(185ab) Bayesian Design of Experiments for Fault Detection and Isolation

Fault detection and isolation (FDI) is a challenging process in modern cyber-physical systems (CPS), which are often characterized by complexity and corresponding parametric and environmental uncertainty.¹ When feasible, optimal test design is necessary for the FDI of these systems, due to the limitations in maintenance budget, time, and the size of datasets available. In systems with capability for down-time or relaxed performance requirements, optimal tests can be designed by manipulating the system input trajectories with the objective to maximize the information extracted from available system sensors.² However, due to the deterministic nature of CPS models and the finiteness of the inputs selected to execute FDI tests, model-based active FDI approaches are vulnerable to uncertainty and error.³ In most approaches, FDI test designs vary with the parameter uncertainty space. For instance, approaches that utilize metrics of the Fisher Information Matrix or Shannon Information are subject to assumptions with respect to the neighborhood around which numerical derivatives expressing parametric sensitivities are calculated. In the majority of methods, these derivatives are, by design, calculated locally, assuming that they hold accurately for the entirety of the parameter space.⁴ The latter, cannot be proven and, in fact, it is not correct for certain classes of problems (e.g., system models that are non-linear with respect to their parameters). To address this issue, this work proposes the use of Bayesian approaches for the design of FDI tests, capable of maximizing test information for the entire model parameter space.

The implications of assuming no dependence of the information extracted from a test on the parameter estimates and the advantages of Bayesian approaches will be illustrated in various implementations of the benchmark 3-tank system model.⁵ We focus this discussion and presentation on the dependence of the system sensitivity matrix on the assumption about the neighborhood around which the sensitivities are estimated using the system model. We showcase that depending on the type of system (non-linearities involved) and the number of errors and uncertainty, assumptions about the effect of our anticipation of fault severity can lead to unique or multiple optimal designs. The latter leads to uncertainty in the decision process for the execution of one set of tests, and lack of certification for the detectability of faults, using model-/sensitivity-based approaches.

Acknowledgment

This work was sponsored by the UTC Institute for Advanced Systems Engineering (UTC-IASE) of the University of Connecticut and the United Technologies Corporation. Any opinions expressed herein are those of the authors and do not represent those of the sponsor.

Literature

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