Bayesian probabilistic approach for model updating and damage detection for a large truss bridge

Abstract

A Bayesian probabilistic methodology is presented for structural model updating using incomplete measured modal data which also takes into account different types of errors such as modelling errors due to the approximation of actual complex structure, uncertainties introduced by variation in material and geometric properties, measurement errors due to the noises in the signal and the data processing. The present work uses Linear Optimization Problems (LOP) to compute the probability that continually updated the model parameters. A real life rail-cum-roadway long steel truss bridge (Saraighat bridge) is considered in the present study, where identified modal data are available from measured acceleration responses due to ambient vibration. The main contributions of this paper are: (1) the introduction of sufficient number of model parameters at the element property level in order to capture any variations in the sectional properties; (2) the development of an accurate baseline model by utilizing limited sensor data; (3) the implementation of a probabilistic damage detection approach that utilizes updated model parameters from the undamaged state and possibly damaged state of the structure.

Recent progress and future trends on damage identification methods for bridge structures

“…Kanta and Samit presented a damage localization and quantification method based on Bayesian framework for railway truss bridges; mode shapes and their derivatives are used to locate the damage, and then in the updating of Bayesian model, the prediction error variance approach based on parameter sensitivity is used to extract the maximum information in modal data to quantify the damage; the method is numerically demonstrated on a truss bridge. Mustafa et al presented a damage identification method for the truss bridge using updated model parameters; first, a reliable baseline model of a large truss bridge is established, and the accurate sectional properties of the bridge components are obtained; then, once the sectional properties change, the damage can be detected using a probabilistic damage identification approach called Bayesian probabilistic methodology; the method is not only capable of identifying the damaged member but also the damage quantification. Pedroza Torres et al proposed a hybrid methodology method based on the results of a comparative study between self‐organizing maps and Bayesian networks in order to reduce computational cost and improve performance in fault condition detection of structures; the proposed method can detect damage efficiently based on numerical results of a truss.…”

Sparse Bayesian learning for structural damage detection using expectation–maximization technique

“…1. In the presented SBL method, the EM algorithm is employed for learning the hyperparameters {α, β, γ} to maximize the evidence function in (17), whereas direct differentiation was used in Huang and Beck 37 and Huang et al 38,39 In fact, it is intractable to maximize the current form of the evidence function in (17) with respect to the hyperparameters {α, β, γ} by direct differentiation. Therefore, the EM algorithm employed here has broader applications for real problems.…”

“…However, the computational efficiency of posterior sampling for the MCMC methods remains a major concern. Mustafa et al utilized linear optimization to identify the posterior statistics of the model parameters for model updating and damage detection, instead of solving the challenging nonlinear optimization problem. A complete review on the recent development of sparse Bayesian learning for structural damage detection and assessment was also provided in Huang et al…”

“…One category is based on the perturbation technique, 8,9,12,13 which assigns a random variable to each uncertainty and then calculates the statistics of the variable. The other widely used category is the Bayesian approach, [14][15][16][17] which explicitly quantifies the posterior probability of the uncertainties according to observations and prior information.…”

Transfer function‐based Bayesian damage detection under seismic excitation

“…For this purpose, it is more expedient to minimize the negative logarithm likelihood function given by One of the major challenges in a Bayesian damage detection or model updating procedure is the application of the method on a large‐scale structure with a large number of unknown parameters. Some researchers studied the Bayesian model updating of a large scale model . Generally, for damage identification in structures with a large number of DOFs, it is necessary to utilize some methods to alleviate computational problems, including substructure methods, model reduction, coarse meshing, and parameter grouping techniques Yuen detected probabilistic damage in a hundred‐story building using a substructuring approach, which allowed for identification of only critical substructures …”