Improving Optimization-based Inverse Analysis using Direct Inverse Maps: A Dynamic Damage Identification Case Study

Abstract

Inverse problems in engineering form routinely part of larger engineering simulations. Therefore, the quality of the solution to an inverse problem directly influences the quality of the larger simulation and, ultimately, the ability to solve an engineering problem. Inverse problems can be challenging and time-consuming to solve, as most inverse strategies require iteration due to the non-linear nature of the problem. As a result, they often remain poorly solved before proceeding to the larger analysis. The quality of the solution to an inverse problem is influenced by the inverse strategy, scaling of the problem, scaling of the data, and initial guesses employed for iterative strategies. Research has focussed considerably on inverse strategies and scaling. However, research into strategies that improve initial guesses of an inverse problem has been largely neglected. This study proposes an elegant strategy to improve the initial guesses for conventional optimization- based inverse strategies, namely direct inverse maps (DIMs) or inverse regression. DIMs form part of modern multivariate statistics. DIM approximates the solution to an inverse problem using regression; popular choices are linear regression, e.g., partial least squares regression (PLSR). These strategies are not iterative but require several independent a- priori simulations to have been conducted. As they are not iterative, one way to improve the solution is to increase the number of independent a-priori simulations to be conducted. Our proposed strategy is to use DIM to generate initial guesses for optimization-based inverse strategies. We conduct a parameter investigation on a truss structure's virtual vibration- based damage identification problem.