Multi-objective topology optimisation for acoustic porous materials using gradient-based, gradient-free, and hybrid strategies.

When designing passive sound-attenuation structures, one of the challenging problems that arise is optimally distributing acoustic porous materials within a design region so as to maximise sound absorption while minimising material usage. To identify efficient optimisation strategies for this multi-objective problem, several gradient, non-gradient, and hybrid topology optimisation strategies are compared. For gradient approaches, the solid-isotropic-material-with-penalisation method and a gradient-based constructive heuristic are considered. For gradient-free approaches, hill climbing with a weighted-sum scalarisation and a non-dominated sorting genetic algorithm-II are considered. Optimisation trials are conducted on seven benchmark problems involving rectangular design domains in impedance tubes subject to normal-incidence sound loads. The results indicate that while gradient methods can provide quick convergence with high-quality solutions, often gradient-free strategies are able to find improvements in specific regions of the Pareto front. Two hybrid approaches are proposed, combining a gradient method for initiation and a non-gradient method for local improvements. An effective Pareto-slope-based weighted-sum hill climbing is introduced for local improvement. Results reveal that for a given computational budget, the hybrid methods can consistently outperform the parent gradient or non-gradient method.

Comparison of heuristics and metaheuristics for topology optimisation in acoustic porous materials.

When designing sound packages, often fully filling the available space with acoustic materials is not the most absorbing solution. Better solutions can be obtained by creating cavities of air pockets, but determining the most optimal shape and topology that maximises sound absorption is a computationally challenging task. Many recent topology optimisation applications in acoustics use heuristic methods such as solid-isotropic-material-with-penalisation (SIMP) to quickly find near-optimal solutions. This study investigates seven heuristic and metaheuristic optimisation approaches including SIMP applied to topology optimisation of acoustic porous materials for absorption maximisation. The approaches tested are hill climbing, constructive heuristics, SIMP, genetic algorithm, tabu search, covariance-matrix-adaptation evolution strategy (CMA-ES), and differential evolution. All the algorithms are tested on seven benchmark problems varying in material properties, target frequencies, and dimensions. The empirical results show that hill climbing, constructive heuristics, and a discrete variant of CMA-ES outperform the other algorithms in terms of the average quality of solutions over the different problem instances. Though gradient-based SIMP algorithms converge to local optima in some problem instances, they are computationally more efficient. One of the general lessons is that different strategies explore different regions of the search space producing unique sets of solutions.

How reproducible is the acoustical characterization of porous media?

There is a considerable number of research publications on the characterization of porous media that is carried out in accordance with ISO 10534-2 (International Standards Organization, Geneva, Switzerland, 2001) and/or ISO 9053 (International Standards Organization, Geneva, Switzerland, 1991). According to the Web of ScienceTM (last accessed 22 September 2016) there were 339 publications in the Journal of the Acoustical Society of America alone which deal with the acoustics of porous media. However, the reproducibility of these characterization procedures is not well understood. This paper deals with the reproducibility of some standard characterization procedures for acoustic porous materials. The paper is an extension of the work published by Horoshenkov, Khan, Bécot, Jaouen, Sgard, Renault, Amirouche, Pompoli, Prodi, Bonfiglio, Pispola, Asdrubali, Hübelt, Atalla, Amédin, Lauriks, and Boeckx [J. Acoust. Soc. Am. 122(1), 345-353 (2007)]. In this paper, independent laboratory measurements were performed on the same material specimens so that the naturally occurring inhomogeneity in materials was controlled. It also presented the reproducibility data for the characteristic impedance, complex wavenumber, and for some related pore structure properties. This work can be helpful to better understand the tolerances of these material characterization procedures so improvements can be developed to reduce experimental errors and improve the reproducibility between laboratories.

On the modeling of visco-thermal dissipations in heterogeneous porous media.

Based on a modified equivalent fluid model, the present work proposes a composite model which analytically includes the shape of the inclusions, whether they are porous or not. This model enables to describe the acoustic behavior of a large range of media from perforated plates to arbitrarily shaped porous composites including configurations of porous inclusions in solid matrix or double porosity media. In addition, possible permeability interactions between the substrate material and the inclusions are accounted for.

An alternative Biot's formulation for dissipative porous media with skeleton deformation.

This paper presents an alternative formulation of Biot's theory to account for the elastic frame effects in a porous medium in which the acoustical properties of the fluid phase are predicted with an equivalent fluid model. This approach was originally developed for a double porosity medium. In this paper, the alternative formulation is applied to predict the transmission loss and absorption coefficient in the case of a single layer fibrous material, a multi-layer system, vibrating perforated plates, and porous composite materials. In the proposed formulation the coupling coefficients in Biot's poroelasticity equations are expressed in terms of the dynamic volumic mass and dynamic bulk modulus. By doing so, the elastic properties of the material frame are considered independently from the properties of the fluid. This formulation is implemented in the form of a transfer matrix algorithm which is validated against experimental data on sound absorption and sound transmission which are obtained for a range of various sound excitations and material arrangements. It is shown that this approach is able to predict accurately the acoustical properties of vibrating perforated plates and porous composites. The proposed approach is sufficiently general to be implemented in a finite element method.

Development of an analytical solution of modified Biot's equations for the optimization of lightweight acoustic protection.

During lift-off, space launchers are submitted to high-level of acoustic loads, which may damage sensitive equipments. A special acoustic absorber has been previously integrated inside the fairing of space launchers to protect the payload. A new research project has been launched to develop a low cost fairing acoustic protection system using optimized layers of porous materials covered by a thin layer of fabric. An analytical model is used for the analysis of acoustic wave propagation within the multilayer porous media. Results have been validated by impedance tube measurements. A parametric study has been conducted to determine optimal mechanical and acoustical properties of the acoustic protection under dimensional thickness constraints. The effect of the mounting conditions has been studied. Results reveal the importance of the lateral constraints on the absorption coefficient particularly in the low frequency range. A transmission study has been carried out, where the fairing structure has been simulated by a limp mass layer. The transmission loss and noise reduction factors have been computed using Biot's theory and the local acoustic impedance approximation to represent the porous layer effect. Comparisons between the two models show the frequency domains for which the local impedance model is valid.

Expressions of dissipated powers and stored energies in poroelastic media modeled by {u,U} and {u,P} formulations.

This paper is devoted to the rigorous obtention of the energy balance in porous materials. The wave propagation in the porous media is described by Biot-Allard's {u,U} and {u,P} formulations. The paper derives the expressions for stored kinetic and strain energies together with dissipated energies. It is shown that, in the case of mixed formulations, these expressions do not correspond to the real and imaginary parts of the variational formulations. A quantitative convergence analysis of finite element scheme is then undertaken with the help of these indicators. It is shown that the order of convergence of these indicators for linear finite-element is one and that they are then well fitted to check the validity of finite-element models.

Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests).

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.