Bayesian damage identification based on autoregressive model and MH-PSO hybrid MCMC sampling method

Bayesian damage identification method, due to its ability to consider the uncertainties, has attracted much attention from researchers. However, there are two key issues to ensure the accuracy of this method, namely, the damage identification objective function and sampling method. The existing objective function based on natural frequencies and mode shapes (FFM), due to the limitation of sensors leading to incomplete measurement, shows poor damage identification ability. Meanwhile, the sampling efficiency of the common sampling method [i.e., the standard Metropolis–Hastings (MH) algorithm] still needs to be enhanced. Aiming at these problems, this study proposes a new objective function based on autoregressive coefficients (FAR), and improves the standard MH algorithm by introducing the particle position updating mechanism in Particle Swarm Optimization (PSO), resulting in MH-PSO hybrid Markov Chain Monte Carlo sampling method (MH-PSO method); both of them are combined to form an improved Bayesian damage identification method. And then, two numerical examples of cantilever beam and American Society of Civil Engineers benchmark frame are exploited to evaluate the effectiveness of the proposed FAR and MH-PSO method, respectively. The results show that FAR has better damage identification ability for multiple damage case than FFM, and the proposed MH-PSO method illustrates better statistical efficiency than the Differential Evolution Monte Carlo method in the case of multi-damage of complex structure. Finally, the effectiveness and feasibility of the proposed improved Bayesian damage identification method has been validated by the experimental frame, whose outcome proves that the proposed method is feasible and accurate.