Probabilistic Digital Twin for Misspecified Structural Dynamical Systems via Latent Force Modeling and Bayesian Neural Networks

TL;DR

This paper introduces a probabilistic digital twin framework that combines Gaussian Process Latent Force Models and Bayesian Neural Networks to improve response prediction in dynamical systems with model misspecification, effectively propagating uncertainty from diagnosis to prognosis.

Contribution

It develops an integrated approach using GPLFM and BNNs for uncertainty-aware diagnosis and prognosis in misspecified dynamical systems, enhancing digital twin reliability.

Findings

Accurately predicts responses in nonlinear systems with model errors.

Effectively propagates uncertainty from diagnosis to prediction.

Demonstrates robustness on benchmark systems.

Abstract

This work presents a probabilistic digital twin framework for response prediction in dynamical systems governed by misspecified physics. The approach integrates Gaussian Process Latent Force Models (GPLFM) and Bayesian Neural Networks (BNNs) to enable end-to-end uncertainty-aware inference and prediction. In the diagnosis phase, model-form errors (MFEs) are treated as latent input forces to a nominal linear dynamical system and jointly estimated with system states using GPLFM from sensor measurements. A BNN is then trained on posterior samples to learn a probabilistic nonlinear mapping from system states to MFEs, while capturing diagnostic uncertainty. For prognosis, this mapping is used to generate pseudo-measurements, enabling state prediction via Kalman filtering. The framework allows for systematic propagation of uncertainty from diagnosis to prediction, a key capability for trustworthy digital twins. The framework is demonstrated using four nonlinear examples: a single degree of freedom (DOF) oscillator, a multi-DOF system, and two established benchmarks -- the Bouc-Wen hysteretic system and the Silverbox experimental dataset -- highlighting its predictive accuracy and robustness to model misspecification.