Bayesian-based methodology for progressive structural health evaluation and prediction by use of monitoring data

Abstract

Despite the continuous evolution and development in the field of structural health monitoring (SHM), interpreting the huge amount of monitoring data from an SHM system to obtain useful information on structural conditions remains a challenge. Furthermore, due to the complexity of structures, measurement noise, inherent uncertainties in measured data and analytical methods, precise models which reflect the actual structural systems are difficult to create. In this regard, this thesis presents novel model-free data-interpretation methodologies within the Bayesian framework for structural health evaluation and prediction. The first part of the thesis is aimed at conducting SHM-based structural condition assessment using Bayesian linear model (BLM) and Bayesian generalized linear model (BGLM). For condition assessment of bridge expansion joints, the relationship pattern between thermal movement of expansion joints and effective temperature of bridge deck is quantified using BLM and long-term monitoring data. The model parameters, model error and their associated uncertainties are estimated by analytical and simulation algorithms. With the established BLM, an anomaly index is defined to evaluate the failure probability of the expansion joints. The maximum and minimum displacements of the expansion joints under design extreme temperatures are predicted and compared with the design allowable values for validation. Then the BLM is extended to BGLM for assessing wind-induced displacement responses of instrumented bridge. With the monitoring data of displacement and wind during typhoons, the correlation pattern between wind-induced displacement and wind speed/direction is explored. The crucial issue of optimizing model structure is dealt with by employing Bayesian model class selection, in terms of maximizing the log-likelihood function. Based on the established model, the bridge displacement responses and the associated confidence intervals under wind speed at serviceability limit state (SLS) are predicted and compared with the design allowable values for validation. In the second part, Bayesian inference-based dynamical linear models (BDLM) are developed for prognosis and damage detection by using the time series of structural response. Firstly, different step ahead predictions by various models considering different component forms, such as trend, seasonal and regression components, are evaluated and compared in accordance with three model criteria. After the most suitable model is determined, a novel detection technique based on the forecasting of BDLM is proposed for local anomaly diagnosis. An index called Bayes factor is introduced for outlier detection. It is carried out by checking the current observation against the forecasting distribution (yielded from the BDLM at current moment) as well as against an alternative model (whose mean value is shifted by a prescribed offset). The detection rule is that if the alternative model better fits the actual observation, a potential outlier is detected. Then, the logic of outlier detection is extended to distinguish between the single outlier and the appearance of a change through defining the cumulative Bayes factors, which can diagnose the anomaly of local component under extreme events or due to structural damage. Finally, Bayesian hypothesis testing is conducted by comparing the time series of structural response before and after the change point to make a judgement on whether the structure is healthy. Two case studies using the in-service monitoring data from a high-speed train and the data from a bridge benchmark problem are provided to show the applicability and effectiveness of the proposed method.