Hybrid framework with regularized model updating and deep learning for structural damage identification

For several decades, much attention has been paid to the field of structural health monitoring (SHM) and damage identification, and numerous methods have been proposed to contribute to its development. Traditional finite element model (FEM) updating-based methods with regularization have the advantages of a clear deduction process and specific physical meaning, but also suffer from the challenges of instability in solution and complication and uncertainty in regularization parameter selection. The powerful fitting ability of deep learning (DL)-based methods effectively advances the capability of damage identification methods. However, these methods are usually criticized as black box models without the physical interpretability. There is no specific guide for network design, which brings obstacles to a wide range of applications. In this study, a physically interpretable hybrid framework for damage identification with a high accuracy is proposed by coupling regularized FEM updating with DL method. In the proposed framework, the regularized FEM updating provides physically meaningful quantities, including damage increments, residual information, and regularization-related terms, which are used to guide the network architecture by domain-mapping analysis. Meanwhile, the DL model learns the updating operation from the dataset, reducing the dependence on manually selected regularization parameters and improving the stability of noise-interference damage identification. Numerical and experimental studies are adopted to validate the proposed approach. Moth-flame optimization, the FEM updating with Tikhonov regularization method and the representative DL methods are also applied to conduct a comparative study to demonstrate the superiority of the proposed hybrid framework. The results show that the proposed framework can achieve accurate and reliable damage identification results under noise effect.