Bayesian ballast damage detection in consideration of uncertainties from measurement noise and modelling error

Abstract

This thesis reports the development of a rigorous theoretical method for permanent way engineers to assess the condition of railway ballast under a concrete sleeper based on the measured vibration of the sleeper. Owing to the high uncertainties induced by measurement noise and modelling error, the probability theory was followed in the development to ensure that the proposed ballast damage detection method can explicitly address the uncertainty problem. The development of the proposed method is divided into three phases. In Phase I, the discrete foundation modelling method, which assumes the ballast stiffness under the sleeper is piecewise constant, is integrated with Bayesian model updating for ballast damage detection. Existing ballast damage detection methods from the literature decides the number of ballast regions under the sleeper by subjective judgement. In Phase I of the proposed method, the probabilities for different numbers of ballast regions conditional on the set of measurement are calculated. The number of ballast regions with the highest probability will be employed in Bayesian model updating. A new sequential algorithm was developed for implementing this idea and identifying the “most plausible” number of ballast regions. It is well known that the minimization processes involved in model updating are easily trapped by local minima in the parameter space. To address the problem of local minima, a hybrid-optimization approach is adopted which consists of two stages. The modified evolutionary algorithm (MEA) was developed in the first stage to estimate the boundaries of the parameter space and a set of initial trials for the active-set algorithm to identify all most probable models in the second stage. This phase of development forms the basic framework in the use of Bayesian probability theory in ballast damage detection. One disadvantage of the method in Phase I is the artificial ballast stiffness discontinuities at the interfaces between two ballast regions. To overcome the stiffness discontinuity problem, a continuous foundation modelling method was developed in Phase II of the proposed method. The basic idea is to approximate the ballast stiffness distribution by a Lagrange polynomial. The newly developed sequential algorithm in Phase I was adopted in Phase II for identifying the “most plausible” polynomial order based on the set of measurement without making any ad hoc assumptions. Evidence from the experimental case studies shows outstanding performance of the newly developed continuous foundation modelling method. In both Phases I and II, the original Bayesian model updating formulations, which consider only the effects of measurement noise in the posterior uncertainties, were employed. The formulations were derived under the assumption that the model updating problem is locally identifiable. To overcome these two limitations, the Bayesian model updating method was re-formulated in Phase III of the proposed method. The new formulations consider the effects of both measurement noise and modelling error. Instead of approximating the posterior probability density function (PDF) of ballast stiffness as a multivariable Gaussian distribution (as in the locally identifiable cases), Phase III of the proposed method approximates the posterior PDF by a group of samples in the important regions of the parameter space. As a result, the proposed method is applicable even when the model updating problem is not locally identifiable. In Phase III, the set of important samples was generated by the Markov chain Monte Carlo (MCMC) method. A newly developed termination criterion was tailor-made for the application of MCMC in Bayesian damage detection. Apart from the theoretical developments, this thesis also reports the development of a practical and cost-effective experimental standard for vibration test of in-situ sleeper for the purpose of ballast damage detection. In the experimental verification, a segment of a full-scale ballasted track was built indoor for simulating the undamaged and various damaged scenarios of the ballasted track. The positive results from the full-scale verification case studies ensure the practical value of the proposed method.

Date of Award	2 Oct 2015
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Heung Fai LAM (Supervisor)