Development of Probabilistic Surrogate Model for Uncertainty Quantification in Low Velocity Impact (LVI) of Caron/Epoxy Woven Composites

Kurzfassung

The design and certification of aero-composite structures rely on the test pyramid, also known as the building block approach. This process currently depends on experimental-based statistical test evidence such as material allowables [1]. Thus, the test pyramid necessitates costly and time-consuming experimental test campaigns up to the full-scale structure. To accelerate the certification process of fibre reinforced polymer (FRP) composite structures, there is growing interest in the aerospace industry for integrating machine learning (ML) models, which can shorten development cycles. For example, surrogate models can replace computationally expensive finite element (FE) simulations with an inverse inference model [2,3]. However, standard surrogate models often fail to capture inherent data variability in the context of the test pyramid. This highlights the need for implementing probabilistic methods that acknowledge real-world variations. To address these growing needs, this study reports a framework to develop a probabilistic surrogate model that connects the coupon level to the sub-element level of the test pyramid. This study uses low velocity impact (LVI) testing as a case study since understanding of impact damages such as barely visible impact damage (BVID) is crucial in certification process to ensure the performance and safety of composite structures. In this study, material properties measured at the coupon level are used for constructing a material card of FE simulation as input features, while the results of impact simulations are served as the target parameters. By establishing correlations between different length scales within the test pyramid, we aim to reduce the reliance on experimental tests conducted at coupon level. Fig. 1 presents the overview of a probabilistic surrogate modelling approach that utilises Bayesian Neural Networks (BNNs) via Monte Carlo (MC) Dropout and Gaussian Process Regression (GPR). This framework not only predicts the energy absorption behaviour of CFRP under impact but also quantifies the uncertainty associated with the predictions. Various mechanical tests at the coupon level are performed to generate a LS-DYNA® material card, MAT_ENHANCED_COMPOSITE_DAMAGE. Subsequently, experimental impact testing is conducted in accordance with ASTM D7136/D7136M to validate the impact FE simulation. The first step in training a surrogate model involves generating a comprehensive dataset that encompasses the design space of interest. To build a robust surrogate model, Latin Hypercube Sampling (LHS) is implemented to cover the multidimensional parameter space efficiently. This ensures that the entire range of each parameter is sampled, significantly improving the convergence rate of the surrogate model compared to random sampling. In the second step, the contribution of each parameter on the model prediction is investigated using SHapley Additive exPlanations (SHAP) [4] to find the importance of each parameter on the prediction for model interpretability. Finally, the surrogate model based on BNN and the GPR model are trained with the reduced input parameters based on their importance. The results from the trained surrogate model enable an accurate prediction of the impact residual energy at reduced time-to-prediction. The output generated by the surrogate model is a distribution rather than a single deterministic prediction. Additionally, the uncertainty within the model helps assess the confidence of the predictions. The comparative study between the BNNs and the GPR models indicates that performance significantly depends on the size of the training dataset. This work represents a first step toward developing a data-driven approach that minimises the reliance on physical experimental testing through probabilistic surrogate modelling. The proposed surrogate model is capable of accurately predicting the impact of residual energy with associated uncertainty. The identified uncertainty can be incorporated into decision-making processes, especially in the early stage of developing composite structures like evaluating operational applicability. Consequently, predictions that include uncertainty can help identify suitable material candidates while reducing the number of required experiments. Furthermore, this work paves the way for a scalable approach for the reduction.

References: [1] Cumbo R, Baroni A, Ricciardi A, et al. Design allowables of composite laminates: A review. Journal of Composite Materials. 2022;56(23):3617-3634. [2] Arndt C, Crusenberry C, Heng B, et al. Reduced-Dimension Surrogate Modeling to Characterize the Damage Tolerance of Composite/Metal Structures. Modelling. 2023;4(4):485-514. [3] Sakaridis E, Karathanasopoulos N, Mohr D. Machine-learning based prediction of crash response of tubular structures. International Journal of Impact Engineering. 2022;166:104240. [4] Lundberg SM, Lee S-I. A Unified Approach to Interpreting Model Predictions. Advances in Neural Information Processing Systems. 2017;30.