Database (Denmark)
Baadsgaard, Mikkel; Nielsen, Jan Nygaard; Madsen, Henrik
2000-01-01
An econometric analysis of continuous-timemodels of the term structure of interest rates is presented. A panel of coupon bond prices with different maturities is used to estimate the embedded parameters of a continuous-discrete state space model of unobserved state variables: the spot interest rate......, the central tendency and stochastic volatility. Emphasis is placed on the particular class of exponential-affine term structure models that permits solving the bond pricing PDE in terms of a system of ODEs. It is assumed that coupon bond prices are contaminated by additive white noise, where the stochastic...
Estimation of pump operational state with model-based methods
Energy Technology Data Exchange (ETDEWEB)
Ahonen, Tero; Tamminen, Jussi; Ahola, Jero; Viholainen, Juha; Aranto, Niina [Institute of Energy Technology, Lappeenranta University of Technology, P.O. Box 20, FI-53851 Lappeenranta (Finland); Kestilae, Juha [ABB Drives, P.O. Box 184, FI-00381 Helsinki (Finland)
2010-06-15
Pumps are widely used in industry, and they account for 20% of the industrial electricity consumption. Since the speed variation is often the most energy-efficient method to control the head and flow rate of a centrifugal pump, frequency converters are used with induction motor-driven pumps. Although a frequency converter can estimate the operational state of an induction motor without external measurements, the state of a centrifugal pump or other load machine is not typically considered. The pump is, however, usually controlled on the basis of the required flow rate or output pressure. As the pump operational state can be estimated with a general model having adjustable parameters, external flow rate or pressure measurements are not necessary to determine the pump flow rate or output pressure. Hence, external measurements could be replaced with an adjustable model for the pump that uses estimates of the motor operational state. Besides control purposes, modelling the pump operation can provide useful information for energy auditing and optimization purposes. In this paper, two model-based methods for pump operation estimation are presented. Factors affecting the accuracy of the estimation methods are analyzed. The applicability of the methods is verified by laboratory measurements and tests in two pilot installations. Test results indicate that the estimation methods can be applied to the analysis and control of pump operation. The accuracy of the methods is sufficient for auditing purposes, and the methods can inform the user if the pump is driven inefficiently. (author)
Estimation of State Transition Probabilities: A Neural Network Model
Saito, Hiroshi; Takiyama, Ken; Okada, Masato
2015-12-01
Humans and animals can predict future states on the basis of acquired knowledge. This prediction of the state transition is important for choosing the best action, and the prediction is only possible if the state transition probability has already been learned. However, how our brains learn the state transition probability is unknown. Here, we propose a simple algorithm for estimating the state transition probability by utilizing the state prediction error. We analytically and numerically confirmed that our algorithm is able to learn the probability completely with an appropriate learning rate. Furthermore, our learning rule reproduced experimentally reported psychometric functions and neural activities in the lateral intraparietal area in a decision-making task. Thus, our algorithm might describe the manner in which our brains learn state transition probabilities and predict future states.
Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner
2017-07-01
A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.
Liu, Peipei; Sohn, Hoon; Park, Byeongjin
2015-06-01
Damage often causes a structural system to exhibit severe nonlinear behaviors, and the resulting nonlinear features are often much more sensitive to the damage than their linear counterparts. This study develops a laser nonlinear wave modulation spectroscopy (LNWMS) so that certain types of damage can be detected without any sensor placement. The proposed LNWMS utilizes a pulse laser to generate ultrasonic waves and a laser vibrometer for ultrasonic measurement. Under the broadband excitation of the pulse laser, a nonlinear source generates modulations at various frequency values due to interactions among various input frequency components. State space attractors are reconstructed from the ultrasonic responses measured by LNWMS, and a damage feature called Bhattacharyya distance (BD) is computed from the state space attractors to quantify the degree of damage-induced nonlinearity. By computing the BD values over the entire target surface using laser scanning, damage can be localized and visualized without relying on the baseline data obtained from the pristine condition of a target structure. The proposed technique has been successfully used for visualizing fatigue crack in an aluminum plate and delamination and debonding in a glass fiber reinforced polymer wind turbine blade.
Application of nonlinear ultrasonic method for monitoring of stress state in concrete
Energy Technology Data Exchange (ETDEWEB)
Kim, Gyu Jin; Kwak, Hyo Gyoung [Dept. of Civil and Environmental Engineering, Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Park, Sun Jong [Dept. of Structural System and Site Safety Evaluation, Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2016-04-15
As the lifespan of concrete structures increases, their load carrying capacity decreases owing to cyclic loads and long-term effects such as creep and shrinkage. For these reasons, there is a necessity for stress state monitoring of concrete members. Particularly, it is necessary to evaluate the concrete structures for behavioral changes by using a technique that can overcome the measuring limitations of usual ultrasonic nondestructive evaluation methods. This paper proposes the use of a nonlinear ultrasonic method, namely, nonlinear resonant ultrasonic spectroscopy (NRUS) for the measurement of nonlinearity parameters for stress monitoring. An experiment compared the use of NRUS method and a linear ultrasonic method, namely, ultrasonic pulse velocity (UPV) to study the effects of continuously increasing loads and cyclic loads on the nonlinearity parameter. Both NRUS and UPV methods found a similar direct relationship between load level and that parameter. The NRUS method showed a higher sensitivity to micro-structural changes of concrete than UPV method. Thus, the experiment confirms the possibility of using the nonlinear ultrasonic method for stress state monitoring of concrete members.
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1994-01-01
In the existing `direct¿ white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation, while a `finitely additive¿ white noise is used to model the observation noise. We remove this asymmetry by modelling the st
White noise theory of robust nonlinear filtering with correlated state and observation noises
Bagchi, Arunabha; Karandikar, Rajeeva
1992-01-01
In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling
Transient and Steady-State Responses of an Asymmetric Nonlinear Oscillator
Directory of Open Access Journals (Sweden)
Alex Elías-Zúñiga
2013-01-01
oscillator that describes the motion of a damped, forced system supported symmetrically by simple shear springs on a smooth inclined bearing surface. We also use the percentage overshoot value to study the influence of damping and nonlinearity on the transient and steady-state oscillatory amplitudes.
Directory of Open Access Journals (Sweden)
Pabitra Pal Choudhury
2011-01-01
Full Text Available Dynamics of a nonlinear cellular automaton (CA is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.
Excited state nonlinear integral equations for an integrable anisotropic spin-1 chain
Energy Technology Data Exchange (ETDEWEB)
Suzuki, J [Department of Physics, Faculty of Science, Shizuoka University, Ohya 836, Shizuoka (Japan)
2004-12-17
We propose a set of nonlinear integral equations to describe the excited states of an integrable the spin-1 chain with anisotropy. The scaling dimensions, evaluated numerically in previous studies, are recovered analytically by using the equations. This result may be relevant to the study of the supersymmetric sine-Gordon model.
Knaus, H.; Blab, G.; Agronskaia, A.V.; van den Heuvel, D.J.; Gerritsen, H.C.; Wösten, H.A.B.
2013-01-01
Label-free nonlinear spectral imaging microscopy (NLSM) records two-photon-excited fluorescence emission spectra of endogenous fluorophores within the specimen. Here, NLSM is introduced as a novel, minimally invasive method to analyze the metabolic state of fungal hyphae by monitoring the autofluore
Rankings & Estimates: Rankings of the States 2015 and Estimates of School Statistics 2016
National Education Association, 2016
2016-01-01
The data presented in this combined report--"Rankings & Estimates"--provide facts about the extent to which local, state, and national governments commit resources to public education. As one might expect in a nation as diverse as the United States--with respect to economics, geography, and politics--the level of commitment to…
Nonlinear Dependence of Global Warming Prediction on Ocean State
Liang, M.; Lin, L.; Tung, K. K.; Yung, Y. L.; Sun, S.
2010-12-01
Global temperature has increased by 0.8 C since the pre-industrial era, and is likely to increase further if greenhouse gas emission continues unchecked. Various mitigation efforts are being negotiated among nations to keep the increase under 2 C, beyond which the outcome is believed to be catastrophic. Such policy efforts are currently based on predictions by the state-of-the-art coupled atmosphere ocean models (AOGCM). Caution is advised for their use for the purpose of short-term (less than a century) climate prediction as the predicted warming and spatial patterns vary depending on the initial state of the ocean, even in an ensemble mean. The range of uncertainty in such predictions by Intergovernmental Panel on Climate Change (IPCC) models may be underreported when models were run with their oceans at various stages of adjustment with their atmospheres. By comparing a very long run (> 1000 years) of the coupled Goddard Institute for Space Studies (GISS) model with what was reported to IPCC Fourth Assessment Report (AR4), we show that the fully adjusted model transient climate sensitivity should be 30% higher for the same model, and the 2 C warming should occur sooner than previously predicted. Using model archives we further argue that this may be a common problem for the IPCC AR4 models, since few, if any, of the models has a fully adjusted ocean. For all models, multi-decadal climate predictions to 2050 are highly dependent on the initial ocean state (and so are unreliable). Such dependence cannot be removed simply by subtracting the climate drift from control runs.
Nonlinear state space model identification of synchronous generators
Energy Technology Data Exchange (ETDEWEB)
Dehghani, M.; Nikravesh, S.K.Y. [Electrical Engineering Department, Amirkabir University of Technology, Tehran (Iran)
2008-05-15
A method for identification of a synchronous generator is suggested in this paper. The method uses the theoretical relations of machine parameters and the Prony method to find the state space model of the system. Such models are useful for controller design and stability tests. The proposed identification method is applied to a third order model of a synchronous generator. In this study, the field voltage is considered as the input and the active output power and the rotor angle are considered as the outputs of the synchronous generator. Simulation results show good accuracy of the identified model. (author)
Quantum state tomography and fidelity estimation via Phaselift
Energy Technology Data Exchange (ETDEWEB)
Lu, Yiping; Liu, Huan; Zhao, Qing, E-mail: qzhaoyuping@bit.edu.cn
2015-09-15
Experiments of multi-photon entanglement have been performed by several groups. Obviously, an increase on the photon number for fidelity estimation and quantum state tomography causes a dramatic increase in the elements of the positive operator valued measures (POVMs), which results in a great consumption of time in measurements. In practice, we wish to obtain a good estimation of fidelity and quantum states through as few measurements as possible for multi-photon entanglement. Phaselift provides such a chance to estimate fidelity for entangling states based on less data. In this paper, we would like to show how the Phaselift works for six qubits in comparison to the data given by Pan’s group, i.e., we use a fraction of the data as input to estimate the rest of the data through the obtained density matrix, and thus goes beyond the simple fidelity analysis. The fidelity bound is also provided for general Schrödinger Cat state. Based on the fidelity bound, we propose an optimal measurement approach which could both reduce the copies and keep the fidelity bound gap small. The results demonstrate that the Phaselift can help decrease the measured elements of POVMs for six qubits. Our conclusion is based on the prior knowledge that a pure state is the target state prepared by experiments.
The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
Dawes, Jonathan
2010-01-01
Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of such problems, where a pattern-forming, or `Turing', instability occurs, rapid progress has been made recently in our understanding of the formation of localized states: patches of regular pattern surrounded by the unpatterned homogeneous background state. ...
Automatic Regionalization Algorithm for Distributed State Estimation in Power Systems
Energy Technology Data Exchange (ETDEWEB)
Wang, Dexin; Yang, Liuqing; Florita, Anthony; Alam, S.M. Shafiul; Elgindy, Tarek; Hodge, Bri-Mathias
2017-04-24
The deregulation of the power system and the incorporation of generation from renewable energy sources recessitates faster state estimation in the smart grid. Distributed state estimation (DSE) has become a promising and scalable solution to this urgent demand. In this paper, we investigate the regionalization algorithms for the power system, a necessary step before distributed state estimation can be performed. To the best of the authors' knowledge, this is the first investigation on automatic regionalization (AR). We propose three spectral clustering based AR algorithms. Simulations show that our proposed algorithms outperform the two investigated manual regionalization cases. With the help of AR algorithms, we also show how the number of regions impacts the accuracy and convergence speed of the DSE and conclude that the number of regions needs to be chosen carefully to improve the convergence speed of DSEs.
Series load induction heating inverter state estimator using Kalman filter
Directory of Open Access Journals (Sweden)
Szelitzky T.
2011-12-01
Full Text Available LQR and H2 controllers require access to the states of the controlled system. The method based on description function with Fourier series results in a model with immeasurable states. For this reason, we proposed a Kalman filter based state estimator, which not only filters the input signals, but also computes the unobservable states of the system. The algorithm of the filter was implemented in LabVIEW v8.6 and tested on recorded data obtained from a 10-40 kHz series load frequency controlled induction heating inverter.
Estimate of Alabama argillacea (Hübner (Lepidoptera: Noctuidae development with nonlinear models
Directory of Open Access Journals (Sweden)
R. S. Medeiros
Full Text Available The objective of this work was to evaluate which nonlinear model [Davidson (1942, 1944, Stinner et al. (1974, Sharpe & DeMichele (1977, and Lactin et al. (1995] best describes the relationship between developmental rates of the different instars and stages of Alabama argillacea (Hübner (Lepidoptera: Noctuidae, and temperature. A. argillacea larvae were fed with cotton leaves (Gossypium hirsutum L., race latifolium Hutch., cultivar CNPA 7H at constant temperatures of 20, 23, 25, 28, 30, 33, and 35ºC; relative humidity of 60 ± 10%; and photoperiod of 14:10 L:D. Low R² values obtained with Davidson (0.0001 to 0.1179 and Stinner et al. (0.0099 to 0.8296 models indicated a poor fit of their data for A. argillacea. However, high R² values of Sharpe & DeMichele (0.9677 to 0.9997 and Lactin et al. (0.9684 to 0.9997 models indicated a better fit for estimating A. argillacea development.
Non-linear parameter estimation for the LTP experiment: analysis of an operational exercise
Congedo, G; Ferraioli, L; Hueller, M; Vitale, S; Hewitson, M; Nofrarias, M; Monsky, A; Armano, M; Grynagier, A; Diaz-Aguilo, M; Plagnol, E; Rais, B
2011-01-01
The precursor ESA mission LISA-Pathfinder, to be flown in 2013, aims at demonstrating the feasibility of the free-fall, necessary for LISA, the upcoming space-born gravitational wave observatory. LISA Technology Package (LTP) is planned to carry out a number of experiments, whose main targets are to identify and measure the disturbances on each test-mass, in order to reach an unprecedented low-level residual force noise. To fulfill this plan, it is then necessary to correctly design, set-up and optimize the experiments to be performed on-flight and do a full system parameter estimation. Here we describe the progress on the non-linear analysis using the methods developed in the framework of the \\textit{LTPDA Toolbox}, an object-oriented MATLAB Data Analysis environment: the effort is to identify the critical parameters and remove the degeneracy by properly combining the results of different experiments coming from a closed-loop system like LTP.
Santaren, D.; Peylin, P.; Viovy, N.; Ciais, P.
2003-04-01
Global model of Carbone, water, and energy exchanges between the biosphere and the atmosphere are usually validated and calibrated with intensive measurement made over specific ecosystem like those of the fluxnet networks.However the nonlinear dependance between fluxes and model parameters generally complicate the optimization of the major parameters.In this study, we estimate few key parameters of the ORCHIDEE french model,using diurnal variation measurements of latent heat,sensible heat and net CO2 fluxes for 3 weeks over pine forest (Landes, France).The model is forced with the observed climatic forcing: Temperature, income solar radiations,wind velocity norm, air humidity, pressure and precipitations. We will first present the inverse methodology and the problem linkedto the non linearity. The result of the optimization shows correlations within the initial ensemble of parameters which allow us to choose only five parameters determined independently from the observations. Directly related to the net CO2 flux, the maximum rate of carboxylation,Vcmax,and the stomatal conductance, gs, are significantly changed from their apriori estimate for that period. The aerodynamic resistance, the albedo and a parameter linked to maintenance respiration were also modified within their physical range.Overall the model fit to the data was largely improved. Note however that some discrepancies remain for sensible heat flux which would probably require some model improvements for the stocking of energy in the soil. Such work is currently extended in time to account for parameter variations between the season. The application to other ecosystems and with the supplementary data of the Leaf Area Index will be also discussed.
Nonlinear optics and solid-state lasers advanced concepts, tuning-fundamentals and applications
Yao, Jianquan
2012-01-01
This book covers the complete spectrum of nonlinear optics and all solid state lasers.The book integrates theory, calculations and practical design, technology, experimental schemes and applications. With the expansion and further development of Laser technology, the wavelength spectrum of Lasers had to be enlarged, even to be tunable which requires the use of nonlinear optical and Laser tunable technology. It systematically summarizes and integrates the analysis of international achievements within the last 20 years in this field. It will be helpful for university teachers, graduate students as well as engineers.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Distributed Consensus of Nonlinear Multi-Agent Systems on State-Controlled Switching Topologies
Directory of Open Access Journals (Sweden)
Kairui Chen
2016-01-01
Full Text Available This paper considers the consensus problem of nonlinear multi-agent systems under switching directed topologies. Specifically, the dynamics of each agent incorporates an intrinsic nonlinear term and the interaction topology may not contain a spanning tree at any time. By designing a state-controlled switching law, we show that the multi-agent system with the neighbor-based protocol can achieve consensus if the switching topologies jointly contain a spanning tree. Moreover, an easily manageable algebraic criterion is deduced to unravel the underlying mechanisms in reaching consensus. Finally, a numerical example is exploited to illustrate the effectiveness of the developed theoretical results.
Directory of Open Access Journals (Sweden)
Baiyu Liu
2014-01-01
Full Text Available We consider a class of coupled nonlinear Schrödinger systems with potential terms and combined power-type nonlinearities. We establish the existence of ground states, by using a variational method. As an application, some symmetry results for ground states of Schrödinger systems with harmonic potential terms are obtained.
State-space model with deep learning for functional dynamics estimation in resting-state fMRI.
Suk, Heung-Il; Wee, Chong-Yaw; Lee, Seong-Whan; Shen, Dinggang
2016-04-01
Studies on resting-state functional Magnetic Resonance Imaging (rs-fMRI) have shown that different brain regions still actively interact with each other while a subject is at rest, and such functional interaction is not stationary but changes over time. In terms of a large-scale brain network, in this paper, we focus on time-varying patterns of functional networks, i.e., functional dynamics, inherent in rs-fMRI, which is one of the emerging issues along with the network modelling. Specifically, we propose a novel methodological architecture that combines deep learning and state-space modelling, and apply it to rs-fMRI based Mild Cognitive Impairment (MCI) diagnosis. We first devise a Deep Auto-Encoder (DAE) to discover hierarchical non-linear functional relations among regions, by which we transform the regional features into an embedding space, whose bases are complex functional networks. Given the embedded functional features, we then use a Hidden Markov Model (HMM) to estimate dynamic characteristics of functional networks inherent in rs-fMRI via internal states, which are unobservable but can be inferred from observations statistically. By building a generative model with an HMM, we estimate the likelihood of the input features of rs-fMRI as belonging to the corresponding status, i.e., MCI or normal healthy control, based on which we identify the clinical label of a testing subject. In order to validate the effectiveness of the proposed method, we performed experiments on two different datasets and compared with state-of-the-art methods in the literature. We also analyzed the functional networks learned by DAE, estimated the functional connectivities by decoding hidden states in HMM, and investigated the estimated functional connectivities by means of a graph-theoretic approach. Copyright © 2016 Elsevier Inc. All rights reserved.
Vehicle State Information Estimation with the Unscented Kalman Filter
Directory of Open Access Journals (Sweden)
Hongbin Ren
2014-01-01
Full Text Available The vehicle state information plays an important role in the vehicle active safety systems; this paper proposed a new concept to estimate the instantaneous vehicle speed, yaw rate, tire forces, and tire kinemics information in real time. The estimator is based on the 3DoF vehicle model combined with the piecewise linear tire model. The estimator is realized using the unscented Kalman filter (UKF, since it is based on the unscented transfer technique and considers high order terms during the measurement and update stage. The numerical simulations are carried out to further investigate the performance of the estimator under high friction and low friction road conditions in the MATLAB/Simulink combined with the Carsim environment. The simulation results are compared with the numerical results from Carsim software, which indicate that UKF can estimate the vehicle state information accurately and in real time; the proposed estimation will provide the necessary and reliable state information to the vehicle controller in the future.
Kumar, K Vasanth; Sivanesan, S
2005-08-31
Comparison analysis of linear least square method and non-linear method for estimating the isotherm parameters was made using the experimental equilibrium data of safranin onto activated carbon at two different solution temperatures 305 and 313 K. Equilibrium data were fitted to Freundlich, Langmuir and Redlich-Peterson isotherm equations. All the three isotherm equations showed a better fit to the experimental equilibrium data. The results showed that non-linear method could be a better way to obtain the isotherm parameters. Redlich-Peterson isotherm is a special case of Langmuir isotherm when the Redlich-Peterson isotherm constant g was unity.
van den Berg, Stéphanie M
2009-01-01
Modeling both genetic and cultural transmission in parent-offspring data in the presence of phenotypic assortment requires the imposition of nonlinear constraints. This article reports a simulation study that determined how well the structural equation modeling software package Mx and the Bayesian-oriented BUGS software package can handle such nonlinear constraints under various conditions. Results generally showed good and comparable results for Mx and BUGS, although BUGS was much slower than Mx. However, since BUGS uses Markov-chain Monte Carlo estimation it could be used for parent-offspring models with non-normal data and/or item-response theory models.
Efficient sensor placement for state estimation in structural dynamics
Hernandez, Eric M.
2017-02-01
This paper derives a computationally efficient algorithm to determine optimal sequential sensor placement for state estimation in linear structural systems subjected to unmeasured excitations and noise contaminated measurements. The proposed algorithm is developed within the context of the Kalman filter and it minimizes the variance of the state estimate among all possible sequential sensor locations. The paper investigates the effects of measurement type, covariance matrix partition selection, spatial correlation of excitation and model selection on optimal sensor placement. The paper shows that the sequential approach reaches the optimal sensor placement as the number of sensor increases.
Collective vs local measurements in qubit mixed state estimation
Bagán, E; Muñoz-Tàpia, R; Rodríguez, A
2004-01-01
We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error in the estimation goes as 1/N. For local measurements we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that standard tomographic techniques lead to an error proportional to $1/N^{1/4}$, while with our optimal data processing it is proportional to $1/N^{3/4}$.
Remote optimal state estimation over communication channels with random delays
Mahmoud, Magdi S.
2014-01-22
This paper considers the optimal estimation of linear systems over unreliable communication channels with random delays. In this work, it is assumed that the system to be estimated is far away from the filter. The observations of the system are capsulized without time stamp and then transmitted to the network node at which the filter is located. The probabilities of time delays are assumed to be known. The event-driven estimation scheme is applied in this paper and the estimate of the states is updated only at each time instant when any measurement arrives. To capture the feature of communication, the system considered is augmented, and the arrived measurements are regarded as the uncertain observations of the augmented system. The corresponding optimal estimation algorithm is proposed and additionally, a numerical simulation represents the performance of this work. © 2014 The authors. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
A new method of modeling and state of charge estimation of the battery
Liu, Congzhi; Liu, Weiqun; Wang, Lingyan; Hu, Guangdi; Ma, Luping; Ren, Bingyu
2016-07-01
Accurately estimating the State of Charge (SOC) of the battery is the basis of Battery Management System (BMS). This paper has introduced a new modeling and state estimation method for the lithium battery system, which utilizes the fractional order theories. Firstly, a fractional order model based on the PNGV (Partnership for a New Generation of Vehicle) model is proposed after analyzing the impedance characteristics of the lithium battery and compared with the integer order model. With the observability of the discrete non-linear model of the battery confirmed, the method of the state observer based on the extended fractional Kalman filter (EFKF) and the least square identification method of battery parameters are studied. Then, it has been applied successfully to estimate the battery SOC using the measured battery current and voltage. Finally, a standard HPPC (Hybrid Pulse Power Characteristic) test is used for parameter identification and several experimental validations are investigated on a ternary manganese-nickel-cobalt lithium battery pack with a nominal capacity of 24 Ah which consists of ten Sony commercial cells (US18650GR G7) in parallels. The results demonstrate the effectiveness of the fractional order model and the estimation method.
Support vector based battery state of charge estimator
Hansen, Terry; Wang, Chia-Jiu
This paper investigates the use of a support vector machine (SVM) to estimate the state-of-charge (SOC) of a large-scale lithium-ion-polymer (LiP) battery pack. The SOC of a battery cannot be measured directly and must be estimated from measurable battery parameters such as current and voltage. The coulomb counting SOC estimator has been used in many applications but it has many drawbacks [S. Piller, M. Perrin, Methods for state-of-charge determination and their application, J. Power Sources 96 (2001) 113-120]. The proposed SVM based solution not only removes the drawbacks of the coulomb counting SOC estimator but also produces accurate SOC estimates, using industry standard US06 [V.H. Johnson, A.A. Pesaran, T. Sack, Temperature-dependent battery models for high-power lithium-ion batteries, in: Presented at the 17th Annual Electric Vehicle Symposium Montreal, Canada, October 15-18, 2000. The paper is downloadable at website http://www.nrel.gov/docs/fy01osti/28716.pdf] aggressive driving cycle test procedures. The proposed SOC estimator extracts support vectors from a battery operation history then uses only these support vectors to estimate SOC, resulting in minimal computation load and suitable for real-time embedded system applications.
Excited-state dynamics and nonlinear optical response of Ge nanocrystals embedded in silica matrix
Razzari, Luca; Gnoli, Andrea; Righini, Marcofabio; Dâna, Aykutlu; Aydinli, Atilla
2006-05-01
We use a dedicated Z-scan setup, arranged to account for cumulative effects, to study the nonlinear optical response of Ge nanocrystals embedded in silica matrix. Samples are prepared with plasma-enchanced chemical-vapor deposition and post-thermal annealing. We measure a third-order nonlinear refraction coefficient of γ =1×10-16m2/W. The nonlinear absorption shows an intensity-independent coefficient of β =4×10-10m/W related to fast processes. In addition, we measure a second β component around 10-9m /W with a relaxation time of 300μs that rises linearly with the laser intensity. We associate its origin to the absorption of excited carriers from a surface-defect state with a long depopulation time.
On the existence of two-dimensional nonlinear steady states in plane Couette flow
Rincon, Francois
2007-01-01
The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids, 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by Mehta and Healey [Phys. Fluids, 17, 4108 (2005)] for small symmetry-preserving perturbations are influenced by an artefact of the modified system of equations used in their paper. However, using a modified version of their model does not help to find plane Couette flow solution in the limit of vanishing symmetry-preserving perturbations either. The issue of the existence of two-dimensional nonlinear steady states in plane Couette flow remains unsettled.
Directory of Open Access Journals (Sweden)
Wen-Jer Chang
2014-01-01
Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.
Non-linear conductivity of NbS{sub 3} in pressure induced metal state
Energy Technology Data Exchange (ETDEWEB)
Dizhur, Eugene; Kostyleva, Irina; Voronovskii, Anatoly [Institute for High Pressure Physics of RAS, Kaluzhskoe sh. 14, 142190 Troitsk (Russian Federation); Zaitzev-Zotov, Sergey [Institute of Radioengineering and Electronics of the RAS, Mokhovaya ul. 11, 125009 Moscow (Russian Federation)
2011-05-15
Temperature and voltage dependencies of conduction of a quasi-one-dimensional conductor NbS{sub 3} after its transition into a metallic state has been studied at pressures higher than 6 GPa. The differential resistance R = dV /dI measured at small biases (the electric field E below 2 V/cm) demonstrate a considerable growth upon cooling below 20 K accompanied by appearance of the non-linear conduction. Both the growth and nonlinear conduction disappear at E > 3 V/cm or when the temperature exceeds 40 K. A narrow dip visible only at much smaller fields E < 20 mV/cm is superimposed over that nonlinear background when cooling below 3.7 K. (copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Energy Technology Data Exchange (ETDEWEB)
Russell, Steven J. [Los Alamos National Laboratory; Carlsten, Bruce E. [Los Alamos National Laboratory
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
Dynamic systems models new methods of parameter and state estimation
2016-01-01
This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamic...
Harding, Brian J; Gehrels, Thomas W; Makela, Jonathan J
2014-02-01
The Earth's thermosphere plays a critical role in driving electrodynamic processes in the ionosphere and in transferring solar energy to the atmosphere, yet measurements of thermospheric state parameters, such as wind and temperature, are sparse. One of the most popular techniques for measuring these parameters is to use a Fabry-Perot interferometer to monitor the Doppler width and breadth of naturally occurring airglow emissions in the thermosphere. In this work, we present a technique for estimating upper-atmospheric winds and temperatures from images of Fabry-Perot fringes captured by a CCD detector. We estimate instrument parameters from fringe patterns of a frequency-stabilized laser, and we use these parameters to estimate winds and temperatures from airglow fringe patterns. A unique feature of this technique is the model used for the laser and airglow fringe patterns, which fits all fringes simultaneously and attempts to model the effects of optical defects. This technique yields accurate estimates for winds, temperatures, and the associated uncertainties in these parameters, as we show with a Monte Carlo simulation.
Directory of Open Access Journals (Sweden)
Gao Dexin
2012-10-01
Full Text Available This paper concentrates on the solution of state feedback exact linearization zero steady-state error optimal control problem for nonlinear systems affected by external disturbances. Firstly, the nonlinear system model with external disturbances is converted to quasi-linear system model by differential homeomorphism. Using Internal Model Optional Control (IMOC, the disturbances compensator is designed, which exactly offset the impact of external disturbances on the system. Taking the system and the disturbances compensator in series, a new augmented system is obtained. Then the zero steady-state error optimal control problem is transformed into the optimal regulator design problem of an augmented system, and the optimal static error feedback control law is designed according to the different quadratic performance index. At last, the simulation results show the effectiveness of the method.
Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.
Dmitriev, Sergey V.; Shigenari, Takeshi
2002-06-01
Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.
Performance emulation and parameter estimation for nonlinear fibre-optic links
DEFF Research Database (Denmark)
Piels, Molly; Porto da Silva, Edson; Zibar, Darko
2016-01-01
Fibre-optic communication systems, especially when operating in the nonlinear regime, generally do not perform exactly as theory would predict. A number of methods for data-based evaluation of nonlinear fibre-optic link parameters, both for accurate performance emulation and optimization...
Performance emulation and parameter estimation for nonlinear fibre-optic links
DEFF Research Database (Denmark)
Piels, Molly; Porto da Silva, Edson; Zibar, Darko;
2016-01-01
Fibre-optic communication systems, especially when operating in the nonlinear regime, generally do not perform exactly as theory would predict. A number of methods for data-based evaluation of nonlinear fibre-optic link parameters, both for accurate performance emulation and optimization, are rev...
Menegaldo, Luciano L
2017-08-01
State-space control of myoelectric devices and real-time visualization of muscle forces in virtual rehabilitation require measuring or estimating muscle dynamic states: neuromuscular activation, tendon force and muscle length. This paper investigates whether regular (KF) and extended Kalman filters (eKF), derived directly from Hill-type muscle mechanics equations, can be used as real-time muscle state estimators for isometric contractions using raw electromyography signals (EMG) as the only available measurement. The estimators' amplitude error, computational cost, filtering lags and smoothness are compared with usual EMG-driven analysis, performed offline, by integrating the nonlinear Hill-type muscle model differential equations (offline simulations-OS). EMG activity of the three triceps surae components (soleus, gastrocnemius medialis and gastrocnemius lateralis), in three torque levels, was collected for ten subjects. The actualization interval (AI) between two updates of the KF and eKF was also varied. The results show that computational costs are significantly reduced (70x for KF and 17[Formula: see text] for eKF). The filtering lags presented sharp linear relationships with the AI (0-300 ms), depending on the state and activation level. Under maximum excitation, amplitude errors varied in the range 10-24% for activation, 5-8% for tendon force and 1.4-1.8% for muscle length, reducing linearly with the excitation level. Smoothness, measured by the ratio between the average standard variations of KF/eKF and OS estimations, was greatly reduced for activation but converged exponentially to 1 for the other states by increasing AI. Compared to regular KF, extended KF does not seem to improve estimation accuracy significantly. Depending on the particular application requirements, the most appropriate KF actualization interval can be selected.
Observability estimate and state observation problems for stochastic hyperbolic equations
2013-01-01
In this paper, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we study a state observation problem for stochastic hyperbolic equations. As a consequence, we also establish a unique continuation property for stochastic hyperbolic equations.
Relevant sampling applied to event-based state-estimation
Marck, J.W.; Sijs, J.
2010-01-01
To reduce the amount of data transfer in networked control systems and wireless sensor networks, measurements are usually sampled only when an event occurs, rather than synchronous in time. Today's event sampling methodologies are triggered by the current value of the sensor. State-estimators are de
Estimation of correlation energy for excited-states of atoms
Hemanadhan, M
2014-01-01
The correlation energies of various atoms in their excited-states are estimated by modelling the Coulomb hole following the previous work by Chakravorty and Clementi. The parameter in the model is fixed by making the corresponding Coulomb hole to satisfy the exact constraint of charge neutrality.
Relevant sampling applied to event-based state-estimation
Marck, J.W.; Sijs, J.
2010-01-01
To reduce the amount of data transfer in networked control systems and wireless sensor networks, measurements are usually sampled only when an event occurs, rather than synchronous in time. Today's event sampling methodologies are triggered by the current value of the sensor. State-estimators are de
Measurement processing for state estimation and fault identification in batch fermentations
Directory of Open Access Journals (Sweden)
R. Dondo
2004-09-01
Full Text Available This work describes an application of maximum likelihood identification and statistical detection techniques for determining the presence and nature of abnormal behaviors in batch fermentations. By appropriately organizing these established techniques, a novel algorithm that is able to detect and isolate faults in nonlinear and uncertain processes was developed. The technique processes residuals from a nonlinear filter based on the assumed model of fermentation. This information is combined with mass balances to conduct statistical tests that are used as the core of the detection procedure. The approach uses a sliding window to capture the present statistical properties of filtering and mass-balance residuals. In order to avoid divergence of the nonlinear monitor filter, the maximum likelihood states and parameters are periodically estimated. The maximum likelihood parameters are used to update the kinetic parameter values of the monitor filter. If the occurrence of a fault is detected, alternative faulty model structures are evaluated statistically through the use of log-likelihood function values and chi2 detection tests. Simulation obtained for xanthan gum batch fermentations are encouraging.
Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok
2016-05-23
This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS) navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s) and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level.
Directory of Open Access Journals (Sweden)
Muhammad Ilyas
2016-05-01
Full Text Available This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF and Unscented Kalman filter (UKF were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level.
Ilyas, Muhammad; Hong, Beomjin; Cho, Kuk; Baeg, Seung-Ho; Park, Sangdeok
2016-01-01
This paper provides algorithms to fuse relative and absolute microelectromechanical systems (MEMS) navigation sensors, suitable for micro planetary rovers, to provide a more accurate estimation of navigation information, specifically, attitude and position. Planetary rovers have extremely slow speed (~1 cm/s) and lack conventional navigation sensors/systems, hence the general methods of terrestrial navigation may not be applicable to these applications. While relative attitude and position can be tracked in a way similar to those for ground robots, absolute navigation information is hard to achieve on a remote celestial body, like Moon or Mars, in contrast to terrestrial applications. In this study, two absolute attitude estimation algorithms were developed and compared for accuracy and robustness. The estimated absolute attitude was fused with the relative attitude sensors in a framework of nonlinear filters. The nonlinear Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) were compared in pursuit of better accuracy and reliability in this nonlinear estimation problem, using only on-board low cost MEMS sensors. Experimental results confirmed the viability of the proposed algorithms and the sensor suite, for low cost and low weight micro planetary rovers. It is demonstrated that integrating the relative and absolute navigation MEMS sensors reduces the navigation errors to the desired level. PMID:27223293
Immune adaptive Gaussian mixture par ticle filter for state estimation
Institute of Scientific and Technical Information of China (English)
Wenlong Huang; Xiaodan Wang; Yi Wang; Guohong Li
2015-01-01
The particle filter (PF) is a flexible and powerful sequen-tial Monte Carlo (SMC) technique capable of modeling nonlinear, non-Gaussian, and nonstationary dynamical systems. However, the generic PF suffers from particle degeneracy and sample im-poverishment, which greatly affects its performance for nonlinear, non-Gaussian tracking problems. To deal with those issues, an improved PF is proposed. The algorithm consists of a PF that uses an immune adaptive Gaussian mixture model (IAGM) based immune algorithm to re-approximate the posterior density. At the same time, three immune antibody operators are embed in the new filter. Instead of using a resample strategy, the newest obser-vation and conditional likelihood are integrated into those immune antibody operators to update the particles, which can further im-prove the diversity of particles, and drive particles toward their close local maximum of the posterior probability. The improved PF algorithm can produce a closed-form expression for the posterior state distribution. Simulation results show the proposed algorithm can maintain the effectiveness and diversity of particles and avoid sample impoverishment, and its performance is superior to several PFs and Kalman filters.
Quantum Enhanced Phase Estimation with an Amplified Bell State
Sahota, Jaspreet
2013-01-01
We propose a phase estimation protocol for optical interferometry that employs a probe state (containing on average n photons) obtained by squeezing each mode, separately, of a single photon path entangled Bell state. This scheme involves a Mach-Zehnder type interferometer for which each mode is squeezed after the first beam splitter. Information about the differential phase is extracted using a parity detection and the resulting measurement signal is super-resolving and supersensitive, with a minimum phase uncertainty 2/(n+1). This probe state can be generated with current technologies where n is in the order of many thousands of photons.