Assessment of Multi-Fidelity Structural Theories for Dynamic Analyses Using Machine Learning

Abstract This paper presents a machine-learning approach to assessing structural theories’ computational cost and accuracy and provides guidelines on the proper finite element modeling for various numerical cases. The proposed approach exploits the Carrera Unified Formulation (CUF) to obtain multi-fidelity refined structural theories and governing equations. Machine learning techniques are used to build surrogate models. CUF provides training data for neural networks, considering higher-order polynomial expansions of the displacement field and problem features, e.g., thickness, geometry, material properties, and boundary conditions. The surrogate model’s training aims to estimate a structural theory’s accuracy, i.e., the fidelity, when providing structural dynamics outputs for a given set of inputs. For instance, the trained network can establish the accuracy of a third-order shear deformation theory in detecting the natural frequencies. Furthermore, indications of the most influential input parameters and generalized primary variables are obtained. Multi-fidelity structural theories are assessed by varying the number of generalized displacement variables, i.e., the nodal degrees of freedom, of finite element models. Low-, first-order theories are incrementally enriched with higher-order terms. The trained network indicates which terms must be retrieved to satisfy a given fidelity requirement.