A Deep Learning Method for Modeling and Uncertainty Evaluation of Nonlinear Dynamic Systems

With the widespread application of nonlinear dynamic systems in modern industrial measurements, ensuring the reliability and stability of measurement results has become increasingly important. However, there is currently a lack of mature and effective methods for addressing dynamic measurement uncertainty assessment. Inspired by the successful application of deep learning techniques in modeling complex dynamic systems, this study explores methods for uncertainty assessment in nonlinear dynamic systems. First, for systems that are difficult to describe with traditional mathematical analytical models, an appropriate neural network is used for modeling. Second, the network structure is optimized by incorporating the system’s physical information. Lastly, methods for system modeling and uncertainty assessment are explored in scenarios with limited data. This study proposes a Physics-Informed Bayesian Network (PIBNN) framework, which integrates the mapping capability of deep learning with physical constraints. By learning the latent structure of nonlinear dynamic systems from measurement data and using uncertainty constraints, the model’s fitting performance is enhanced. Simulation and experimental results demonstrate that this framework outperforms traditional methods in terms of generalization ability and physical interpretability, and exhibits significant effectiveness in uncertainty assessment and reliability analysis of measurement results.