A refined TMCMC algorithm for adaptive model updating for the probabilistic analysis of complex engineering structures

Modelling complex engineering structures involves numerous parameters that are difficult to determine. Many uncertainties in the model parameters cannot be resolved through standards and experiments alone, necessitating model updating methods. The Bayesian model updating method is one of the most popular approaches for this purpose; and it has led to the development of numerous improved algorithms. However, the traditional Bayesian model updating algorithms are time-consuming and may not always yield the most likely posterior distributions of the model parameters in engineering applications. Therefore, this paper introduces a refined transitional Markov chain Monte Carlo (rTMCMC) algorithm based on the TMCMC algorithm and improved TMCMC (iTMCMC) algorithm. The rTMCMC algorithm is an adaptive Bayesian model updating method designed for engineering applications; it can adaptively find the most likely posterior distributions of model parameters without increasing the computation time. The efficiency of the rTMCMC algorithm is validated via a numerical example, which compares it with the TMCMC and iTMCMC algorithms. Finally, two examples at both the component and structural levels, updated by the rTMCMC algorithm, and compared with the iTMCMC algorithm, are presented, demonstrating the effectiveness of the rTMCMC algorithm in engineering applications.