A novel Bayesian blind source separation approach for extracting non-stationary and discontinuous components from structural health monitoring data

We propose a new method to explore the blind source separation (BSS) of heterogeneous structural health monitoring (SHM) data containing non-stationary and temporally discontinuous components in the framework of Bayesian inference. Specifically, Gaussian process (GP) with a specially defined time-varying kernel function is introduced to encode the prior information about the unknown sources. The time-varying kernel function encompasses a state indicator hyperparameter which enables the expressivity of intermittently active and inactive source signals and incorporates smooth switch and composite kernels catering for the interpretation of complex sources. With the likelihood function elicited from monitoring data alongside with the priors for sources, mixing matrix and noise, the unknown sources are extracted from the posterior distributions formalized by Bayes’ theorem, where a sequential Metropolis − Hasting sampling algorithm is adopted to numerically compute the source statistics in a high-dimensional realm. Numerical simulations demonstrate that the proposed method performs satisfactorily in (i) extracting intermittently active and inactive (abruptly appearing and disappearing) non-stationary source signals, (ii) estimating inconsistent levels of noise contaminated in different sensors, and (iii) handling unknown number of sources. In the verification using real-world strain monitoring data collected from the Tsing Ma Bridge carrying both highway and railway traffic, it is shown that the proposed method well extracts the railway-induced non-stationary strain component with intermittence, and the structural condition index formulated by the Bayesian dynamic linear model (BDLM) is more robust when adopting the separated highway-induced strain data than using the combined railway- and highway-induced strain data. The results obtained by the proposed method are also compared with those by the two most common BSS techniques — the independent component analysis (ICA) and second-order statistics (SOS) methods.