PGVAE-VBAKF: A robust strategy for complex system response prediction and noise variance estimation considering modeling errors and nonstationary noises

Document Type

Article

Publication Date

1-15-2026

Abstract

Accurate system response prediction is essential in understanding the latent physics and assessing the performance, safety, and durability of structures. Although numerous model- and data- based methods have been developed for structural response prediction, the combined effects of modeling errors and time-varying measurement noises can significantly reduce the response prediction accuracy. To address this issue, the present study proposes a Physics-Guided Variational Auto-Encoder with Variational Bayesian Adaptive Kalman Filter (PGVAE-VBAKF) strategy for complex system response prediction and noise variance estimation. First, to mitigate the impact of modeling errors on complex system learning, this study proposes a PGVAE-based approach that integrates state-space modeling with neural networks. This method enhances the accuracy of response modeling for complex systems. Compared to data-driven methods, the proposed PGVAE-based approach can significantly reduce the relative root mean square error (RRMSE) of response prediction. Second, this study employs a well-trained PGVAE to replace the transition and observation models in the Kalman filter, which can effectively mitigate the influence of inaccurate system matrices and yield precise response estimation. Third, to handle nonstationary noises, this study integrates PGVAE with VBAKF to enable effective response estimation for complex systems subject to modeling errors and nonstationary noises, which can quantify time-varying noise variances. Furthermore, a model reduction strategy that integrates PGVAE with Z-score normalization, modal superposition, and residual neural network is proposed to improve the training efficiency and high-dimensional system learning accuracy. Numerical and experimental studies are implemented to validate the performance of the proposed method. Research results show that the proposed method can accurately predict the complex system response and quantify the uncertainty of noise variances. The proposed method can effectively mitigate the combined adverse effects of modeling errors and nonstationary noises for complex system learning and has the potential to be applied for structural health monitoring (SHM) of complex nonlinear structures.

Publication Source (Journal or Book title)

Mechanical Systems and Signal Processing

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