From Generalized Gauss Bounds to Distributionally Robust Fault Detection with Unimodality Information

The need for exact distributions in probabilistic fault detection design is hardly fulfilled. recent moment-based distributionally robust (DRFD) secures robustness against inexact but suffers from over-pessimism. To address this issue, we develop a new DRFD scheme by using unimodality, ubiquitous property of real-life distributions. evaluate worst-case false alarm rates, generalized Gauss bound first attained, which less conservative than known Chebyshev bounds that underpin DRFD. This also yields analytical solutions to problems, are suboptimal provably ones disregarding unimodality. A tightened further derived assuming bounded uncertainty, based on convex programming approximation problems developed. Results physical system data elucidate the proposed can reduce conservatism unimodality information, and attaining better robustness-sensitivity trade-off prevalent data-centric with moderate sample sizes.