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.

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.…”

Adaptive Image Processing for Bubbles in Flotation Process

“…To describe the dynamic stochastic process the conditional probability of output is defined. To approximate conditional output PDF many literatures have been devoted to the nonparametric estimation including kernel methods, orthogonal methods, the histogram and their varieties 22 . More recently Wang et al proposed the B-spline expansion models that successfully tracked the output PDFs to a target distribution shape by using various control approaches 22 .…”

“…To approximate conditional output PDF many literatures have been devoted to the nonparametric estimation including kernel methods, orthogonal methods, the histogram and their varieties 22 . More recently Wang et al proposed the B-spline expansion models that successfully tracked the output PDFs to a target distribution shape by using various control approaches 22 . The characteristics of the size distribution of froth segmentation results show that the output PDF is smooth but with spikes, with an obvious long tail skewed to the left.…”

Fault detection and diagnosis for general discrete-time stochastic systems using output probability density estimation

“…This method was the first attempt focussing on the application of the PDF model. However, there was a criticism that the used linear B-spline model cannot guarantee the output PDF of the model is positive [23], [26]. Subsequently, an improved design approach has been applied for the general stochastic system by using a square root B-spline model and nonlinear filter design [26].…”

“…For stochastic systems, many significant schemes have been introduced and applied to practical process successfully. In general, the following approaches have been widely applied and developed for this problem: filter-or observer-based approaches [22], [23], identification-based approaches [24], and static approaches based likelihood approaches [25]. For dynamic stochastic systems, the filter based FDD approaches, have been presented as an effective way for Gaussian variables in stochastic systems.…”