Input Design for Model Discrimination and Fault Detection via Convex Relaxation

TL;DR

This paper develops a convex relaxation-based approach for designing input signals that effectively discriminate among models in dynamic systems, aiding fault detection within finite time intervals.

Contribution

It introduces a novel optimization framework using semidefinite relaxation for input design in model discrimination and fault detection, including a suboptimal solution analysis.

Findings

Effective input signals for model discrimination are generated using convex relaxation.

The proposed method improves fault detection accuracy in benchmark wind turbine problems.

The approach offers a computationally feasible solution for nonconvex optimization challenges.

Abstract

This paper addresses the design of input signals for the purpose of discriminating among a finite set of models dynamic systems within a given finite time interval. A motivating application is fault detection and isolation. We propose several specific optimization problems, with objectives or constraints based on signal power, signal amplitude, and probability of successful model discrimination. Since these optimization problems are nonconvex, we suggest a suboptimal solution via a random search algorithm guided by the semidefinite relaxation (SDR) and analyze the accuracy of the suboptimal solution. We conclude with a simple example taken from a benchmark problem on fault detection for wind turbines.