A Novel Method for Damage Identification Based on Tuning-Free Strategy and Simple Population Metropolis-Hastings Algorithm

The most commonly used method for sampling damage parameters from the posterior distribution is the Markov chain Monte Carlo (MCMC) method. The population MCMC method as one of the MCMC methods has been utilized for damage identification by some researchers recently. Nevertheless, for the conventional population MCMC methods, these sampling methods often require significant computational resources and tuning of a large number of algorithm parameters. Aiming at the problem of difficulty in selecting the proposal distribution and low computational efficiency in the conventional MCMC method, this paper proposed a simple population Metropolis-Hastings (SP-MH) algorithm for the damage identification, which is realized by exchanging information among chains in a relatively small population and using tuning-free strategy. Then, a numerical cantilever beam and an experimental frame are utilized to verify the effectiveness and feasibility of the proposed algorithm, it can be seen that the convergence rate of the SP-MH algorithm is faster than that of the Differential Evolution Monte Carlo (DE-MC) algorithm, and in a small population state, the SP-MH algorithm can still maintain convergence, saving plenty of computing time for damage identification. The results show that the SP-MH algorithm is feasible and accurate in practice damage identification, and the SP-MH algorithm performs better than the DE-MC algorithm. Compared with the DE-MC algorithm, the SP-MH algorithm is simple and convenient for damage identification due to its tuning-free strategy and relatively small population.