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ScienceDirect IFAC-PapersOnLine 49-3 (2016) 073–077 Approach for Rail Failures in Probabilistic Defect-Based Risk Assessment Probabilistic Defect-Based Risk Assessment Approach for Rail Failures in Probabilistic Risk Assessment Approach for Rail Failures in Infrastructure Probabilistic Defect-Based Defect-BasedRailway Risk Assessment Approach for Rail Failures in Railway Infrastructure Railway Infrastructure Railway Infrastructure Ali Jamshidi*. Shahrzad Faghih Roohi**, Alfredo Núñez*, Robert Babuska**,
Ali Jamshidi*. Shahrzad Roohi**, Núñez*, Robert Babuska**, Bart DeFaghih Schutter**, Rolf Alfredo Dollevoet*, Zili Li* Ali Jamshidi*. Shahrzad Shahrzad Faghih Roohi**, Alfredo Núñez*, Robert Babuska**, Ali Roohi**, Núñez*, Robert Bart DeFaghih Schutter**, Rolf Alfredo Dollevoet*, Zili Li* Ali Jamshidi*. Jamshidi*. Shahrzad Faghih Roohi**, Alfredo Núñez*, Robert Babuska**, Babuska**, Bart De Schutter**, Rolf Dollevoet*, Zili Li* Bart De Schutter**, Rolf Zili * Section of Railway Engineering, Delft of Technology, Stevinweg 1, 2628CN Delft, The Netherlands Bart DeUniversity Schutter**, Rolf Dollevoet*, Dollevoet*, Zili Li* Li* *(email:
[email protected]; of Railway Engineering, Delft University of Technology, Stevinweg 1, 2628CN Delft,
[email protected]) The Netherlands
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[email protected]; **(email: Section of Railway Engineering, Delft University of Technology, Stevinweg 1, 2628CN Delft, The Netherlands Section of Railway Engineering, Delft University of Technology, Stevinweg 1, 2628CN Delft, TheThe Netherlands
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[email protected]) * Section of Railway Engineering, Delft University of Technology, Stevinweg 1, 2628CN Delft, The Netherlands ** Delft Center for Systems and Control, Delft University of Technology Mekelweg 2, 2628CD Delft, Netherlands (email:
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[email protected]) ** Delft Center for Systems and Control, Delft University of Technology Mekelweg 2, 2628CD Delft, The Netherlands (email:
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[email protected]) ** Delft Center for Systems and Control, Delft University of Technology Mekelweg 2, 2628CD Delft, The Netherlands ** Delft Center for Systems and Control, Delft University of Technology Mekelweg 2, 2628CD Delft, The (email:
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[email protected]) ** Delft Center for Systems and Control, Delft University of Technology Mekelweg 2, 2628CD Delft, The Netherlands Netherlands (email:
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[email protected]) Abstract: This paper develops a defect-based risk analysis methodology for estimating rail failure risk. Abstract: This paper develops a defect-based risk analysisthe methodology forofestimating raildefect, failurecalled risk. The methodology relies on an evolution modelrisk addressing severity level rail surface Abstract: This paper develops aa defect-based analysis methodology for estimating rail failure risk. Abstract: This paper develops defect-based risk analysis methodology for estimating rail failure risk. The methodology relies on an evolution model addressing the severity level of rail surface defect, called Abstract: develops aisdefect-based analysissquat methodology forofestimating failurecalled risk. squat. TheThis riskpaper ofrelies rail failure assessed by risk analyzing failure level probability usingrail a probabilistic The methodology on an evolution model addressing the severity rail surface The methodology on an evolution model addressing the severity level of rail surface defect, called squat. The risk ofrelies railcracks. failure is assessed by analyzing squat failuremethod probability using a defect, probabilistic The methodology relies on an evolution model addressing the severity level of rail surface defect, called analysis of the squat For this purpose, a Bayesian inference is employed to capture a squat. of rail failure is assessed by analyzing squat failure probability using aa probabilistic squat. The risk of rail failure is assessed by analyzing squat failure probability using probabilistic analysisThe of risk theofsquat cracks. For this purpose, athe Bayesian inference method is employed to capture a squat. The risk of rail failure is assessed by analyzing squat failure probability using a probabilistic robust model squat failure probability when squat becomes severe. Moreover, an experimental analysis of the cracks. For this athe Bayesian inference method is to a analysis of between theofsquat squat cracks. For this purpose, purpose, Bayesian inference method is employed employed to capture capture robust model squat failure probability when squat becomes severe. Moreover, an experimental analysis of the squat cracks. For this purpose, Bayesian inference method is employed to capture correlation squat visual length andwhen squataathe crack depth is obtained in order to define four severityaa robust model of squat failure probability squat becomes severe. Moreover, an experimental robust model of squat squat failure probability when the squat becomes severe. Moreover, an risk experimental correlation between squat visual length andwhen squat crack depth is obtained in of order to define fourofseverity robust model of probability the squat becomes severe. Moreover, an experimental categories. Relying on failure thevisual failure probability and the severity categories the to squats, future correlation between squat length and squat crack depth is obtained in order define four correlation between squat visual length and squat crack depth is obtained in order to define four severity categories. Relying on the failure probability and the severity categories of the squats, risk ofseverity future correlation between squat visual length and squat crack depth is obtained in order to define four severity failure is categorized inthethree different scenarios (optimistic, average andofpessimistic). To show the categories. Relying on failure probability and the severity categories the squats, risk of future categories. Relying on the failure probability and the severity categories of the squats, risk of future failure is categorized in three different scenarios (optimistic, average and pessimistic). To show the categories. Relying oninthethree probability and (optimistic, the severity categories ofpessimistic). the squats, risk of future practicality and efficiency offailure thedifferent proposed methodology, a real example isand illustrated. failure is categorized scenarios average To show the failure is categorized in three different scenarios (optimistic, average and pessimistic). To show the practicality and efficiency of the proposed methodology, a real example is illustrated. failure is categorized in three different scenarios (optimistic, averageisand pessimistic). To show the practicality and efficiency the proposed methodology, aa real example illustrated. Keywords: Squat, Railwayoftrack, Bayesian inference, Failure risk, Severity analysis © 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. practicality efficiency the example is practicality and efficiency oftrack, the proposed proposed methodology, a real real example is illustrated. illustrated. Keywords: and Squat, Railwayof Bayesianmethodology, inference, Failure risk, Severity analysis Keywords: Squat, Railway track, Bayesian inference, Failure risk, Severity analysis Keywords: Keywords: Squat, Squat, Railway Railway track, track, Bayesian Bayesian inference, inference, Failure Failure risk, risk, Severity Severity analysis analysis squat could pose a safety threat due to potential derailment 1. INTRODUCTION squat could pose a safety threat due to potential derailment (Prescott et al., 2013). 1. INTRODUCTION squat could pose aa safety threat due to potential derailment squat could pose (Prescott et al., 2013). 1. INTRODUCTION squat could pose a safety safety threat threat due due to to potential potential derailment derailment In the recent years, railways has been promoted in the whole 1. INTRODUCTION (Prescott et al., 2013). 1. INTRODUCTION In this paper, risk of rail failure is assessed relying on a (Prescott et al., 2013). In the recent years, railways has been promoted in the whole (Prescott et al., 2013). world as a means of reducing traffic congestion and In this paper, risk of rail failure is assessed relying on a In the recent years, railways has road been promoted in the whole probabilistic approach usingfailure a Bayesian inference method. In the years, been in whole world as levels. a means of reducing traffic congestion and In this paper, risk is relying on In the recent recent years, railways has been promoted in the thewithout whole emission In railways order to has keeproad the promoted trains running In this paper,approach risk of of rail rail failure is assessed assessed relying on aaa probabilistic using a Bayesian inference method. world as a means of reducing road traffic congestion and In this paper, risk of rail failure is assessed relying on The Bayesian approach provides robust inferences together world as a means of reducing road traffic congestion and emission levels. In order to keep the trains running without probabilistic approach using a Bayesian inference method. world as a means of reducing road traffic congestion and disruptions, an efficient maintenance policy based on risk probabilistic approach using Bayesian inference method. The approach provides robust rate inferences together emission levels. In order to keep the trains running without approach using aaofBayesian inference method. with Bayesian a more realistic treatment growth uncertainties. A emission levels. In order to keep running without disruptions, efficient policy based on risk probabilistic The Bayesian approach provides robust inferences together emission levels. Indifferent order maintenance tocomponents keep the the trains trains running without assessment ofan the of the infrastructure The Bayesian approach provides robust inferences together with a more realistic treatment of growth rate uncertainties. A disruptions, an efficient maintenance policy based on risk The Bayesian approach provides robust inferences together few studies have been carried out on the application of disruptions, an efficient maintenance policy based on risk assessment of the different components of the infrastructure with a more realistic treatment of growth rate uncertainties. A disruptions, an efficient maintenance policy based on risk is essential to anticipate problems before they occur. with a more realistic treatment of growth rate uncertainties. A few studies have been carried out on the application of assessment of the components of infrastructure with astudies moremethods realistic treatment ofof growth rate uncertainties. A in safety railway infrastructures. assessment ofanticipate the different different components of the the infrastructure Bayesian is essential to problems before they occur. few have been carried out on the application of assessment of the different components of the infrastructure few studies have been carried out on the application of Bayesian methods in safety of railway infrastructures. is essential to anticipate problems before they occur. few studies have been carried out on the application of Andrade et al. (2015) employ Hierarchical Bayesian models Among all railway infrastructures, the track plays an is essential essential to to anticipate anticipate problems problems before before they they occur. occur. Bayesian methods safetyHierarchical of railway infrastructures. is Bayesian methods in of railway infrastructures. Andrade al.evolution (2015)in Bayesian models Among allrole railway infrastructures, the system. track plays an to Bayesian methods inemploy safety of quality railwayindicators infrastructures. predictet the ofsafety the main related important in the entire railway In the Andrade et al. (2015) employ Hierarchical Bayesian models Among all railway infrastructures, the track plays an Andrade et al. (2015) employ Hierarchical Bayesian models to predict the evolution of the main quality indicators related Among all railway infrastructures, the track plays an important role in the entire railway system. In the Andrade et al. (2015) employ Hierarchical Bayesian models Among all railway infrastructures, the track plays an to railway track geometry degradation including the standard Netherlands almost half of the maintenance budget is to predict the evolution of the main quality indicators related important role in the entire railway system. In the predict the evolution of the main quality indicators related to railway track geometry degradation including the standard important role in the entire railway system. In the Netherlands almost half of the maintenance budget is to predict the evolution of the main quality indicators related important in maintenance the entire railway system. In The the deviation of longitudinal level defects and the standard allocated torole track (Zoeteman, 2014). to railway track geometry degradation including the standard Netherlands almost half of the maintenance budget is to railway track geometry degradation including the deviation of longitudinal level defects and the standard Netherlands almost half of the maintenance budget is allocated to track maintenance (Zoeteman, 2014). The to railway track geometry degradation including the standard Netherlands almost half of the maintenance budget is deviation of horizontal alignment defects. The goal is to use purpose of to the track budgetmaintenance is to keep the(Zoeteman, track at a high reliability deviation of longitudinal level defects and the standard allocated 2014). The ofhorizontal longitudinal level defects and goal the standard deviation of defects. The is to use allocated to track maintenance (Zoeteman, 2014). The purpose of to the track budget is to keep the(Zoeteman, track at a high reliability of longitudinal defects and the standard allocated 2014). the modelled indicatorsalignment in level planning of track maintenance level. Moreover, a maintenance robust track maintenance plan The can deviation deviation of horizontal alignment defects. The goal is to use purpose of the budget is to keep the track at a high reliability deviation of horizontal alignment defects. The goal is to the modelled indicators in planning of track maintenance purpose of the budget is to keep the track at a high reliability level. Moreover, a robust track maintenance plan can deviation of horizontal alignment defects. The goal is to use use purpose of the budget is to keep the track at a high reliability operations. Anindicators investigation on railway ballastmaintenance failures is facilitate infrastructure management by capturing plan a setcan of the modelled in planning of track level. Moreover, a robust track maintenance the modelled indicators in planning of track maintenance operations. An investigation on railway ballast failures is level. Moreover, a robust track maintenance plan can facilitate infrastructure management by capturing a set of the modelled indicators in planning of track maintenance level. Moreover, a robust track maintenance plan can done by Lam et al. (2014) using Bayesian inference to realistic infrastructure cases of component degradation. Then, the operations. An investigation on railway ballast failures is facilitate management by capturing a set of operations. An investigation on railway ballast failures is done by Lam et al. (2014) using Bayesian inference to facilitate infrastructure management by capturing a set of realistic cases of component degradation. Then, the An et investigation on ballastinference failures is facilitate infrastructure management by capturing a set of operations. analyse uncertainty induced byrailway measurement errors of infrastructure manager would bedegradation. able to define which done by Lam al. (2014) using Bayesian to realistic cases of component Then, the done by Lam et al. (2014) using Bayesian inference to analyse uncertainty induced by measurement errors of realistic cases of component degradation. Then, the infrastructure manager would be able to define which done by Lam et al. (2014) using Bayesian inference to realistic cases of component degradation. Then, the vibrations in the ballast failure zones. Two integrated scenarios are the most relevant to consider and how to uncertainty induced by measurement errors of infrastructure manager beto able to define which analyse uncertainty induced by errors vibrations inforthetrack ballast failure zones. Twomaintenance integrated infrastructure manager would able to which scenarios themaintenance most would relevant consider and horizon. how to analyse analyse uncertainty induced by measurement measurement errors of of infrastructure manager would bemaintenance able to define define which frameworks degradation and rail manage theare track in abe time vibrations in the ballast failure zones. Two integrated scenarios are the most relevant to consider and how to vibrations in the ballast failure zones. Two integrated frameworks for track degradation and rail maintenance scenarios the most relevant to consider and how to manage theare track maintenance in a maintenance time horizon. vibrations in the ballast failure zones. Two integrated scenarios are the most relevant to consider and how to decisions are proposed relying on Bayesian networks in As a high percentage of the railway system failures occur in for track degradation and maintenance manage the track in aa maintenance time horizon. frameworks for track Mahboob, degradation and rail rail maintenance decisions are proposed relying on2014). Bayesian networks in manage thepercentage track maintenance maintenance inrisk maintenance time occur horizon. As atracks, high of failure the railway systembyfailures in frameworks frameworks for track degradation and rail maintenance manage the track maintenance in a maintenance time horizon. (Bouillaut el al. 2008; A nonparametric the analysing the caused surface defects decisions are proposed relying on Bayesian networks in As aatracks, high percentage of the railway system failures occur in decisions are proposed relying on Bayesian networks in (Bouillaut el al. 2008; Mahboob, 2014). A nonparametric As high percentage of the railway system failures occur in the analysing the failure risk caused by surface defects decisions are proposed relying on Bayesian networks in As a high percentage of the railway system failures occur in Bayesian approach with Mahboob, a Dirichlet2014). ProcessAMixture Model is crucial for the track maintenance planby(Burstow et al., (Bouillaut el al. 2008; nonparametric the tracks, analysing the failure risk caused surface defects (Bouillaut el al. 2008; Mahboob, 2014). A nonparametric Bayesian approach with a Dirichlet Process Mixture Model the tracks, analysing the failure risk caused by surface defects is crucial for the track maintenance plan (Burstow et al., (Bouillaut el al. 2008; Mahboob, 2014). A nonparametric the tracks, analysing the failure risk caused by surface defects is used to approach facilitate reliability analysisProcess in a railway system by 2002; Zhaoforetthe al.,track 2006;maintenance Liu et al., plan 2001;(Burstow Hassankiadeh, Bayesian with a Dirichlet Mixture Model is crucial et al., Bayesian with Dirichlet Process Mixture Model used to approach facilitate reliability analysis inconsequences a railway system by is crucial maintenance plan (Burstow et al., 2002; Zhao etthe al., 2006; Liuisetto al., 2001;the Hassankiadeh, Bayesian approach with aaTrain Dirichlet Process Mixture Model is crucial foridea the track maintenance plan (Burstow et one al., is Mokhtarian et al. (2013). accident can be 2011). Thefor oftrack this paper analyse effect of is used to facilitate reliability analysis in a railway system by 2002; Zhao et al., 2006; Liu et al., 2001; Hassankiadeh, is used to facilitate reliability analysis in a railway system by Mokhtarian et al. (2013). Train accident consequences can be 2002; Zhao et al., 2006; Liu et al., 2001; Hassankiadeh, 2011). The idea of this paper is to analyse the effect of one is used to facilitate reliability analysis in a railway system by 2002; Zhao et al., 2006; Liu et al., 2001; Hassankiadeh, modelled by Bayesian networks where human errors and common defect in railway networks called squat. To assess a Mokhtarian et al. (2013). Train accident consequences can be 2011). The idea of this paper is to analyse the effect of one Mokhtarian et al. (2013). Train accident consequences can be modelled by Bayesian networks where human errors and 2011). The idea of this paper is to analyse the effect of one common defect in railway networks called squat. To assess a et Bayesian al. (2013). Train accident consequences be 2011). The idea ofrailway this paper isfactors to analyse thebeeffect of into onea Mokhtarian track degradation are addressed (Bearfield et errors al., can 2005, defect-based risk, two major must taken modelled by networks where human and common defect in networks called squat. To assess modelled by Bayesian networks where human errors and track degradation are addressed (Bearfield et al., 2005, common defect in railway networks called squat. To assess a defect-based risk, two major factors must be taken into modelled by Bayesian networks where human errors and common defect in railway networks called squat. To assess a Marsh, 2004; Castillo at al., 2015). This paper is organized account. First, the track stochastic variables such as the track degradation are (Bearfield etis al., 2005, defect-based risk, major factorsvariables must besuch taken into track degradation are addressed (Bearfield al., 2005, 2004; ataddressed 2015). This paper organized defect-based two major must taken into account. First, the two track stochastic the track degradation are2, addressed (Bearfield etthe al., 2005, defect-based risk, two major factors must be be takenas into as follows. In Castillo Section aal., short background onet squats is growth rate ofrisk, defects where thefactors rail structure deteriorates as Marsh, Marsh, 2004; Castillo at al., 2015). This paper is organized account. First, the track stochastic variables such as the Marsh, 2004; Castillo at al., 2015). This paper is organized as follows. In Section 2, a short background on the squats is account. First, the track stochastic variables such as the growth rate of defects where the rail structure deteriorates as Marsh, 2004; Castillo at al., 2015). This paper is organized account. First, the track stochastic variables such as the presented. Section 3 addresses the Bayesian model of rail the traffic passes along the rails. Second, the spatial as follows. In Section 2, a short background on the squats is growth rate of defects where the rail structure deteriorates as as follows. In Section 2, a short background on the squats is presented. Section 3 addresses the Bayesian model of rail growth rate of defects where the rail structure deteriorates as the traffic passes along the rails. Second, the spatial as follows. In Section 2, a short background on the squats is growth rate of defects where the rail structure deteriorates as failure. Section 4 presents the riskthe assessment model together characteristics of the along track since the track characteristics vary presented. Section 3 addresses Bayesian model of rail the traffic passes the rails. Second, the spatial presented. Section 3 addresses the Bayesian model of rail failure. Section 4 presents the risk assessment model together the traffic passes along the rails. Second, the spatial characteristics of the track since the track characteristics vary presented. Section 3 addresses the Bayesian model of rail the traffic passes along the rails. Second, the spatial with a real-life Finally, in Section model 4, conclusions in space. The idea is to capture the evolution rate of the squat failure. Section 4example. presents the risk assessment together characteristics of the track since the track characteristics vary failure. Section presents risk together a real-life Finally, in Section model 4, conclusions characteristics of the track since the track characteristics vary in space. idea is to capture the rate ofwhere the squat failure. Section 44example. presents the the risk assessment assessment model together characteristics of can the track since theevolution track characteristics vary are presented. when the The growth affect the track reliability and the with with a real-life example. Finally, in Section 4, conclusions in space. The idea is to capture the evolution rate of the squat with a real-life example. Finally, in Section 4, conclusions are presented. in space. The idea is to capture the evolution rate of the squat when the growth can affect the track reliability and where the with a real-life example. Finally, in Section 4, conclusions in space. The idea is to capture the evolution rate of the squat track is prone to rail failure. Moreover, in extreme cases, the presented. when the growth can affect the track reliability and where the are when the growth can affect track and track is to rail Moreover, in extreme cases, the are presented. presented. when theprone growth can failure. affect the the track reliability reliability and where where the are track is prone to rail failure. Moreover, in extreme cases, the track track is is prone prone to to rail rail failure. failure. Moreover, Moreover, in in extreme extreme cases, cases, the the
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2. SQUAT IN RAILWAY INFRASTRUCTURES
3. BAYESIAN MODEL FOR RAIL FAILURE
Surface defects can affect track availability. Those rolling contact fatigue (RCF) defects can be classified as rail corrugation, squats, head checks, shatter cracking, vertical splits, head horizontal splits, and wheel burns (Magel , 2001). Appearance of those defects results in the increase of maintenance operations needed, more frequent track monitoring required, and rail failure when not detected in time in the worst case.
Bayesian methods are widely used as a statistic technique to evaluate robustness in stochastic data behaviours in particular, for analysis of hazard rates with a small number of data samples. Potential benefits of the Bayesian approach in comparison with the usual Maximum Likelihood Estimate (MLE) method are computationally explained by Ahn et al. (2007). The MLE is an effective tool to estimate hazard rate as long as a sufficient amount of data is available. Using the MLE, a single point value for the failure rate, which maximizes the likelihood function, can be estimated. However, our prior beliefs about the likely values for the failure rates are not injected into the estimation model with the MLE. In contrast to the MLE, Bayesian inference treats failure rates as random variables. Thus, the difference is that in the Bayesian model, the estimation output is a probability density function rather than a single point as in the MLE.
In this paper, we investigate squats, which are surfaceinitiated defects. The squats are observed in tracks, either ballast tracks or slab tracks, and in all possible traffic volumes (Kaewunruen et al., 2014). Fig 1 shows a reference photo of severe squats with cracks already propagated beneath the rail surface.
In Bayesian inference, prior knowledge and beliefs about unknown parameters are represented by the probability density distribution π 0 ( λ ) , and statistical observations y
have the likelihood f ( y|λ ) where λ is the failure rate. Then, according to Bayes’ theorem, the posterior distribution of rail failure probability is expressed as:
π ( λ|y ) =
f ( y|λ ) π 0 ( λ ) ∝ f ( y|λ ) π 0 ( λ ) f ( y)
(1)
Let us assume that the failure probability is constructed by considering a nonlinear regression model over the crack depth. The data include observations of the crack depth, the number of cracks with the same depth, and the number of cracks with the growth above 4 mm (see Fig 2). The nonlinear regression model shows the likelihood distribution of parameters a (intercept) and b (slope) in the Bayesian inference model:
Fig 1: Example of severe squats on a rail Typically, the squats evolve from indentations into defects with surface cracks growing along the depth beneath the rail surface (Li et al., 2010). Once the squat gets severe in terms of crack depth and visual length, the train ride quality and safety become considerably low (Remennikov and Kaewunruen, 2008). In practice, squats can be detected and analysed using different methods, such as inspection using human inspectors, on-board measurements via photo/video records, axle box acceleration (ABA) measurements, and other non-destructive testing (NDT), such as ultrasonic and eddy current testing. While axle box acceleration (ABA) measurements are efficient in detecting both early stage and severe squats (Molodova et al. 2014; Li et al. 2015), in this paper the focus is the analysis of severe defects in terms of crack lengths. Thus, we rely on ultrasonic and surface photos of the defects.
f ( y | ( a, b)) = exp( −1 / ( a + b ⋅ y ))
(2)
where y is the crack depth. When no prior information is available about the values of parameters a and b, we assume uniform prior distributions (Faghih-Roohi et al., 2014):
Ultrasonic (US) testing is currently one of the most extensively employed automatic inspection technique for squats. This method can only be used to reliably detect cracks with depths higher than 4 mm, depending on the instruments. When a rail includes squats with cracks larger than 4 mm, the evolution of the defects generates a potential risk of the rail failure. This paper employs US measurements to model crack growth of squat. In the next two sections, the rail failure probability model is presented.
π 0 (a) = Uniform ( A1 , A2 )
(3)
π 0 (b) = Uniform ( B1 , B2 )
(4)
By Bayes' theorem, the joint posterior distribution of the model parameters is proportional to the product of the likelihood and the priors. Monte Carlo methods are often used in Bayesian data analysis to describe the posterior distribution. The objective is to generate random samples 74
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from the posterior distribution and use them when it is not possible to compute analytically the posterior distribution. For this purpose, a slice sampling algorithm is chosen to obtain N samples of the distribution with an arbitrary density function (Neal, 2003). The slice sampling algorithm is a type of a Markov Chain Monte Carlo (MCMC) algorithm. Among all the MCMC methods such as Gibbs sampling, and the Metropolis–Hastings algorithm, slice sampling is easier to implement as only the posterior needs to be specified (Gilks, 1996).
sample means. This produces a smoother plot than the raw sample traces, and can make it easier to identify and understand any non-stationarity. The first fifty values of Fig. 3 are not comparable to the rest of the figure. However, the rest of each plot shows that the parameter posterior means have converged to stationarity.
Mean of the intercept, a
1.5
4. FAILURE RISK ASSESSMENT 4.1 Rail Failure Probability
Growth, mm
Mean of the slope, b
3 3 3 0
2
4
6
8
300
400 500 600 Number of samples
700
800
900
1000
0.6 0.4 0.2 100
200
300
400 500 600 Number of samples
700
800
900
1000
The probability failure regression models resulted from N samples of MCMC simulation are depicted in Fig. 5, where N is equal to 1000. The idea of Fig. 5 is to show how squat will be prone for rail break in the future. In this figure, the nonlinear regression models of s1, s2, s3 are used to reflect the optimistic failure scenario, the average scenario and the pessimistic scenario, respectively. Thus, relying on the figure, for each available crack depth, the probability of the squat to develop into a rail break is estimated within a time horizon, sufficient to guarantee a timely maintenance. For example, the squats with crack depth 7 mm induces rail to be broken if we do not maintenance operations in a long time horizon, with probabilities increasing according the scenario: 0.8554 for s1, 0.8668 for s2 and 0.9068 for s3. Point estimates and Bayesian confidence intervals, representing uncertainty about parameters after data analysis are presented in Table 1.
2
-2
200
Fig 4: Posterior distributions of regression parameter b
3
-1
100
0.8
0 0
4
4
0
1
5
5
0.5
Fig 3: Posterior distributions of regression parameter a
6
0
1
0
In this section, the risk model is presented. First, failure probability is calculated by considering squats with over 4 mm in crack depth measured by US. The probability of failure indicate how likely is a squat to develop into a rail break in the future. To evaluate the failure probability, we consider squats with crack depths ranging from 1 mm to 9 mm. By measuring the depths every one year, we see how many cracks have reached depth of 4 mm or even more, and how the cracks growth over time. Then, we enumerate the squats with the same growth and crack depth, to capture the typical behaviour of squats in the particular track. Fig. 2 shows the occurrence of cracks of more than 4 mm over a track segment of around 2.35 kilometres during a period of 4 years. The Mega Gross Tone (MGT) is equal to 3.719 per year in this track. The data collected in the Fig. 2 is used to estimate the Bayesian parameters, a and b, in order to capture the failure rate. The idea is to use crack depths for several different squats over time to calculate growth with regards to number of the squats with same growth in depth.
1
75
10
Crack depth, mm
Fig 2: The cracks length over 4 mm versus crack growth. Numbers indicate the occurrence of the data point.
Table 1: Bayesian point and interval estimates 95 % confidence Scenario Parameter Mean interval a1 0.8001 s1 b1 0.8000 [0.9860,1.0089] a2 1.0009 s2 b2 0.8624 [0.8589, 0.8667] a3 1.9592 s3 b3 1.1346
The posterior distribution of the regression parameters (a, b) is calculated based on the MCMC simulation generated in one thousand samples. Fig. 3 and Fig. 4 show how the parameters (a, b) vary over the samples. The posterior distributions show updated state of the mean value and the level of the uncertainty of the model parameters. As seen in the figures, the purpose is to check for convergence using 75
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1
4.3 Rail failure risk
0.9
Relying on the failure probability scenarios and the severity categories, the risk can be defined as:
Probability of failure
0.8 0.7
s3
0.6
s2
0.5
Rsz
s1
= wz
lzi+1
∫
Ps (l )dl
(5)
lzi
0.4 0.3 0.2 0
1
2
3
4 5 Crack depth, mm
6
7
8
where Rsz is the rail failure probability for scenario s and Category z, wz is the severity weight of Category z and lzi , lzi+1 is the interval of crack depths that defines Category
9
Fig 5: Bayesian estimates for rail failure probability after a time horizon sufficiently long to guarantee a timely maintenance.
z. The idea is to use the failure probability of the crack depth l, Ps(l), for each category of severity, z, by considering the severity weight wz.Table 2 shows the resulting risk values of each scenario at different categories. To illustrate, as expected, the risk of failure in scenario s3 for Category 1 is the highest where the crack are most severe both in the length and the depth while the risk for scenario s1 in the Category 4 contains the lowest value.
4.2 Squat Severity Analysis As the visual lengths of squats follow a specific growth model classifying the squats according to its severity, in this section, a relation on how the visual lengths and the crack lengths are linked to each other is investigated. The idea is to classify the severity of the squat when it is getting worse in terms of both, the visual length and the crack length. For this purpose, the visual length and the crack depth of 36 squats were registered every six months over 2 years (see Fig. 5).
Table 2. Failure risk results Risk Scenario s1 s2 s3
As depicted in Fig. 6, the squat growth space is divided into four categories representing the squat severity. The reason behind specifying the category boundaries is that the squats with visual length above 20 mm will potentially reappear after a grinding operation. Thus, Category 1 shows the most severe growth of squats where the crack length and visual length both are sufficiently high to require maintenance as soon as possible. Contrary to the Category 1, Category 4 is a safe category reflecting all the squats which are located in the early stage of growth. There are a few squats observed in categories 2 and 3. Even though the squats situated in Category 2 are in early stage of growth in terms of visual length, the crack depth are considerably high. In Category 3 the visual length is high whereas the crack depth is below 4 mm.
Crack depth, mm
Category 1
Category 4
Category 3
6 5 4 0
5
10
15 20 25 Visual length, mm
30
35
Category 3 0.1621 0.1654 0.1753
Category 4 0.0811 0.0827 0.0876
5. CONCLUSIONS
8
Category 2
Category 2 0.5172 0.5241 0.5449
The failure risk values can be used as risk Key Performance Indicators (KPIs) to address health condition of the rail, so to keep informed infrastructure manager of the status of track. In combination with other KPIs as defined in Jamshidi et al. (2015), the risk values can be employed to support a condition-based maintenance plan.
9
7
Category 1 0.7758 0.7862 0.8173
40
Fig 6: Experimental categories of squat based on crack depths and the visual lengths 76
In this paper, a probabilistic approach is used to model rail failure considering the squat growth. A Bayesian method was employed to make robust failure estimation, including optimistic, average and pessimistic scenarios. Furthermore, uncertainties of the method are also obtained and used to calculate Bayesian confidence intervals per failure scenario. Then, according to where the squat is in the severity categories, the rail failure risk is obtained per failure scenario. In future studies, we will develop the methodology to analytically predict the rail failure over a time horizon using risk key performance indicators relying on different measurement sources. Parameters like mechanical strength values, material properties and geometrical values of the rail such as area of cross section, can give further details about the way the crack will evolve over time. The evaluation on how those parameters influence the risk assessment is part of the further research.
IFAC CTS 2016 May 18-20, 2016. Istanbul, Turkey
Ali Jamshidi et al. / IFAC-PapersOnLine 49-3 (2016) 073–077
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Lam, H. F., Hu, Q., and Wong, M. T. (2014). The Bayesian methodology for the detection of railway ballast damage under a concrete sleeper. Journal of Engineering Structures, 81:289-301. Doi: 10.1016/j.engstruct.2014.08.035. Li, Z., Molodova, M., Núñez, A., and Dollevoet, R., (2015), Improvements in axle box acceleration measurements for the detection of light squats in railway infrastructure. IEEE Transactions on Industrial Electronics 62(7): 4385-4397. Doi:10.1109/TIE.2015.2389761 Li, Z., Zhao, X., Molodova, M., Dollevoet, R. P. B., (2010). Squat treatment by way of minimum action based on early detection to reduce life cycle costs. Proceedings of the Joint Rail Conference JRC, Urbana, Illinois, 27-29 April. Liu, X., Barkan, C., and Saat, M. (2011). Analysis of derailments by accident cause: evaluating railroad track upgrades to reduce transportation risk. Transportation Research Record: Journal of the Transportation Research Board (2261),178-185. Magel, E. E. (2001). Rolling Contact Fatigue: A Comprehensive Review, Report, DOT/FRA/ORD-11/24, Federal Railroad Administration. Mahboob, Q. (2014). A Bayesian Network methodology for railway risk, safety and decision support, Doctoral dissertation, TU Dresden. Marsh, W., and Bearfield, G. (2004). Using Bayesian networks to model accident causation in the UK railway industry. Probabilistic Safety Assessment and Management, 3597-3602. Doi: 10.1007/978-0-85729410-4_575. Mokhtarian, P., Namzi-Rad, M. R., Ho, T. K., and Suesse, T. (2013). Bayesian nonparametric reliability analysis for a railway system at component level. IEEE International Conference on Intelligent Rail Transportation (ICIRT), 197 – 202, Beijing, 30 August1 September. doi: 10.1109/ICIRT.2013.6696293. Molodova, M., Li, Z., Núñez, A., and Dollevoet, R. P. B. (2014) Automatic detection of squats in the railway infrastructures. IEEE Transactions on Intelligent Transportation Systems 15(5):1980-1990. Doi: 10.1109/TITS.2014.2307955 Neal, R. M. (2003). Slice sampling. Annals of Statistics, 31 (3), 705-741. Prescott, D., and Andrews, J. (2013). Modelling maintenance in railway infrastructure management. In Reliability and Maintainability Symposium (RAMS), Orlando, FL. Zhao, J., Chan, A. H., and Stirling, A. B. (2006). Risk analysis of derailment induced by rail failures-a probabilistic approach. In Reliability and Maintainability Symposium, 2006. RAMS'06 Annual, 486-491. 23-26 January, Newport Beach, CA. Doi: 10.1109/RAMS.2006.1677421 Zoeteman, A., Dollevoet, R. P. B., and Li, Z. (2014). Dutch research results on wheel/rail interface management: 2001-2013 and beyond. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 228(6), 642-651. Doi: 10.1177/0954409714524379.
ACKNOWLEDGEMENTS This research is supported by ProRail and MAGW, and by the Dutch Technology Foundation STW, which is part of the Netherlands Organization for Scientific Research (NWO), and which is partly funded by the Ministry of Economic Affairs. REFERENCES Ahn, S., Park, C., and Kim, H. (2007). Hazard rate estimation of a mixture model with censored lifetimes. Stochastic Environmental Research and Risk Assessment, 21(6), 711–716. Doi: 10.1007/s00477-006-0082. Andrade, A. R., and Teixeira, P. F. (2015). Statistical modelling of railway track geometry degradation using hierarchical Bayesian models. Journal of Reliability Engineering & System Safety, 142, 169-183. Doi: 10.1016/j.ress.2015.05.009. Bearfield, G., and Marsh, W. (2005). Generalising event trees using Bayesian networks with a case study of train derailment. The 35th International Conference on Computer Safety, Reliability, and Security, (3688), 5266. Trondheim, Norway, 20-23 September. Doi: 10.1007/11563228. Bouillaut, L., François, O., Leray, P., Aknin, P., and Dubois, S. (2008). Dynamic Bayesian networks modelling maintenance strategies: Prevention of broken rails. 8th World Congress on Railway Research, Seul, South Korea. 18-22 May 2008. Burstow, M. C., Watson, A. S., and Beagles, M. (2002). Application of the whole life rail model to control rolling contact fatigue. Proceedings of the International Conference Railway Engineering, London, UK, July 2002. Castillo, E., Calviño, A., Grande, Z., Sánchez‐Cambronero, S., Gallego, I., Rivas, A., and Menéndez, J. M. (2015). A Markovian–Bayesian Network for Risk Analysis of High Speed and Conventional Railway Lines Integrating Human Errors. Journal of Computer‐Aided Civil and Infrastructure Engineering, 1467-8667. Doi: 10.1111/mice.12153. Faghih-Roohi, S., Xie, M., and Ng, K. M. (2014). Accident risk assessment in marine transportation via Markov modelling and Markov Chain Monte Carlo simulation. Ocean Engineering, 91, 363-370. Doi: 10.1016/j.oceaneng.2014.09.029. Gilks, W., Richardson S., and Spiegelhalter, D. (1996). Markov Chain Monte Carlo in Practice, Chapman & Hall, London. Hassankiadeh, S. J., (2011). Failure Analysis of Railway Switches and Crossings for the purpose of Preventive Maintenance, M.Sc thesis. KTH Stockholm Sweden. Jamshidi, A. Núñez, A. Li, Z., and Dollevoet, R. P. B. (2015). Maintenance decision indicators for treating squats in railway infrastructures. Proceedings of the 94th Annual Meeting of the Transportation Research Board, Washington, USA, January 11-15 2015. Kaewunruen, S., and Ishida, M. (2014). Field monitoring of rail squats using 3D ultrasonic mapping technique, Journal of the Canadian Institute for Non-Destructive Evaluation. 35(6), 5-11. 77
