Inverse Gaussian process-based corrosion growth modeling and its application in the reliability analysis for energy pipelines

This paper describes an inverse Gaussian process-based model to characterize the growth of metal-loss corrosion defects on energy pipelines. The model parameters are evaluated using the Bayesian methodology by combining the inspection data obtained from multiple inspections with the prior distributions. The Markov Chain Monte Carlo (MCMC) simulation techniques are employed to numerically evaluate the posterior marginal distribution of each individual parameter. The measurement errors associated with the ILI tools are considered in the Bayesian inference. The application of the growth model is illustrated using an example involving real inspection data collected from an in-service pipeline in Alberta, Canada. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. Parametric analyses associated with the growth model as well as reliability assessment of the pipeline based on the growth model are also included in the example. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.     

Probabilistic characterisation of metal-loss corrosion growth on underground pipelines based on geometric Brownian motion process

This article describes a geometric Brownian motion process-based model to characterise the growth rate of the depth of corrosion defects on underground steel pipelines based on inspection data subjected to measurement uncertainties. To account for the uncertainties from different sources, the hierarchical Bayesian method is used to formulate the growth model, and the Markov Chain Monte Carlo simulation techniques are used to numerically evaluate the probabilistic characteristics of the model parameters. The growth model considers the bias and random scattering error associated with the in-line inspection (ILI) tool as well as the correlations between the random scattering errors associated with different ILI tools. The application of the growth model is illustrated through an example involving real ILI data collected from an in-service pipeline in Canada. The results indicate that the model in general can predict the growth of corrosion defects reasonably well. The proposed model can be used to facilitate the development and application of reliability-based pipeline corrosion management.     

Reliability-based temporal and spatial maintenance strategy for integrity management of corroded underground pipelines

In this work, a novel stochastic model framework for predicting the external corrosion growth in buried pipeline structures has been developed, and a reliability-based temporal and spatial maintenance strategy is presented. The spatial correlation of soil properties is modelled via hidden Markov random field. The temporal correlation of the corrosion rate is characterised by the geometric Brownian bridge process. A Bayesian inferential framework is employed to estimate the model parameters of the corrosion growth model using in-line inspection data. The proposed corrosion growth model was validated with actual inspection data. In the reliability analysis, the impact of device detectability is considered and hence the estimated failure probability is more realistic. The proposed maintenance strategy is directly based on the time-specific and location-specific failure probability. The application of the proposed model and maintenance strategy is illustrated through a real-life pipeline system. The results indicate that the proposed maintenance strategy is an adaptive and dynamic scheme that is able to improve the efficiency of inspections.     

Structural failure assessment of buried steel water pipes subject to corrosive environment

It is essential to predict the lifetime of buried pipelines since they are not easily accessible for inspection. In this study a time-dependent, non-linear state model has been introduced for the structural analysis of corrosion affected steel water pipes, stressed by external forces. Using limit state concept, the simultaneous effect of externally applied loading and material corrosion are considered through failure modes. A non-linear corrosion model is used to simulate the loss of pipe wall thickness during the operation period. In order to take the uncertainty associated with the design and environmental variables into account, a Monte Carlo simulation technique has been adopted using MATLAB. A parametric sensitivity analysis is also carried out to measure the effectiveness of each parameter on the probability of pipe failure. Results obtained for a steel water pipeline in Eastern Sydney are presented and discussed.     

Life-cycle reliability assessment of reinforced concrete bridges under multiple hazards

This paper proposes a novel probabilistic methodology for estimating the life-cycle reliability of existing reinforced concrete (RC) bridges under multiple hazards. The life-cycle reliability of an RC bridge pier under seismic and airborne chloride hazards is compared to that of a bridge girder under traffic and airborne chloride hazards. When conducting a life-cycle reliability assessment of existing RC bridges, observational data from inspections can provide the corrosion level in reinforcement steel. Random variables related with the prediction of time-variant steel weight loss can be updated based on the inspection results using Sequential Monte Carlo Simulation (SMCS). This paper presents a novel procedure for identifying the hazards that most threaten the structural safety of existing RC bridges, as well as the structural components with the lowest reliability when these bridges are exposed to multiple hazards. The proposed approach, using inspection results associated with steel weight loss, provides a rational reliability assessment framework that allows comparison between the life-cycle reliabilities of bridge components under multiple hazards, helping the prioritisation of maintenance actions. The effect of the number of inspection locations on the updated reliability is considered by incorporating the spatial steel corrosion distribution. An illustrative example is provided of applying the proposed life-cyle reliability assessment to a hypothetical RC bridge under multiple hazards.     

Evaluating the system reliability of corroding pipelines based on inspection data

This paper presents a methodology for evaluating the time-dependent system reliability of a pressurised gas pipeline segment containing multiple active metal-loss corrosion defects. The methodology incorporates three distinctive failure modes of the pipe segment due to corrosion, namely small leak, large leak and rupture. The growth of the depth of individual corrosion defect is assumed to follow a power-law function of time. The Bayesian updating and Markov Chain Monte Carlo (MCMC) simulation techniques are used to quantify the parameters of the power-law growth model based on data obtained from multiple inspections carried out at different times. The simple Monte Carlo and MCMC techniques are combined to evaluate the system reliability. A numerical example involving an in-service gas pipeline located in Alberta, Canada, is used to illustrate the proposed methodology. Results of the sensitivity analysis suggest that the use of a defect-specific or segment-specific growth model for the defect depth has a marked impact on the evaluated system reliability. The proposed methodology can be incorporated in reliability-based pipeline corrosion management programmes to assist integrity engineers in making informed decisions about defect repair and mitigation.     

钢筋坑蚀对混凝土梁抗弯性能的影响

与钢筋均匀锈蚀相比,钢筋坑蚀具有显著的不确定性和截面损失等特点,对混凝土构件的抗弯性能具有一定的影响。结合国内外相关资料,通过实际工程中钢筋坑蚀的试验统计,验证了坑蚀系数服从极值I型的分布。基于钢筋的坑蚀概率模型,借助MonteCarlo模拟,分析了锈蚀钢筋混凝土梁的抗弯承载力,研究了钢筋坑蚀对混凝土受弯构件承载能力的影响。结果表明,钢筋坑蚀的随机性对梁的可靠性有很大影响,钢筋坑蚀构件抗弯承载力的下降速度比均匀锈蚀更快,对梁的耐久性具有潜在危害。     

Corrosion initiation time updating by epistemic uncertainty as an alternative to schedule the first inspection time of pre-stressed concrete vehicular bridge beams

As traffic demands grow constantly and some vehicle bridges deteriorate because of corrosion issues, bridge agencies require non-expensive procedures to support decisions about cost-effective maintenance schedules. In this article, a reliability-based formulation is proposed for the prediction of the optimal first inspection time including both the corrosion deterioration and the epistemic uncertainty on the corrosion initiation time. For the identification of the bridge integrity state, where little or no follow-up has been previously developed, the prediction of a damage state implies a great deal of epistemic uncertainty. The impact of this kind of uncertainty on the corrosion initiation time prediction is appraised in order to include the conservative estimations of such a time, according to the bridge revenues/cost ratio of further and more detailed studies. The time-varying bridge reliability is calculated in terms of the bridge corrosion deterioration, which induces a moment capacity reduction of the bridge beams. Epistemic uncertainty is introduced in the corrosion initiation time, and the optimal first inspection time is obtained as a probability distribution. Consequently, a procedure to calculate the first time for inspection on girder bridges has been proposed, based on updating a known distribution after considering the effect of epistemic uncertainty, using a lognormal distributed factor as ‘evidence’, by means of the Markov chain Monte Carlo technique.     

Calculation of Posterior Probabilities for Bayesian Model Class Assessment and Averaging from Posterior Samples Based on Dynamic System Data

Abstract: In recent years, Bayesian model updating techniques based on dynamic data have been applied in system identification and structural health monitoring. Because of modeling uncertainty, a set of competing candidate model classes may be available to represent a system and it is then desirable to assess the plausibility of each model class based on system data. Bayesian model class assessment may then be used, which is based on the posterior probability of the different candidates for representing the system. If more than one model class has significant posterior probability, then Bayesian model class averaging provides a coherent mechanism to incorporate all of these model classes in making probabilistic predictions for the system response. This Bayesian model assessment and averaging requires calculation of the evidence for each model class based on the system data, which requires the evaluation of a multi‐dimensional integral involving the product of the likelihood and prior defined by the model class. In this article, a general method for calculating the evidence is proposed based on using posterior samples from any Markov Chain Monte Carlo algorithm. The effectiveness of the proposed method is illustrated by Bayesian model updating and assessment using simulated earthquake data from a ten‐story nonclassically damped building responding linearly and a four‐story building responding inelastically.     

Improved Bayesian network configurations for probabilistic identification of degradation mechanisms: application to chloride ingress

Probabilistic modelling of deterioration processes is an important task to plan and quantify maintenance operations of structures. Relevant material and environmental model parameters could be determined from inspection data; but in practice, the number of measures required for uncertainty quantification is conditioned by time-consuming and expensive tests. The main objective of this study was to propose a method based on Bayesian networks for improving the identification of uncertainties related to material and environmental parameters of deterioration models when there is limited available information. The outputs of the study are inspection configurations (in space and time) that could provide an optimal balance between accuracy and cost. The proposed methodology was applied to the identification of random variables for a chloride ingress model. It was found that there is an optimal discretisation for identifying each model parameter and that the combination of these configurations minimises identification errors. An illustration to the assessment of the probability of corrosion initiation showed that the approach is useful even if inspection data are limited.     

A sensor-driven structural health prognosis procedure considering sensor performance degradation

This article presents a general framework for sensor-driven structural health prognosis and its application to probabilistic maintenance scheduling. Continuously collected sensor data is used to update the parameters of the stochastic structural degradation model. Uncertainty in sensor data (i.e. measurement error) is explicitly modelled as an evolving stochastic process. The proposed framework utilises Bayesian theorem and Markov Chain Monte Carlo (MCMC) sampling to calculate the posterior distributions of stochastic parameters of the structural degradation model. Bayesian updating allows the use of dynamic diagnostic information with prior knowledge for improved prognosis including risk analysis and remaining useful life (RUL) estimation. Although the proposed sensor-driven structural health prognosis procedure is illustrated with a fatigue-related example, it is applicable to more general applications such as corrosion and pavement cracking. A case study of the fatigue details found in a prototype steelgirder bridge has been conducted to demonstrate the proposed prognosis and maintenance scheduling procedure.     

考虑随机腐蚀作用的埋地管线地震反应分析

利用齐次马尔可夫过程模拟埋地管线腐蚀的发生,并利用线性腐蚀模型模拟埋地管线腐蚀的发展,将线性腐蚀模型中腐蚀速率考虑为确定性参数,推导给出了管线面积腐蚀率随服役时间变化的概率密度函数,并获得了管线截面面积随服役时间变化的均值和方差。在此基础上,根据弹性地基梁模型,将管线周围土体位移正交展开为余弦级数的形式,获得了地震作用下腐蚀管线位移反应和应力反应的解析表达式。对腐蚀管线地震反应进行线性展开,采用随机摄动理论推导给出了腐蚀管线在地震激励下位移和应力反应的均值和标准差。利用上述分析模型对一根200 m长的埋地管线进行了实例分析,结果表明建议模型可以反映管线面积随服役时间的变化规律,并能反映腐蚀管线在地震作用下位移反应和应力反应的基本概率特征。     

Prediction of Onset of Corrosion in Concrete Bridge Decks Using Neural Networks and Case-Based Reasoning

Abstract:   This article proposes a methodology for predicting the time to onset of corrosion of reinforcing steel in concrete bridge decks while incorporating parameter uncertainty. It is based on the integration of artificial neural network (ANN), case-based reasoning (CBR), mechanistic model, and Monte Carlo simulation (MCS). A probabilistic mechanistic model is used to generate the distribution of the time to corrosion initiation based on statistical models of the governing parameters obtained from field data. The proposed ANN and CBR models act as universal functional mapping tools to approximate the relationship between the input and output of the mechanistic model. These tools are integrated with the MCS technique to generate the distribution of the corrosion initiation time using the distributions of the governing parameters. The proposed methodology is applied to predict the time to corrosion initiation of the top reinforcing steel in the concrete deck of the Dickson Bridge in Montreal. This study demonstrates the feasibility, adequate reliability, and computational efficiency of the proposed integrated ANN-MCS and CBR-MCS approaches for preliminary project-level and also network-level analyses.     

Probabilistic assessment to predict the time to corrosion of steel in reinforced concrete tunnel box exposed to sea water

This study concerned the service life prediction, in terms of chloride-induced steel corrosion, of a concrete tunnel-box structure placed on seabed. To calculate the time to steel corrosion, the rate of chloride transport in the identical concrete mix to the structure was tested, and the chloride threshold level for corrosion was assumed by a literature review from 65 published data. Then, the Monte Carlo Simulation was used to calculate the probability of steel corrosion and its corresponding service life, assuming that the corrosion initiates at 10% of the probability of corrosion. As a result, the service life depended on the time dependency of chloride transport. The service life was equated to 31, 51, 85, and 147 years, at 0.1, 0.2, 0.3 and 0.4 of the age factors, respectively, while the time independent model indicated only 27 years of the service life. Finally, methods to raise the service life were discussed.     

Probabilistic Neural Network for Reliability Assessment of Oil and Gas Pipelines

A fuzzy artificial neural network (ANN)–based approach is proposed for reliability assessment of oil and gas pipelines. The proposed ANN model is trained with field observation data collected using magnetic flux leakage (MFL) tools to characterize the actual condition of aging pipelines vulnerable to metal loss corrosion. The objective of this paper is to develop a simulation-based probabilistic neural network model to estimate the probability of failure of aging pipelines vulnerable to corrosion. The approach is to transform a simulation-based probabilistic analysis framework to estimate the pipeline reliability into an adaptable connectionist representation, using supervised training to initialize the weights so that the adaptable neural network predicts the probability of failure for oil and gas pipelines. This ANN model uses eight pipe parameters as input variables. The output variable is the probability of failure. The proposed method is generic, and it can be applied to several decision problems related with the maintenance of aging engineering systems.     

基于截尾概率分布的基坑突涌模糊可靠度分析

岩土工程可靠度分析中,计算参数具有随机性,稳定性评价具有模糊性。传统的Monte Carlo模拟方法计算可靠度时,往往假定参数概率分布在正负无穷之间分布,与真实情况不符,而且其计算效率也往往较低。规范推荐的基坑突涌验算公式,计算结果往往偏于保守。引入截尾概率分布的确定方法,对参数概率分布进行截尾处理;提出拉丁超立方抽样与最大熵原理结合来确定结构响应概率分布的方法,并将其与模糊可靠度原理结合,构建了基于抽样模拟的模糊可靠度计算模型;推荐了考虑土体抗剪强度的突涌验算公式。将所提方法应用于某深基坑工程突涌分析中,其结果表明,基于截尾分布的抽样可以有效避免参数抽样值为负数的情况,所提计算模型效率明显优于传统的Monte Carlo模拟方法,模糊可靠度的计算结果比经典可靠度更符合工程实际情况。     

基于不确定性的氯离子侵蚀环境下普通混凝土结构的耐久性研究

针对氯盐侵蚀环境下普通混凝土结构的锈胀开裂,通过分析普通混凝土结构的腐蚀损伤发展特点,建立氯离子侵蚀环境下普通混凝土结构的耐久性失效准则。基于工程实例,采用不确定性分析方法,通过Monte Carlo随机模拟,对氯离子侵蚀环境下普通混凝土结构的锈胀开裂时间开展了可靠性分析研究,得出了其近似概率密度分布,通过假设检验,确定其服从对数正态分布,并给出其在不同保证率情况下锈胀开裂时间的取值。     

Bayesian method for the correlated competitive bidding model

A multivariate competitive bidding model takes into account the correlation among competitors in determination of markup size. However, parameter estimation for the multivariate model is a challenging issue. A simplified, piecemeal style statistical method was proposed for low-dimension problems. However, this method may cause significant estimation errors when applied to complex bidding situations. A refined Bayesian statistical method based on Markov chain Monte Carlo (MCMC) simulation is developed that can be employed in practical bidding problems. To deal with missing values in bid data, a data augmentation technique is integrated in the MCMC process. The proposed Bayesian method is shown through case studies to be robust for complex bidding situations and also insensitive to the selection of the prior models of the correlation matrix. An important feature of the proposed Bayesian method is that it allows a project manager to quantify statistical uncertainties of parameter estimation and their effects on markup decisions. The optimal markup is represented by a posterior distribution which paints a complete picture of the uncertainties involved in the markup size decision.     

基桩完整性检测的概率分析及质量动态评估

基于概率理论，对基桩完整性检测的概率分布进行了详细的分析，分析表明抽检结果与总体不合格率和抽检桩数有关，因此建议将总体不合格率作为评价整批桩质量的标准。利用 Bayesian 方法推导出总体不合格率的先验分布服从标准的 Beta 分布，由共轭分布原理得出后验分布也服从 Beta 分布。然后分析了总体不合格率后验分布的期望和方差，得出结论：后验分布的期望是先验分布的期望和当前抽样检测不合格率的加权和；后验分布的方差是当前抽检不合格率及先验分布方差的加权和。通过分析抽检桩数对加权系数和后验分布的期望和方差的影响，结果表明：当抽检桩数小于 10 时，抽检桩数对检测结果有显著影响；当抽检桩数大于 10 时，抽检桩数对抽检结果的影响变小；尤其当抽检桩数大于 20 时，对抽检结果无显著影响。最后利用先验分布的期望和方差与后验分布的期望和方差的关系建立起质量检测的动态评估模型。算例分析表明该动态模型可更准确地估计出总体不合格率，具有较重要的工程实际意义。