Identification for distributed parameter systems

This thesis considers the parameter identification problem for systems governed by partial differential equations. The various identification methods sire grouped into three disjoint classes namely: "Direct Methods", "Reduction to a Lumped Parameter System", and "Reduction to an Algebraic Equation". The major subject investigated here is concerned with the applicability of stochastic approximation algorithms for identifying distributed parameter systems (DPS) operating in a stochastic environ­ment, where no restriction on probability distributions is imposed. These algorithms are used as a straightforward identification procedure, converge to the real value of the parameters with probability one, and are suitable for on-line applications. In this way, a new identification method is developed for DPS described by linear models, driven by random inputs, and observed through noisy measurements. The very real case of noisy observations taken at a limited number of discrete points located in the spatial domain is considered. The proposed identifica­tion method assumes that a previous system classification has been performed, such that the model to be identified is known up to a set of space-varying parameters, where extraneous terms may be included

Sign-perturbed sums: A new system identification approach for constructing exact non-asymptotic confidence regions in linear regression models

We propose a new system identification method, called Sign - Perturbed Sums (SPS), for constructing nonasymptotic confidence regions under mild statistical assumptions. SPS is introduced for linear regression models, including but not limited to FIR systems, and we show that the SPS confidence regions have exact confidence probabilities, i.e., they contain the true parameter with a user-chosen exact probability for any finite data set. Moreover, we also prove that the SPS regions are star convex with the Least-Squares (LS) estimate as a star center. The main assumptions of SPS are that the noise terms are independent and symmetrically distributed about zero, but they can be nonstationary, and their distributions need not be known. The paper also proposes a computationally efficient ellipsoidal outer approximation algorithm for SPS. Finally, SPS is demonstrated through a number of simulation experiments

Consistent parameter identification of partial differential equation models from noisy observations

This paper introduces a new residual-based recursive parameter estimation algorithm for linear partial differential equations. The main idea is to replace unmeasurable noise variables by noise estimates and to compute recursively both the model parameter and noise estimates. It is proven that under some mild assumptions the estimated parameters converge to the true values with probability one. Numerical examples that demonstrate the effectiveness of the proposed approach are also provided

Identification of Stochastic Wiener Systems using Indirect Inference

We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is difficult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e.,~linear dynamic systems with process noise where the output is measured using a non-linear sensor with additive measurement noise. It is in principle possible to evaluate the log-likelihood cost function using numerical integration, but the corresponding optimization problem can be quite intricate. This motivates studying consistent, but sub-optimal, identification methods for stochastic Wiener systems. We will consider indirect inference using the best linear approximation as an auxiliary model. We show that the key to obtain a reliable estimate is to use uncertainty weighting when fitting the stochastic Wiener model to the auxiliary model estimate. The main technical contribution of this paper is the corresponding asymptotic variance analysis. A numerical evaluation is presented based on a first-order finite impulse response system with a cubic non-linearity, for which certain illustrative analytic properties are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015, Beijing, China, October 19-21, 201

Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Iterative procedures for identification of nonlinear interconnected systems

This work addresses the identification problem of a discrete-time nonlinear system composed by linear and nonlinear subsystems. Systems in this class will be represented by Linear Fractional Transformations. Iterative identification procedures are examined, that alternate between the estimation of the linear and the nonlinear components. The burden of identification falls naturally on the nonlinear subsystem, as techniques for identification of linear systems have long been established. Two approaches are examined. A point-wise identification of the nonlinearity, recently proposed in the literature, is applied and its advantages and drawbacks are outlined. An alternative procedure that employs piecewise affine approximation techniques is proposed. Numerical examples demonstrate the efficiency of the proposed algorithm

Perturbed Datasets Methods for Hypothesis Testing and Structure of Corresponding Confidence Sets

Hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately. The method of sign-perturbed sums (SPS) is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric. This paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution. It is shown that the SPS method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability. In the case of linear regression problems it is shown that the confidence regions are connected, bounded and possibly non-convex sets in both cases. To highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the SPS method can have non-connected parts, which have far reaching consequences

Thermal and Electrical Parameter Identification of a Proton Exchange Membrane Fuel Cell Using Genetic Algorithm

[EN] Proton Exchange Membrane Fuel Cell (PEMFC) fuel cells is a technology successfully used in the production of energy from hydrogen, allowing the use of hydrogen as an energy vector. It is scalable for stationary and mobile applications. However, the technology demands more research. An important research topic is fault diagnosis and condition monitoring to improve the life and the efficiency and to reduce the operation costs of PEMFC devices. Consequently, there is a need of physical models that allow deep analysis. These models must be accurate enough to represent the PEMFC behavior and to allow the identification of different internal signals of a PEM fuel cell. This work presents a PEM fuel cell model that uses the output temperature in a closed loop, so it can represent the thermal and the electrical behavior. The model is used to represent a Nexa Ballard 1.2 kW fuel cell; therefore, it is necessary to fit the coefficients to represent the real behavior. Five optimization algorithms were tested to fit the model, three of them taken from literature and two proposed in this work. Finally, the model with the identified parameters was validated with real data.This research was funded by COLCIENCIAS (Administrative department of science, technology and innovation of Colombia) scholarship program PDBCEx, COLDOC 586, and the support provided by the Corporacion Universitaria Comfacauca, Popayan-ColombiaAriza-Chacón, HE.; Correcher Salvador, A.; Sánchez-Diaz, C.; Pérez-Navarro, Á.; García Moreno, E. (2018). Thermal and Electrical Parameter Identification of a Proton Exchange Membrane Fuel Cell Using Genetic Algorithm. Energies. 11(8):1-15. https://doi.org/10.3390/en11082099S115118Mehta, V., & Cooper, J. S. (2003). Review and analysis of PEM fuel cell design and manufacturing. Journal of Power Sources, 114(1), 32-53. doi:10.1016/s0378-7753(02)00542-6Wang, Y., Chen, K. S., Mishler, J., Cho, S. C., & Adroher, X. C. (2011). 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K., Ahmed, N. A., Al-Fares, F. S., & AlSharidah, M. E. (2015). Parameter Identification of PEM Fuel Cell Using Quantum-Based Optimization Method. Arabian Journal for Science and Engineering, 40(9), 2619-2628. doi:10.1007/s13369-015-1711-0Methekar, R. N., Prasad, V., & Gudi, R. D. (2007). Dynamic analysis and linear control strategies for proton exchange membrane fuel cell using a distributed parameter model. Journal of Power Sources, 165(1), 152-170. doi:10.1016/j.jpowsour.2006.11.047KUNUSCH, C., HUSAR, A., PULESTON, P., MAYOSKY, M., & MORE, J. (2008). Linear identification and model adjustment of a PEM fuel cell stack. International Journal of Hydrogen Energy, 33(13), 3581-3587. doi:10.1016/j.ijhydene.2008.04.052Li, C.-H., Zhu, X.-J., Cao, G.-Y., Sui, S., & Hu, M.-R. (2008). Identification of the Hammerstein model of a PEMFC stack based on least squares support vector machines. 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