Evaluation of the Influence of Generalized Variables and Geometry on the Dynamic Response of Structures Using Explainable Machine Learning Techniques

This work exploits Machine Learning (ML) for evaluating 1D structural theories, with a particular focus on the influence of generalized displacement variables and physical parameters on the accuracy of dynamic analysis. The structural cases analyzed are clamped-free beams with stiffened thin-walled cross-sections. The structural theories are generated using the Carrera Unified Formulation (CUF), which enables systematic multi-fidelity analysis by varying the order of the kinematic expansion. A Neural Network (NN) is developed and trained using a set of input features that represent the generalized variables. The NN aims to estimate how accurately a given theory detects dynamic behavior for a given set of problem features, e.g., cross-section geometries and boundary conditions. To interpret the predictive behavior of the trained model, eXplainable Machine Learning (XML) tools based on SHapley Additive exPlanations (SHAP) values are employed to evaluate the importance of each input variable on the output, providing a measure of how much each input variable influences the accuracy achieved by each kinematic theory. The aim is to extract the most influential terms and use them to build optimized reduced models with the minimum number of unknown variables and the maximum fidelity. The results highlight the importance of higher-order terms in improving the accuracy of the structural theory and their dominance over linear terms in structural cases with very low slenderness ratios.