Efficient learning of uncertainty distributions in coupled multidisciplinary systems through sensory data

Coupled multidisciplinary systems are fundamental to many complex engineering systems, such as those in cyber–physical systems, aerospace engineering, automotive systems, energy networks, and robotics. Accurate analysis, control, and monitoring of these systems depend on effectively inferring their inherent uncertainties. However, the dynamic nature of these systems, along with the interconnectivity of various disciplines, poses significant challenges for uncertainty estimation. This paper presents a framework for learning uncertainty distributions in partially observed coupled multidisciplinary systems. By employing a non-linear/non-Gaussian hidden Markov model (HMM) representation, the authors capture the stochastic nature of system states and observations. The proposed methodology leverages particle filtering techniques and Bayesian optimisation for efficient parameter estimation, accounting for the inherent uncertainties in input statistics. Numerical experiments on a coupled aerodynamics-structures system and a power converter system demonstrate the efficacy of the proposed method in estimating input distribution statistics. The results highlight the critical importance of accounting for non-stationary behaviours in coupled multidisciplinary systems for capturing the true variability of input statistics and showcase the superiority of our method over approaches that assume data derive from the stationary state of the system.