Comparing reduced order model forms for nonlinear dynamical systems

Massegur, David, Clifford, Declan, Ronch, Andrea Da and Symon, Sean (2022) Comparing reduced order model forms for nonlinear dynamical systems. In Proceedings of the 33rd Congress of the International Council of the Aeronautical Sciences, ICAS 2022. vol. 6, International Council of the Aeronautical Sciences. pp. 4039-4071 .

Abstract

The time domain solution of a chaotic system governed by a set of nonlinear equations is computationally expensive and ill suited for parametric searches. This work investigates the use of reduced order models to distill, both from data and equations, an equivalent but more advantageous mathematical representation. Two types of reduced order model are presented, data-driven, non-intrusive approaches and a model-derived, intrusive alternative. Three test cases are used for assessing the predictive capability of the models: a) Lorenz 1963 model; b) Moehlis model; and c) Lorenz 1996 model. Various key performance indices are selected to quantify the accuracy of the reduced order models, including over the short and long time scales. The small size of the test cases, up to 220 states for Lorenz 1996 model, prevented us from executing a projection of the reduced order models onto a smaller basis. Hence, the focus was on recovering the underlying governing equations and on the reconstruction of the physical features. For each reduced order model, details concerning the practical implementation and the model generation are also given.

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Contributors

Author: David Massegur

Author: Andrea Da Ronch

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