Fault detection and identification for a class of continuous piecewise affine systems with unknown subsystems and partitions

Abstract

This paper establishes a novel online fault detection and identification strategy for a class of continuous piecewise affine (PWA) systems, namely, bimodal and trimodal PWA systems. The main contributions with respect to the state-of-the-art are the recursive nature of the proposed scheme and the consideration of parametric uncertainties in both partitions and in subsystems parameters. In order to handle this situation, we recast the continuous PWA into its max-form representation and we exploit the recursive Newton-Gauss algorithm on a suitable cost function to derive the adaptive laws to estimate online the unknown subsystem parameters, the partitions, and the loss in control authority for the PWA model. The effectiveness of the proposed methodology is verified via simulations applied to the benchmark example of a wheeled mobile robot.

Statistical Inference for Piecewise Affine System Identification

“…Le Quang et al [21] investigate the identification of continuous piecewise affine systems in state space form with jointly unknown partition and subsystem matrices. A novel online fault detection and identification strategy was established for a class of continuous piecewise affine systems, namely, bimodal and trimodal piecewise affine systems in [22], where the recursive nature of the proposed scheme and the consideration of parametric uncertainties in both partitions and in subsystems parameters were proposed there.…”

The modified extended Kalman filter based recursive estimation for Wiener nonlinear systems with process noise and measurement noise

“…12,13 When the nonlinear block of the Wiener system has static property, that is, the output nonlinearity is expressed as a linear combination of known bases, the Wiener system can be parameterized into a linear regressive model and the conventional identification algorithms for the linear systems can be used. 14,15 In this literature, Kazemi and Arefi assumed that the bases of the nonlinear block are the polynomial functions and presented a least squares based iterative algorithm based on the key term separation principle. 16 Yang et al considered the identification of Wiener nonlinear systems with time-delay and outliers and derived a robust expectation-maximization algorithm by using the Laplace distribution to model the output data with outliers.…”

“…The reason mainly lies in two‐folds: (a) the structure of Wiener systems is highly simple in contrast to other nonlinear models such as the NARMAX models and Volterra models; 10,11 and (b) the Wiener systems are judged to have the ability to represent nonlinear systems with arbitrary precision 12,13 . When the nonlinear block of the Wiener system has static property, that is, the output nonlinearity is expressed as a linear combination of known bases, the Wiener system can be parameterized into a linear regressive model and the conventional identification algorithms for the linear systems can be used 14,15 . In this literature, Kazemi and Arefi assumed that the bases of the nonlinear block are the polynomial functions and presented a least squares based iterative algorithm based on the key term separation principle 16 .…”

Piecewise affine identification of a hydraulic pumping system using evolutionary computation

“…The PWA identification procedures can be classified into five categories [13]: optimisation, clustering, algebraic and recursive methods. Among them, the following approaches stand out: (i) procedure based on mixed integer programming [18]; (ii) methods based on clustering [12, 17, 34]; (iii) Bayesian approach [20]; (iv) bounded error procedure [19]; (v) evolutionary approaches [28, 29] and (vi) recursive or on‐line algorithms [13, 24, 35, 36]. A simple and efficient clustering method based on GMMs, trained by the expectation‐maximisation algorithm – presented in [21] – will be used as a framework in what follows.…”