Finite Element Model Updating for Bridges Based on Adaptive Nested Sampling and Bayesian Theory

In bridge health monitoring based on finite element models, Bayesian model updating techniques are commonly used to quantify the uncertainties of important parameters in the finite element models, so as to address the issue of non-uniqueness in model updating caused by measurement errors, modeling errors, computational errors, etc. To resolve the problem of low efficiency in model updating due to the large number of finite element simulations required, a Bayesian model updating method based on an adaptive nested sampling (ANS) algorithm was proposed. The method used the modal parameters to construct the probability objective function and adopted the ANS algorithm to approximate it. ANS retained the nature of nested sampling (NS), which made the samples ultimately approximate the optimal parameters by narrowing the sampling range layer by layer, and it simplified the computation process of the evidence value and the a posteriori probability density value by transforming the high-dimensional integration problem into a simple one-dimensional integration problem through layer-by-layer approximation. On this basis, the ANS algorithm could also reduce the call of the finite element model by adaptively adjusting the number of samples during the iteration process. Finally, a pedestrian truss bridge was used as a case study for Bayesian finite element model updating experiments. The results demonstrate that under the same algorithm parameter settings, the ANS algorithm reduces the number of finite element simulation calls by approximately 84% compared to the traditional NS algorithm. This leads to approximately 86% computational time savings while obtaining uncertainty updating results with equal accuracy.