(456e) Active Fault Diagnosis for Stochastic Linear Systems: Design Criteria and Implementation Issues

Reliable diagnosis of faults in engineering systems is increasingly challenging because of their growing complexity and stricter requirements on performance, safety, and availability in operating such systems. The majority of available methods for fault detection and diagnosis passively relies on input-output data, which may not be sufficiently informative for timely and reliable diagnosis [1]. Two of the primary reasons the data may fail to reveal that a fault has occurred is the presence of feedback controllers and system uncertainty [2].

Methods for active fault diagnosis, or AFD, improve diagnosis time and confidence by increasing the amount of diagnostically relevant information in the input-output data. AFD involves acting on the system through injecting input signals that are specifically designed for investigating whether potential faults have occurred. When uncertainties are described using probability distributions, the input signals generally increase some statistical distance between the predicted outputs associated with a set of models for the faults. The larger the statistical distance, the higher the chance of reconciling the input-output data with the model that corresponds to the current fault status, which in turn results high-confidence diagnosis. However, input design for AFD is a challenging problem even in the case of linear systems, generally relying on solving nonconvex optimization problems; see, e.g., [3,4,5,6].

We here present results on a recently developed method for AFD for linear stochastic systems. The method involves minimizing a bound on the probability of misdiagnosis [7], subject to a set of models for the potential faults, bounds on the input, and probabilistic constraints on the state. Our discussion is focused on the tightness of the bound and numerical challenges in its minimization, and we demonstrate the performance of the proposed approach on a benchmark problem. Preliminary results suggest that locally optimal solutions can be determined efficiently and result in fast and reliable diagnosis. We further compare the method to other similar approaches, including [4] and [6], and discuss challenges of state chance constraints, receding-horizon implementation, and global optimization.

References

[1] M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and Fault-Tolerant Control. Berlin, Germany: Springer, 2nd ed., 2006.

[2] S.L. Campbell and R. Nikoukhah, Auxiliary Signal Design for Failure Detection. Princeton, NJ: Princeton University Press, 2004.

[3] R. Nikoukhah, “Guaranteed active failure detection and isolation for linear dynamical systems,” Automatica, vol. 34, no. 11, pp. 1345–1358, 1998.

[4] L. Blackmore and B.C. Williams, “Finite horizon control design for optimal discrimination between several models,” in Proceedings of the IEEE Conference on Decision and Control, (San Diego, CA), pp. 1147–1152, 2006.

[5] J.K. Scott, R. Findeisen, R.D. Braatz, and D.M. Raimondo, “Input design for guaranteed fault diagnosis using zonotopes,” Automatica, vol. 50, no. 6, pp. 1580–1589, 2014.

[6] J.A. Paulson, T.A.N. Heirung, R.D. Braatz, and A. Mesbah, “Closed-loop active fault diagnosis for stochastic linear systems,” in Proceedings of the American Control Conference, (Milwaukee, WI), 2018.

[7] T. Kailath, “The divergence and Bhattacharyya distance measures in signal selection,” IEEE Transactions on Communication Technology, vol. 15, no. 1, pp. 52–60, 1967.