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.     

Bayesian Modeling of External Corrosion in Underground Pipelines Based on the Integration of Markov Chain Monte Carlo Techniques and Clustered Inspection Data

In this study, a model is developed to assess external corrosion in buried pipelines based on the unification of Bayesian inferential structure derived from Markov chain Monte Carlo techniques using clustered inspection data. This proposed stochastic model combines clustering algorithms that can ascertain the similarity of corrosion defects and Monte Carlo simulation that can give an accurate probability density function estimation of the corrosion rate. The metal loss rate is chosen as the indicator of corrosion damage propagation, obeying a generalized extreme value (GEV) distribution. Bayesian theory was employed to update the probability distribution of metal loss rate as well as the GEV parameters in order to account for the model uncertainty. The proposed model was validated with direct and indirect inspection data extracted from a 110‐km buried pipeline system.     

改进DE-TMCMC法及其在高级模型参数识别上的应用

目前基于贝叶斯结合马尔可夫链蒙特卡罗（MCMC）的参数识别方法仅在某些传统的简单本构模型的参数识别上得到了验证。鉴于此,提出了一种效率更高的基于差分进化算法的过渡马尔可夫链蒙特卡罗方法（DE-TMCMC）,并基于此提出了一种高效的贝叶斯参数识别方法,应用于高级土体本构模型的参数识别。为了验证其稳健性和有效性,选取丰浦砂的常规室内试验结果作为目标试验来识别考虑临界状态的砂土本构模型的参数。通过对比原始TMCMC方法在参数识别上的表现,突显了DE-TMCMC在识别砂土高级本构模型参数方面的能力。     

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.     

Advanced Markov Chain Monte Carlo Approach for Finite Element Calibration under Uncertainty

Uncertainty involved in the experiment data prohibits the wide applications of the finite element (FE) model updating technique into engineering practices. In this article, the Markov Chain Monte Carlo approach with a Delayed Rejection Adaptive Metropolis algorithm is investigated to perform the Bayesian framework for FE updating under uncertainty. A major advantage of this algorithm is that it adopts global and local adaptive strategies, which makes the FE model updating be robust to uncertainty. Another merit of the studied method is that it not only quantitatively predicts structural responses, but also calculates their statistical parameters such as the confidence interval. Impact test data of a grid structure are investigated to demonstrate the effectiveness of the presented FE model updating technique, in which the uncertainty parameters include the vertical and longitudinal spring stiffness that simulate the boundary
conditions, the end‐fixity factor for modeling semi‐rigid connections, and the elastic modulus for simulating the uncertainty associated with material property.     

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.     

赣江大桥基于应力谱的疲劳寿命可靠度分析

结合对南昌赣江大桥南桥第 1 0孔桁梁桥的疲劳寿命评估 ,介绍了采用蒙特卡罗法模拟疲劳荷载的情况 ,随后对比了实测数据与模拟数据 ,确定模拟数据可以用于实际疲劳寿命评估。利用模拟数据分析了赣江大桥的疲劳损伤的概率分布情况 ,确定了在给定概率下的赣江大桥的疲劳寿命     

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.     

Adaptive Markov chain Monte Carlo algorithms for Bayesian inference: recent advances and comparative study

Abstract

Condition assessments of structures require prediction models such as empirical model and numerical simulation model. Generally, these prediction models have model parameters to be estimated from experimental data. Bayesian inference is the formal statistical framework to estimate the model parameters and their uncertainties. As a result, uncertainties associated with the model and measurement can be accounted for decision making. Markov Chain Monte Carlo (MCMC) algorithms have been widely employed. However, there still remain some implementation issues from the inappropriate selection of the proposal mechanism in Markov chain. Since the posterior density for a given problem is often problem-dependent and unknown, users require a trial-and-error approach to select and tune optimal proposal mechanism. To relieve this difficulty, various adaptive MCMC algorithms have been recently appeared. Users must understand their mechanism and limitations before applying the algorithms to their problems. However, there is no comprehensive work to provide detailed exposition and their performance comparison together. This study aims to bring together different adaptive MCMC algorithms with the goal of providing their mechanisms and evaluating their performances through comparative study. Three algorithms are chosen as the representative proposal mechanism. From comparative studies, the discussions were drawn in terms of performances, simplicity and computational costs for less-experienced users.     

Slope reliability and back analysis of failure with geotechnical parameters estimated using Bayesian inference

A Bayesian approach is proposed for the inference of the geotechnical parameters used in slope design. The methodology involves the construction of posterior probability distributions that combine prior information on the parameter values with typical data from laboratory tests and site investigations used in design. The posterior distributions are often complex, multidimensional functions whose analysis requires the use of Markov chain Monte Carlo (MCMC) methods. These procedures are used to draw representative samples of the parameters investigated, providing information on their best estimate values, variability and correlations. The paper describes the methodology to define the posterior distributions of the input parameters for slope design and the use of these results for evaluation of the reliability of a slope with the first order reliability method (FORM). The reliability analysis corresponds to a forward stability analysis of the slope where the factor of safety (FS) is calculated with a surrogate model from the more likely values of the input parameters. The Bayesian model is also used to update the estimation of the input parameters based on the back analysis of slope failure. In this case, the condition FS = 1 is treated as a data point that is compared with the model prediction of FS. The analysis requires a sufficient number of observations of failure to outbalance the effect of the initial input parameters. The parameters are updated according to their uncertainty, which is determined by the amount of data supporting them. The methodology is illustrated with an example of a rock slope characterised with a Hoek-Brown rock mass strength. The example is used to highlight the advantages of using Bayesian methods for the slope reliability analysis and to show the effects of data support on the results of the updating process from back analysis of failure.     

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.     

Seismic design requirements for reinforced concrete piers considering aftershock-induced seismic hazard

The main purpose of this study is to develop an estimation procedure of seismic design level setting for reinforced concrete (RC) piers considering aftershock-induced seismic hazards. This work develops an assessment method of the seismic hazards induced by aftershocks and takes an example of the Chi–Chi Earthquake in Taiwan. The number of aftershocks is assumed to follow the modified Gutenberg–Richter law with lower and upper bounds when analysing the cumulative density function of the magnitude of the aftershock within a specified post-mainshock period for the earthquake. Additionally, this work considers the spatial uncertainty in the hypocentres of aftershocks to assess the aftershock-induced seismic hazards. Fragility curves and residual factors of damaged RC piers are used in the transition probability matrix of Markov Chain model for considering the cumulative damage induced by aftershocks by incorporating uncertainty into aftershock events, as well as into structural capacity and residual factors corresponding to a specified damage state, the exceedance probabilities for various damage states can be estimated using Markov Chain model and Monte Carlo Simulation. Finally, in the case study, the proposed procedure is used to determine the important factor in the preliminary seismic design of typical RC piers for the Chi–Chi Earthquake in Taiwan.     

基于随机多项式展开的流固耦合非饱和土坡概率反分析

降雨入渗条件下非饱和土坡流固耦合作用复杂,具有高度非线性的特点,一般采用数值方法模拟。数值模型计算量大已成为监测数据概率反分析的重要制约因素。提出一种基于随机多项式展开(PCE)的概率反分析方法。该方法采用随机多项式展开构建土性参数与数值模型响应的显式函数,作为概率反分析中原数值模型的代替模型,与基于贝叶斯理论和马尔可夫链蒙特卡罗(MCMC)模拟的概率反分析方法相结合,从而有效提高非饱和土坡流固耦合参数概率反分析的效率。通过降雨入渗非饱和土坡算例研究,结果表明,与基于数值模型的常规随机反分析相比,两种方法在后验分布统计值、95%置信区间等结果非常接近,基于PCE的概率反分析计算效率显著提高,结果可靠。     

桥梁损伤识别的实用模型修正方法研究

对面向损伤识别的桥梁结构模型修正实用方法进行了研究。提出了基于振动特性测量的三步模型修正策略和综合利用通用有限元程序ANSYS的优化功能进行模型修正的方法。为了缩减待修正的参数,根据计算目标函数对每个单元参数的敏感性,进行子结构划分,通过对子结构参数的修正进行结构损伤的大致定位,然后对确定为损伤的子结构的每个单元进行参数修正,进行结构的损伤定量识别和状态评估。修正算法的优化方法采用ANSYS一阶优化方法和随机搜索方法,敏感性分析和模型修正完全基于ANSYS软件进行,较适合于实际工程的应用。为了说明方法的可行性,以某一实际三跨预应力钢筋混凝土连续箱梁桥为仿真算例,以结构模型的单元刚度衰减来模拟损伤,进行损伤识别,达到了较好的效果。     

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.     

桅杆结构风振疲劳及可靠性分析

运用Monte Carlo方法对桅杆结构的非线性风振响应进行了计算。应用雨流法统计了纤绳节点板焊缝在服役期间内的应力幅及对应的循环次数。基于Miner线性累积损伤准则,计算得到了结构的疲劳寿命。以桅杆结构纤绳节点板焊缝的极限疲劳循环次数作为随机变量,利用可靠度理论分析了焊缝在不同服役期的疲劳可靠度。     

Maintenance management of offshore structures using Markov process model with random transition probabilities

The robustness of an offshore engineering design is highly dependent on the maintenance management, where the latter needs a full knowledge of engineering analysis and predictions. An accurate estimation of offshore structural performance with time-varying effect is a keen technical issue. The traditional Markov chain model used for structural strength predictions suffers from the difficulty that some of the measurements or inspection data are largely different from the predicted damage condition. This paper presents a deterioration prediction method for maintenance planning in offshore engineering using the Markov models. Instead of traditional deterministic approaches, the Markov chain model is refined by expressing the transition probabilities as random variables. Through such development, the proposed model is able to estimate an interval for the deterioration of an offshore structure. An existing offshore structure located in South China Sea is used in this study for the demonstration purpose. The selection of transition periods of the Markov chain model is investigated. The use of the stochastic model in the prediction of maintenance timing is also discussed. The results show that the proposed approach can provide more reliable information on structural integrity compared to the conventional method.     

Optimization of site investigation program for improved statistical characterization of geotechnical property based on random field theory

This paper presents a framework for optimization of site investigation program, within which the robustness of the site investigation program and the investigation effort are optimized. A site investigation program is judged robust if the derived statistics of the geotechnical property of interest are robust against the uncertainties caused by limited data availability and test error. In this study, a Markov chain Monte Carlo simulation-based Bayesian inference approach was used to characterize the statistics of the intended geotechnical property. The robustness of the site investigation program was formulated as a byproduct of the Bayesian inference of the geotechnical property statistics. The proposed framework for optimization of the site investigation program was implemented as a bi-objective optimization problem that considers both robustness and investigation effort. The concepts of Pareto Front and knee point were employed to aid in making an informed decision regarding selection of site investigation program. The effectiveness and significance of the proposed framework were demonstrated through a simulation study.     

Dynamic alongwind fatigue of slender vertical structures

The wind-excited vibrations of structures induce fluctuating stresses around mean deformation states that lead to fatigue damage accumulation and can determine structural failure without exceeding design wind actions. This paper proposes a mathematical model aimed at deriving a histogram of the stress cycles, the accumulated damage and the fatigue life of slender vertical structures (e.g. towers, chimneys, poles and masts) in alongwind vibrations. The formulation, integrally in closed form, is based on a probabilistic counting cycle method inspired by narrow-band processes. An example illustrates the proposed procedure and shows, through the comparison with Monte Carlo simulations, the entity of the approximations involved by treating the response as narrow-banded instead of broad-banded.     

拱梁组合结构桁架桥的随机疲劳荷载谱分析

疲劳荷载谱的研究是钢桥疲劳分析的基础。通过对蕴藻浜大桥路段交通情况的实地调查,得到车辆重量及交通流量的一些统计参数值,并利用统计学蒙特卡罗理论及数据拟合的方法得到随机疲劳荷载谱。它为分析嘉定蕴藻浜大桥的疲劳应力提供理论基础。