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.     

Integration of structural health monitoring in a system performance based life-cycle bridge management framework

In this paper, an approach for integrating the information obtained from structural health monitoring in a life-cycle bridge management framework is proposed. The framework is developed on the basis of life-cycle system performance concepts that are also presented in this paper. The performance of the bridge is quantified by incorporating prior knowledge and information obtained from structural health monitoring using Bayesian updating concepts. This performance is predicted in the future using extreme value statistics. Advanced modelling tools and techniques are used for the lifetime reliability computations, including incremental nonlinear finite element analyses, quadratic response surface modelling using design of experiments concepts, and Latin hypercube sampling, among other techniques. The methodology is illustrated on an existing bridge in the state of Wisconsin.     

Long-term bridge health monitoring and performance assessment based on a Bayesian approach

This study presents a damage detection approach for the long-term health monitoring of bridge structures. The Bayesian approach comprising both Bayesian regression and Bayesian hypothesis testing is proposed to detect the structural changes in an in-service seven-span steel plate girder bridge with Gerber system. Both temperature and vehicle weight effects are accounted in the analysis. The acceleration responses at four points of the bridge span are utilised in this investigation. The data covering three different time periods are used in the bridge health monitoring (BHM). Regression analyses showed that the autoregressive exogenous model considering both temperature and vehicle weight effects has the best performance. The Bayesian factor is found to be a sensitive damage indicator in the BHM. The Bayesian approach can provide updated information in the real-time monitoring of bridge structures. The information provided from the Bayesian approach is convenient and easy to handle compared to the traditional approaches. The applicability of this approach is also validated in a case study where artificially generated damage data is added to the observation data.     

A Bayesian Probabilistic Approach for Acoustic Emission‐Based Rail Condition Assessment

The investigation described in this article aims at developing a Bayesian‐based approach for probabilistic assessment of rail health condition using acoustic emission monitoring data. It comprises the following three phases: (i) formulation of a frequency‐domain structural health index (SHI), via a linear transformation method, tailored to damage‐sensitive frequency bandwidth; (ii) establishment of data‐driven reference models, using Bayesian regression about the real and imaginary parts of the SHI derived with monitoring data from the intact rail; and (iii) quantitative evaluation of discrimination between the new observations representative of current rail health condition and the baseline model predictions in terms of Bayes factor. If the deviation of the new observations from the predictions is within an acceptable tolerance, no damage is flagged, and the new data are further used to update and refine the reference models. If the observations deviate substantially from the model predictions in a probabilistic sense, damage is signaled, damage severity is quantified, and damage location determined. The proposed approach is examined by using field monitoring data acquired from an instrumented railway turnout, and the coincidence between the assessment results and the actual health conditions demonstrates its effectiveness in damage detection, localization, and quantification.     

Structural health monitoring of a cable-stayed bridge with Bayesian neural networks

In recent years, there has been an increasing interest in permanent observation of the dynamic behaviour of bridges for long-term monitoring purpose. This is due not only to the ageing of a lot of structures, but also for dealing with the increasing complexity of new bridges. The long-term monitoring of bridges produces a huge quantity of data that need to be effectively processed. For this purpose, there has been a growing interest on the application of soft computing methods. In particular, this work deals with the applicability of Bayesian neural networks for the identification of damage of a cable-stayed bridge. The selected structure is a real bridge proposed as benchmark problem by the Asian-Pacific Network of Centers for Research in Smart Structure Technology (ANCRiSST). They shared data coming from the long-term monitoring of the bridge with the structural health monitoring community in order to assess the current progress on damage detection and identification methods with a full-scale example. The data set includes vibration data before and after the bridge was damaged, so they are useful for testing new approaches for damage detection. In the first part of the paper, the Bayesian neural network model is discussed; then in the second part, a Bayesian neural network procedure for damage detection has been tested. The proposed method is able to detect anomalies on the behaviour of the structure, which can be related to the presence of damage. In order to obtain a confirmation of the obtained results, in the last part of the paper, they are compared with those obtained by using a traditional approach for vibration-based structural identification.     

Monitoring Structural Health Using a Probabilistic Measure

A Bayesian probabilistic methodology for structural health monitoring is presented. The method uses a sequence of identified modal parameter data sets to continually compute the probability of damage. In this approach, a high likelihood of a reduction in model stiffness at a location is taken as a proxy for damage at the corresponding structural location. The concept extends the idea of using as indicators of damage the changes in model parameters identified using a linear finite-element model and modal parameter data sets from the structure in undamaged and possibly damaged states. This extension is needed because of uncertainties in the updated model parameters that in practice obscure health assessment. These uncertainties arise due to effects such as variation in the identified modal parameters in the absence of damage, as well as unavoidable model error. The method is illustrated by simulating on-line monitoring, wherein specified modal parameters are identified on a regular basis and the probability of damage for each substructure is continually updated. Examples are given for abrupt onset of damage and progressive deterioration.     

Damage Pattern Recognition for Structural Health Monitoring Using Fuzzy Similarity Prescription

Abstract:   Structural health monitoring (SHM) is a systematic method for non-destructive evaluation of a structure's performance by sensing, extracting, patterning, and recognizing features of the structural response. Most SHM approaches focus on statistical analysis for damage identification considering only random uncertainties. This article introduces a method that allows accommodating other types of uncertainties due to ambiguity, vagueness, and fuzziness which are statistically non-describable. The proposed method deals primarily with epistemic uncertainty. The method improves damage identification by performing damage pattern recognition using fuzzy sets. In this approach, healthy observations are used to construct a fuzzy set representing healthy performance characteristics. Additionally, the bounds on the similarities among the structural damage states are prescribed. Thus, an optimal group of fuzzy sets representing damage states such as little, moderate, and severe damage can be inferred as an inverse problem from healthy observations only. Piecewise linear functions are used as fuzzy membership functions representing the states of healthy and damaged. The optimal group of damage fuzzy sets is used to classify a set of observations at any unknown state of damage using the principles of fuzzy pattern recognition based on maximum approaching degree. A case study for damage pattern recognition of a model steel bridge is presented and discussed. The approach is capable of identifying damage patterns accurately.     

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。     

An efficient algorithm for architecture design of Bayesian neural network in structural model updating

There has been growing interest in applying the artificial neural network (ANN) approach in structural system identification and health monitoring. The learning process of neural network can be more robust when presented in the Bayesian framework, and rational architecture of the Bayesian neural network is critical to its performance. Apart from number of hidden neurons, the specific forms of the transfer functions in both hidden and output layers are also crucially important. To the best of our knowledge, however, the simultaneous design of proper number of hidden neurons, and specific forms of hidden‐ and output‐layer transfer functions has not yet been reported in terms of the Bayesian neural network. It is even more challenging when the transfer functions of both layers are parameterized instead of using fixed shape forms. This paper proposes a tailor‐made algorithm for efficiently designing the appropriate architecture of Bayesian neural network with simultaneously optimized hidden neuron number and custom transfer functions in both hidden and output layers. To cooperate with the proposed algorithm, both the Jacobian of the network function and Hessian of the negative logarithm of weight posterior are derived analytically by matrix calculus. This is much more accurate and efficient than the finite difference approximation, and also vital for properly designing the Bayesian neural network architecture as well as further quantifying the confidence interval of network prediction. The validity and efficiency of the proposed methodology is verified through probabilistic finite element (FE) model updating of a pedestrian bridge by using the field measurement data.     

Structural parameter identification and damage detection for a steel structure using a two-stage finite element model updating method

A two-stage eigensensitivity-based finite element (FE) model updating procedure is developed for structural parameter identification and damage detection for the IASC-ASCE structural health monitoring benchmark steel structure on the basis of ambient vibration measurements. In the first stage, both the weighted least squares and Bayesian estimation methods are adopted for the identification of the connection stiffness of beam-column joints and Young’s modulus of the structure; then the damage detection is conducted via the FE model updating procedure for detecting damaged braces with different damage patterns of the structure. Comparisons between the FE model updated results and the experimental data show that the eigensensitivity-based FE model updating procedure is an effective tool for structural parameter identification and damage detection for steel frame structures.     

Sensitivity of uncertainties in performance prediction of deteriorating concrete structures

Deterioration models for the condition and reliability prediction of civil infrastructure facilities involve numerous assumptions and simplifications. Furthermore, input parameters of these models are fraught with uncertainties. A Bayesian methodology has been developed by the authors, which uses information obtained through health monitoring to improve the quality of prediction. The sensitivity of prior and posterior predicted performance to different input parameters of the deterioration models, and the effect of instrument and measurement uncertainty, is investigated in this paper. The results quantify the influence of these uncertainties and highlight the efficacy of the updating methodology based on integrating monitoring data. It has been found that the probabilistic posterior performance predictions are significantly less sensitive to most of the input uncertainties. Furthermore, updating the performance distribution based on ‘event’ outcomes is likely to be more beneficial than monitoring and updating of the input parameters on an individual basis.     

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.     

Image‐based post‐disaster inspection of reinforced concrete bridge systems using deep learning with Bayesian optimization

Many bridge structures, one of the most critical components in transportation infrastructure systems, exhibit signs of deteriorations and are approaching or beyond the initial design service life. Therefore, structural health inspections of these bridges are becoming critically important, especially after extreme events. To enhance the efficiency of such an inspection, in recent years, autonomous damage detection based on computer vision has become a research hotspot. This article proposes a three‐level image‐based approach for post‐disaster inspection of the reinforced concrete bridge using deep learning with novel training strategies. The convolutional neural network for image classification, object detection, and semantic segmentation are, respectively, proposed to conduct system‐level failure classification, component‐level bridge column detection, and local damage‐level damage localization. To enable efficient training and prediction using a small data set, the model robustness is a crucial aspect to be taken into account, generally through its hyperparameters’ selection. This article, based on Bayesian optimization, proposes a principled manner of such selection, with which very promising results (well over 90% accuracies) and robustness are observed on all three‐level deep learning models.     

基于径向基神经网络的桥梁有限元模型修正

基于某预应力混凝土大跨刚构-连续梁桥的ANSYS有限元模型,提出一种基于径向基神经网络的有限元模型修正方法。该方法以不同设计参数条件下有限元模型模态分析频率作为输入向量,以对应的桥面单元、中墩、边墩的弹性模量、密度等设计参数修正值作为输出向量,利用径向基神经网络来逼近两者之间的非线性映射关系。结合该桥梁结构健康监测系统中加速度传感器监测的桥梁结构动力反应的加速度数据,利用神经网络的泛化特性,直接计算出有限元模型设计参数的修正值。研究结果表明:修正后的有限元模型能更真实地反映结构的物理状态,较好地反映该桥梁结构的真实动力特性。     

铁路简支梁桥下部结构健康状态动力评估方法研究

提出一种以实测横桥向整体振动、横桥向局部振动和顺桥向局部振动模态的不同组合为输入,采用模型修正技术和优化算法识别铁路简支梁桥下部结构的物理参数,从而实现对墩身、基础和支座病害进行定位和定量分析的动力学方法。进一步,建立了针对下部结构系统中各构件的评估准则和评估流程。对两座铁路桥梁进行现场试验,并依据所提评估方法和评估准则对其健康状态进行评估,理论分析结果现场评估结果一致,从而证明所提方法的准确性和有效性。     

SHM-based F-AHP bridge rating system with application to Tsing Ma Bridge

This paper aims at developing a structural health monitoring (SHM)-based bridge rating method for bridge inspection of long-span cable-supported bridges. The fuzzy based analytic hierarchy approach is employed, and the hierarchical structure for synthetic rating of each structural component of the bridge is proposed. The criticality and vulnerability analyses are performed largely based on the field measurement data from the SHM system installed in the bridge to offer relatively accurate condition evaluation of the bridge and to reduce uncertainties involved in the existing rating method. The procedures for determining relative weighs and fuzzy synthetic ratings for both criticality and vulnerability are then suggested. The fuzzy synthetic decisions for inspection are made in consideration of the synthetic ratings of all structural components. The SHM-based bridge rating method is finally applied to the Tsing Ma suspension bridge in Hong Kong as a case study. The results show that the proposed method is feasible and it can be used in practice for longspan cable-supported bridges with SHM system.     

Probabilistic Baseline of Finite Element Model of Bridges under Environmental Temperature Changes

The material properties and structural stiffness of actual bridges fluctuate with variations in environmental temperature; therefore, it is not appropriate to use a determined finite element model (FEM) as the baseline model for localizing the structural damage of bridges. To address this issue, we proposed the concept of the probabilistic baseline of FEM of bridges under variable environmental temperature, that is, we established reasonable probability distributions of the physical parameters of bridges that are suitable for damage localization with varying environmental temperature. First, a method is presented to obtain the probabilistic baseline of FEM of bridges, which imports cluster analysis into stochastic FEM updating. Unlike the conventional methods, the measured natural frequencies first are classified into different clusters using the Gaussian mixture method (GMM), with each cluster consisting of measured data that satisfy the same Gaussian distribution. Then, the conventional methods of stochastic FEM updating can be conveniently implemented to obtain the probabilistic baseline of FEM for each cluster. Second, for each cluster, the mean values and covariance of the updating parameters are updated in two sequential steps, and a new approach is proposed for determining the initial covariance of the updating parameters. The results of an actual example show that predetermining a reasonable initial covariance for the updating parameters can accurately and efficiently obtain the updated results. Finally, the effectiveness of the presented method is verified through the monitoring data of an actual bridge.     

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。     

Maintenance decision model for steel bridges: a case in the Netherlands

A probabilistic model is developed to investigate the crack growth development in welded details of orthotropic bridge decks. Bridge decks may contain many of these vulnerable details and bridge reliability cannot always be guaranteed upon the attainment of a critical crack. Therefore, insight into the crack growth development is crucial in guaranteeing bridge reliability and scheduling efficient maintenance schemes. The probabilistic nature of the crack growth development model and the dependence of this model on many interdependent random variables result in significant uncertainties regarding model outcome. To reduce some of these uncertainties, the probabilistic model is combined with a monitoring system installed on a part of the bridge. In addition, a Bayesian network is used to determine the dependence structure between the different details (monitored and non-monitored) of the bridge. This dependence structure enables us to make more accurate crack growth predictions for all details of the bridge while monitoring only a limited number of those details and updating the remaining uncertainties.     

Life-Cycle Performance of RC Bridges: Probabilistic Approach

This article addresses the problem of reliability assessment of reinforced concrete (RC) bridges during their service life. First, a probabilistic model for assessment of time-dependent reliability of RC bridges is presented, with particular emphasis placed on deterioration of bridges due to corrosion of reinforcing steel. The model takes into account uncertainties associated with materials properties, bridge dimensions, loads, and corrosion initiation and propagation. Time-dependent reliabilities are considered for ultimate and serviceability limit states. Examples illustrate the application of the model. Second, updating of predictive probabilistic models using site-specific data is considered. Bayesian statistical theory that provides a mathematical basis for such updating is outlined briefly, and its implementation for the updating of information about bridge properties using inspection data is described in more detail. An example illustrates the effect of this updating on bridge reliability.