POD Reduced-Order Modeling for Inverse Material Characterization from Transient Dynamic Tests

摘要

Inverse problem solution methods have been widely used for nondestructive material characterization problems in a variety of fields, including structural engineering, material science, aerospace engineering and medicine. A traditional inverse problem solution approach for material characterization is to create a numerical representation of the system, such as a finite element model, combined with nonlinear optimization techniques to minimize the difference between the experimental response and the numerical representation. Unfortunately, due to the high computational cost of analyzing the numerical representation of many systems, it can often be impractical to solve a given inverse problem by this traditional method.parudA strategy for using reduced-order modeling, in particular the proper orthogonal decomposition (POD) model reduction approach in inverse material characterization problems is presented in this work. POD is used to derive a low-dimensional basis from a finite set of full-order numerical analyses of the system. The governing equations of the system are projected onto the obtained POD basis to construct a reduced-order model (ROM). The ROM is then used to replace the full-order modeling to reduce the high computational cost, while still keeping the accuracy of the response close to that of the full-order model. After that, the ROM is combined with a global optimization algorithm to identify an estimation of the material properties in the system. A case study of a damaged aluminum plate, which is subjected to a time-dependent harmonic sinusoidal excitation, is chosen to demonstrate that the ROM strategy is capable of accurately identifying material parameters of a system with minimal computational cost.