3 Case studies of model order reduction for acoustics and vibrations

doi:10.1515/9783110499001-003

Cited by 5 publications

(4 citation statements)

References 43 publications

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“…Therefore it can be used in the automatic approximation of ϕ i (s) given only the function values, a tolerance, and a maximum order. AAA has been successfully used to solve nonlinear eigenvalue problems [28] and to linearize dynamic systems with nonlinear frequency dependency [16,53]. Such linearization allows the direct use of standard model order reduction methods, but the system's structure is changed and the order is increased from n to n (d + 1) prior to the reduction, d being the maximum polynomial order of the nonlinear terms.…”

Section: Automatic Approximation Of Frequency Dependent Nonlinearitiesmentioning

confidence: 99%

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Automatic model order reduction for systems with frequency-dependent material properties

Aumann

Deckers

Jonckheere

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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Section: Automatic Approximation Of Frequency Dependent Nonlinearitiesmentioning

confidence: 99%

“…A reduced order model with the original matrix structure may preserve spectral properties and allows a physical interpretation of its matrices. If the reduced order model is coupled to other systems, preserving the matrix structure is beneficial as the same coupling conditions for the full and the reduced order models can be applied [16].…”

Section: Introductionmentioning

confidence: 99%

Automatic model order reduction for systems with frequency-dependent material properties

Aumann

Deckers

Jonckheere

et al. 2022

Computer Methods in Applied Mechanics and Engineering

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“…For efficient numerical computations, ideas for Arnoldi-like algorithms have been extended to the second-order system case [6,39] for application to structural and vibro-acoustic systems [5,54,59]. Further related methods for vibro-acoustic systems with poroelastic materials can be found in, e.g., [25,48,49]. An important aspect in interpolatory model order reduction is the choice of appropriate interpolation points.…”

Section: Introductionmentioning

confidence: 99%

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods

Aumann,

Werner

2022

Preprint

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Vibration and dissipation in vibro-acoustic systems can be assessed using frequency response analysis. Evaluating a frequency sweep on a full-order model can be very costly, so model order reduction methods are employed to compute cheap-to-evaluate surrogates. This work compares structure-preserving model reduction methods based on rational interpolation and balanced truncation with a specific focus on their applicability to vibro-acoustic systems. Such models typically exhibit a second-order structure and their material properties as well as their excitation may be depending on the driving frequency. We show and compare the effectiveness of all considered methods by applying them to numerical models of vibro-acoustic systems depicting structural vibration, sound transmission, acoustic scattering, and poroelastic problems.

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“…In addition, the preservation of internal system structures such as (4) and ( 5) is desired as this typically yields more accurate approximations as well as the preservation of structure inherent properties. Also, if the reduced-order model is to be coupled to other systems, preserving the structure is advantageous because the same coupling conditions as for the full-order model can be applied to the reduced surrogate [22].…”

Section: Introductionmentioning

confidence: 99%

Predicting near optimal interpolation points for parametric model order reduction using regression models

Aumann

Müller

2021

Proc Appl Math and Mech

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The design of vibro-acoustic systems, such as vehicle interiors, regarding optimal vibrational or sound radiation properties requires the solution of many numerical models under varying parameters, as often material or geometric uncertainties have to be considered. Vibro-acoustic systems are typically large and numerically expensive to solve, so it is desirable to use an efficient parametrized surrogate model for optimization tasks. High quality reduced models of non-parametric systems can be computed by projection, given a set of optimal expansion points. However, finding a set of optimal expansion points can be computationally expensive and each set is valid for a specific parameter realization only. The method presented in this contribution learns the map between a model's parameter realizations and the corresponding sets of expansion points using data-driven methods. Queried with an unknown set of parameters, the learned model returns a set of expansion points which are used to compute the corresponding reduced model efficiently. Numerical experiments on two vibro-acoustic models of different complexity are performed and three data driven regression methods are evaluated: multivariate polynomial regression, k-nearest neighbors, and support vector regression. Especially k-nearest neighbors regression yields accurate results for different types of physical models while being computationally inexpensive to fit.

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3 Case studies of model order reduction for acoustics and vibrations

Cited by 5 publications

References 43 publications

Automatic model order reduction for systems with frequency-dependent material properties

Automatic model order reduction for systems with frequency-dependent material properties

Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods

Predicting near optimal interpolation points for parametric model order reduction using regression models

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