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Title: Measurement and forecasting of high-speed rail track slab deformation under uncertain SHM data using Variational Heteroscedastic Gaussian Process
Authors: Wang, QA
Ni, YQ 
Issue Date: 1-Aug-2019
Source: Sensors (Switzerland), 1 Aug. 2019, v. 19, no. 15, 3311
Abstract: Uncertainty in sensor data complicates the construction of baseline models for the measurement and forecasting (M&F) of high-speed rail (HSR) track slab deformation. Standard Gaussian process (GP) assumes a uniform noise throughout the input space. However, in the application to modelling of HSR structural health monitoring (SHM) data, this assumption can be unrealistic, because of its unique heteroscedastic uncertainty that is induced by dynamic train loading, electromagnetic interference, large temperature variation, and daily maintenance actions of railway track infrastructure. Therefore, this study firstly develops a novel online SHM system enabled by fiber Bragg grating (FBG) technology to eliminate electromagnetic interference on SHM data for continuous and long-term monitoring of track slab deformation, with the capacity of temperature self-compensation. To deal with different sources of uncertainty, the study explores Variational Heteroscedastic Gaussian Process (VHGP) approach while using variational Bayesian and Gaussian approximation for data modelling, estimation of the monitoring data uncertainty, and further data forecasting. The results demonstrate that the VHGP framework yields more robust regression results and the estimated confidence level can better depict the heteroscedastic variances of the noise in HSR data. Higher accuracy for both regression and forecasting is gained through VHGP and the position with maximum noise can be more accurately forecasted with a smooth varying confidence interval. Based on in-situ measurement data, the uncertainty levels for all sensors are estimated together with corresponding deformation profiles for the instrumented segment and three typical types of uncertainty are summarized during the M&F process of HSR track slab deformation.
Keywords: Fiber Bragg grating
Heteroscedastic Gaussian Process
High-speed rail
Measurement and forecasting
Structural health monitoring
Publisher: Molecular Diversity Preservation International (MDPI)
Journal: Sensors (Switzerland) 
ISSN: 1424-8220
DOI: 10.3390/s19153311
Rights: © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
The following publication Wang Q-A, Ni Y-Q. Measurement and Forecasting of High-Speed Rail Track Slab Deformation under Uncertain SHM Data Using Variational Heteroscedastic Gaussian Process. Sensors. 2019; 19(15):3311, is available at
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