Model reduction by CPOD and Kriging

Xiao, Manyu; Breitkopf, Piotr; Coelho, Rajan Filomeno; Knopf-Lenoir, Catherine; Sidorkiewicz, Maryan; Villon, Pierre

doi:10.1007/s00158-009-0434-9

Cited by 71 publications

(20 citation statements)

References 12 publications

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“…A similar process has been employed by [38] in the prediction of transient turbine blade and compressor casing temperatures and by [39] in the prediction of a velocity eld inside the combustion chamber of a reciprocating engine. In this case, the method of snapshots proposed by [40] is employed with the number of modal coecients selected so as to represent more than 99.99% of the variation.…”

Section: Two Variable Rotor Optimization and Prediction Of Transiementioning

confidence: 99%

Multifidelity Multidisciplinary Whole-Engine Thermomechanical Design Optimization

Toal¹,

Keane²,

Benito³

et al. 2014

Journal of Propulsion and Power

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Traditionally the optimization of a turbomachinery engine casing for tip clearance has involved either 2D transient thermo-mechanical simulations or 3D mechanical simulations. The following paper illustrates that 3D transient whole engine thermomechanical simulations can be used within tip clearance optimizations and that the eciency of such optimizations can be improved when a multi-delity surrogate modeling approach is employed. These simulations are employed in conjunction with a rotor sub-optimization utilizing surrogate models of rotordynamics performance, stress,

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Section: Two Variable Rotor Optimization and Prediction Of Transiementioning

confidence: 99%

Multifidelity Multidisciplinary Whole-Engine Thermomechanical Design Optimization

Toal¹,

Keane²,

Benito³

et al. 2014

Journal of Propulsion and Power

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“…The reduced-order model is then built either by interpolation of Ψ e.g. [25] interpolated the basis Ψ vectors onto the manifold of symmetric positive-definite matrices, or by interpolation of the β's using kriging/Radial Basis Functions [21]/Diffuse Approximation [17,26]. Assuming that only the projection coefficients β's depend on theV and that Ψ is constant for the design problem, followed by truncating the basis Ψ to a small number (m << M ) of highly energetic modes, we get…”

Section: Output Space Rommentioning

confidence: 99%

“…For this we introduce the concept of the α-manifold. The output space (physics) is modeled using constrained Proper Orthogonal Decomposition [21] giving the smallest set of coefficients β 1 ...β m needed to conserve linear objective and constraint functions. The POD coefficients for the shape and physics are then analyzed together to get the local parametric expression for both α's as well as β's in the neighborhood of the evaluation point.…”

Section: Introduction Literature Reviewed and Motivation For Researchmentioning

confidence: 99%

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

Raghavan¹,

Xia²,

Breitkopf³

et al. 2013

Computer Methods in Applied Mechanics and Engineering

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International audienceEngineering design problems generally involve a high-dimensional input space of design variables yielding an output space by means of costly high-fidelity evaluations. In order to decrease the overall cost, reduced-order models for the output space such as Proper Orthogonal Decomposition (POD) and Proper Generalized Decomposition (PGD) are an active area of research. However, little research has been conducted into alleviating the problems associated with a high-dimensional input space. In addition to higher dimensionality being an impediment to efficient design by itself, complex shapes involve a high number of explicit/implicit constraints restricting the design space. Geometric parameterization methods in traditional CAD present difficulties in expressing these constraints leading to a high failure rate and the generation of inadmissible shapes. In this paper, we propose a simultaneous meta-modeling protocol for both input and output spaces. We perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an alpha-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using metamodeling for both spaces, we facilitate interactive design space exploration for the purpose of design. The proposed approach is applied to the industrial problem of designing a car engine intake port

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“…This has been used in the scope of an optimization framework of coupled problems [8], in metal forming process [10], aerodynamic design [7] and flow optimization [20]. [9] combines RSM with PGD for optimization of the pultrusion process.…”

Section: Introductionmentioning

confidence: 99%

Proper orthogonal decomposition with high number of linear constraints for aerodynamical shape optimization

Xiao

Breitkopf

Coelho

et al. 2014

Applied Mathematics and Computation

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Model reduction by CPOD and Kriging

Cited by 71 publications

References 12 publications

Multifidelity Multidisciplinary Whole-Engine Thermomechanical Design Optimization

Multifidelity Multidisciplinary Whole-Engine Thermomechanical Design Optimization

Towards simultaneous reduction of both input and output spaces for interactive simulation-based structural design

Proper orthogonal decomposition with high number of linear constraints for aerodynamical shape optimization

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