Using NNMs to Evaluate Reduced Order Models of Curved Beam

VanDamme, Christopher I.; Allen, Matthew S.

doi:10.1007/978-3-319-30084-9_42

Cited by 4 publications

(2 citation statements)

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“…The value of the scaling factor determines the amount of nonlinearity that is excited in the system and thus the coefficients to be estimated. Previous works [17,18] sought to find a set of optimal loads for which to excite the structure such that the ROM is accurate. This approach, although shown to be effective in certain cases, does not evaluate the ability of the ROM to generalize to other load cases and may be case dependent.…”

Section: Introductionmentioning

confidence: 99%

“…This procedure evaluates the core function of the nonlinear ROM, its ability to accurately predict the nonlinear internal force for a given displacement state. Most works in the field have used subsequent evaluation metrics, such as static displacement [5,11], random response [5,11], and nonlinear normal modes [17,18]. These more complex and computationally expensive metrics indirectly evaluate the ability of the ROM to predict the nonlinear internal force.…”

Section: Introductionmentioning

confidence: 99%

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Simultaneous Regression and Selection in Nonlinear Modal Model Identification

Damme

Madrid²,

Allen

et al. 2021

Vibration

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High fidelity finite element (FE) models are widely used to simulate the dynamic responses of geometrically nonlinear structures. The high computational cost of running long time duration analyses, however, has made nonlinear reduced order models (ROMs) attractive alternatives. While there are a variety of reduced order modeling techniques, in general, their shared goal is to project the nonlinear response of the system onto a smaller number of degrees of freedom. Implicit Condensation (IC), a popular and non-intrusive technique, identifies the ROM parameters by fitting a polynomial model to static force-displacement data from FE model simulations. A notable drawback of these models, however, is that the number of polynomial coefficients increases cubically with the number of modes included within the basis set of the ROM. As a result, model correlation, updating and validation become increasingly more expensive as the size of the ROM increases. This work presents simultaneous regression and selection as a method for filtering the polynomial coefficients of a ROM based on their contributions to the nonlinear response. In particular, this work utilizes the method of least absolute shrinkage and selection (LASSO) to identify a sparse set of ROM coefficients during the IC regression step. Cross-validation is used to demonstrate accuracy of the sparse models over a range of loading conditions.

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Section: Introductionmentioning

confidence: 99%