scholarly journals Robustness Analysis of the Estimators for the Nonlinear System Identification

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 834
Author(s):  
Wiktor Jakowluk ◽  
Karol Godlewski
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Adaptive Filtering ◽  
Nonlinear System Identification ◽  
Robustness Analysis ◽  
Estimation Methods ◽  
Function Evaluation ◽  
Model Parameters ◽  
Maximum Information ◽  
Plant Model

The main objective of the system identification is to deliver maximum information about the system dynamics, while still ensuring an acceptable cost of the identification experiment. The focus of such an idea is to design an appropriate experiment so that the departure from normal working conditions during the identification task is minimized. In this paper, the adaptive filtering (AF) scheme for plant model parameter estimation is proposed. The experimental results are obtained using the nonlinear interacting water tanks system. The adaptive filtering is expressed by minimizing the error between the system and the plant model outputs subject to the white noise signal affecting system output. This measurement error is quantified by the comparison of Minimum Error Entropy Renyi (MEER), Least Entropy Like (LEL), Least Squares (LS), and Least Absolute Deviation (LAD) estimators, respectively. The plant model parameters were obtained using sequential quadratic programming (SQP) algorithm. The robustness tests for the double-tank water system parameter estimators are performed using the ellipsoidal confidence regions. The effectiveness analysis for the above-mentioned estimators relies on the total number of iterations and the number of function evaluation comparisons. The main contribution of this paper is the evaluation of different estimation methods for the nonlinear system identification using various excitation signals. The proposed empirical study is illustrated by the numerical examples, and the simulation results are discussed.

scholarly journals Efficient implementation of the third order RLS adaptive Volterra filter

2006 ◽  
Vol 19 (1) ◽  
pp. 133-141 ◽  
Author(s):  
Georgeta Budura ◽  
C. Botoca
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Adaptive Filtering ◽  
Adaptive Filter ◽  
Nonlinear System Identification ◽  
Third Order ◽  
Volterra Filter ◽  
The Third ◽  
Nonlinear Adaptive Filtering ◽  
Made In

Nonlinear adaptive filtering techniques are widely used for the nonlinearities identification in many applications. This paper proposes a new implementation of the third order RLS Volterra filter based on the decomposition of the input vector. Its performances are evaluated in a typical nonlinear system identification application. Different degrees of nonlinearity for the nonlinear system are considered. Comparations, based on the adaptive filter error, are made in all cases with a linear identifier. The experimental results show that the proposed nonlinear identifier has better performances than the linear one.

Heuristic Order Reduction of NARX-OBF models Applied to Nonlinear System Identification

2020 ◽  
Vol 1 (2) ◽  
Author(s):  
Elder Oroski ◽  
Beatriz Do Santos Pês ◽  
Adolfo Bauchspiess ◽  
Marco Egito Coelho
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Nonlinear System Identification ◽  
Model Performance ◽  
Order Reduction ◽  
Computational Effort ◽  
Model Parameters ◽  
Auto Regressive ◽  
Narx Models

Nonlinear system identification concerns the determination of the model structure and its parameters. Although the designers often seek the best model for each system, it can be tricky to determine, at the same time, the best structure and the parameters which optimize the model performance. This paper proposes the use of a Genetic Algorithm, GA, and the Levenberg-Marquardt, LM, method to obtain the model parameters, as well as perform the order reduction of the model. In order to validate the proposed methodology, the identification of a magnetic levitator, operating in closed loop, was performed. The class NARX-OBF, Nonlinear Auto Regressive with eXogenous input-Orthonormal Basis Function, was used. The use of OBF functions aims to reduce the number of terms in NARX models. Once the model is found, the order reduction is performed using GA and LM, in a hybrid application, capable of determining the model parameters and reducing the original model order, simultaneously. The results show, considering the inherent trade-of between accuracy and computational effort, the proposed methodology provided an implementation with good mean square error, when compared with the full NARX-OBF model.

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