Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis

Degroote, Joris; Vierendeels, Jan; Willcox, Karen

doi:10.1002/fld.2089

Cited by 111 publications

(118 citation statements)

References 48 publications

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“…The paper [100] compares projection-based reduced models to stochastic spectral approximations in a statistical inverse problem setting and concludes that, for an elliptic problem with low parameter dimension, the reduced model requires fewer offline simulations to achieve a desired level of accuracy, while the polynomial chaos-based surrogate is cheaper to evaluate in the online phase. In [74] parametric reduced models are compared with Kriging models for a thermal fin design problem and for prediction of contaminant transport. For those examples, the Kriging models are found to be rapid to solve, to be implementable with a nonintrusive approach, and to provide an accurate approximation of the system output for conditions over which they were derived.…”

Section: Parametric Model Reduction In Actionmentioning

confidence: 99%

“…An approach to overcome this problem in the general nonaffine case is to interpolate reduced state-space quantities as opposed to the basis matrices themselves. This idea was recently introduced in [5,9,74,161,188]. The methods proposed in [9,188] first perform a congruence transformation of the local basis matrices in {V 1 , .…”

Section: Interpolating the Local Reduced Model Matricesmentioning

confidence: 99%

“…Then the reduced-order coefficient matrices constructed from these transformed projection matrices can be interpolated by using matrix manifold interpolation [9] and direct interpolation [188]. In [74], global basis vectors V k = V and W k = W are used for all p k , and therefore there is no need to perform the congruence transformation on the bases before interpolating the reduced models.…”

Section: Interpolating the Local Reduced Model Matricesmentioning

confidence: 99%

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A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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Abstract. Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for which the equations governing the system behavior depend on a set of parameters. Examples include parameterized partial differential equations and large-scale systems of parameterized ordinary differential equations. The goal of parametric model reduction is to generate low-cost but accurate models that characterize system response for different values of the parameters. This paper surveys state-of-the-art methods in projection-based parametric model reduction, describing the different approaches within each class of methods for handling parametric variation and providing a comparative discussion that lends insights to potential advantages and disadvantages in applying each of the methods. We highlight the important role played by parametric model reduction in design, control, optimization, and uncertainty quantification-settings that require repeated model evaluations over different parameter values.

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Section: Parametric Model Reduction In Actionmentioning

confidence: 99%

Section: Interpolating the Local Reduced Model Matricesmentioning

confidence: 99%

Section: Interpolating the Local Reduced Model Matricesmentioning

confidence: 99%

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A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

2015

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“…In this work the approach of PMOR by state-space matrices interpolation is chosen. This method has been successfully applied in the past in aeroelasticity, for fast flutter clearance of a wing-store configuration [33], in control system design of a flexible aircraft [34], in unsteady CFD [35] and in other engineering domains [36], but not for gust and manoeuvre loads prediction. Hereafter, the PMOR framework proposed in [37] is followed.…”

Section: Parametric Model Order Reductionmentioning

confidence: 99%

Parametric reduced order model approach for rapid dynamic loads prediction

Castellani¹,

Lemmens

Cooper³

2016

Aerospace Science and Technology

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A parametric reduced order methodology for loads estimation is described that produces a fast and accurate prediction of gust and manoeuvre loads for different flight conditions and structural parameter variations. The approach enables efficient prediction of the peak loads whilst maintaining the correlated time histories for different loads. It is then possible to determine correlated loads plots with reduced computation without losing accuracy. The effectiveness of the methodology is demonstrated by considering loads arising from families of gusts and pitching manoeuvres acting upon a numerical transport aircraft aeroservoelastic model with varying flight conditions and structural properties.

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“…Henceforth, we refer to this approach as interpolation in the frequency domain. Instead of interpolating the reduced transfer functions, it has been proposed in [3,5,18,37] to interpolate the reduced system matrices to get the reduced-order model on the whole parameter domain. From now on, this approach will be referred to as interpolation in the time domain.…”

Section: Is Reciprocal If H(s) = Sh(s)mentioning

confidence: 99%