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Wheel condition assessment is of great significance to ensure the operation safety of trains and metro systems. This study is intended to develop a Bayesian probabilistic method for online and quantitative assessment of railway wheel conditions using track-side strain-monitoring data. The proposed method is a fully data-driven, nonparametric approach without the need of a physical model. To enable defect identification using only response measurement, the measured dynamic strain responses of rail tracks during the passage of trains are processed to elicit the normalized cumulative distribution function values representative of the effect of individual wheels, which in conjunction with the frequency points are used to formulate a probabilistic reference model in terms of sparse Bayesian learning. Through cleverly realizing sparsity by introducing hyper-parameters and their priors, the sparse Bayesian learning makes the resulting model to exempt from overfitting and generalize well on unseen data. Only the monitoring data in healthy state are needed in formulating the reference model. A novel Bayesian null hypothesis significance testing in terms of scale-invariant intrinsic Bayes factor, which does not suffer from the Jeffreys–Lindley paradox, is then pursued in the presence of new monitoring data collected from possibly defective wheel(s) to detect wheel defects and quantitatively assess wheel condition. The proposed method in fully Bayesian inference framework is verified by utilizing the real-world monitoring data acquired by a distributed fiber Bragg grating–based track-side monitoring system and comparing with the offline inspection results.

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This paper proposes an improved most likely heteroscedastic Gaussian process (MLHGP) algorithm to handle a kind of nonlinear regression problems involving input-dependent noise. The improved MLHGP follows the same learning scheme as the current algorithm by use of two Gaussian processes (GPs), with the first GP for recovering the unknown function and the second GP for modeling the input-dependent noise. Unlike the current MLHGP pursuing an empirical estimate of the noise level which is provably biased in most of local noise cases, the improved algorithm gives rise to an approximately unbiased estimate of the input-dependent noise. The approximately unbiased noise estimate is elicited from Bayesian residuals by the method of moments. As a by-product of this improvement, the expectation maximization (EM)-like procedure in the current MLHGP is avoided such that the improved algorithm requires only standard GP learnings to be performed twice. Four benchmark experiments, consisting of two synthetic cases and two real-world datasets, demonstrate that the improved MLHGP algorithm outperforms the current version not only in accuracy and stability, but also in computational efficiency. Index Terms-Gaussian process regression, most likely heteroscedastic Gaussian process, input-dependent noise, Bayesian residual, method of moments. Qiu-Hu Zhang received his B.Eng. and M.Sc. degrees from Hefei University of Technology, China, in 2009 and 2014, respectively. He is currently pursuing Ph.D. degree at The Hong Kong Polytechnic University, Hong Kong. His research interests include Bayesian machine learning, Bayesian decision theory, and structural health monitoring. Yi-Qing Ni received his B.Eng. degree

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