Active Fault Diagnosis for Nonlinear Systems with Probabilistic Uncertainties

Stringent requirements on safety and availability of high-performance systems necessitate reliable fault detection and isolation in the event of system failures. This paper investigates active fault diagnosis of nonlinear systems with probabilistic, time-invariant uncertainties of the parameters and initial conditions. A probabilistic model-based approach is presented for the design of auxiliary input signals enhancing fault diagnosability by separation of multiple nonlinear models pertaining to nominal and faulty system operations in the presence of the probabilistic uncertainties. To obtain a computationally tractable formulation, polynomial chaos expansions are used to propagate the probabilistic uncertainties through the system models. The input design problem is formulated in terms of a metric that characterizes the similarity of arbitrarily shaped distributions of the model outputs. An optimal input sequence is generated while considering hard input and state constraints. The simulation results for active diagnosis of multiple faults in a three-tank system indicate the capability of the presented approach to improve fault detectability and isolability under probabilistic uncertainties of the parameters and initial conditions.