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 optimizationbased 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 apriori 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.
