Frequentist and bayesian approaches for probabilistic fatigue life assessment of high-speed train using in-service monitoring data

Abstract

Rapid development of high-speed rail has made high-speed trains one of the most favorable transportation means in recent decades. With the extension of in-service period, train bogie components experience more and more stresses due to the cyclic loadings during routine high-speed train journeys, resulting in cumulative fatigue damage and eventually leading to fatigue failure. With safety being the paramount factor for public transport, the fatigue life of a high-speed train needs to be properly and reliably assessed. As a paradigm of integrating on-board monitoring data into condition assessment of train components, the continuously collected in-service strain data from on-board monitoring systems is significantly useful for evaluation of the fatigue life of high-speed trains. However, the complex operating environment of high-speed trains indicates that various types of uncertainties exist in the monitoring data and established models. This phenomenon brings forward a challenge in obtaining fatigue life assessment results with sufficient accuracy and precision. The research in this thesis is dedicated to developing a probabilistic methodology for integrating in-service monitoring data into fatigue life assessment of high-speed trains. It consists of two branches, as described in the following. One branch leads to the investigations of monitoring-based fatigue life assessment of high-speed trains in the framework of frequentist probabilistic inference. An initial effort is made to address stress modeling technique to formulate probability density functions (PDFs) for both stress range and mean stress, which will be used for fatigue life analysis of train components in light of in-service monitoring data. For modeling of the multi-modal PDF of mean stress acquired from in-service stress history, different types of finite mixture distributions and hybrid mixture parameter estimations are employed. Using the Akaike information criterion (AIC) or Bayesian information criterion (BIC), the best fitted models for the PDFs of stress range and mean stress are obtained, respectively. Based on this modeling technique, the joint PDF of stress range and mean stress is derived through a frequentist modeling technique. Further, this technique provides a foundation for the establishment of a frequentist fatigue life assessment method. In this method, mean stress effect is quantified through a newly defined indicator Q. This indicator is then introduced to formulate a fatigue life assessment method based on the stress-life (S-N) theory. Then the PDFs of both stress range and Q are established and jointly determined with the Miner's cumulative rule to evaluate the fatigue life of high-speed train components with the use of on-board monitoring data. For verification purpose, the method is adopted to assess the fatigue life using the monitoring data acquired from an in-service train running on a high-speed railway in China. The other branch of the present study explores the development of a probabilistic fatigue life assessment approach for in-service high-speed trains in the framework of Bayesian inference. Firstly, Bayesian modeling technique for the stress spectrum of monitoring data is introduced. Analytical solution is used to estimate the derived PDF for the stress spectrum. By integrating prior knowledge and continuous monitoring data, the PDF of the stress spectrum can consider the uncertainties in the continuous monitoring data to predict and update the modeling results. The performance of the technique is shown through the estimated model parameters, model errors and the associated uncertainties. With the formulated Bayesian modeling technique, a fatigue life assessment method is proposed for high-speed trains under in-service environment. Uncertainties in the component material and in-service monitoring data can be considered in deriving the posterior PDF of the fatigue life. This method is verified with the monitoring data of a welded component of a train running on a high-speed railway in China. In addition, as stress concentration largely affects fatigue life of a welded joint, the hot spot stresses obtained from the monitoring data are also integrated into the method. Assessment and prediction results show capability and good performance of the proposed method. This Bayesian method is especially implementable to the fatigue life assessment of a high-speed train when the monitoring period becomes sufficient that prior information and continuous monitoring data can be obtained.