Reverse Variational Autoencoder: A probabilistic inference framework for structural health monitoring and inverse analysis in engineering

• Proposed RVAE: A Bayesian deep learning framework for efficient inverse analysis. • RVAE incorporates causality by reversing the VAE compression-decompression structure. • RVAE reveals multiple possible solutions with high accuracy and efficiency. • RVAE outperforms traditional methods, achieving 1,000x faster inverse analysis. • RVAE offers flexibility with label-free inversion and adaptable prediction ranges. Inverse analysis in structural engineering involves inferring uncertain parameters from limited external observations, which is crucial for structural health monitoring and maintenance. However, real-world applications often face under-constrained problems with multiple possible solutions due to sparse measurements. This study proposes a Bayesian deep learning-based framework, termed Reverse Variational Auto-Encoder (RVAE), to fulfill efficient probabilistic structural inverse analysis. The RVAE framework modifies the original VAE structure to consider the causality relationship underlying inverse problems, enabling a semi-supervised learning paradigm for label-agnostic scenarios. The effectiveness of the RVAE framework is validated through a grid structure experiment. The implemented model successfully reveals all possible solutions for bending amplitudes, strains, and node displacements, with root-mean-squared reconstruction errors of 1.21 %, 2.77 %, and 1.36 %, respectively. A comparative analysis is conducted between mainstream inversion algorithms and RVAE. The results demonstrate that while all the other inversion algorithms achieve low reconstruction errors, they provide single-solution estimation, thus highlighting RVAE's capability to provide the most comprehensive information. RVAE's capability for real-time probabilistic estimation of structural parameters is further discussed and demonstrated in a full-scale bridge tower experiment, where it utilizes multi-sensor data to infer critical structural parameters, showing strong adaptability to noisy, incomplete, and heterogeneous monitoring inputs. In summary, RVAE tackles the challenges of large-scale parameter inversion in engineering structures by enabling efficient probabilistic inference under sparse observations. It supports semi-supervised learning in label-agnostic scenarios and real-time prediction of multiple plausible solutions, thereby fulfilling the synchronous updating requirements of digital twin systems.