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

Model uncertainty quantification is essential for enhancing the validity of simulations of nonlinear dynamic systems. However, its effectiveness may be affected when 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 but distinct systems. In this paper, we propose a novel population-based model bias correction (PMBC) framework that employs federated learning (FL) to enable distributed, privacy-preserving bias correction for a population of distinct but similar nonlinear dynamic systems. 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-form errors and parameter uncertainty. FL 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, and the original simulation model. The results indicate that the proposed PMBC method consistently produces the lowest prediction errors, maintaining generalization under new input excitations.