Proper Orthogonal Decomposition and Radial Basis Functions for Fast Simulations

Buljak, Vladimir

doi:10.1007/978-3-642-22703-5_3

Cited by 22 publications

(38 citation statements)

References 15 publications

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“…Moreover, the smoothing coefficient c has been assumed herein equal to 1. It is computationally of advantage to select this value within the 0−1 range [2]. Substituting all the sample points and their corresponding function values in equation 4 and organizing the unknowns in a linear equation system, the unknown coefficients a i can be obtained.…”

Section: Pod With Rbfmentioning

confidence: 99%

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Application of Metamodelling Techniques for Mechanized Tunnel Simulation

Khaledi¹,

Schanz²,

Miro³

2014

Journal of Theoretical and Applied Mechanics

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Complex engineering problems require using computationally expensive simulations which take relatively long time. In such cases, routine tasks such as design optimization, parameter identification, or sensitivity analysis become impractical since they require thousands or even millions of simulations. A common practice for engineers to solve this problem is to use metamodels in place of actual simulation models. In this paper, we investigate the performance of four metamodelling approaches, namely, Response Surface Methodology, Moving Least Squares, POD-RBF, and Neighborhood Approximation considering the effect of sample size and sampling methods. Our main goal in this work is to find a reliable and robust metamodel technique in order to construct an approximated function for mechanized tunnel simulation. For this reason, a numerical study is carried out on a 3D tunnel modeled in Plaxis3D and the accuracy and robustness of the aforementioned metamodelling techniques are discussed.

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Section: Pod With Rbfmentioning

confidence: 99%

“…[2,6,9], (2) papers which perform comparative study between existing metamodelling approaches; see, e.g. [4,5,8,11] and papers which apply the metamodelling concept for engineering problems; see, e.g.…”

Section: Introductionmentioning

confidence: 99%

Application of Metamodelling Techniques for Mechanized Tunnel Simulation

Khaledi¹,

Schanz²,

Miro³

2014

Journal of Theoretical and Applied Mechanics

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“…In this dissertation, Proper Orthogonal Decomposition (POD) combined with Radial Basis Functions (RBF) is employed in the sensitivity analysis of a rock salt cavern to evaluate the corresponding system responses. This technique is proposed by Buljak (2010), for more details about the approach and its implementation process see Khaledi et al (2014).…”

Section: Metamodelmentioning

confidence: 99%

Probabilistic Analysis of a Rock Salt Cavern with Application to Energy Storage Systems

et al. 2016

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“…POD is a powerful technique for low-order approximation of some high dimensional processes, which is also known as principal component analysis (PCA), Karhunen-Loeve Decomposition (KLD) or singular value Decomposition (SVD). Several contributions on equivalence and connection among these three methods can refer to [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…A detailed overview of POD can refer to [18,21]. Though POD widely used in the computation of statics, fluid dynamics, structural dynamics, etc., it is mainly applied to perform the principal component analysis and search the main behavior of a dynamic system [22].…”

Section: Introductionmentioning

confidence: 99%