A spatio-temporal Gaussian process with change-points for image-based degradation data

Abstract

Condition monitoring and fault diagnosis using big-data analytic and artificial intelligence (AI) have been an essential tool for reliable operation and timely maintenance of machines, facilitating condition-based maintenance (CBM). To continuously monitor the health of machining tools, we propose a spatio-temporal Gaussian process with change-points (CP-STGP) for modeling image-based degradation patterns. Introducing the concept of change-points, we aim to detect degradation transitions in space-time domain to determine the optimal replacement time for machining tools. The proposed model adopts spectral representation through partial derivatives for complex correlation structure of covariance function in space-time domain. We also introduce the Kalman filter algorithm after transforming original image data using the fast Fourier transform to attempt computational efficiency of re-parameterization. By sequentially applying the likelihood-ratio test (LRT) for multivariate normal models, we derive maximum likelihood estimates (MLEs) of the parameters of the CP-STGP model by determining the number of change-points a priori. Inference on the model parameters is then derived, based on the asymptotic distribution of the LRT statistic. The analysis of a cylinder system in an automobile and simulation results show that the CP-STGP model effectively captures varying image patterns over time by separately modeling them before and after change-points. The proposed modeling approach is expected to help maintenance engineers automatically determine the best replacement time for machining tools as an alternative to manual inspection in practice.