Probabilistic outlier detection for robust regression modeling of structural response for high-speed railway track monitoring

Outlier detection is an important procedure taken in structural health monitoring (SHM) to create clean and reliable data. A robust time series outlier detection method incorporating a Bayesian perspective and an extreme learning machine (ELM) neural network model is proposed, with application to long-term monitoring data of ballastless tracks for high-speed railway systems. A robust sparse Bayesian ELM (SBELM) model is first established by computing the posterior probability density function of the ELM weight parameters and then marginalizing over the prediction-error precision parameter to obtain a robust nonlinear regression model between the track temperature and structural response. Both the posterior mean and the associated uncertainties of the robust SBELM model are then taken into account to compute the outlier probability for each suspicious data point, which quantifies their degree of data “outlier-ness.” It effectively takes into account the prediction uncertainty of the SBELM regression model. The method is applied to long-term monitoring data for track temperatures, and track strain and relative displacement responses, from two high-speed rail track systems where there are both slight and serious outliers. The results demonstrate that the proposed method can reliably detect outliers by quantifying the outlier probability and that the final results are robust to the selection of the “thresholds.” It is also shown that our new algorithm produces significantly improved model prediction performance after the outliers are detected and removed.