Acoustic sensitivity analysis considering ground reflection using Bayesian neural network-accelerated isogeometric boundary element method

A multi-domain boundary element formulation for acoustic frequency sensitivity analysis

The fast multipole boundary element method (FMBEM), based on the Burton-Miller formulation for 3-D acoustic sensitivity analysis, is presented in this paper in order to overcome the difficulties in the shape sensitivity analyses using the boundary element method based on the direct differentiation method.The Burton-Miller formulation, which is a linear combination of the conventional boundary integral equation (CBIE) and its normal derivative (NDBIE), is applied to circumvent the difficulty caused by the so-called fictitious eigenfrequencies.The fast multipole method (FMM) is also employed to improve the overall computational efficiency.The sensitivity boundary integral equations of hypersingular type are obtained by the direct differentiation method.The correctness and validity of the method are demonstrated through some numerical results, from which the effectiveness of the present method is shown for 3-D acoustic shape sensitivity analyses.

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures.

SummaryThe complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher‐order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural–acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural–acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd.

Acoustic sensitivity analysis is an essential technique to determine the direction of structural-acoustic optimization by evaluating the gradient of the objective functions with respect to the design variables. However, acoustic sensitivity analysis with respect to acoustic impedance, which is an important parameter representing the interior absorbent material in automotive acoustics, is lacking in the study. Moreover, acoustic sensitivity analysis implemented with conventional numerical methods is time and effort-consuming in automotive acoustics, due to the large-scale mesh generation. In this work, the impedance sensitivity analysis for automotive acoustics based on the discontinuous isogeometric boundary element method is presented. The regularized boundary integral equation with impedance boundary conditions is established, then the sensitivity is derived by differentiating the boundary integral equation. The efficiency of the proposed method is improved by employing the parallel technique and generalized minimal residual solver. A long duct example with an analytical solution validates the accuracy of the proposed method, and an automotive passenger compartment subjecting to impedance boundary conditions illustrates that the computing time of the proposed method is one order of magnitude less than the conventional method. This work presents an easily implementable and efficient tool to investigate acoustic sensitivity with respect to impedance, showing great potential in the application of automotive acoustics.

The main content of this paper is to explain that the acoustic sensitivity of the trimmed body of the vehicle can be improved by optimizing the installation form of battery pack, and then the interior noise of the whole vehicle can be reduced. Firstly, based on the acoustic sensitivity theory and simulation analysis method, the analysis model of the trimmed body with battery pack structure is established, and the acoustic sensitivity of the key connection points of the trimmed body is simulated and analyzed. Secondly, the acoustic sensitivity of the trimmed body is effectively improved by optimizing the installation form of the battery pack and the structure of the battery pack bracket. Finally, the improved scheme is verified and tested on the real vehicle road, and the expected experimental results are obtained.KeywordsAcoustic sensitivityOptimizationPower battery packODSRoad noiseDynamic stiffness

Explicit evaluation of hypersingular boundary integral equations for acoustic sensitivity analysis based on direct differentiation method

The experimental modal analysis is widely utilized in dynamic design of machines to meet the requirement for less vibration and noise, and further the sensitivity analysis is newly adopted to find the appropriate points to reduce the vibration due to structural modification for better dynamics. On the contrary, concerning about the noise induced by the vibration, the present analysis consists of two steps: after the vibrational sensitivity analysis, the noise may be predicted through coefficient of sound radiation, for instance, which yields rather time consuming and inaccuracy. This paper describes the development of a new acoustic sensitivity analysis, which is directly based on the result of acoustic modal analysis when measuring the sound with a microphone against the excitation force. This analysis can provide very useful informations on which parts of the structure should be modified in order to reduce the noise with easy-use and enough accuracy. A simple plate structure and a complex automobile engine are used to confirm the effectiveness of the acoustic sensitivity analysis developed.

A program, global acoustic design sensitivity analyzer, is developed that can perform a global acoustic design sensitivity analysis of exterior noise with respect to structural sizing design variables. A system for global acoustic design sensitivity is introduced and implemented numerically by employing the continuum sensitivity analysis. A half-scale automobile cavity model is considered as a numerical example. By using a continuum method, we obtained accurate and efe cient sensitivities when the number of design variables was large. Also, the tendency plotsof element sensitivities and energy contribution for global acousticsensitivities areavailable. Finally, a design optimization was performed to simultaneously reduce the weight and sound pressure level at interesting points and frequencies. I. Introduction T HE range of engineering problems that can be solved through numericalanalyses hasbeen greatlybroadened with the advent of high-speed digital computers. In addition, the development of the e nite element method (FEM)and the boundary element method (BEM) has also been important to engineering analysis. These two typesofanalysesareassociatedwithanalyticalstructure-bornenoise prediction. FEM is commonly used to compute the vibration of the structure emitting noise, and BEM can be used to predict the generated noise. Other methods for acoustic prediction, such as statistical energy analysis, are also available. In this paper, the focus is on FEM and BEM. In a gradient-based optimization scheme, it is important to have accurate gradients (sensitivities ) of the objective function and constraints with respect to the design variables. Formulation of global acoustic sensitivity through chain-ruled derivatives using FEM and BEM has been studied and implemented by many researchers. Coyette et al. 1 have previously investigated the computation and utilizationofacousticsensitivitieswith respecttosizingdesignvariables. Two types of sensitivities were considered. One was acoustic sensitivity with respect to the normal velocity ofvibratingstructure, and the other was structural sensitivity of structural velocities with respect to physical sizing design variables such as thickness. The acoustic sensitivities and structural sensitivities were calculated using BEM and FEM, respectively, and then these sensitivities were combined to obtain a globalacousticsensitivity.In addition,this approach was implemented to the commercial code, SYSNOISE. The same approach was presented in the articles by Cunefare et al., 2;3 who focused on e nding the best optimization formulation by comparing the relative performance and results obtained through the use of several different objective functions and constraints. They obtained acoustic sensitivities and structural sensitivities from the commercial codes NASTRAN and COMET. They also developed COMIN to combine the acoustic and structural sensitivities. Most researchers who studied global acoustic design sensitivity analysis (DSA) and acoustic optimization have used the structural sensitivity analysis module supported by commercial codes and have thus faced limitations in the accuracy and number of design variables. There are several reasons for the limitations of the semianalytical method. First, when the semianalytical method is used forstructural sensitivity analysis, a slight error could occur due to the amount of perturbation. For this paper, we used a continuum approach 4i6 to calculate the structural sensitivity combined with acoustic sensitiv

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters can provide a method to low-noise design of mechanical structure objectively and quantitatively. Using the Distributed source energy boundary point method, the expressions of the change of the acoustical energy density with respect to design variable is presented in this paper. The Distributed source energy boundary point method is a speedy and precise method which can avoid the complex computing of the singularity integral in EBEM. The correctness and availability is validated by the numerical simulation.

In order to predict car interior noises at the car design and development stage, the statistical energy analysis (SEA) method was used. All the input parameters – modal density (MD), damping loss factor (DLF) and coupling loss factor (CLF) were calculated with SEA principle. Meanwhile, the sound excitation was calculated with sound power experiment data of internal combustion engine given by the engine manufacturer and sound source radiation formula. Engine mount excitation was also computed through the acceleration at initiative side of the engine mount and the transmissibility. A car virtual prototype was built to calculate a car body suspension receiving excitation from road roughness. A computational fluid dynamics (CFD) model was also built up to analyze the wind excitation on the outside surfaces. The car interior noises were predicted by the SEA model with all of the parameters and excitations. A good agreement was indicated by comparing predicted results with measured ones. The maximum relative error between prediction and measurement results is less than 3%, and the maximum absolute error is less than 2.5 dB (A). The above predicted results satisfy engineering precision requirements and as well as showing that using SEA method to predict car internal noises is feasible. The acoustic sensitivity analysis was made at the end. The car internal noise prediction method presented in the paper can be used at car design and development stage.

The vibration and noise of automobiles by lightening might cause decreasing the product value. In this study, an improvement of the door closing sound of lightened door and a structural modification of the door outer panel were investigated in consideration of human sensibility. To forecast by CAE easily, a series of verifications was done with a simplified door experiment model. Acoustic sensitivity analysis was used to detect an effective position for structural changing. Finally, an actual door closing sound was designed to a pleasant sound.

This paper proposes a novel approach for broadband acoustic shape sensitivity analysis based on the direct differentiation approach. Since the system matrices of the boundary element method (BEM) for the analysis of acoustic state and acoustic sensitivity have frequency dependence, repeated calculations are needed at different frequencies. This is very time-consuming, especially for sensitivity calculations used in shape optimization design. The Taylor series expansion of the Hankel function is carried out to separate the frequency-dependent and frequency-independent terms in the acoustic shape sensitivity boundary integral equation to construct a frequency-independent system matrix. In addition, due to the formation of asymmetric full-coefficient matrices in acoustic shape sensitivity equations based on the BEM, repeatedly solving system equations is also extremely time-consuming at broadband frequencies for large scale issues. The second-order Arnoldi approach was employed to create a reduced-order model that maintains the key features of the initial full-order model. The strong singular and supersingular integrals within the sensitivity equations can be calculated directly utilizing the singularity elimination technique. Finally, several numerical examples confirm the accuracy and efficiency of the proposed algorithm.

<div class="htmlview paragraph">Global acoustic sensitivity analysis [<span class="xref">1</span>] is a technique used to identify structural modifications to a component that can reduce the total radiated power of a vibrating structure or the sound pressure levels at specified field points. This report describes the use of global sensitivity analysis within SYSNOISE to determine what structural changes are required to reduce radiated noise from flexible structures in an open duct system. The technique can help optimize design parameters that define the behavior of a flexible structure such as shell thickness and Young's Modulus. The sensitivity analysis approach consists of separately evaluating structural and acoustic sensitivities. A structural finite element model (FEM) of an open duct system is used to compute the sensitivity of the structural response to changes in thickness. A boundary element model (BEM) is then used to relate changes in the calculated acoustic response to changes in the structural design variables.</div> <div class="htmlview paragraph">This paper includes both a baseline design and a revised design to demonstrate global sensitivity analysis. The development of sensitivity methodology allows for optimizing structural-acoustic design of engine air induction systems.</div>

In a recent study of noise from a T-7A-installed GE F404 engine, microphones along 38 and 76 m (125 and 250 ft) arcs were mounted 1.5 m (5 ft) above the ground to quantify human impact. While helpful for this purpose, the resulting multipath effects pose challenges for other acoustical analyses. For jet noise runup measurements, these effects are complicated by the fact that the noise source is extended and partially correlated and its spatial properties are frequency dependent. Furthermore, a finite-impedance ground surface and atmospheric turbulence affect interference nulls. This study applies a ground-reflection method developed previously [Gee et al., Proc. Mtgs. Acoust. 22, 040001 (2014)] for rocket noise measurements. The model accounts for finite ground impedance, atmospheric turbulence, and extended source models that are treated as coherent and incoherent arrays of monopoles. Application to the ground runup data to correct the 38 and 76 m spectra at a range of angles suggests the incoherent line source model is more appropriate at sideline angles whereas the coherent source model is more appropriate for upstream and downstream propagation. Comparisons with near-field data and similarity spectra show that, while imperfect, this method represents an advancement in correcting jet noise spectra for ground reflection effects. [Work supported by ONR Grant No. N00014-21-1-2069.]