The Bayesian pattern search, a deterministic acceleration of Bayesian model updating in structural health monitoring

Finite element (FE) model updating is a popular tool for damage localisation and quantification in structural health monitoring (SHM) of buildings, infrastructure and wind turbines. Considering the prevailing uncertainty in these applications is very important to achieving reliable results. Bayesian model updating (BMU) is a promising and well-investigated method for uncertainty quantification in SHM. BMU methods require many model evaluations to solve the updating problem. Therefore, they cannot always be applied to real-world examples, where FE simulations with considerable computational time must be performed for every model evaluation. In this work, the global pattern search algorithm (GPS), a deterministic global optimisation, is used to accelerate BMU in a two-step approach. The approach is therefore called "Bayesian pattern search" (BPS). The efficient deterministic GPS algorithm is used as a first step to solve the model-updating problem deterministically. After this, the well-established Bayesian model-updating method, the transitional Markov chain Monte Carlo (TMCMC) method, is used to quantify the influence of the prevailing uncertainty associated with the model-updating problem. The BPS method is tested using a simulated two-mass oscillator and a laboratory steel beam featuring a reversible damage mechanism and real measurement data. The results show that the new approach BPS is able to produce results similar to those of the conventional Bayesian TMCMC approach, but at a significantly improved numerical performance, which can make it approximately 17 times faster.