A Variational Bayesian Approach for Temporally Correlated Source Separation and Application to Thermal Strain Extraction of High-Speed Rail

Abstract

Strain experienced by an in-service high-speed train is extremely important for ensuring the train’s structural safety because it gives a direct and unique insight into the real structural performance under various excitations. However, environmental factors, such as temperature, will significantly alter the monitoring data of strain and seriously affect the health assessment results. To eliminate the thermal effect on strain monitoring data, a hierarchical Bayesian approach in the context of Blind Source Separation (BSS) is explored in this study. Compared with the conventional independent component analysis (ICA) and second-order blind identification (SOBI) techniques, the Bayesian blind source separation approach can explicitly account for and quantify the measurement errors and uncertainty. More importantly, it directly gives rise to the (posterior) probability density distributions of the source signals, which greatly facilitate the reliability assessment of structural components making use of monitoring data. To accommodate non-i.i.d. temporal structure of the source signals, the Gaussian process kernel function is introduced in this study to define the prior distribution of the unknown sources. With this prior distribution in conjunction with appropriate priors for the mixing matrix and noise, the joint posterior distribution of the three groups of unknown parameters is derived by the Bayesian theorem. The Variational Bayesian (VB) learning is then applied to numerically obtain the probabilistic characteristics of the sources, mixing matrix, and noise separately. The real strain data acquired from a bogie in a high-speed train during its in-service operation is used to evaluate the performance of the proposed method through comparison with the ICA and SOBI techniques.