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The three-dimensional acoustic intensimetry employing multiple probe-modules are implemented for estimating the source distance by calculating the nearest intersection points of the vectors. The probe spacing, source localization error, and source distance affect the estimation error. It is found that the intensity vectors indicating the source location diverge in some directions due to the geometric singularity. Numerical and experimental tests are conducted with three probe-modules configured as an equilateral triangle on a plane. The result reveals that the large error due to geometric singularity can be significantly reduced by only excluding the corresponding vectors that cause the divergence.

In the analysis of interior acoustic problems, the time domain boundary element method (TBEM) suffers the monotonically increasing instability when using the direct Kirchhoff integral. This instability is related to the non-oscillatory static acoustic mode describing the constant spatial response in an enclosure. In this work, nonphysical natures of non-oscillatory static mode influencing the instability of TBEM calculation are investigated, and a method for stabilization is studied. In TBEM calculation, the static mode is represented by two non-oscillatory eigenmodes with different eigenvalues. The monotonically increasing instability is caused by the unstable poles of non-oscillatory eigenmodes as well as very small, very low frequency noise of an input signal. Interior problems with impedance boundary condition also exhibit the monotonically increasing instability stemming from its pseudo non-oscillatory static mode due to the lack of dissipation at very low frequencies. Calculation of transient sound fields within rigid and lined boxes provides numerical evidences. It is noted that the stabilization effort by modifying the coefficient matrix based on the spectral decomposition can be used only for correcting the unstable pole. The filtering method based on the eigen-analysis must be additionally used to avoid the remaining instability caused by very low frequency noise of input signal.

The time domain boundary element method (TBEM) to calculate the exterior sound field using the Kirchhoff integral has difficulties in non-uniqueness and exponential divergence. In this work, a method to stabilize TBEM calculation for the exterior problem is suggested. The time domain CHIEF (Combined Helmholtz Integral Equation Formulation) method is newly formulated to suppress low order fictitious internal modes. This method constrains the surface Kirchhoff integral by forcing the pressures at the additional interior points to be zero when the shortest retarded time between boundary nodes and an interior point elapses. However, even after using the CHIEF method, the TBEM calculation suffers the exponential divergence due to the remaining unstable high order fictitious modes at frequencies higher than the frequency limit of the boundary element model. For complete stabilization, such troublesome modes are selectively adjusted by projecting the time response onto the eigenspace. In a test example for a transiently pulsating sphere, the final average error norm of the stabilized response compared to the analytic solution is 2.5%.

The time domain boundary element method (BEM) is associated with numerical instability that typically stems from the time marching scheme. In this work, a formulation of time domain BEM is derived to deal with all types of boundary conditions adopting a multi-input, multi-output, infinite impulse response structure. The fitted frequency domain impedance data are converted into a time domain expression as a form of an infinite impulse response filter, which can also invoke a modeling error. In the calculation, the response at each time step is projected onto the wave vector space of natural radiation modes, which can be obtained from the eigensolutions of the single iterative matrix. To stabilize the computation, unstable oscillatory modes are nullified, and the same decay rate is used for two nonoscillatory modes. As a test example, a transient sound field within a partially lined, parallelepiped box is used, within which a point source is excited by an octave band impulse. In comparison with the results of the inverse Fourier transform of a frequency domain BEM, the average of relative difference norm in the stabilized time response is found to be 4.4%.

The time-domain solution from the Kirchhoff integral equation for an exterior problem is not unique at certain eigen-frequencies associated with the fictitious internal modes as happening in frequency-domain analysis. One of the solution methods is the CHIEF (Combined Helmholtz Integral Equation Formulation) approach, which is based on employing additional zero-pressure constraints at some interior points inside the body. Although this method has been widely used in frequency-domain boundary element method due to its simplicity, it was not used in time-domain analysis. In this work, the CHIEF approach is formulated appropriately for time-domain acoustic boundary element method by constraining the unknown surface pressure distribution at the current time, which was obtained by setting the pressure at the interior point to be zero considering the shortest retarded time between boundary nodes and interior point. Sound radiation of a pulsating sphere was used as a test example. By applying the CHIEF method, the low-order fictitious modes could be damped down satisfactorily, thus solving the non-uniqueness problem. However, it was observed that the instability due to high-order fictitious modes, which were beyond the effective frequency, was increased.

Near-field acoustical holography (NAH) is a useful tool for the identification and visualization of vibro-acoustic sources. In particular, NAH can be applied to many practical sources having irregular shape if the inverse boundary element method (BEM) is employed. Once the relation between the source and the radiated field is defined in the transfer matrix modeled by the BEM, the reconstruction of acoustic parameters on the source surface can be conducted by the multiplication of the inverse transfer matrix and the field data measured over the hologram surface. The usual practical way to measure the field data radiated from an irregular shaped source is to adopt a regular hologram surface, which can be a flat, cylindrical, or spherical shape, for the measurement ease. Then, the hologram surface is not conformal to the source surface and the resulting transfer matrix becomes further ill-posed than the conformal case. To investigate the effect of sensor proximity and distance variability on the reconstruction error, simulation and measurement were conducted for an interior problem comprised of a parallelepiped rigid box with a vibrating end plate. Flat, tilted, and randomized hologram surfaces were adopted in the test. It was shown that the reconstruction error is greatly affected by the conditioning of transfer matrix which is related to the positioning of sensor. To improve the reconstruction accuracy, an investigation was conducted to find proper field points among a large number of overdetermined field points. The number of field data was reduced gradually under various reduction schemes using condition number, effective independence value, and sensor distance. It was demonstrated that the quality of reconstruction result given by the non-conformal measurement can be improved by removing some field points that contribute to the ill-conditioning of the inverse problem. A small improvement of the reconstruction accuracy was observed by reducing the field points in the overdetermined situation. However, further reduction of the field points, becoming an underdetermined situation, yielded a drastic improvement of the reconstruction accuracy.

The phased beam tracing method (PBTM) was suggested as a medium-frequency simulation technique for the calculation of impulse response, although main assumptions of geometric acoustics still hold. The phased method needs the reflection coefficient for characterizing the acoustic property of a surface and the complex wave number for describing the propagation characteristics. In this study, two types of approximate real reflection coefficients derived from the measured absorption coefficient were tested for a practical applicability. As a test example, pressure impulse responses and energy impulse responses computed from the PBTM were compared with those from the measurement and the ordinary beam tracing method. The PBTM employing the approximate reflection coefficients greatly increased the accuracy of the prediction compared to the ordinary beam tracing method, in particular at the medium-frequency range in octave bands above the Schroeder cutoff frequency. A comparison was made between angle-dependent and angle-independent reflection coefficients in the calculation of acoustic measures. Although the angle-dependent reflection coefficient yielded best matched results with measured data, but the simple angle-independent reflection coefficient can be also used with a reasonably good precision.

In using the near-field acoustical holography based on the inverse boundary element method (BEM) for the reconstruction of vibroacoustic source parameters, an enormous number of measurements required in practice have limited the extended application of this method. To obtain the sufficient field data with a small number of actual measured data, the regeneration method of the radiated field using the multipoint equivalent sources is attempted in this paper. In using the equivalent source method, a vibrating source can be represented by distributed spherical sources inside the actual source surface. In this paper, the radiated field is expressed with a series of spherical Hankel functions and spherical harmonics. For suppressing the adverse effect of high-order spherical functions, spatial filtering of coefficients and wave-vector components by a regularization scheme is adopted. Restored field data appended with actual measured data can be used as input for the inverse BEM to reconstruct the source field. Numerical tests for spherical sources were performed for investigating the characteristics of the proposed technique. In order to validate the usefulness of the proposed method to actual irregular sources, a vacuum cleaner was taken as a demonstration example and good agreement between measured and reconstructed results could be observed.

In applying the boundary element method to an acoustic interior problem modeled as a single domain, even a small change of the cavity geometry affects the whole system matrix. Thus, calculating sensitivities for each intermediate shape is performed independently during iterations for an optimum shape. By utilizing the sub-domain modularization capability of the MBEM, however, the matrix inversion task is performed only once for the initial shape during whole iterations. This can reduce the total computational costs of finding an optimum shape design and the computational efficiency increases as the number of iterations increases. A demonstration example is given by a two-dimensional automotive interior cavity.

The calculation efficiency of the conventional single-domain acoustic BEM (SBEM) is important for analyzing large scaled or complicated acoustic cavity systems. Although the multi-domain BEM (MBEM) has been developed to deal with such complex shaped and large size acoustic systems effectively, it is generally known that the MBEM requires more computation time and computer memory space than the SBEM. However, if the proper division were applied on a single cavity, it is thought that the MBEM could be the better method than the SBEM in the viewpoint of accuracy and efficiency. This might be possible when one reminds the fact that the effort in the MBEM calculations also depends strongly on the shape of the total acoustic cavity. In this article, the general computational characteristics of the MBEM for analyzing the interior acoustic fields are investigated to provide a guideline in the division of a single cavity into several subdomains for having better computational performance than using the SBEM. A two-dimensional long duct comprised of a number of linear elements is taken as a demonstration example. It is clearly shown that the modification of MBEM model through the present guidelines achieves more accurate and efficient computation than using the SBEM.

A simplified boundary element method (BEM) for dealing with high-frequency sound is proposed. The boundary integral equation is modified into a quadratic form to enable the prediction of sound levels in the one-third octave band analysis. Monopole and dipole source terms in the conventional BEM are transformed into the auto- and cross-spectra of two vibrating sources, in which the cross-spectra are eventually neglected by assuming that the correlation coefficients involved are negligible. The present method is compared with the Rayleigh integral for calculating the sound pressure radiated from a baffled panel, in terms of the application limit. The characteristic length of the boundary element and the applicable frequency range can be determined by the lower limit value of the correlation coefficient. As a test example, the field pressure radiated from a partially vibrating sphere is predicted and the resultant trend is in good agreement with the analytic solution as far as the related correlation coefficient satisfies the assumption. The overdetermination process for overcoming nonuniqueness in exterior radiation problems is unnecessary in the present method because phase information can be ignored. The results of the calculation show that the proposed method is acceptable for solving the exterior radiation problem at a high-frequency range in a timely manner.

In near-field acoustical holography using the boundary element method, the reconstructed field often diverges due to the presence of small measurement errors. In order to handle this instability in the inverse problem, the reconstruction process should include some form of regularization for enhancing the resolution of source images. The usual method of regularization has been the truncation of wave vectors associated with small singular values, although the determination of an optimal truncation order is difficult. In this article, an iterative inverse solution technique is suggested in which the mean-square error prediction is used. A statistical estimation of the minimum mean-square error between measured pressures and the model solution is required for yielding the optimal number of iterations. The continuous curve of an optimal wave-vector filter is designed, for suppressing the high-order modes that can produce large reconstruction errors. Experimental results from a baffled radiator reveal that the reconstruction errors can be reduced by this form of regularization, by at least 48% compared to those without any regularization. In comparison to results using the optimal truncation method of regularization, the new scheme is shown to give further reductions of truncation error of between 7% and 39%, for the example in this article.

In applying the conformal near-field acoustical holography (NAH) to actual source identification problems, it is often possible to determine the velocity at certain points of the source surface in advance. This partially known velocity data would reduce the problem size and permit better reconstruction accuracy. In this paper, the effectiveness of using partially measured source data in the conformal NAH is investigated, which uses the boundary element method. A vibro-acoustic transfer matrix and measured field pressure data, which is involved with the boundary integral equation, are reorganized in order to deal with the partially measured surface velocities. For a baffled vibrating panel, simulations were performed by varying the number of velocity-known nodes. In addition, the effect of measurement error is investigated for two extreme positioning methods of velocity-known nodes. Without regularization, the reconstructed error can be reduced considerably by employing some of the source data and this error can be further reduced by increasing those surface points. However, the velocity reconstruction error is not reduced substantially when the number of velocity-known nodes is less than 30%-40% of the total nodes. The reduction in the reconstruction error is not large if the regularization technique is applied to the restored field.

Boundary integral equations are formulated for the shape sensitivity analysis of the acoustic problems. The concept of the material derivative is employed in deriving the sensitivity equations. Since the equation is derived by the direct differentiation of the boundary integrals containing the field values, it is expected that the sensitivity would be computed more effectively and accurately than the conventional finite difference method. In addition, the equation has the potential to be applied to many complex acoustic problems, because the derived equation is regularized by using the integral identity that incorporates the one-dimensional propagating wave and its material derivative. The validity of the formulations is demonstrated through examples having regular shapes such as the three-dimensional pulsating sphere and the one-dimensional duct, for which the analytical solutions are available. As an example for an irregular domain, the two-dimensional model of an automotive interior cavity is dealt with in the view point of the noise level at the passenger’s ear position. The results show that the present method can be an effective tool for the shape optimization in designing the desired sound field. It is noted that the present method permits accurate sensitivities of the acoustic pressure on the boundary as well as at the field points. The present method is thought to be an alternative to the previous finite difference techniques for computing the shape sensitivity using the boundary element method and the formal derivative method using the finite element method.

Nowadays, the two-microphone method is accepted as the standard as specified in ASTM E1050-90 for measuring in-duct acoustic properties. However, research results on using the least square method with multiple measurement points and broadband excitation have been reported for enhancing the frequency response of the two-microphone method. In this paper, the effects of varying the relative measurement positions on errors in the estimation of the acoustic quantities is studied for the multiple microphone method. Both the theoretical and experimental results show that, among possible sensor positioning configurations, the equidistant positioning of sensors yields the smallest error within the effective measurement frequency range. In addition, it is noted that the measurement accuracy can be increased and the effective frequency range can be widened by increasing the number of equidistant sensors. Measurement examples are shown and the results support the findings.

The two most popular frequency response function estimators,Ĥ1andĤ2give biased estimates when measured input and output signals are contaminated by uncorrelated noises. Recently, an improved frequency response function estimatorĤswas proposed for reducing the bias error due to measurement noises, but without any analysis on the random error. In this paper, the random error formula forĤshas been derived for accurate estimation of desired function. The result shows that the random error in the magnitude ofĤsis always smaller than that ofĤ2, but larger than that ofĤ1.

This appendix contains sections titled: Introduction Kirchhoff-Helmholtz Integral Equation Discretization Solution Strategy of Acoustic Boundary Element Method Nonuniqueness Problem References

This chapter gives a brief review of the acoustics necessary for acoustic array signal processing. In particular, two approaches of representing the sound field are described. Remarks are made on the ill-posedness associated with inverse problems.

The vibrational velocity, sound pressure, and acoustic power on the vibrating boundary comprising an enclosed space are reconstructed by the boundary element method based on the measured field pressures. The singular value decomposition is used to obtain the inverse solution in the least‐square sense and to express the acoustic modal expansion between the measurement and source fields. In general, such an inverse operation has been considered an ill‐posed problem having a divergence phenomenon involved with extremely small measurement errors. The ill‐conditioned nature of the acoustic inverse problem is caused by the singularity of the transfer matrix which produces nonradiating wave components. In order to minimize the singularity and to also reduce the number of measurement points, optimal measurement positions are determined by the effective independence method. Regularization methods are used to stabilize the reconstructed field by suppressing nonradiating components resulting in the singular transfer...

A weakly singular boundar integral equation and a non-singular one are derived for acoustic problems. By using the one-dimensional wave propagation mode, the degree of the singularities appearing in the conventional boundary integral equation can be reduced. Since the strong singularity is removed in the weakly singular equation, the jump term of the field pressure expression in the very vicinity of the boundary disappears. It is shown that the weak singularity can be also removed for a smooth boundary in the non-singular representation, and thus special treatments for singular integral are no longer needed. In order to test the proposed method, several simple problems have been solved by employing the triangular element with standard Gaussian quadrature integration points. The results obtained show the accuracy of the method in the near field as well as on the boundary.

A theoretical formulation is carried out of acoustic wave propagation in a narrow capillary tube with steady gas flow. The transverse variations of the particle velocity, temperature, and viscosity are considered. A fully developed laminar steady flow is assumed and the concept of a complex propagation constant is introduced in the formulation. The final equation form reduces to a Kummer-type differential equation and its solution is obtained in terms of confluent hypergeometric functions. The dispersion equation for the complex propagation constants takes on a recursive form. A simplified form of the analysis permits comparison with previous results dealing with visco-thermal effects and includes the features of Poiseuille-type laminar steady flow for low and medium shear wave numbers. Numerical simulation results show that the effect of steady flow is very significant for the backward traveling waves, and the assumption of a parabolic velocity profile for shear wave numbers less than four should be used carefully when the flow Mach number is greater than 0·1. The present theory is applicable for shear wave numbers up to 10 or more, with the non-parabolic axial velocity fluctuations included, which encompasses almost all the possible situations of capillary duct dimension, temperature and flow velocity. The theory?!would be useful as an approximation in solving the acoustic problems of the monolith in catalytic converters for automotive exhaust systems and of the propagation of sound in a porous medium.

Knowledge of the temperature distribution of an in-duct gaseous medium is essential in the monitoring of combustion status. To obtain the temperature distribution, an inverse relationship based on the Radon transform is formulated by using the measured time retardation data from a set of acoustic sensors and actuators. The entire spatial distribution can be obtained by interpolating the estimated discrete temperature data using either a path-based or spaced-based method. An interpolation method then determines the precision of the final imaging result. The characteristics and performance of two interpolation methods are investigated in a simulation study by reconstructing the temperature distribution of a rectangular cross-section. To calculate the temperature field, the path-based interpolation method adopts a direct expression of temperature variation along the propagation path, whereas the space-based interpolation method uses data obtained at predetermined points deployed inside the field. The average reconstruction accuracy of the space-based interpolation for temperature fields with 1 and 4 local maxima is 22% and 183% better than that of path-based interpolation, respectively. Also, the space-based interpolation method is more robust with regard to measurement noise than the path-based interpolation method.

It is well known that the presence of a grazing mean flow affects the acoustic impedance of an aperture, but the detailed nature and understanding of the influence is still unknown. In this paper, results from a recent theoretical analysis of the problem are compared with a new set of experimental results. The purpose is twofold. First, the experimental results are used to validate the theory. It is found that the theory predicts the resistance quite well, but not the reactance. Second, the theory is used to try and give some physical understanding to the experimental results. In particular, some scaling laws are confirmed, and it is also shown that measured negative resistance values are to be expected. They are not erroneous, as previously thought. Former sets of experimental data for this problem are notable for the amount of variation that they display. Thus, both the theory and the new experimental results are also compared with those earlier detailed results that most closely conform to the conditions assumed here, namely fully developed turbulent pipe flow of low Mach number past circular orifices. The main field of application is in flow ducts, in particular, flow through perforated tubes in exhaust mufflers.

The in-duct source can be characterized by two acoustical parameters such as the source strength and the source impedance, which permit the prediction of radiated sound pressure or insertion loss of the whole duct system. One-port acoustic characteristics of an in-duct source can be measured by the multiload method using an overdetermined set of open pipes or side-branch pipes with different lengths as applied loads. The input data, viz. load pressure and load impedance, are usually contaminated by measurement error in the actual measurements, which result in errors in the calculated source parameters. In this paper, the effects of the errors in the input data on the results have been studied numerically, varying the number of loads and their impedances in order to determine what combination of the loads will yield the best result. It is noted that, frequently, only a set of open pipes is used when applying the multiload method to the internal combustion engine sources. A set of pipe lengths, which cause the calculated results to be least sensitive to the input data error, can be found when using open pipe loads. The present work is intended to produce guidelines for preparing an appropriate load set in order to obtain accurate source properties of fluid machines.

In the conformal near-field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro-acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular shaped boundaries. When the vibro-acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff–Helmholtz integral equation has the singularity problem in the close near field of the source surface. This problem stems from the singular kernel of the Green function of the boundary integral equation (BIE) and the singularity can influence the reconstruction accuracy greatly. In this paper, the nonsingular BIE is introduced to the NAH calculation and the holographic BIE is reformulated. The effectiveness of nonsingular BEM has been investigated for the reduction of reconstruction error. Through interior and exterior examples, it is shown that the resolution of predicted field pressure could be improved in the close near field by employing the nonsingular BIE. Because the BEM-based NAH inevitably requires the field pressure measured in the close proximity to the source surface, the present approach is recommended for improving the resolution of the reconstructed source field.

The one-port source characteristics in a duct system, viz., source impedance and strength, can be determined by using the four-load method. In this paper, to avoid the instability problem of the conventional four-load method, a new formulation for the multiload method has been proposed, which employs an error function based on the linear, time-invariant source model. It is shown that the method is less sensitive to input errors compared to the previous methods. For a 10% input error, the proposed method yields a relative error in the source resistance that is about 1/100 times smaller than for the conventional method. The effectiveness of the present method is demonstrated by two test examples, a loudspeaker and a blower, each operating in a duct. It is observed that the conventional and least-squares methods result in large errors, whereas the present method yields far better agreement with the actual source parameters, as measured by the direct method. The present method is then used to obtain the source parameters on the exhaust side of an operating internal combustion engine. The radiated sound spectrum from the exhaust opening is predicted by using the measured source parameters and the calculated result agrees very well with the measured one.

An approximation of speed of sound in the measurement plane is essential for the inverse estimation of temperature. To this end, an inverse problem relating the measured retarded time data in between set of sensors and actuators array located on the wall is formulated. The involved transfer matrix and its coefficient vectors approximate speed of sound of the measurement plane by using the radial basis function with finite number of interpolation points deployed inside the target field. Then, the temperature field can be reconstructed by using spatial interpolation technique, which can achieve high spatial resolution with proper number of interpolation points. A large number of retarded time data of acoustic paths in between sensors and arrays are needed to obtain accurate reconstruction result. However, the shortage of interpolation points due to practical limitations can cause the decrease of spatial resolution and deterioration of the reconstruction result. In this works, a regeneration for obtaining the additional retarded time data for an arbitrary acoustic path is suggested to overcome the shortage of interpolation points. By applying the regeneration technique, many interpolation points can be deployed inside the field by increasing the number of retarded time data. As a simulation example, two rectangular duct sections having arbitrary temperature distribution are reconstructed by two different data set: measured data only, combination of measured and regenerated data. The result shows a decrease in reconstruction error by 15 % by combining the original and regenerated retarded time data.

The sound field radiated from a vibrating structure is reconstructed by using the equivalent source modeling. In this method, the equivalent multipole sources which are similar to the spherical harmonics in the Helmholtz equation least‐squares (HELS) method are distributed over or inside a vibrating surface. To improve the accuracy and usefulness, the effective independence (EfI) method is used to determine the optimal position of equivalent sources and the regularization scheme is adopted to determine the optimal expansion number of spherical harmonics and to suppress the high order poles. After regenerating field pressures using those optimized equivalent source modeling, the vibrating source is effectively reconstructed with minimal measurement combining the proposed method with the near‐field acoustic holography (NAH) using the inverse boundary element method (BEM). In this study, an application example of a commercial vacuum cleaner using the equivalent source modeling will be demonstrated. [Work supported by the BK21 project and NRL.]

Time-domain acoustic solution from the Kirchhoff integral equation for the exterior problem is not unique due to the presence of fictitious internal modes and also suffers from the instability that stems from the time marching scheme. In this work, methods to stabilize the time-domain acoustic boundary element calculation were suggested. Low-order fictitious internal modes within the effective frequency range of boundary element calculation were suppressed by the newly formulated time-domain CHIEF (Combined Helmholtz Integral Equation Formulation) method. Additional interior points were included, similar to frequency-domain problems, to satisfy the zero pressure constraint considering the shortest retarded time between boundary nodes and interior points. However, the calculation was yet unstable due to remaining unstable high-order modes beyond the effective frequency limit. To further stabilize the computation, unstable high-order internal modes were nullified using the wave vector filtering method. In comparison with the time-domain Burton-Miller formulation, the proposed method has no hyper-singular integral and the monotonically increasing instability was not observed. As a test example, sound radiation from a pulsating sphere was used and a good stabilization performance was shown. Average relative-difference norm of the stabilized time response from the analytic solution was 2.7%. (This work was partially supported by BK21 project)

In the acoustic pyrometry for the measurement of temperature distribution of a cross section in a furnace, the temperature can be reconstructed from the measured time‐of‐flights between sensor‐actuator array systems. The calculated transfer matrix is composed of the approximated slowness function and its coefficient vector. In this study, the least‐squares method is used to inversely reconstruct the temperature. If the transfer matrix is highly singular, reconstruction result will be deteriorated in the presence of the measurement error. To reduce the effect of the singularity, the redundancy of the sensor data can be removed and/or the regularization of the restored field can be employed. As a simulation example, a thermal field within a rectangular cross section of a 1‐D infinite duct with asymmetrical temperature distribution was considered. Condition number of the transfer matrix revealed a highly singular state of the system, regardless of the number of sensors. Sensor/actuator positions were selecte...

Existing loudness models are specified only to diotic sounds in spite of the fact that normal human beings hear dichotic sounds. The arithmetic mean of loudness values of both ear signals has been suggested for the approximated value of the resultant perceived loudness. In this study, the dependence of overall loudness perception on the interaural level differences was investigated by the subjective tests. It was found that the larger the interaural level difference, the louder the perception than the mean of calculated loudness values at both ears and the lower the critical band rate or the reference level, the louder the perception than the mean value. A modified loudness model was proposed for the application to dichotic sounds by using the equivalent diotic levels.

In the conformal near‐field acoustical holography (NAH), using the boundary element method (BEM), the vibroacoustic information on the source surface can be indirectly reconstructed by utilizing the measured field pressure and the inverse transfer matrix. The involved vibroacoustic transfer matrix is generally ill conditioned and the reconstruction process should include the singular value decomposition (SVD) in order to solve the problem in the inverse procedure. The accuracy of the reconstructed field is deteriorated substantially due to the ill conditioning of the transfer matrix and the inevitable measurement noise of field pressure related to the nonpropagating wave components. In this study, the computational processes of SVD and wave‐vector filtering in the BEM‐based NAH are discussed and their physical meanings are investigated through a simulation example. The vibroacoustic transfer matrix decomposed by SVD permits an effective regularization of the source field: This is possible because the involved information in the transfer matrix can be separated into the radiation efficiency and the wave modes at the source and surface fields. In particular, it is clearly shown that the restored source image can be improved dramatically by adopting the wave‐vector filter that suppresses the nonpropagating wave components appropriately that cause the deterioration of the reconstruction accuracy.

In the conformal near‐field acoustic holography (NAH) using the boundary element method (BEM), the transfer matrix relating the vibro‐acoustic properties of source and field depends solely on the geometrical condition of the problem. This kind of NAH is known to be very powerful in dealing with the sources having irregular boundaries. When the vibro‐acoustic source field is reconstructed by using this conformal NAH, one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components. The conventional acoustic BEM based on the Kirchhoff–Helmholtz integral equation has the singularity problem in the very‐near field of the source surface: computation error increases very rapidly as approaching from the far field. This problem originated from the singular kernel of the fundamental solution of the BIE and can influence the reconstruction accuracy. In this paper, the holographic BIE is reformulated to remove the singularity by introducing an additional propagating plane wave. Reconstructed results by the conventional and the nonsingular BIE are compared for a simple radiator model. It is observed that the nonsingular formulation can yield accurate vibro‐acoustic transfer matrix and thus improve the resolution of the reconstructed source field.

The BEM‐based acoustic holography is applied to predicting vibroacoustic parameters on the boundary enclosing the interior space. The singular value decomposition method is utilized for inverse operation of the transfer matrix. Such backward reconstruction usually suffers from the divergence phenomenon due to the inversion of ill‐conditioned matrix produced by nonradiating wave components involved with extremely small measurement errors. In order to minimize the reconstruction error arising from the divergence phenomenon, optimal measurement positions are determined by the effective independence method. In addition, regularization methods are used to enhance the resolution of reconstructed field by suppressing the nonradiating wave components. The interior field of a rectangular box is considered as an example for validating and demonstrating the proposed reconstruction process and the experimental verification is carried out. It is noted that the present method can effectively improve the resolution of the reconstructed field, thus vibroacoustic parameters on the vibrating boundary can be estimated with reasonably good precision.