Filter-based fault detection and diagnosis using output PDFs for stochastic systems with time delays

Abstract

In this paper, a fault detection and diagnosis (FDD) scheme is studied for general stochastic dynamic systems subjected to state time delays. Different from the formulation of classical FDD problems, it is supposed that the measured information for the FDD is the probability density function (PDF) of the system output rather than its actual value. A B-spline expansion technique is applied so that the output PDF can be formulated in terms of the dynamic weights of the B-spline expansion, by which a time delay model can be established between the input and the weights with non-linearities and modelling errors. As a result, the concerned FDD problem can be transformed into a classic FDD problem subject to an uncertain non-linear system with time delays. Feasible criteria to detect the system fault are obtained and a fault diagnosis method is further presented to estimate the fault. Simple simulations are given to demonstrate the efficiency of the proposed approach.

Fault Detection for Non-Gaussian Stochastic Systems with Time-Varying Delay

“…Remark 5. Theorem 4 is based on a newly proposed augmented Lyapunov functional of form (17), which contains a structure more general than the traditional ones as those in [19,20] for involving( ) and ( − ( )) in the first term of (17). In addition, the importance of augmented Lyapunov functional is that it separates Lyapunov function matrix 1 from , ; that is, there are no terms containing the product of 1 and any of them, which makes the design of the fault detection observer more easier.…”

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

“…However, it cannot do so in [16]. Thus, less conservative fault detection criterion can be obtained in this note.…”

“…Suppose these output PDFs can be approximated using a square root B-spline model as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi cðz; uðtÞÞ It is assumed that the identified weighting system is formulated by (6) with the following coefficient matrices The parameters can be chosen as k 1 = 1, k 2 = 1. The fault is supposed as The threshold can be calculated b = 0.0193 in Theorem 1, which is obtained as 0.0869 in [16]. Figure 1 shows the three-dimensional (3D) mesh plot of the output PDFs when the fault occurs.…”

Function Based Fault Detection for Uncertain Multivariate Nonlinear Non-Gaussian Stochastic Systems Using Entropy Optimization Principle

“…There is no need to measure the system output pdf. This constitutes a major advantage compared with [37][38][39], which require the output pdf to be measurable.…”