Active Fault Diagnosis for Stochastic Systems With Incipient Actuator and Sensor Faults

ABSTRACT To overcome the limited adaptability of passive fault diagnosis and the modeling and uncertainty constraints in existing active fault diagnosis (AFD) approaches, this paper proposes a Bayesian minimum probability of error input design framework for discrete time stochastic systems with incipient actuator faults, incipient sensor faults, and their mixed cases. A key contribution is an analytically derived closed form Chernoff upper bound on the multi‐mode misclassification probability based on the full output sequence, resulting in a tractable optimization problem with an expected Chernoff distance objective and an explicit linear discriminant rule for multi‐mode decision making. To improve computational efficiency, a hierarchical discretization strategy for the Chernoff parameter is developed to decouple bound tightening from excitation input optimization, reducing the overall design to a sequence of constrained quadratic programs. Simulations on the benchmark four tank system demonstrate improved separability for incipient hybrid faults under stochastic disturbances, highlighting the practical potential of the proposed stochastic AFD method.