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Gradient-Enhanced Parametric Optimization of Vibro-Acoustic Problem using Xfem and a Dedicated Metamodel

Abstract : Noise reduction is a design constraint which is more and more took into account. For instance, this con- straint occurs in aircraft cabin design on which the noise propagation is minimized by finding the optimal arrangement. Classical design processes requires many expensive numerical computations. In order to reduce the computation time, a new strategy is proposed based on two specific tools integrated in a dedicated optimiza- tion strategy: (1) a finite element solver which provides responses and gradients of the objective function to (2) a gradient-enhanced metamodel which interpolates both kinds of information. Solving the mechanical problem remains to solve a coupled problem composed of structural and fluid domains. The acoustic fluid problem is governed by the Helmoltz’s equation. A porous material present in the acoustic cavity is modeled by the Biot-Allard’s constitutive law [1, 2]. The structural problem corresponds to thin walls placed in the fluid and governed by elasto-dynamics equation. The air-structure problem is solved using xfem [3, 4] in order to be able to consider an arbitrary structure placed in the acoustic cavity. In order to reduce the computation time, a reduced model is built from the full coupled problem using a Craig- Bampton’s approach [5]. In addition of the resolution of the coupled problem, the calculation of the gradients with respect to the design parameters is proposed by considering an intrusive approach. Due to the fact that design parameters govern only the position of the structure in the acoustic cavity, the calculation of the gradients requires only calculation of gradients of the xfem’s operators which can be done analytically. The global optimization based on this mechanical problem requires a large number of calls of the mechan- ical solver. Therefore a gradient-enhanced surrogate-based optimization is used. The approach is based on the Efficient Global Optimization [6] composed of two phases: (1) a gradient-enhanced cokriging [7] metamodel is built using only a few sample points and associated responses and gradients and (2) an iterative scheme using the expected improvement [8] allows us to find the global minimum by adding smartly new sample points to the initial surrogate model. The whole strategy has been applied on some 2D and 3D cavity on which the position of a wall is determined in order to minimize the mean quadratic pressure in a control volume. Some examples will be presented for illustrating the performance of the proposed approach. References [1] Maurice A. Biot. Theory of Propagation of Elastic Waves in a FluidSaturated Porous Solid. I. LowFre- quency Range. The Journal of the Acoustical Society of America, 28(2):168–178, 1956. [2] Jean-François Allard and Noureddine Atalla. Sound propagation in porous media: modelling sound ab- sorbing materials. Elsevier, London, 1(0):11, 1993. [3] Antoine Legay. An extended finite element method approach for structural-acoustic problems involving immersed structures at arbitrary positions. International Journal for Numerical Methods in Engineering, 93(4):376–399, 2013. [4] Antoine Legay. The extended finite element method combined with a modal synthesis approach for vibro- acoustic problems. International Journal for Numerical Methods in Engineering, 101(5):329–350, 2015. [5] Mervyn C. C. Bampton and Roy R. Craig Jr. Coupling of substructures for dynamic analyses. AIAA Journal, 6(7):1313–1319, 2016/11/25 1968. [6] Donald R. Jones, Matthias Schonlau, and William J. Welch. Efficient global optimization of expensive black-box functions. Journal of Global optimization, 13(4):455–492, 1998. [7] Luc Laurent, Rodolphe Le Riche, Bruno Soulier, and Pierre-Alain Boucard. An overview of gradient- enhanced metamodels with applications. Archives of Computational Methods in Engineering, Jul 2017. [8] Matthias Schonlau. Computer Experiments and Global Optimization. PhD thesis, University of Waterloo, 1997.
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Submitted on : Monday, July 30, 2018 - 5:58:11 PM
Last modification on : Wednesday, March 24, 2021 - 2:40:02 PM

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  • HAL Id : hal-01851746, version 1

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Luc Laurent, Antoine Legay. Gradient-Enhanced Parametric Optimization of Vibro-Acoustic Problem using Xfem and a Dedicated Metamodel. 13th World Congress on Computational Mechanics, WCCM XIII and the 2nd Pan American Congress on Computational Mechanics, University Jul 2018, New York, United States. ⟨hal-01851746⟩

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