A unified framework for fault detection and isolation of sensor and actuator biases in linear time invariant systems using marginalized likelihood ratio test with uniform priors

• Introduction of extended data window based on the statistical FDT/FCT tests and historical data.
• Using the realistic uniform priors for marginalization of faults in sensor and actuators.
• Introduction of normalized state space equations based on the realistic uniform priors and computation of the relevant fault signature matrices.
• Decoupling detection and isolation phases from estimation of fault magnitude.
• Development of MLR test statistic for detection/isolation of the fault.

This study aims to present a fault detection and isolation (FDI) framework based on the marginalized likelihood ratio (MLR) approach using uniform priors for fault magnitudes in sensors and actuators. The existing methods in the literature use either flat priors with infinite support or the Gamma distribution as priors for the fault magnitudes. In the current study, it is assumed that the fault magnitude is a realization of a uniform prior with known upper and lower limits. The method presented in this study performs detection of time of occurrence of the fault and isolation of the fault type simultaneously while the estimation of the fault magnitude is achieved using a least squares based approach. The newly proposed method is evaluated by application to a benchmark CSTR problem using Monte Carlo simulations and the results reveal that this method can estimate the time of occurrence of the fault and the fault magnitude more accurately compared to a generalized likelihood ratio (GLR) based approach applied to the same benchmark problem. Simulation results on a benchmark problem also show significantly lower misclassification rates.