LAUSR

Abstract Compared with classic probability or statistical theories, Bayesian inference could be a better option for real-world damage identification problems since it can simultaneously utilize both prior knowledge and current measurements of a structure. However for a complex problem, a Bayesian identification procedure should face the challenge of unknown likelihood functions and unacceptable computational expenses. Due to it, approximate Bayesian computation (ABC) is adopted and incorporated with the Metropolis Hastings sampling (MHS) algorithm and stochastic response surface (SRS). Likelihood functions are no longer required during the inference. A stable Markov chain is obtained containing qualified parameter samples, whose random responses are then fast computed by SRSs. Additionally, a nested Bayesian updating procedure with a dynamic tolerance is proposed for fast estimation convergence of posterior probability distributions. After that a probabilistic damage index is defined based on the statistical features of the estimated posterior probability distributions. Lastly, the feasibility of the proposed method has been validated using both numerical and experimental beams. Their damage was indicated by the magnitude variations of the damage index.