结构性能退化的评估和贝叶斯动态预测

 结构性能的退化影响因素复杂、时间跨度长、不确定性大，其预测不可避免地要考虑具体结构的实际情况，即在一般规律认识的基础上，不断利用在具体结构生命周期中得到的新信息，更新对结构未来性能退化的预测，进而得到更确切合理的可靠度分析和决策。基于这一思路，引入贝叶斯动态模型理论，设计模型结构，用于结构性能退化的预测。同时，根据结构性能退化的多阶段特点和目前工程实践可获取的结构检测信息的实际情况，提出状态指标的概念，用于描述结构性能退化。计算实例验证贝叶斯动态预测的优越性及信息更新对结构性能退化预测和寿命评估的影响，同时说明状态指标具有简便实用的特点。     

结构性能退化的评估和贝叶斯动态预测

结构性能的退化影响因素复杂、时间跨度长、不确定性大,其预测不可避免地要考虑具体结构的实际情况,即在一般规律认识的基础上,不断利用在具体结构生命周期中得到的新信息,更新对结构未来性能退化的预测,进而得到更确切合理的可靠度分析和决策。基于这一思路,引入贝叶斯动态模型理论,设计模型结构,用于结构性能退化的预测。同时,根据结构性能退化的多阶段特点和目前工程实践可获取的结构检测信息的实际情况,提出状态指标的概念,用于描述结构性能退化。计算实例验证贝叶斯动态预测的优越性及信息更新对结构性能退化预测和寿命评估的影响,同时说明状态指标具有简便实用的特点。     

Evaluation and Bayesian dynamic prediction of deterioration of structural performance

The deterioration of structural performance is a time-variant process with a large amount of uncertainties and incompleteness of load and environmental effects. It seems inevitable that the prediction of structural deterioration should be based on a philosophy of information updating. In the present paper, a new model system for structural performance prediction is introduced based on Bayesian dynamic linear model (DLM) theory. The system can implement Bayesian updating on the prediction of the time series process of structural deterioration. It can effectively incorporate useful information through the deterioration process of structures to update the prediction. Intervention and monitoring techniques are also designed to ensure the stability of the model system. This paper also defines an indicator of the so-called ‘condition index’ to evaluate the structural performance. Using condition indexes, the qualitative condition rating of structural performance based on visual inspection in current engineering practice can be integrated into the Bayesian DLMs. Case studies validate the advantages of Bayesian DLMs. The information updating has a favourable effect on reliability analysis and life prediction. The condition indexes are simple and convenient used in practice.     

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.     

Active learning structural model updating of a multisensory system based on Kriging method and Bayesian inference

Model updating techniques are often applied to calibrate the numerical models of bridges using structural health monitoring data. The updated models can facilitate damage assessment and prediction of responses under extreme loading conditions. Some researchers have adopted surrogate models, for example, Kriging approach, to reduce the computations, while others have quantified uncertainties with Bayesian inference. It is desirable to further improve the efficiency and robustness of the Kriging-based model updating approach and analytically evaluate its uncertainties. An active learning structural model updating method is proposed based on the Kriging method. The expected feasibility learning function is extended for model updating using a Bayesian objective function. The uncertainties can be quantified through a derived likelihood function. The case study for verification involves a multisensory vehicle-bridge system comprising only two sensors, with one installed on a vehicle parked temporarily on the bridge and another mounted directly on the bridge. The proposed algorithm is utilized for damage detection of two beams numerically and an aluminum model beam experimentally. The proposed method can achieve satisfactory accuracy in identifying damage with much less data, compared with the general Kriging model updating technique. Both the computation and instrumentation can be reduced for structural health monitoring and model updating.     

Probabilistic prediction of urban water consumption using the SCEM-UA algorithm

Prediction of urban water consumption can help to improve the performance of water distribution systems. Despite the obvious presence of uncertainty in measurements and in assumed model types/structures, most of the existing water consumption prediction models are developed and used in a deterministic context. Methods for more realistic assessment of parameter and model prediction uncertainties have begun to appear in literature only recently. A novel application of the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) for the calibration of a water consumption prediction model is proposed here. The model is applied to a case study of the city of Catania (Italy) with the aim to predict daily water consumption. The SCEM-UA algorithm is used to calibrate the parameters of the artificial neural network based prediction model and in turn to determine the associated parameter and model prediction uncertainties. The results obtained using the SCEM-UA ANN approach were compared to the corresponding results obtained using other predictive models developed recently by the authors of the paper. When compared to the these models, the SCEM-UA ANN based water consumption prediction model shows similar predictive capability but also the ability to identify simultaneously the prediction uncertainty bounds associated with the posterior distribution of the parameter estimates.     

Substructure Identification and Health Monitoring Using Noisy Response Measurements Only

Abstract:   A probabilistic substructure identification and health monitoring methodology for linear systems is presented using measured response time histories only. A very large number of uncertain parameters have to be identified if one considers the updating of the entire structure. For identifiability, one then would require a very large number of sensors. Furthermore, even when such a large number of sensors are available, processing of vast amount of the corresponding data raises computational difficulties. In this article a substructuring approach is proposed, which allows for the identification and monitoring of some critical substructures only. The proposed method does not require any interface measurements and/or excitation measurements. No information regarding the stochastic model of the input is required. Specifically, the method does not require the response to be stationary and does not assume any knowledge of the parametric form of the spectral density of the input. Therefore, the method has very wide applicability. The proposed approach allows one to obtain not only the most probable values of the updated model parameters but also their associated uncertainties using only one set of response data. The probability of damage can be computed directly using data from the undamaged and possibly damaged structure. A hundred-story building model is used to illustrate the proposed method.     

碳化概率模型及混凝土结构碳化失效概率分析

混凝土碳化分析是评估混凝土结构长期性能的重要内容。该文分析总结了现有混凝土碳化理论和经验模型。在现有确定性模型基础上,通过添加模型修正项的方法修正确定性模型的误差,建立混凝土碳化概率模型。概率模型中模型参数的后验统计分布特征利用已有检测数据通过贝叶斯更新手段获得。基于建立的碳化概率模型,构建混凝土结构碳化时变失效概率的分析方法,该方法充分考虑模型不确定性对混凝土结构碳化时变失效概率的影响。运用该方法对一钢筋混凝土简支板的碳化性能进行了分析评估。     

Prediction of thrust and torque requirements of TBMs with fuzzy logic models

For successful tunnel excavations, selection of proper tunnel boring machine (TBM), optimization of design parameters and prediction of their performance are critical. Normal and rolling forces of disc cutters are used for determination of thrust, torque and power requirement of TBMs as well as prediction of their performance. Much research has been conducted to predict these parameters of disc cutters using analytical, empirical and numerical approaches. In recent years alternative methods, such as fuzzy logic, have been extensively used to deal with subjects having ambiguities and uncertainties. A model was established to predict normal forces of constant cross section (CCS) disc cutters in the rock cutting process by using fuzzy logic method. The other model which predicts specific energy requirement of disc cutter can also be used for predicting the rolling forces of these cutters. These models are based on experience and verified the database which consists of linear cutting test results generated at the Earth Mechanics Institute of the Colorado School of Mines. The models predict forces of disc cutters using uniaxial compressive and tensile strength of rocks, disc diameter and tip width, penetration and spacing of cuts.     

复杂条件下岩石工程安全性的智能分析评估 和时空预测系统

 采用人工智能、系统科学、岩石力学与工程地质学等多学科交叉,提出复杂条件下岩石工程安全性的智能分析评估和时空预测系统的新思路和新方法,包括赋存环境的认识、工程结构特征需求分析与施工约束条件识别、岩石工程稳定性(安全性)综合集成智能分析评估、岩石工程智能反馈分析方法、岩体模型和参数动态更新的岩石工程稳定性时空演化的综合集成智能分析方法、岩石工程安全性的分区自适应调控方法、岩石工程稳定性多元信息与多任务智能反馈分析集成系统。该系统在龙滩、八尺门、水布垭、拉西瓦等多个大型工程的边坡和地下厂房中的成功应用,显示了其科学性和先进性。     

Analysis of a combined cooling, heating, and power system model under different operating strategies with input and model data uncertainty

Combined cooling, heating, and power (CCHP) system models have been used by many researchers to compare their performance with conventional systems. However, decisions based on the results of computer simulations need to take into account the uncertainty of these results to get insight into the level of confidence in the predictions. This paper presents an analysis of a CCHP system model under different operating strategies with input and model data uncertainty. However, the uncertainties that underlie the variation in input parameters such as the thermal load, natural gas prices and electricity prices are not readily available. Additionally, engine performance uncertainty can be difficult to characterize because of the nonlinearity of engine efficiency curves. This paper presents practical and novel approaches to estimating the uncertainty in these and other input parameters. A case study using a small office building located in Atlanta, GA, is described to illustrate the importance of the use of uncertainty and sensitivity analysis in CCHP system performance predictions, and how the primary energy consumption, operational cost, and carbon dioxide emissions are affected by the uncertainty associated with the model input parameters.     

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.     

Eutrophication research of West Lake,Hangzhou, China: modeling under uncertainty

The models such as the eutrophication ecosystem model of West Lake, Hangzhou (EEM), are always used to make policy decisions for eutrophication management. Thus it is important to know the uncertainty in the model predictions due to the combined effects of uncertainty in the full set of input variables, and the individual input parameters whose variations have the greatest effect on variations in model predictions. In this study, randomized methods based on Monte Carlo technique have been developed and applied to the model (EEM). The technique consists of parameter sensitivity analysis, randomly sampling from underlying probability distributions and multivariate regression analysis. With this technique, model uncertainties during modeling are clarified and their propagation evaluated. Results show that among the five input parameters selected for uncertainty analysis, the settling rate of algae SVS and water temperature TEM have the largest contribution to model prediction uncertainty of the model outputs (PC, PS and PHYT).     

基于ANN的岩土体热阻系数预测模型研究

为准确预测土体热阻系数,通过室内热探针测试与数据分析,简要分析了含水量、干密度、矿物成分和颗粒形态等因素对土体热传导特性的影响,利用人工神经网络(ANN)技术,建立了计算土体热阻系数的预测模型,并与传统经验关系模型进行对比,明确所提计算模型的可靠性与优越性.结果表明:土体传热性能受众多因素影响,其热阻系数难以准确估算,基于ANN的计算模型可以较好地解决这一问题;以含水量和干密度为输入参数的单个模型适用于特定类型土体,而4个输入参数(含水量、干密度、黏粒含量和石英含量)的广义模型不受此限制,增加相关输入参数可有效保证模型计算结果的精确度;单个模型和广义模型的计算结果与实测结果吻合良好,预测能力均显著优于传统经验关系模型;对于工程性质差异显著、沉积环境复杂的不同类型土体,建议优先选用广义模型来估算其热阻系数.     

Analysis of randomly vibrating structures under hybrid uncertainty

In the analysis of several structural systems some parameters always suffer from a level of scattering and others have an intrinsic unpredictable nature. In these circumstances, conventional deterministic-based approaches can lead to excessive approximations and the final results may be very far from the real ones. In this paper, a hybrid approach for the analysis of randomly vibrating structures is presented, to take into account both stochastic processes and epistemic variables. In detail, the dynamic loading has been modelled as a random process whereas the parameters for describing the input process as well as the structural systems are treated as fuzzy variables. This hypothesis has been performed to describe the random meanings and behaviours of some dynamic loads (i.e. earthquake, wind or sea waves) but also to incorporate “non-conventional” sources of uncertainties in the adopted mathematical models. Some numerical examples are presented at the end of the paper in order to illustrate the consequences of the developed methodology. First, the problem regarding a linear tuned mass damper under non-stationary excitation is presented and a sensitivity analysis is conducted for the structural response by considering different values of the input parameters. The second example deals with the dynamic analysis of a broadcasting antenna subject to double filtered stationary base motion. Numerical results demonstrate that the proposed methodology provides an efficient support for assessing the dynamic response under hybrid uncertainty.     

Bayesian analysis of uncertainty for structural engineering applications

There has been recent interest in differentiating aleatory and epistemic uncertainties within the structural engineering context. Aleatory uncertainty, which is related to the inherent physical randomness of a system, has substantially different effects on the analysis and design of structures as compared with epistemic uncertainty, which is knowledge based. Bayesian techniques provide powerful tools for integrating, in a rigorous manner, the two types of uncertainties. In a purely probabilistic viewpoint, the uncertainties merge, resulting in widened probability densities. From the viewpoint of design or experimentation, however, the two types of uncertainties have widely different effects. The purpose of this paper is to develop insight into these effects, using Bayesian-based analytical expressions for the aleatory and epistemic uncertainties. The paper goes beyond standard Bayesian conjugate distributions by incorporating the effects of model uncertainty, where the applicability of two or more analytical models are used to describe the structure of interest. The influence of multiple model uncertainties is explored for two problems: the Bayesian updating process as data is acquired, and the design of simple parallel systems.     

Trivariate analysis of soil ranking-correlated characteristics and its application to probabilistic stability assessments in geotechnical engineering problems

An important issue in the probabilistic prediction modelling of multivariate soil properties (usually including cohesion, friction angle, and unit weight) is the measurement of dependence structure among these properties. The use of Pearson's correlation as a dependence measure has several pitfalls; therefore, it may not be appropriate to use probabilistic prediction models in geotechnical engineering problems based on this correlation. As an alternative, a copula-based methodology for prediction modelling and an algorithm to simulate multivariate soil data are proposed.In this method, all different random variables are transformed to a rank/uniform domain in order to form a copula function by applying cumulative distribution function transformations. The technique of copulas, representing a promising alternative for solving multivariate problems to describe their dependence structure by a ranked correlation coefficient, is highlighted. Two existing observed soil data sets from river banks are used to fit a trivariate normal copula and a trivariate fully nested Frank copula. The ranking correlation coefficient Kendall's τ and the copula model parameters are estimated. The goodness-of-fit test to choose the best-fitting model is discussed.A series of triplet samples (i.e., cohesion, friction angle, and unit weight) simulated from the trivariate normal copula with flexible marginal distributions are used as input parameters to evaluate the uncertainties of soil properties and to define their correlations. The influence of the cross-correlation of these soil properties on reliability-based geotechnical design is demonstrated with two simple geotechnical problems: (a) the bearing capacity of a shallow foundation resting on a clayey soil and (b) the stability of a cohesive-frictional soil in a planar slope. The sensitivity analysis of their correlations of random variables on the influence of the reliability index provides a better insight into the role of the dependence structure in the reliability assessment of geotechnical engineering problems.     

Prediction of roadheader performance by artificial neural network

Performance prediction of the roadheaders is one of the main subjects in determining the economics of the underground excavation projects. During the last decades, researchers have focused on developing performance prediction models for roadheaders. In the first stage of this study, the performance of a roadheader used in Kucuksu sewage tunnel (Istanbul) was recorded in detail and the instantaneous cutting rate (ICR) of the machine was determined. The uniaxial compressive strength (UCS) and rock quality designation (RQD) are used as input parameters in previously developed empirical models in order to point out the efficiency of these models, and the relationships between measured and predicted ICR for different encountered formations. In the second stage of the study, Artificial Neural Network (ANN) technique is used for predicting of the ICR of the roadheader. A data set including UCS, RQD, and measured ICR are established. It is traced that a neural network with two inputs (RQD and UCS) and one hidden layer can be sufficient for the estimation of ICR. In addition, it is determined that increase in number of neurons in hidden layer has positive optimizing on the performance of the ANN and a hidden layer larger than 10 neurons does not have a significant effect on optimizing the performance of the neural network. Furthermore, probability of memorizing is being recognized in this situation. Based on this study, it is concluded that the prediction capacity of ANN is better than the empirical models developed previously.     

Bridge condition modelling and prediction using dynamic Bayesian belief networks

The development of a condition-based deterioration modelling methodology at bridge group level using Bayesian belief network (BBN) is presented in this paper. BBN is an efficient tool to handle complex interdependencies within elements of engineering systems, by means of conditional probabilities specified on a fixed model structure. The advantages and limitations of the BBN for such applications are reviewed by analysing a sample group of masonry bridges on the UK railway infrastructure network. The proposed methodology is then extended to develop a time dependent deterioration model using a dynamic Bayesian network. The condition of elements within the selected sample of bridges and a set of conditional probabilities for static and time dependent variables, based on inspection experience, are used as input to the models to yield, in probabilistic terms, overall condition-based deterioration profiles for bridge groups. Sensitivity towards various input parameters, as well as underlying assumptions, on the point-in-time performance and the deterioration profile of the group are investigated. Together with results from ‘what if’ scenarios, the potential of the developed methodology is demonstrated in relation to the specification of structural health monitoring requirements and the prioritisation of maintenance intervention activities.     

Structural Model Updating and Health Monitoring with Incomplete Modal Data Using Gibbs Sampler

Abstract:   A new Bayesian model updating approach is presented for linear structural models. It is based on the Gibbs sampler, a stochastic simulation method that decomposes the uncertain model parameters into three groups, so that the direct sampling from any one group is possible when conditional on the other groups and the incomplete modal data. This means that even if the number of uncertain parameters is large, the effective dimension for the Gibbs sampler is always three and so high-dimensional parameter spaces that are fatal to most sampling techniques are handled by the method, making it more practical for health monitoring of real structures. The approach also inherits the advantages of Bayesian techniques: it not only updates the optimal estimate of the structural parameters but also updates the associated uncertainties. The approach is illustrated by applying it to two examples of structural health monitoring problems, in which the goal is to detect and quantify any damage using incomplete modal data obtained from small-amplitude vibrations measured before and after a severe loading event, such as an earthquake or explosion.