Koopman Operator Based Fault Diagnostic Methods for Mechanical Systems

Traditionally, dynamical systems can be simulated with physics-based model when the design parameters and material property are pre-known. However, when a system is deployed in field and has suffered potential degradation, a physics-based model might be infeasible to obtain. Moreover, the non-linearity and unknown coupling between the system and contacting constraints are often hard to determine accurately. The analysis of those systems becomes practically problematic. In this paper, the Koopman operator is used to learn and represent a dynamic system in a data driven manner. This paper proposes two methods of using the Koopman operator to extract and classify critical parameters of a non-linear dynamic mechanical system for fault diagnosis. The first method proposes a model to extract key features from a dynamic system and feed the features to a neural network to classify the existence of a fault. The second method uses parameters derived from the Koopman operator to create a prediction model with healthy data. This prediction model is then used to predict future system dynamics for a measured time evolution and compare that with direct measurements when future dynamics become available. Both methods are then tested via an experimental case study and the results are discussed.