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Non-intrusive techniques for Reduced Order Modelling

Authors: Girish, Shreyas;

Non-intrusive techniques for Reduced Order Modelling

Abstract

This thesis focuses on the development, implementation, and validation of nonintrusive Reduced Order Modeling (ROM) techniques for structural dynamic systems. Full-Order Models (FOM) are generated using Kratos Multiphysics for a two-dimensional cantilever beam subjected to varying multi-directional load cases. The displacement, velocity, and acceleration snapshots are collected to build the high-fidelity dataset. Proper Orthogonal Decomposition (POD) is employed to extract dominant modes, achieving a dimensionality reduction of over 98% while preserving more than 99.99% of the system energy. Two ROM approaches are explored. The Direct ROM method constructs reduced mass and stiffness matrices through Galerkin projection using the reduced basis. The Operator Inference ROM, on the other hand, infers system operators directly from the snapshot data without requiring access to the full governing equations, offering a non-intrusive and data-driven alternative. Both ROMs are solved using Newmark integration coupled with Newton-Raphson iterations to capture nonlinear dynamic behavior. Validation is performed by comparing the ROM outputs against the FOM solutions across displacement, velocity, acceleration, and force responses. Results show that the Direct ROM method achieves excellent agreement with the FOM, particularly for displacement predictions. The Operator Inference ROM demonstrates slightly higher reconstruction errors in displacement but outperforms the Direct ROM in velocity and acceleration predictions for certain cases. Additionally, the Operator Inference method shows promise for complex systems where access to full matrices is limited. Finally, a detailed comparison of solution times and error metrics highlights the efficiency and potential trade-offs of both approaches, providing critical insights into the practical deployment of ROM techniques for real-time structural simulations. The findings establish Operator Inference ROM as a competitive alternative for rapid dynamic simulations while maintaining acceptable levels of accuracy.

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Keywords

Operator Inference, Simplified Models, Cantilever Beam, Sistemes no lineals, Dinàmica estructural, Proper Orthogonal Decomposition, Nonlinear systems, Structural dynamics, Reduced Order Models, Real-Time Simulation, Kratos Multiphysics, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics, Structural Dynamics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average