Copula-Based Multi-structure Damage Co-diagnosis and Prognosis for the Fleet Maintenance Digital Twin

Digital-twin-based structural diagnosis and prognosis are growing topics that have an important role in improving in-service safety and the economy. However, current research focuses primarily on individual structures using Bayesian-based updating approaches, leaving little attention to the multiple similar structures at the fleet level. Given the nonlinear and non-Gaussian nature of the structural damage evolution, direct modeling of multiple structures would require a larger number of particles. The study presents a novel copula-based approach for efficiently modeling multi-structure damage diagnosis and prognosis in a fleet. The proposed approach leverages the particle filter to model the damage growth in each structure and utilizes the copula function to capture the relationship between structures as the joint probability distribution. The relevant parameters in the copula function are estimated using the maximum mean discrepancy metric based on the similarity of the predicted damage state, and structural parameters. Once an observation is available for a structure, the damage states of the structure and other structures in the fleet are updated using the approximate copula-based joint distribution. The results from hypothetical datasets demonstrate that the proposed approach improves prediction accuracy compared to traditional individual-based methods and effectively controls uncertainties for each structure, even during intervals of no observations. This approach holds promise for integration into the fleet maintenance digital twin.