Optimal Discrete-time Fault Detection and Diagnosis Filtering

Abstract

For the FDD problem of stochastic plants, one main approach is the filter-based or observer-based methodology, where the (extended) Kalman filtering results were widely used and Gaussian systems were considered (see [20, 41]). However, nonlinearity may lead to non-Gaussian outputs, where (especially for asymmetric distributions with multiple peaks) mean and variance are insufficient to characterize their statistical behavior precisely (see [63, 66, 157, 161]). It is noted that many effective robust and nonlinear filtering and filter-based FDD approaches have been provided (see [55, 110, 144, 176, 195, 203] and references therein) to date. For example, in [55], robust performance optimization has been applied to the filtering problems of linear systems. In [176], feasible filtering approaches based on algebraic algorithms have been provided for linear plants with uncertainties and time delays. In [110, 144], it has been shown how robust filtering and robust control approaches can be used for FDD problems. However, few results can be found to solve FDD problems for the transformed discrete-time system, when nonlinearity and time delays are included and measurements are a nonlinear function of the state.

To overcome the obstacles and improve FDD performance, a discrete-time dynamical weighting system with nonlinearity, uncertainty and time delays is established. As such, the problem for dynamic stochastic systems can be transformed into a classical discrete-time nonlinear FDD problem, where nonlinearity exists in both the dynamical equation and the measurement one. In this chapter, robust guaranteed cost performance is introduced for the weighting model to enhance FDD performance. Feasible approaches are given to design the FDD filter by means of optimization techniques in terms of LMIs, with which the stochastic faults can be detected and diagnosed using the measured output PDFs.