Delay-dependent fault detection and diagnosis using B-spline neural networks and nonlinear filters for time-delay stochastic systems

Abstract

A new fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (PDFs) of the system. The square-root B-spline neural networks is used to formulate the output PDFs with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Delay-dependent criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. It is shown that this new criterion can provide higher sensitivity performance than the existing result. Simulations are given to demonstrate the efficiency of the proposed approach.

Fault Tolerant Control for Non-Gaussian Stochastic Distribution Systems

“…Remark 1 Compared with the models considered in [3,10,19], there are the following several features: first of all, a radial basis function (RBF) neural network technique is proposed so that the PDF model is more practically reasonable; secondly, in the model adopted in [1], ω(y, u(t), F ) is omitted, which can lead to the conservative result.…”

“…So there is a need to further develop the FDD methods that can be applied to the stochastic systems subject to non-Gaussian distribution. Motivated by these factors, studies on stochastic distribution systems and stochastic distribution control have been investigated in [1,3,4,6,7,10,19,20,[22][23][24][25][31][32][33]. Differently from conventional FDD problems, the measurement information for the FDD is the output PDFs rather than the mean or variance of the output, and the stochastic variables involved in are not confined to the Gaussian ones.…”

Fault Detection and Diagnosis for Non-Gaussian Singular Stochastic Distribution Systems via Output PDFs

“…As shown in reference [14] and [15], the output PDFs γ(z,u(t),F(t)) can be approximated by using square root Bspline expansions as the following form:…”

“…Corollary 1: If for the parameters κ i > 0 (i=1,2), there exists matrices R and P with being non-singular and constant γ > 0 satisfying (14), then fault F can be detected by the following criterion:…”

“…while the control objective of SDC systems is to control the shape of the output PDFs, the aim of FDD in SDC It is noted that if only output PDFs can be measured rather than the output vector itself,most existing observer-based FDD approaches are invalid. As a result, an observer-based fault detection and diagnosis approaches have been developed in reference( [3], [7], [11], [14], [15], [16],and reference therein) to detect and diagnose the fault in the non-Gaussian SDC system. However, concerning the FDD problem, few literatures have been reported to the singular non-gaussian stochastic distribution control systems.…”