Uncertainty quantification of bistable variable stiffness laminate using machine learning assisted perturbation approach

Morphing structures have received growing interest in aerospace structures and wind turbines due to their rapid shape-changing ability in response to the change in operating conditions. Bistable laminates using variable stiffness composites are considered potential candidates in morphing structures for their ability to tailor the design space with a plethora of multiple stable configurations and satisfy the conflicting requirements of load -carrying capacity and deformability. Even though extensive works have been reported on the analysis and design of the cured shape of unsymmetrical variable stiffness laminates for morphing application, the effect of uncertainty in design variables on the behavior of bistable laminates is not profoundly assessed in the literature. In particular, uncertainty propagation through a highly non-linear map can lead to a significant discrepancy between the numerically predicted and experimental observations. Therefore, for adaptability in practical application, it is imperative to quantify the uncertainty as well as to characterize the non-linearity present near the design point of interest. In this work, a general purpose machine learning assisted uncertainty quantification (MLAUQ) framework is developed and demonstrated on unsymmetrical bistable laminate. The study considers three different variants of the approach based on the order of approximation (O(hk)) used for the training purpose. It is found that the MLAUQ - 3 approach performs better than other approaches, and a theoretical justification for the same is provided. The method relies on the fact that expensive computation of the Hessian required for standard perturbation approaches can be bypassed by training a neural network while retaining accurate gradient information near the design point of interest. In the case of bistable laminate, a network trained with a few training samples can capture the local model non-linearity. Further, numerical investigations reveal that the proposed approach is computationally efficient and accurate compared to traditional uncertainty quantification (UQ) approaches.