Nonlinear Modelling of a Rail-Sleeper-Ballast System and Its Application in the Bayesian Ballast Damage Detection
軌道-軌枕-道砟系統的非線性建模及其在基於貝葉斯方法的道砟損傷檢測中的應用
Student thesis: Doctoral Thesis
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Award date | 25 Aug 2017 |
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Permanent Link | https://scholars.cityu.edu.hk/en/theses/theses(ff690344-a5e4-4506-a241-f860a23c20f4).html |
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Other link(s) | Links |
Abstract
This thesis reports the stage by stage development of a novel and practical ballast damage detection method for assisting permanent way engineers and inspectors to quantify the “health” condition of ballast under the concrete sleepers with the consideration of the nonlinear stiffness of ballast under large amplitude vibration.
Firstly, an appropriate modelling method was developed for capturing the time-domain behaviour of a linear rail-sleeper-ballast system utilizing impact hammer field test data (under small amplitude vibration) obtained from a ballasted track at Tsuen Wan.
Secondly, the time-domain ballast damage detection methodology based on the linear rail-sleeper-ballast model was developed. The Bayesian statistical system identification framework was followed to explicatively address the uncertainties introduced by modelling error and measurement noise. To ensure the robustness of the developed method, the Markov chain Monte Carlo (MCMC) simulation was adopted in generating samples for the approximation of the posterior probability density function (PDF) of ballast stiffness values under the concrete sleeper. A new Bayesian model class selection method utilizing MCMC samples was formulated. A comprehensive numerical case study was carried out to study the effect of the quantity (i.e., the number of sensors) and quality (i.e., the level of measurement noise) on the performance of the newly developed method. The results show that the uncertainty of the identified ballast stiffness is at acceptable level even when measured data from only one sensor was employed. To ensure the applicability of the method, impact hammer field test data from another railway track at Siu Ho Wan was employed to verify the developed method.
Thirdly, the proposed time-domain ballast damage detection methodology with the consideration of the nonlinear stress-strain behaviour of ballast was developed, which can be conceptually divided into four components: (1) nonlinear modelling method for the rail-sleeper-ballast system, in which nonlinear ballast stiffness in supporting the sleeper is incorporated; (2) the discrete ballast modelling method for representing different ballast damage scenarios by different model classes; (3) MCMC-based Bayesian model class selection method for detecting the damaged region of ballast; and (4) MCMC-based Bayesian model updating for calculate the posterior PDF of nonlinear ballast stiffness to quantify the damage. The newly developed methodology was verified using impact hammer tests from the indoor test panel, where ballast damage can be simulated. The damage detection results are encouraging.
Finally, train induced track vibration was measured from a ballasted track at Siu Ho Wan for the verification of the proposed methodology in model updating of ballasted track system. Since it is impossible to simulate damage to operating ballasted track, only undamaged case is considered. The train-track vibration test was detailly reported in this thesis. Important observations from the train induced track vibration were discussed.
Apart from the theoretical and algorithmic developments, this thesis also contributes in the design and implementation of various practical vibration measurement method for obtaining the dynamic responses of the ballasted track under either impact hammer or train induced vibration.
Firstly, an appropriate modelling method was developed for capturing the time-domain behaviour of a linear rail-sleeper-ballast system utilizing impact hammer field test data (under small amplitude vibration) obtained from a ballasted track at Tsuen Wan.
Secondly, the time-domain ballast damage detection methodology based on the linear rail-sleeper-ballast model was developed. The Bayesian statistical system identification framework was followed to explicatively address the uncertainties introduced by modelling error and measurement noise. To ensure the robustness of the developed method, the Markov chain Monte Carlo (MCMC) simulation was adopted in generating samples for the approximation of the posterior probability density function (PDF) of ballast stiffness values under the concrete sleeper. A new Bayesian model class selection method utilizing MCMC samples was formulated. A comprehensive numerical case study was carried out to study the effect of the quantity (i.e., the number of sensors) and quality (i.e., the level of measurement noise) on the performance of the newly developed method. The results show that the uncertainty of the identified ballast stiffness is at acceptable level even when measured data from only one sensor was employed. To ensure the applicability of the method, impact hammer field test data from another railway track at Siu Ho Wan was employed to verify the developed method.
Thirdly, the proposed time-domain ballast damage detection methodology with the consideration of the nonlinear stress-strain behaviour of ballast was developed, which can be conceptually divided into four components: (1) nonlinear modelling method for the rail-sleeper-ballast system, in which nonlinear ballast stiffness in supporting the sleeper is incorporated; (2) the discrete ballast modelling method for representing different ballast damage scenarios by different model classes; (3) MCMC-based Bayesian model class selection method for detecting the damaged region of ballast; and (4) MCMC-based Bayesian model updating for calculate the posterior PDF of nonlinear ballast stiffness to quantify the damage. The newly developed methodology was verified using impact hammer tests from the indoor test panel, where ballast damage can be simulated. The damage detection results are encouraging.
Finally, train induced track vibration was measured from a ballasted track at Siu Ho Wan for the verification of the proposed methodology in model updating of ballasted track system. Since it is impossible to simulate damage to operating ballasted track, only undamaged case is considered. The train-track vibration test was detailly reported in this thesis. Important observations from the train induced track vibration were discussed.
Apart from the theoretical and algorithmic developments, this thesis also contributes in the design and implementation of various practical vibration measurement method for obtaining the dynamic responses of the ballasted track under either impact hammer or train induced vibration.
- Nonlinear ballast modelling, rail-sleeper-ballast system, Bayesian approach