Model-Free Geometric Fault Detection and Isolation for Nonlinear Systems Using Koopman Operator

Abstract

This paper presents a model-free fault detection and isolation (FDI) method for nonlinear dynamical systems using Koopman operator theory and linear geometric technique. The key idea is to obtain a Koopman-based reduced-order model of a nonlinear dynamical system and apply the linear geometric FDI method to detect and isolate faults in the system. Koopman operator is an infinite-dimensional, linear operator which lifts the nonlinear dynamic data into an infinite-dimensional space where the correlations of dynamic data behave linearly. However, due to the infinite dimensionality of this operator, an approximation of the operator is needed for practical purposes. In this work, the Koopman framework is adopted toward nonlinear dynamical systems in combination with the linear geometric approach for fault detection and isolation. In order to demonstrate the efficacy of the proposed FDI solution, a mathematical nonlinear dynamical system, and an experimental three-tank setup are considered. Results show a remarkable performance of the proposed geometric Koopman-based fault detection and isolation (K-FDI) technique.