Parametric model order reduction without a priori sampling for low rank changes in vibro-acoustic systems

Ophem, S. van; Deckers, Elke; Desmet, Wim

doi:10.1016/j.ymssp.2019.05.035

Cited by 14 publications

(26 citation statements)

References 23 publications

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“…This formulation is an extension to second-order systems of the formulation shown in [10]. An alternative formulation was previously shown in [1].…”

Section: Low Rank Model Order Reduction Formulation For Vibro-acoustimentioning

confidence: 98%

“…The application of MOR on vibro-acoustic systems comes with specific challenges, such as time-stability and the modeling of parametric variations that are related to the physical system, such as structural boundary conditions, a change of material properties, etc [5]. Recently, a novel reduction scheme for lowrank parametric variations in vibro-acoustic systems was derived [1], using earlier derived techniques for first order system as starting point [6], [7]. The technique from [1] allows for the modeling of lowrank parametric variations, such as those that appear for the application of boundary conditions or the placement of local stiffeners/masses [8].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, a novel reduction scheme for lowrank parametric variations in vibro-acoustic systems was derived [1], using earlier derived techniques for first order system as starting point [6], [7]. The technique from [1] allows for the modeling of lowrank parametric variations, such as those that appear for the application of boundary conditions or the placement of local stiffeners/masses [8]. Furthermore, this technique does not rely on a-priori parameter sampling, in contrast to other common pMOR schemes.…”

Section: Introductionmentioning

confidence: 99%

“…2. Since the authors of [10] mention several potential advantages, as compared to other approaches, a comparison between this approach and the formulation in [1] is done in Sec. 3, specifically on stability and accuracy aspects, where it is shown that for this specific application both methods lead to equivalent reduced order models.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems

Ophem¹,

Deckers²,

Desmet³

2021

14th WCCM-ECCOMAS Congress

Self Cite

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Recently, a novel parametric model order reduction formulation has been derived for vibroacoustic systems that allows for the reduction of systems with low-rank parametric changes [1]. This scheme does not require sampling of the parameter space, in contrast to conventional parametric model reduction techniques. This means that a single reduction basis, obtained with conventional non-parametric model order reduction schemes, can be used for a wide range of parameter values. This is done by rewriting the system in a non-parametric form, in which the low-rank contributions act as inputs. A disadvantage of this scheme is that the size of the input matrix scales with the amount of chosen parameters, leading to a potentially large reduced basis when many parameters are considered.

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“…This formulation is an extension to second-order systems of the formulation shown in [10]. An alternative formulation was previously shown in [1].…”

Section: Low Rank Model Order Reduction Formulation For Vibro-acoustimentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems

Ophem¹,

Deckers²,

Desmet³

2021

14th WCCM-ECCOMAS Congress

Self Cite

View full text Add to dashboard Cite

show abstract

“…This allows us to better control the fidelity of the final model, and as we described in Section 2.3, we are able to guarantee asymptotic stability of H(s; p) uniformly in p, so long as each reduced model H i (s), i = 1, 2, 3, 4 is asymptotically stable and the single reduced H 3 (s) is also positive real. Naturally, these assertions may also be made with the approach of [8] or its recent formulation for second-order systems [55], but it can be substantially more difficult to guarantee these properties using a single choice of projecting bases, Z r and W r . We are able to exploit the flexibility of reducing the four subsystems independently of one another and do not suffer under these constraints.…”

Section: 4mentioning

confidence: 99%

Sampling-free parametric model reduction of systems with structured parameter variation

Beattie

Gugercin

Tomljanović

2018

Preprint

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We consider a parametric linear time invariant dynamical systems represented in state-space form as $$E \dot x(t) = A(p) x(t) + Bu(t), \\ y(t) = Cx(t),$$ where $E, A(p) \in \mathbb{R}^{n\times n}$, $B\in \mathbb{R}^{n\times m} $ and $C\in \mathbb{R}^{l\times n}$. Here $x(t)\in \mathbb{R}^{n} $ denotes the state variable, while $u(t)\in \mathbb{R}^{m}$ and $y(t)\in \mathbb{R}^{l}$ represent, respectively, the inputs and outputs of the system. We assume that $A(p)$ depends on $k\ll n$ parameters $p=(p_1, p_2, \ldots, p_k)$ such that we may write $$A(p)=A_0+U\,\diag (p_1, p_2, \ldots, p_k)V^T,$$ where $U, V \in \mathbb{R}^{n\times k}$ are given fixed matrices.We propose an approach for approximating the full-order transfer function $H(s;p)=C(s E -A(p))^{-1}B$ with a reduced-order model that retains the structure of parametric dependence and (typically) offers uniformly high fidelity across the full parameter range. Remarkably, the proposed reduction process removes the need for parameter sampling and thus does not depend on identifying particular parameter values of interest. Our approach is based on the classic Sherman-Morrison-Woodbury formula and allows us to construct a parameterized reduced order model from transfer functions of four subsystems that do not depend on parameters, allowing one to apply well-established model reduction techniques for non-parametric systems. The overall process is well suited for computationally efficient parameter optimization and the study of important system properties. One of the main applications of our approach is for damping optimization: we consider a vibrational system described by $$ \begin{equation}\label{MDK} \begin{array}{rl} M\ddot q(t)+(C_{int} + C_{ext})\dot q(t)+Kq(t)&=E w(t),\\ z(t)&=Hq(t), \end{array} \end{equation} $$ where the mass matrix, $M$, and stiffness matrix, $K$, are real, symmetric positive-definite matrices of order $n$. Here, $q(t)$ is a vector of displacements and rotations, while $ w(t) $ and $z(t) $ represent, respectively, the inputs (typically viewed as potentially disruptive) and outputs of the system. Damping in the structure is modeled as viscous damping determined by $C_{int} + C_{ext}$ where $C_{int}$ and $C_{ext}$ represent contributions from internal and external damping, respectively. Information regarding damper geometry and positioning as well as the corresponding damping viscosities are encoded in $C_{ext}= U\diag{(p_1, p_2, \ldots, p_k)} U^T$ where $U \in \mathbb{R}^{n\times k}$ determines the placement and geometry of the external dampers. The main problem is to determine the best damping matrix that is able to minimize influence of the disturbances, $w$, on the output of the system $z$. We use a minimization criteria based on the $\mathcal{H}_2$ system norm. In realistic settings, damping optimization is a very demanding problem. We find that the parametric model reduction approach described here offers a new tool with significant advantages for the efficient optimization of damping in such problems.

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A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence

Jelich

Baydoun

Voigt³

et al. 2021

Numerical Meth Engineering

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In this article, a greedy reduced basis algorithm is proposed for the solution of structural acoustic systems with parameter and implicit frequency dependence. The underlying equations of linear time‐harmonic elastodynamics and acoustics are discretized using the finite element and boundary element method, respectively. The solution within the parameter domain is determined by a linear combination of reduced basis vectors. This basis is generated iteratively and given by the responses of the structural acoustic system at certain parameter samples. A greedy approach is followed by evaluating the next basis vector at the parameter sample which is currently approximated worst. The algorithm runs on a small training set which bounds the memory requirements and allows applications to large‐scale problems with high‐dimensional parameter domains. The computational efficiency of the proposed scheme is illustrated based on two numerical examples: a point‐excited spherical shell submerged in water and a satellite structure subject to a diffuse sound pressure field excitation.

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Parametric model order reduction without a priori sampling for low rank changes in vibro-acoustic systems

Cited by 14 publications

References 23 publications

Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems

Automatic and Sampling-Free Parametric Model Order Reduction of Vibro-Acoustic Systems

Sampling-free parametric model reduction of systems with structured parameter variation

A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence

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