Jump Hidden Markov Models for Fault Diagnosis: A Hybrid Bayesian Filtering Approach

We address the challenge of temporal change detection and estimation in nonlinear dynamical systems. Traditionally, model-based fault diagnosis methods rely on the parallel execution of multiple filters, each corresponding to different system models (nominal and faulty). Although effective, this approach becomes computationally expensive, especially when using numerical techniques such as the particle filter instead of closed-form, Gaussian filters. In this work, we propose a novel fault diagnosis framework that integrates a Bernoulli state variable, in the form of a jump Hidden Markov Model, governed by a task-specific probabilistic mode switching mechanism, to represent the presence or absence of a fault (or change) within a dynamic system. By embedding this binary state within a Bayesian filtering framework, we develop a hybrid state filter that significantly reduces the computational complexity traditionally associated with particle filtering approaches for fault diagnosis. The proposed filter enables real-time evaluation of fault hypotheses based on the statistical moments of a single posterior probability density function, thereby eliminating the requirement for maintaining multiple parallel filters. The proposed method is validated through a numerical benchmark example demonstrating its efficiency and effectiveness.