Surrogate models of complex dynamic systems from energy distributions

Abstract

Engineers who design complex dynamic systems do not have the luxury of iteration. Numerical analysis of a single design, typically by finite element analysis, requires enormous amounts of CPU time. Therefore, improving a design by trying out many design modifications is impossible. Moreover, it is also impossible to identify which subsystem designs have the largest effects on the dynamic response of the system. The present work addresses this challenge by constructing surrogate models from energy distributions in a nominal design. These surrogate models are surprisingly effective at identifying subsystems that have the largest effects on the dynamic response, and therefore guide engineers to design modifications that matter most. A significant advantage of these surrogate models is the very low cost of creating them, as they are created directly from the frequency response of a nominal design and therefore do not require additional linear solves or other time-intensive calculations. This presentation begins with an analytical justification for considering energy distributions as surrogate models. Next, Monte Carlo Simulations are presented to show strong correlations between energy distributions and the effects of design changes on dynamic responses. These simulations include random structures as well as beams. Work supported by ONR under Grant N00014-19-1-2100.