<p>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 reproduce the dynamics accurately, whilst providing a substantial reduction of computational resources and a near real-time evaluation. Reduced Order Models (ROMs) have emerged as efficient low-order representations in this context. A dominant approach to derive reliable ROMs is projection-based reduction, relying on POD or similar techniques to approximate the subspace where the principal components of the dynamic response lie. The dynamics are subsequently projected and propagated in the respective manifold, coupled with a second-tier approximation termed hyper-reduction to address the bottleneck of evaluating the nonlinear terms on the reduced coordinate space. Although this class of reduction strategies has been proven effective, both in terms of approximating the real-life system’s dynamic behavior and providing an efficient evaluation with respect to computational time, the derived ROMs suffer from two significant bottlenecks. First, the ROM performance is directly related to the reconstruction error of the actual response manifold. Thus, the linear nature of the POD operator (or equivalent ones) imposes accuracy limitations, as it constrains the dynamics to evolve in a linear approximation of the original manifold. Additionally, the hyper-reduction strategy becomes the primary source of error, as it necessarily sacrifices the nonlinear mapping’s accuracy to achieve a reduction in the computational cost. Our work explores the potential of employing machine learning tools to derive a reduction framework able to address and potentially overcome the aforementioned bottlenecks, drawing inspiration from similar works in this context. We capitalize on two fundamental aspects. On the one hand, we tackle the reconstruction error minimization via the use of autoencoders in order to approximate the nonlinear response manifold, as an initial step towards substituting POD-based projection. This attempts to define a more appropriate, nonlinear scheme to approximate the respective response manifolds leading to more accurate approximations. At the same time, our efforts scrutinize the possibility of exploiting LSTM-based neural network schemes as a more accurate surrogate of the nonlinear mapping on the reduced space, as opposed to the adoption of hyper-reduction. The proposed ROM features are validated with respect to their ability to outperform the linear, POD-based ROM.</p>

A Machine Learning Framework for Alleviating Bottlenecks of Projection-Based Reduced Order Models

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

ASME 2021 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2021)

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