Fault Diagnosis and Fault Tolerant Control for Non-Gaussian Stochastic Systems with Random Parameters

This chapter discusses the design of fault diagnosis and its related fault tolerant control for non-Gaussian stochastic systems subjected to parameter randomness. At first, a new formulation of fault diagnosis algorithm is proposed for linear fixed parameter systems that are subjected to non-Gaussian input. For this type of system, the residual signals are controlled, by the estimated fault, to reach a statistic state that is only affected by the original random inputs to the system and the uncontrollable part caused by the rate of changes of the unknown fault. This is followed by the design of fault diagnosis algorithm for non-Gaussian systems that are also subjected to random parameter changes. In this case, the fault is taken as the unexpected changes of the probability density functions of the random parameters. The Laplace transform is used to convey the output probability density function of the system into a simple form, where functional parameter estimation is applied to estimate the faults. Fault tolerant control has been formulated for both systems through an adaptive framework. A simulated example for the Thermal Mechanical Pulping process has been included to demonstrate the use of the proposed algorithm and interesting results have been obtained.

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