Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems

Abstract

Abstract-Sophisticated fault detection (FD) algorithms often include nonlinear mappings of observed data to fault decisions, and simulation studies are used to support the methods. Objective statistically supported performance analysis of FD algorithms is only possible for some special cases, including linear Gaussian models. The goal here is to derive general statistical performance bounds for any FD algorithm, given a non-linear non-Gaussian model of the system. Recent advances in numerical algorithms for nonlinear filtering indicate that such bounds in many practical cases are attainable. This paper focuses on linear non-Gaussian models. A couple of different fault detection setups based on parity space and Kalman filter approaches are considered, where the fault enters a computable residual linearly. For this class of systems, fault detection can be based on the best linear unbiased estimate (BLUE) of the fault vector. Alternatively, a nonlinear filter can potentially compute the maximum likelihood (ML) state estimate, whose performance is bounded by the Cramér-Rao lower bound (CRLB). The contribution in this paper is general expressions for the CRLB for this class of systems, interpreted in terms of fault detectability. The analysis is exemplified for a case with measurements affected by outliers.

Enhanced Performance of FH Detection System Using Adaptive Threshold Level

“…From Figure (14) the desired threshold T is 9.64 dB. Interpolating between T = 5 dB and T = 10 dB in Figure ( Tables (4) and (5) illustrates the percentage number of ones versus SNR computed as a pure theoretical threshold which is equal to 100% and 0 % respectively, theoretical threshold as in table (3) for P F =10 -3 but applied in simulink and threshold level guessed experimentally in ATL mode, the final field for percentage number of errors for theoretical threshold level applied in simulink and ATL experimental mode, demonstrates the slight difference between them as in Figures (16) and (17).…”

Statistical signal processing approaches to fault detection

“…It turns out that this upper bound depends on something called the intrinsic accuracy of the probability density function of the noise process, see Kay and Sengupta (1993);Hendeby (2005). The more nonGaussian noise in terms of intrisic accuracy, the higher performance bound.…”

Performance Issues in Non-Gaussian Filtering Problems

“…Several estimators are used: EKF, MMF (only Example I), PF, and PMF (representing the truth). The MMF uses a pruning algorithm, where the least probable branches in the hypotheses tree are cut off, after the introduction of the measurement information, to keep the number of parallel hypotheses at the desired level [22,23].…”