A MACHINE LEARNING FRAMEWORK FOR ALLEVIATING BOTTLENECKS OF PROJECTION-BASED REDUCED ORDER MODELS.

Abstract

Digital twins and virtual representations have become critical components in structural health monitoring applications of real-life engineering systems. These numerical surrogates should capture nonlinear effects and accurately recover the involved dynamics, whilst providing a substantial reduction of computational resources and a near real-time evaluation [7]. In this context, Reduced Order Models (ROMs) have emerged as efficient low-order representations, featuring in various monitoring applications ranging from vibration control to residual life estimation. A dominant approach to derive physics-based ROMs is projection-based reduction. This exploits Proper Orthogonal Decomposition, or similar projection techniques, to approximate the subspace where the principal components of the dynamic response lie [2]. To achieve this, POD is applied on a series of response time series produced from the full-order model evaluation, henceforth termed as snapshots. This leads to the assembly of a basis, subsequently employed to project the governing equations in a linear subspace, thus enabling the propagation of the dynamics in a reduced coordinate space. Integrating the projected, low-order system of equations forward in time can potentially lead to substantial computational savings, while maintaining an accurate approximation, which additionally comes with physical connotation. The ROM is additionally coupled with a second-tier approximation termed hyper-reduction to address the bottleneck of evaluating the nonlinear terms on the reduced coordinate space [3]. Although this class of reduction strategies has been proven effective, both in terms of approximating nonlinear dynamic behavior and providing an efficient evaluation with respect to computational time, the derived ROMs suffer from two significant bottlenecks [6]. As already described, the