State estimation and fault detection and identification for constrained stochastic linear hybrid systems

In this study, a fault detection and identification (FDI) scheme are proposed for constrained stochastic linear hybrid systems (CSLHSs) based on our proposed constrained innovation hybrid estimator (CIHE). CSLHSs are stochastic linear hybrid systems that have state equality constraints on the dynamics of each mode. The CIHE is derived to estimate the CSLHS in such a way that the expectation of the innovations of the mode-matched filters satisfy the constraints. Therefore the constraint information is available in the residual of the CIHE for FDI of not only system dynamic faults but also constraint violations. Each constrained, mode-matched filter is proved to be unbiased, satisfy the constraint, and have smaller estimation error than corresponding unconstrained filters. It is also proved that the CIHE is unbiased and that three residuals from the CIHE have zero mean with a given covariance for different cases of system faults. By monitoring the statistical properties of these residuals, both constraint and discrete faults are detected and identified. The estimation and FDI characteristics of the CIHE algorithm are illustrated using a water tank system as an example.