Accelerated Bayesian Inference of Structural Damage Detection Using a Convolutional Neural Network Surrogate Model

Performing Bayesian inference of structural damage detection is always computationally intractable, as the corresponding posterior probability density function (PDF) is commonly configured with hundreds/thousands of parameters. For Markov Chain Monte Carlo (MCMC) methods, thousands of likelihood calls are required for stochastic exploration of the parameter space, while evaluation of the likelihood function requires complex forward modeling for each set of structural parameters explored during the sampling process. This study proposes an accelerated Bayesian inference (ABI) algorithm for structural damage identification based on a convolutional neural network (CNN)‐based surrogate model. As an emulator for the likelihood function, the CNN is constructed using samples from the prior distribution of damage parameters, and the weighted sampling is employed to select uniformly distributed samples in the parameter space for model training. The Metropolis–Hasting (MH) algorithm with this surrogate model is then integrated into the delayed acceptance framework, in which the surrogate model behaves as an approximate model to generate easily computed proposals transferred to the exact model, thus reducing the computational burden imposed by repeated evaluations of the computationally expensive likelihood. Considering the non‐negligible bias of the surrogate model, the enhanced error model is used to adaptively correct the surrogate model using online posterior samples. An experimental three‐story frame and a numerical cable‐stayed bridge are utilized to verify the effectiveness of the proposed method. Compared to traditional sampling methods, the computational cost of damage detection can be reduced by up to 75%, and at the same time the damage identification accuracy has been improved, especially for large‐scale complex structures. Although the proposed algorithm is developed for a particular structural damage identification problem, it can be extended to all other models with a costly likelihood for accelerating uncertainty quantification. Moreover, the proposed CNN surrogate model can be incorporated into other sampling‐based methods.