Prediction Error Variances in Bayesian Model Updating Employing Data Sensitivity

Abstract

Efficiency of a Bayesian model updating algorithm is greatly affected by the choice of variance of prediction error models of different data points (evidence) used for model updating. In the context of structural model updating, a sensitivity-based novel approach is proposed in this work to find these variances without increasing the dimensionality of the model updating problem. Well-established relations of modal data sensitivity toward structural parameters are incorporated in the Bayesian framework to evaluate the prediction error variances. A high-rise shear building is considered for numerical illustration of the approach. Markov chain Monte Carlo (MCMC) simulation technique is employed using the Metropolis-Hastings algorithm to simulate the samples from the posterior distribution. Results are presented as a comparison of unknown parameters obtained using the proposed approach and an approach in which all prediction error variances are assumed to be equal. The study shows that the proposed approach is highly efficient in extracting appropriate information from the data, and therefore enhancing the efficiency of Bayesian algorithm. It also illustrates that the damage locations play an important role in the selection of variances of prediction error models. Furthermore, each data point of evidence can be very effective in estimating the model parameters, if the information contained in the data is exploited effectively.