Ensuring the accuracy of indirect nonlinear dynamic reduced-order models

Numerous powerful methods exist for developing reduced-order models (ROMs) from finite element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra d...

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Bibliographic Details
Published inNonlinear dynamics Vol. 112; no. 3; pp. 1997 - 2019
Main Authors Xiao, Xiao, Hill, Thomas L., Neild, Simon A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.02.2024
Springer Nature B.V
Subjects
Accuracy
Automotive Engineering
Classical Mechanics
Control
Curved beams
Dynamical Systems
Energy levels
Engineering
Finite element method
Mechanical Engineering
Nonlinear dynamics
Original Paper
Reduced order models
Vibration
Reduced-order models (ROMs)
Finite element model
Geometric nonlinearity
Error metric
Load case selection
Multi-dimensional fitting procedure
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Summary:Numerous powerful methods exist for developing reduced-order models (ROMs) from finite element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra dynamic FE simulations. It has been shown that the well-established implicit condensation and expansion (ICE) method can produce an accurate ROM when the FE model’s static behaviour are captured accurately. However, this is achieved via a fitting procedure, which may be sensitive to the selection of load cases and ROM’s order, especially in the multi-mode case. To alleviate this difficulty, we define an error metric that can evaluate the ROM’s fitting error efficiently within the displacement range, specified by a given energy level. Based on the fitting result, the proposed method provides a strategy to enrich the static dataset, i.e. additional load cases are found until the ROM’s accuracy reaches the required level. Extending this to the higher-order and multi-mode cases, some extra constraints are incorporated into the standard fitting procedure to make the proposed method more robust. A curved beam is utilised to validate the proposed method, and the results show that the method can robustly ensure the accuracy of the static fitting of ROMs.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-09094-2