A Population-Based Model Bias Correction Framework Using Federated Learning for Simulation Models of Nonlinear Dynamic Systems

Abstract Model uncertainty quantification is essential for enhancing the validity of simulations of nonlinear dynamic systems. However, its effectiveness may be significantly affected when experimental or monitoring data are sparse. To tackle this challenge, we drew inspiration from population-based structural health monitoring, which enhances damage diagnostics by facilitating information sharing across a population of similar (in some context) but different systems. In this article, we propose a novel population-based model bias correction (PMBC) framework that employs federated learning (FL) to enable distributed, privacy-preserving bias correction for populations of nonlinear dynamic systems sharing a common design framework but with different system models in reality due to uncertainty in unit-specific model parameters and model-structural errors. The model uncertainty in a population of nonlinear dynamic systems is first analyzed using the Kennedy and O’Hagan (KOH) framework. The proposed method then constructs a shared nonlinear autoregressive with eXogenous inputs (NARX) surrogate model for the simulation model and develops system-specific bias datasets that capture both model-structural errors and parameter uncertainty. Federated training is employed to collaboratively learn a global bias correction model, which is subsequently fine-tuned into system-specific bias models using local datasets to correct biases in a population of nonlinear dynamic systems. The effectiveness of the proposed framework is demonstrated through two case studies, namely a population of Duffing oscillators and a fleet of three ship-heading models. In both cases, the PMBC approach is compared with a conventional single-system bias correction method, a centralized approach with and without fine-tuning, and the original simulation model. The results indicate that the proposed PMBC method consistently produces the lowest prediction errors, maintaining robust generalization under untested new input excitations.