Acoustic Topology Optimization Research Articles

Evolutionary topology optimization approach to design multiphase soundproof systems with poroelastic media

SummaryWith the constant development of cities, noise sources have become increasingly present inside and outside living environments. Consequently, soundproof systems comprised of porous materials have been widely adopted as filling fabric of closed‐space structures, such as in the components of buildings, airplanes or automobiles. However, in many situations, simply filling spaces may not be the most effective approach. In that scenario, this work introduces a multiphase acoustic topology optimization methodology to design closed‐space structures for sound attenuation. Based on the Bi‐directional Evolutionary Structural Optimization (BESO) algorithm, the proposed approach combines Biot's poroelasticity equations, expressed in the mixed /p form, and the Unified Multiphase (UMP) technique to fully describe the multiphysics involved in the acoustic, poroelastic and elastic model relations. An objective function contemplating different combinations of structural, viscous and thermal dissipated powers is maximized over multiple frequencies. Volume constraints in each material phase and a novel material interpolation scheme are also considered. The resultant topologies present enhanced dissipated power levels and manufacturability, even when compared with various baseline configurations of similar volume fractions.

Low noise optimization of two-stage gearbox housing structure based on acoustic contribution analysis and topology optimization

Low noise optimization of two-stage gearbox housing structure based on acoustic contribution analysis and topology optimization

Multi-domain acoustic topology optimization based on the BESO approach: applications on the design of multi-phase material mufflers

Multi-domain acoustic topology optimization based on the BESO approach: applications on the design of multi-phase material mufflers

Topology Optimization of Sound-Absorbing Materials for Two-Dimensional Acoustic Problems Using Isogeometric Boundary Element Method

In this work, an acoustic topology optimization method for structural surface design covered by porous materials is proposed. The analysis of acoustic problems is performed using the isogeometric boundary element method. Taking the element density of porous materials as the design variable, the volume of porous materials as the constraint, and the minimum sound pressure or maximum scattered sound power as the design goal, the topology optimization is carried out by solid isotropic material with penalization (SIMP) method. To get a limpid 0–1 distribution, a smoothing Heaviside-like function is proposed. To obtain the gradient value of the objective function, a sensitivity analysis method based on the adjoint variable method (AVM) is proposed. To find the optimal solution, the optimization problems are solved by the method of moving asymptotes (MMA) based on gradient information. Numerical examples verify the effectiveness of the proposed topology optimization method in the optimization process of two-dimensional acoustic problems. Furthermore, the optimal distribution of sound-absorbing materials is highly frequency-dependent and usually needs to be performed within a frequency band.

Acoustic Topology Optimization of Sound Absorbing Materials Directly from Subdivision Surfaces with IGA-FEM/BEM

Acoustic Topology Optimization of Sound Absorbing Materials Directly from Subdivision Surfaces with IGA-FEM/BEM

Auxiliary algorithm to approach a near-global optimum of a multi-objective function in acoustical topology optimization

In this study, an auxiliary algorithm is proposed to avoid local optima in solving an acoustical topology optimization problem by using a gradient-based optimizer. A local optimum convergence issue often occurs in the multi-objective function problem because the sub-objective functions are non-convex in general. In order to overcome this issue and find a near-global optimum, the sign change of sensitivity is heuristically conducted based on the objective function difference at every step of design variable updating. An acoustical topology optimization problem is formulated for improving a noise attenuation performance of a muffler. The heuristic-based auxiliary algorithm is combined with a well-known optimization algorithm to solve the topology optimization problem for a single target frequency as well as a multi-target frequency. Diverse optimal topologies were successfully obtained for various design conditions. Comparison of the optimized solutions by the proposed method and the previous methods strongly supported the validity of the proposed auxiliary algorithm. The application of the proposed method to a suction muffler design problem showed the industrial applicability of the method.

Efficient acoustic topology optimization with the Multifrequency Quasi-Static Ritz vector (MQSRV) method

Efficient acoustic topology optimization with the Multifrequency Quasi-Static Ritz vector (MQSRV) method

Multi-frequency acoustic topology optimization of sound-absorption materials with isogeometric boundary element methods accelerated by frequency-decoupling and model order reduction techniques

The paper presents a novel approach for multi-frequency acoustic topology optimization of sound-absorption materials. In this work, the isogeometric boundary element method based on subdivision surfaces is used to solve Helmholtz equations. To avoid time-consuming frequency sweep, we adopt a series expansion method to decouple the frequency-dependent terms from the integrand in the boundary element method, including the terms associated with the impedance boundary conditions that were introduced to model the absorption materials. Moreover, the second-order Arnoldi (SOAR) approach is employed to reduce the order of the systems. Three dimensional numerical examples were given to demonstrate the effectiveness of the proposed algorithm.

Topology optimization of acoustic systems with a multiconstrained BESO approach

This work details a new acoustic topology optimization methodology with applications on the design of systems composed of rigid and porous materials. The Bi-directional Evolutionary Structural Optimization (BESO) algorithm is combined with the Virtual Temperature Method to minimize the occurrence of air cavities and rough surfaces inside rigid and porous domains, hence configuring a multiconstrained optimization approach. The modeling of porous materials is done by the Johnson–Champoux–Allard (JCA) formulation, while the Finite Element Method is used to approximate the governing equations of the physical system. Two different optimization problems are considered separately: first, a rigid–acoustic metasurface is optimized to reduce regional sound pressure levels (SPL) in a set of observed frequencies, while also considering wind permeability through the structure. Secondly, a coupled poro-acoustic absorptive system is treated in order to enhance the sound absorption coefficient in the low frequency range. Both problems are systematized by the implementation of acoustic–rigid and acoustic–porous material interpolation schemes, respectively. The effectiveness of the proposed approach is explored through numerical examples. Here, it is remarked that the methodology maintains the uniformity of rigid barriers, by guaranteeing the absence of internal holes to them. In addition, well-defined cavities are formed in porous domains, increasing their absorption coefficients, but without inflicting macroscopic closed spaces within such structures. In these cases, comparison with appropriate literature is also provided. • Multiconstrained topology optimization algorithm for acoustic problems. • Implementation of the Virtual Temperature Method for connectivity. • Optimization of metasurfaces for reduction of sound pressure levels. • Optimization of porous structures for enhancements of sound absorption coefficient.

Acoustic topology optimization using moving morphable components in neural network-based design

Acoustic topology optimization using moving morphable components in neural network-based design

Measuring and Characterizing the Noise Emission of a Small Combustion Engine after Acoustical Topology Optimization of the Muffler

Measuring and Characterizing the Noise Emission of a Small Combustion Engine after Acoustical Topology Optimization of the Muffler

Analytical and numerical modeling, sensitivity analysis, and multi-objective optimization of the acoustic performance of the herschel-quincke tube

This study presents the assessments of the acoustic performance of a Herschel-Quincke (HQ) tube, which includes sensitivity analysis and multi-objective optimization of its design variables. A proper model introduced using the flow characteristics of the HQ tube. Input variables were frequency (f), temperature (T), the ratio of areas (R), and tube length (L). These variables were chosen to be varied in a specified range to best characterize the exhaust flow in internal combustion engines. Then a proper multi-objective genetic algorithm (MOGA) was developed for the acoustic performance and geometry optimization of a two-duct HQ tube; the objectives were maximizing the transmission loss (TL) and at the same time minimizing the backpressure (BP). Besides, the local sensitivity analysis using numerical derivative and variance-based global sensitivity analysis (GSA) using Monte Carlo sampling was performed for the analytical model of the HQ tube. The results showed that the length of the bypass tube is a crucial factor for the maximum sensitivity index (SI) of the TL, while the SI of the BP was maximum for the ratio of areas. The proposed analytical model was proved to be reliable for the TL, showing low values of the error of the sensitivity index (eSI) and less reliable for the BP parameter, showing higher eSI values. For the evaluation of the TL sensitivity, Monte Carlo sampling is relatively inaccurate in the small sample size of 200. It was also observed that the Uniform distribution had lower eSI in lower sample sizes; however, Sobol sampling showed better performance in higher sample sizes. The MOGA optimization proved to be successful in maximizing the TL for the frequencies between 105.84 and 1981.11 Hz, with the TL greater than 20 dB, and the BP less than 0.1. The most efficient solution among the Pareto set after a tradeoff was at 105.84 Hz, for which the TL and the BP were 36.47 dB and 1.50E−02, respectively. The model with the best goodness of fit to represent the Pareto front was the power model with two terms. Then, the acoustic performance of the optimized geometry was investigated using computational aeroacoustics (CAA) in the presence of mean flow in Fluent software. Using the CAA approach, the maximum TL value was obtained for 104 0.4 Hz as 12.14 dB. The simulated TL by CAA had more broadband behaviors with fewer peaks than the analytical approach. The results of this study demonstrated the remarkable potential of the MOGA optimization and sensitivity analysis for acoustic performance and topology optimization for possible applications in internal combustion engines.

Fictitious domain models for topology optimization of time-harmonic problems

A new fictitious domain model for topology optimization of time-harmonic problems based on a wave to diffusion equation transition is proposed. By employing negative values of appropriate material coefficients, a tuneable exponential decay of the field amplitude in the fictitious domains can be obtained, whereas for the conventional model a finite field amplitude is always present. To demonstrate the applicability of the model, we consider two topology optimization problems; a volume minimization problem for acoustic topology optimization for which intuitive meaningful designs are obtained with the proposed model unlike the case with a conventional contrast model. For a structural topology optimization example, the proposed model is shown to remove problematic issues with structural artifacts found for a certain dynamic compliance minimization problem.

Reliability-based acoustical topology optimization of mufflers under noise frequency and temperature uncertainties

A reliability-based topology optimization method is proposed to optimally design mufflers under noise frequency and temperature uncertainties. The optimal mufflers designed with deterministic noise frequency and temperature frequently fail to reduce duct noise effectively when the noise frequency or temperature varies. To resolve this problem, a reliability-based acoustical topology optimization problem is formulated for a two-dimensional expansion chamber muffler. The partition volume inside the muffler is selected as the objective function, and its acoustical reliability and transmission loss are used as constraints so as to design a simple but highly reliable muffler. To expedite finding an optimal solution, a gradient-based optimizer is used; further, to calculate the acoustical reliability and its sensitivity, the first-order reliability method and the weighted uniform sampling method are selectively employed. The formulated design problem is solved for various design conditions, and the acoustical reliabilities of optimal mufflers designed according to the proposed method and the deterministic muffler method are compared. Finally, the noise attenuation performance of the optimally designed muffler is experimentally validated.

Efficient Acoustic Topology Optimization Using Vibro-Acoustic Coupled Craig–Bampton Mode Synthesis

Continuum topology optimization is an effective way to reduce vibration and noise of vibro-acoustic coupling system. However, the high computation time required for calculating the vibro-acoustic responses during topology optimization is a major obstacle for practical applications. In this paper, a novel symmetric method of vibro-acoustic system matrix is proposed, and a new model reduction method is developed based on Craig–Bampton mode synthesis method to compute dynamic responses with adequate efficiency and accuracy for topology optimization. The comparison results show that the proposed method substantially reduces the degrees of freedom (DOFs) and calculation time. The response values and eigenfrequencies calculated by the model reduction method are exactly the same as those of the full model. Furthermore, the bidirectional evolutionary structural optimization (BESO) algorithm is applied to solve the problem of minimizing the response of a single frequency and a certain range of frequency excitation at a specified target point. The results show that the optimization algorithm converges fast, the iterative process is robust and the response values of different coupling systems can be reduced to a higher extend, which indicates the applicability of the optimization algorithm.

Aeroacoustic topology optimization of noise barrier based on Lighthill's acoustic analogy

Topology optimization for the shape of noise barrier taking into account the aeroacoustic sound source is presented based on Lighthill's acoustic analogy approach. In the previous acoustic topology optimization based on the Helmholtz equation, only simple acoustic sound sources were taken into account. To overcome this limitation, the present aeroacoustic topology optimization is performed using Lighthill's equation that represents the sound propagation by an aeroacoustic sound source. In this study, aeroacoustic sound sources are randomly generated through the stochastic noise generation and radiation method. As an interpolation method of material properties by continuous design variables, the linear filter and the sigmoid penalty function are used. The top shape of noise barrier is designed by the optimization examples for various conditions, such as random aeroacoustic sound sources, interpolation methods, and target frequencies.

Acoustic topology optimization of sound absorbing materials directly from subdivision surfaces with isogeometric boundary element methods

This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spline functions that generate limit smooth subdivision surfaces are employed to discretize the acoustic boundary integral equations. The effect of sound-absorbing materials on the acoustic response is characterized by acoustic impedance boundary conditions. The optimization problem is formulated in the framework of Solid Isotropic Material with Penalization methods and the sound absorption coefficients on elements are selected as design variables. The potential of the proposed topology optimization approach for engineering prototyping is illustrated by numerical examples.

Acoustic model topology optimization for large vocabulary speech recognition

Acoustic model topology selection work in constructing large vocabulary speech recognition systems is being done empirically or heuristically. In this paper, we propose two improved algorithms, which are based on Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) respectively, on the basis of our previously proposed algorithms to select and optimize model topologies for small or medium vocabulary speech recognition systems. Our improved algorithms attain the goal of optimizing acoustic model topologies for large vocabulary speech recognition systems mainly through modifying the encoding schemes of our previously proposed algorithms. Experiments on the dialogue corpus of Inner Mongolia University show that, compared with the conventional acoustic model topology selection method, our newly proposed algorithms are able to bring much higher recognition performance for large vocabulary speech recognition systems by optimizing their acoustic model topologies.

Methods for evaluating in-duct noise attenuation performance in a muffler design problem

In this study, methods for evaluating the noise attenuation performance of a muffler in a muffler design problem are investigated, and a proper evaluation method is suggested for actual noise reduction in a duct when an optimally designed muffler is mounted on a duct. Mathematical expressions of the transmission loss, insertion loss, and level difference for a simple expansion chamber muffler are developed from basic acoustic equations. The effects of the locations of the measurement points, tailpipe length, and impedance at the end of the duct on the noise attenuation performance calculated using the three evaluation methods are discussed. The TL and IL maximization problems formulated using topology optimization are solved for a muffler unit, and the noise attenuation performances of the optimally designed mufflers are compared when mounted on a duct. Another acoustical topology optimization problem, a partition volume minimization problem for a muffler design, is formulated to reduce the in-duct broadband noise, and the noise attenuation performance of the optimal muffler obtained using this formulation is experimentally validated. These research results will contribute to the development of a muffler design method with high accuracy by reducing the discrepancy between the noise attenuation performances of a muffler unit and a muffler mounted on a duct.

Acoustic topology optimization of porous material distribution based on an adjoint variable FMBEM sensitivity analysis

We develop an acoustic topology optimization approach in this work for the surface design of structures covered by porous materials. The fast multipole boundary element method (FMBEM) is employed for the sound scattering analysis. The acoustic absorption characteristics of porous materials are numerically modeled using the Delany–Bazley–Miki empirical model. Based on the solid isotropic material with penalization (SIMP) method, the optimization is performed by setting the artificial element densities of porous material as the design variables, minimizing the sound pressure or the dissipated sound power as the design objective. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method (AVM) and the fast multipole method (FMM) to calculate the sensitivities of the objective function with respect to a large number of design variables. The FMM is applied to accelerate the vector-matrix product required by the AVM. According to the gradient information, the method of moving asymptotes (MMA) is used for solving the optimization problem to find the optimal solution. We validate the proposed topology optimization approach through numerical examples of acoustic scattering over a single cylinder and multi cylinders, and demonstrate its ability to handle large-scale problems.