Data-Driven Fault Diagnostic Methods of Mechanical Systems Based on Koopman Operator

Abstract

The Koopman operator is a linear evolution operator that can represent non-linear dynamical systems. Traditionally, there are several methods of analyzing linear dynamical systems. However, when introducing the non-linearity, the analysis of that system becomes exponentially more problematic. This method of linear representations of non-linear dynamical systems is becoming more pertinent as data-driven systems are becoming more abundant. The novel use of the Koopman operator in this paper is to extract and classify significant parameters of a mechanical non-linear dynamic system. This thesis proposes two distinct methods of using the Koopman operator for fault diagnosis. The first method proposes a model to extract key features from a dynamic system and through a neural network is able to classify the existence of a fault. The second method uses parameters derived from the Koopman operator to create a prediction model. This prediction model is used to reconstruct the original system dynamics for a desired time evolution. The two methods are then tested via two separate case studies and the results are discussed.