Binaural simulation is the recreation of a three-dimensional audio environment around a listener's head. The binaural simulation of structural acoustic data would open new opportunities in virtual prototyping and simulation. By modeling the structure as an array of vibrating monopoles and applying Head Related Transfer Functions (HRTFs) to each of the sources, a binaural simulation of this type can be created. Unfortunately, this simulation method requires an extensive amount of computer power and speed for real-time simulation, more so than is available with current technology. The objective of this research is to reduce the number of computations required in the binaural simulation of structural acoustic data. This thesis details two methods of reducing the number of real-time calculations required in this binaural analysis: singular value decomposition (SVD), and equivalent source reduction (ESR). The SVD method reduces the complexity of the HRTF computations by breaking the HRTFs into dominant singular values and vectors. The ESR method reduces the number of sources to be analyzed in real-time by replacing sources on the scale of a structural wavelength with sources on the scale of an acoustic wavelength. The ESR and SVD reduction methods can be combined to provide an estimated computation time reduction of 99.4%. In addition, preliminary tests show that there is a 97% correlation between the results of the combined reduction methods and the results found with current binaural simulation techniques. / Master of Science

FDTD is an electromagnetic field computation method with the ability of considering circuit elements. Traditional lump element method is insufficient for simulating circuit. In this thesis, we use equivalent source method to combine non-linear circuit elements like active devices into the FDTD simulation. The advantages of this is powerful and time-saving. The accuracy of this method is checked of transmission line driving by CMOS circuits. By employing this method, we find that it will increase EMI phenomenon by strengthening current of driving load, and the load of coupling line will affect noise due to impedance mismatch.

Virtual acoustic prototyping (auralization) is the rendering of a virtual sound field that is created from the calculated acoustic response of a modeled structure. Auralization is useful in the design and subjective evaluation of buildings, automobiles, and aircraft. The virtual acoustic prototyping method in this thesis uses finite element modeling (FEM), the equivalent source method (ESM), and head-related transfer functions (HRTFs). A tradeoff exists between the accuracy of the auralization process and the number of equivalent sources (and thus computational power) that are required. The goal of this research is to validate (numerically and subjectively) a virtual acoustic prototyping method for use in structural design; this thesis illustrates the first attempt to apply the aforementioned methods to a structure that represents a typical building or automobile. The structure's acoustics were modeled using FEM, ESM, and HRTFs. A prototype of the modeled structure was built. A 36% correlation was achieved between the model and prototype. Slight variations in boundary conditions caused significant FEM error, but the data represented a typical structure. Psychoacoustic comparison testing was performed to determine the number of equivalent sources that must be used in an auralization to accurately recreate the sound field. The number was found to be dependent on the type of noise that is played to the test subject. A clear relationship between the numerical correlation of two sounds and the percentage of subjects who could hear a difference between those two sounds was established for impulsive, broadband, and engine noises. / Master of Science

Pass-by noise testing is an important step in vehicle design and regulation compliance. Finite element analysis simulations have been used to cut costs on prototyping and testing, but the high computational cost of simulating surface vibrations from complex geometries and the resulting airborne noise propagation is making the switch to digital twin methods not viable. This paper aims at investigating the use of equivalent source methods as an alternative to the before mentioned simulations. Through the use of a simple 2D model, the difficulties such as ill-conditioning of the transfer matrix and the required regularisation techniques such as TSVD and the Tikhonov L-curve method are tested and then applied to a mesh of a 3D engine model. Source and pressure field errors are measured and their origins are explained. A heavy emphasis is put on the model geometry as a source of error. Finally, rules of thumb based on the regularisation balance and the wavelength dependent pressure sampling positions are formulated in order to achieve usable results. / Bullerprovning vid passage är ett viktigt steg i fordonsdesign och regelefterlevnad. Simuleringar med finita elementanalyser har använts för att minska kostnaderna för prototypframtagning och provning, men de höga beräkningskostnaderna för att simulera ytvibrationer från komplexa geometrier och den resulterande luftburna bullerspridningen gör att övergången till digitala tvillingmetoder inte är genomförbar. Denna uppsats syftar till att undersöka användningen av ekvivalenta källmetoder som ett alternativ till de tidigare nämnda simuleringarna. Genom att använda en enkel 2D-modell testas svårigheterna som dålig konditionering av överföringsmatrisen och de nödvändiga regulariseringsteknikerna som TSVD och Tikhonov L-kurvmetoden och tillämpas sedan på ett nät av en 3D-motormodell. Käll- och tryckfältsfel mäts och deras ursprung förklaras. Stor vikt läggs vid modellgeometrin som en felkälla. Slutligen formuleras tumregler baserade på regulariseringsbalansen och de våglängdsberoende tryckprovtagningspositionerna för att uppnå användbara resultat.

Dans cette thèse, nous nous intéressons à la modélisation mathématique des hétérogénéités de longueurs caractéristiques beaucoup plus petites que la longueur d'ondes. La thèse consiste en deux parties. La partie théorique est dédiée à l'obtention d'un développement asymptotique raccordé: la solution est décrite à l'aide d'un développement de champ proche au voisinage de l'obstacle et par un développement de champ lointain hors de ce voisinage. Le développement de champ lointain met en jeu des solutions singulières de l'équation des ondes tandis que le champ proche lui est régi par un modèle quasi-statique. Ces deux développements sont alors raccordés dans une zone intermédiaire dite de raccord. Nous obtenons alors des estimations d'erreurs permettant de rendre rigoureux ce développement asymptotique formel. La deuxième partie est numérique. Elle décrit à la fois la méthode de Galerkine discontinue, une méthode de raffinement de maillage espace-temps et propose une discrétisation des modèles asymptotiques obtenues précédemment. Elle est illustrée par un certain nombre de tests numériques. / In this thesis, we focus our attention on the modeling of heterogeneities which are smaller than the wavelength. The document is decomposed into two parts : a theoretical one and a numerical one. In the first part, we derive a matched asymptotic expansion composed of a far-field expansion and a near-field expansion. The terms of the far-field expansion are singular solutions of the wave equation whereas the terms of the near-field expansion satisfy quasistatic problems. These expansions are matched in an intermediate region. We justify mathematically this theory by proving error estimates. In the second part, we describe the Discontinuous Galerkin method, a local time stepping method and the implementation of the matched asymptotic method. Numerical simulations illustrate these results.