The detection of multiple faults in a Bayesian setting using dynamic programming approaches

Abstract

Inspired by the need for improving the reliability and safety of complex dynamic systems, this paper tackles the multiple faults detection problem using Dynamic Programming (DP) based methods under the Bayesian framework. These methods include (i) Maximum-A-Posteriori (MAP) estimator approach, (ii) Monte Carlo Markov Chain (MCMC) posteriors, (iii) Set Membership (SM) approach, (iv) probability of fault and (v) alternative methods. Using Bernoulli and Poisson priors, the Bayesian DP-type MAP estimate of all unknown parameters is presented. To derive the posterior distributions of Bayesian point estimations, the MCMC method is applied. For the SM approach, the Bayesian feasible parameter space is derived, as Bayesian confidence interval. The SM criteria are proposed to detect multiple faults which also reduces the Bayesian complexity of MAP estimator. For online fault detection, using the Bayesian model selection technique and the MAP estimator, the DP-based probability of faults is given, serving as a Bayesian early warning system. Since running DP algorithms is a time-consuming, alternative methods are also proposed using the modified MAP estimator. These methods use iterative approximations of MAP estimates, via the application of an iterative Expectation–Maximization algorithm technique. Numerical simulations are conducted and analysed to evaluate the performance of the proposed methods.