Optimal Adaptive Threshold and Mode Fault Detection for Model-Based Fault Diagnosis of Hybrid Dynamical Systems

Selection of suitable residual thresholds is a crucial factor for robust model-based fault diagnosis of a dynamical system. Usually, the residual thresholds for robust diagnosis, called adaptive thresholds, are generated based on the worst case conditions of parameter and measurement uncertainties. The adaptive thresholds are robust because they consider that all parameters can have maximum possible deviations in arbitrary directions, i.e. either higher or lower than the corresponding measured or estimated parameter values. This inflates the thresholds and for small faults, the residuals may not cross the adaptive thresholds. For larger faults, the time taken to cross the thresholds may be significant leading to detection delay. The situation is more complex in a hybrid dynamical system because both discrete mode faults and parametric faults are possible and the diagnosis scheme must discriminate between those two types of faults. This chapter presents a common bond graph model-based framework for the hybrid system modelling, simulation, residual and threshold equations derivation, and parametric and discrete mode fault detection and isolation. To improve the fault detection and isolation, an optimization technique is proposed to select a set of optimal adaptive thresholds in the presence of uncertainties. Also, a new technique is proposed to discriminate the parametric faults from the discrete mode faults by an initial hypothesis based on magnitude of residual deviation after a fault. This discrimination improves further diagnosis tasks, especially the parameter estimation process. The proposed diagnosis and thresholding techniques are applied to an academic example system.