A Koopman operator approach for machinery health monitoring and prediction with noisy and low-dimensional industrial time series

Abstract Data-driven methods for machinery health monitoring and prediction, such as machine learning and statistical pattern recognition techniques, normally requires high quality (less noised), frequently-sampled and large volume time-series data to estimate proper models between system inputs and outputs. However, most of the industrial time-series are highly noisy and only few types of sensory data are available, which challenges the estimation accuracy. This paper proposes a data-driven spectral decomposition framework (denoted as Koopman-CBM) for the machinery health monitoring and prediction problem. Specifically, considering noisy industrial signals in the form of one dimensional time-series, we use the higher-order dynamic mode decomposition (DMD) embeds time-lagged snapshots to increase the spatial complexity of low-dimensional time series and use the total-least-square algorithm to compensate the effect of measurement noise, thereby, extracting accurate dynamical features. The obtained de-noised model characteristics (i.e., eigenvalues, eigenfunctions, Koopman operator) is effective in predicting the system health stages. In parallel, using the Koopman operator as the linear predictor associated with the nonlinear dynamics, we can then perform remaining useful life (RUL) predictions with high accuracy. The experimental validation of the proposed framework is carried out on a rolling bearing datasets for degradation health-stage inspection and RUL prediction. Results show that– compared with other mainstream methods– our approach is capable of identifying the critical degradation stages and achieving higher RUL prediction accuracies.