MODAL-DRN-BL: A Framework for Modal Analysis Based on Dilated Residual Broad Learning Networks

Abstract Each object has unique inherent frequencies and vibration modes, which are known as modal parameters. The modal analysis aims to study the free vibration characteristics of an object under an external force action. In modal analysis, finite element method (FEM) is widely used to build dynamic model structures and solve for modal parameters. Nevertheless, despite its widespread application, FEM does come with certain drawbacks related to computational efficiency. FEM necessitates the construction of stiffness and mass matrices for the structure, alongside an eigenvalue analysis during modal analysis, which can result in extensive computational time. Additionally, meshing the object is a fundamental requirement for FEM, and achieving proper meshing can be a laborious and time-consuming task. In the case of nonlinear problems, FEM demands iterative solutions, with each iteration addressing a linear system. To that end, in this article, we propose a MODAL-DRN-BL framework to improve the computational efficiency against FEM. MODAL-DRN-BL utilizes convolution operation to effectively expand the receptive field and capture vibration information at longer distances. It also handles sparse interaction between features through a broad learning module. Experimental results demonstrate that our proposed MODAL-DRN-BL framework achieves a mean absolute error of 1.49 in modal analysis benchmark ansys apdl (Ansys Parametric Design Language). Moreover, in terms of computational time, the MODAL-DRN-BL framework exhibits significant optimization compared to ansys apdl, resulting in a five-order-of-magnitude improvement in computational efficiency.