This research focuses on the utilization of model-based active fault detection and isolation (FDI) techniques for optimal design of maintenance tests under uncertainty. The goal here is to improve the robustness of system fault diagnostics (i.e., reliability and maintainability) to uncertainty, subsequently improving the cost of maintenance throughout a system’s lifecycle. This can be accomplished by designing admissible inputs that produce unique system responses to every potential fault for any realization of system uncertainty.
We extend the work of Stuber et al.  and formulate the problem as a worst-case FDI design problem. Furthermore, we apply novel implicit function theory to transform the equality-constrained bilevel worst-case FDI design problem into a semi-infinite program (SIP) with embedded implicit functions, significantly reducing its size . This problem is to be solved globally, using the SIP cutting-plane algorithm of  with modification to accommodate implicit functions , to provide guarantees on feasibility for detecting and isolating all faults. As an example, the figure shows the uniqueness of the system responses to faults as it relates to system inputs at their worst-case realization of uncertainty, and highlights the positive impact inputs can have during fault diagnostics.
- Hale, W. T., Wilhelm, M.E., Palmer, K.A., Stuber, M.D., and G.M. Bollas. Semi-Infinite Programming for Global Guarantees of Robust Fault Detection and Isolation in Safety-Critical Systems. Computers & Chemical Engineering. 126, 218-230 (2019). DOI: 10.1016/j.compchemeng.2019.04.007
- Hale, W.T., Palmer, K. A., Stuber, M. D., and Bollas, G. M. Design of Built-in Tests for Robust Active Fault Detection and Isolation of Discrete Faults in Uncertain Systems. In Proceedings, ACC 2018, Milwaukee, WI, Jun 29, 2018. (paper)
 Stuber, M. D. & Barton, P. I. Semi-Infinite Optimization with Implicit Functions. Industrial & Engineering Chemistry Research, 2015, 54, 307-317.
 Stuber, M. D.; Wechsung, A.; Sundaramoorthy, A. & Barton, P. I. Worst-case design of subsea production facilities using semi-infinite programming. AIChE Journal, 2014, 60, 2513-2524.
 Mitsos, A. Global optimization of semi-infinite programs via restriction of the right-hand side. Optimization, Taylor & Francis, 2011, 60, 1291-1308.