on measurement scale and scaling the relationships between measurement scale and scaling are discussed and analyzed in detail it is pointed out that only certain fundamental properties can be measured and that these properties do not include constitutive variables the interrelationships between scale and measurement are shown to manifest themselves in two types of heterogeneity which we label as explicit and implicit an important issue that is addressed for the first time is the necessity of scaling instruments when scaling laboratory experiments up to field scale or vice versa explicit constraints that scaled instruments must satisfy are derived for the frequency response of the instrument it is shown that linear interpolators can be viewed as filters instruments but that these interpolators don t preserve the scale constraints of the instrument used in making the field measurements the relationship between signal conditioning and the instrument s window is isolated and shown to be a multiple convolution over the spatial coordinates corresponding to the window followed by a temporal convolution for the signal conditioning

study of the comparison of the methods of equivalent sources and boundary element methods for near field acoustic holography boundary element methods bem based near field acoustic holography nah has been used successfully in order to reconstruct the normal velocity on an arbitrarily shaped structure surface from measurements of the pressure field on a nearby conformal surface an alternative approach for this reconstruction on a general structure utilizes the equivalent sources method esm in esm the acoustic field is represented by a set of point sources located over a surface that is close to the structure surface this approach is attractive mainly for its simplicity of implementation and speed in this work esm as an approximation of bem based nah is studied and the necessary conditions for the successful application of this approach in nah is discussed a cylindrical fuselage surface excited by a point force as an example to validate the results is used

effective hydraulic conductivity of bounded strongly heterogeneous porous media we develop analytical expressions for the effective hydraulic conductivity ke of a three dimensional heterogeneous porous medium in the presence of randomly prescribed head and flux boundaries the log hydraulic conductivity y forms a gaussian statistically homogeneous and anisotropic random field with an exponential autocovariance by effective hydraulic conductivity of a finite volume in such a field we mean the ensemble mean expected value of all random equivalent conductivities that one could associate with a similar volume under uniform mean flow we start by deriving a first order approximation of an exact expression developed in 1993 by neuman and orr we then generalize this to strongly heterogeneous media by invoking the landau lifshitz conjecture upon evaluating our expressions we find that ke decreases rapidly from the arithmetic mean ka toward an asymptotic value as distance between the prescribed head boundaries increases from zero to about eight integral scales of y the more heterogeneous is the medium the larger is ke relative to its asymptote at any given separation distance our theory compares well with published results of spatially power averaged expressions and with a first order expression developed intuitively by kitanidis in 1990

combined helmholtz equation least squares method for reconstructing acoustic radiation from arbitrarily shaped objects a combined helmholtz equation least squares chels method is developed for reconstructing acoustic radiation from an arbitrary object this method combines the advantages of both the hels method and the helmholtz integral theory based near field acoustic holography nah as such it allows for reconstruction of the acoustic field radiated from an arbitrary object with relatively few measurements thus significantly enhancing the reconstruction efficiency the first step in the chels method is to establish the hels formulations based on a finite number of acoustic pressure measurements taken on or beyond a hypothetical spherical surface that encloses the object under consideration next enough field acoustic pressures are generated using the hels formulations and taken as the input to the helmholtz integral formulations implemented through the boundary element method bem the acoustic pressure and normal component of the velocity at the discretized nodes on the surface are then determined by solving two matrix equations using singular value decomposition svd and regularization techniques also presented are in depth analyses of the advantages and limitations of the chels method examples of reconstructing acoustic radiation from separable and nonseparable surfaces are demonstrated

frictional contact problem for a rigid cylindrical stamp and an elastic layer resting on a half plane abstract the frictional contact problem for a layer resting on a homogeneous half plane is handled using linear elasticity theory in this study the layer is in contact with a rigid cylindrical stamp that is on the layer and applies a concentrated force in the normal and tangential directions friction between the component couples of layer stamp and layer half plane is taken into account the problem is reduced to a system of singular integral equations in which the contact pressures and the contact areas are the unknowns and it is treated using fourier transforms and the boundary conditions for the problem the system of singular integral equations is solved numerically using the gauss jacobi integration formula with equilibrium and consistency conditions numerical results for the contact pressures and the contact areas are given as a solution for both the frictional and the frictionless cases this work is the first study that investigates the effect of friction on the receding contact problem of a layer and a half plane with two contact areas

spectral matrix completion by cyclic projection and application to sound source reconstruction from non synchronous measurements a fundamental limitation of the inverse acoustic problem is determined by the size of the array and the microphone density a solution to achieve large array and or high microphone density is to scan the object of interest by moving sequentially a small prototype array which is referred to as sequential measurements in comparison to a large array and or high microphone density array that can acquire simultaneously all the information of the spectral matrix in particular all cross spectra sequential measurements can only acquire a block diagonal spectral matrix while the cross spectra between the sequential measurements remain unknown due to the missing phase relationships between consecutive positions nevertheless these unknown cross spectra are necessary for sound source reconstruction the objective of this paper is to propose an algorithm to recover the missing elements of the spectral matrix in the case where the acoustical field is highly coherent this issue is shown to boil down to a matrix completion problem subject to given constraint of hermitian symmetry measurements fitting reduced rank and spatial continuity of the sound field a cyclic projection cp algorithm is proposed in this work to find an optimal solution at the intersection between three predefined sets the proposed method is analyzed through numerical simulations of diverse setups and is also validated experimentally

inverse problem with beamforming regularization matrix applied to sound source localization in closed wind tunnel using microphone array abstract microphone arrays have become a standard technique to localize and quantify source in aeroacoustics the simplest approach is the beamforming that provides noise source maps with large main lobe and strong side lobes at low frequency since a decade the focus is set on deconvolution techniques such as damas or clean sc while the source map is clearly improved these methods require a large computation time in this paper we propose a sound source localization technique based on an inverse problem with beamforming regularization matrix called hybrid method with synthetic data we show that the side lobes are removed and the main lobe is narrower moreover if the sound noise source map provided by this method is used as input in the damas process the number of damas iterations is highly reduced the hybrid method is applied to experimental data obtained in a closed wind tunnel in both cases of acoustic or aeroacoustic data the source is correctly detected the proposed hybrid method is found simple to implement and the computation time is low if the number of scan points is reasonable

a stochastic approach to the problem of upscaling of conductivity in disordered media theory and unconditional numerical simulations a general problem in groundwater modeling is how to assign conductivity values to blocks of a numerical model in this study a method is proposed to upscale the conductivity measurements observed at a given scale to block conductivity values for arbitrary block size assuming a multilognormal distribution for the point conductivities the block conductivity appears as a random function whose distribution conditional to point measurements can be derived this conditional distribution allows filling the flow simulator blocks with equiprobable realizations of block conductivities locally conditioned to actual data these realizations could also be conditioned to conductivity values measured at any scale if the size of the measurement support is known the analytical results are compared to results obtained through a monte carlo analysis and a good agreement was found even for variances of ln t larger than 1

regularization methods for near field acoustical holography the reconstruction of the pressure and normal surface velocity provided by near field acoustical holography nah from pressure measurements made near a vibrating structure is a linear ill posed inverse problem due to the existence of strongly decaying evanescentlike waves regularization provides a technique of overcoming the ill posedness and generates a solution to the linear problem in an automated way we present four robust methods for regularization the standard tikhonov procedure along with a novel improved version landweber iteration and the conjugate gradient approach each of these approaches can be applied to all forms of interior or exterior nah problems planar cylindrical spherical and conformal we also study two parameter selection procedures the morozov discrepancy principle and the generalized cross validation which are crucial to any regularization theory in particular we concentrate here on planar and cylindrical holography these forms of nah which rely on the discrete fourier transform are important due to their popularity and to their tremendous computational speed in order to use regularization theory for the separable geometry problems we reformulate the equations of planar cylindrical and spherical nah into an eigenvalue problem the resulting eigenvalues and eigenvectors couple easily to regularization theory which can be incorporated into the nah software with little sacrifice in computational speed the resulting complete automation of the nah algorithm for both separable and nonseparable geometries overcomes the last significant hurdle for nah

reconstructing the vibro acoustic quantities on a highly non spherical surface using the helmholtz equation least squares method this paper presents helpful guidelines and strategies for reconstructing the vibro acoustic quantities on a highly non spherical surface by using the helmholtz equation least squares hels this study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces the key is to select the optimal origin of the coordinate system behind the planar surface choose a target structural wavelength to be reconstructed set an appropriate stand off distance and microphone spacing use a hybrid regularization scheme to determine the optimal number of the expansion functions etc the reconstructed vibro acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength and produce much more satisfactory results than a straight application of the original hels formulations experiment validations on a baffled square plate were conducted inside a fully anechoic chamber

sound source reconstruction using inverse boundary element calculations whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure the aim in this work is to reverse the process i e to determine vibration from acoustic field data this inverse problem is brought on a form suited for solution by means of an inverse boundary element method since the numerical treatment of the inverse source reconstruction results in a discrete ill posed problem regularization is imposed to avoid unstable solutions dominated by errors in the present work the emphasis is on tikhonov regularization and parameter choice methods not requiring an error norm estimate for choosing the right amount of regularization several parameter choice strategies have been presented lately but it still remains to be seen how well these can handle industrial applications with real measurement data in the present work it is demonstrated that the l curve criterion is robust with respect to the errors in a real measurement situation in particular it is shown that the l curve criterion is superior to the more conventional generalized cross validation gcv approach for the present tire noise studies

spatial resolution limits for the reconstruction of acoustic source strength by inverse methods one method for deducing the strength of an acoustic source distribution from measurement of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution in practice the frequency response function matrix to be inverted may very often be ill conditioned this ill conditioning will also often result in an ill posed problem and thus regularization algorithms are used to produce reasonable solutions for this purpose tikhonov regularization has been applied and generalized cross validation gcv has been introduced as an effective method for determining the proper amount of regularization without prior knowledge of either the source distribution or the contaminating errors in the present work the emphasis is placed on the relationship between the spatial resolution of the reconstructed source distribution and the small singular values of the frequency response function matrix to be inverted however the use of tikhonov regularization often suppresses the effect of small singular values and these are in turn often associated with high spatial frequencies of the source distribution thus the process of regularization produces a useful estimate of the acoustic source strength distribution but with a limited spatial resolution furthermore in the field of fourier acoustics the spatial resolution of the reconstructed source distribution is usually limited by the wavelength of the radiation this paper expresses the relationship between estimation accuracy spatial resolution noise level and source sensor geometry when a range of inverse sound radiation problems are regularised using tikhonov regularization with gcv the results presented form the basis of guidelines that enable the reconstruction of acoustic source strength with a resolution that is finer than the intrinsic half wavelength limit

approximations of inverse boundary element methods with partial measurements of the pressure field boundary element methods bems based near field acoustic holography nah requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby conformal surface there are practical cases when measurements are available over a patch from the measurement surface in which conventional inverse bem based nah ibem cannot be applied directly but instead as an approximation in this work two main approximations based on the indirect implicit methods are considered patch ibem and ibem with cauchy data patch ibem can be applied with a continuation procedure which as its predecessor patch nah a well known technique that can be used on separable geometries of the wave equation continues the pressure field using an iterative procedure or it can be applied by a direct procedure on the other hand ibem with cauchy data requires measurements over two conformal patches and it will be shown that this technique will be reliable regardless of the position of the source the theory behind each method will be justified and validated using a cylindrical surface with numerical data generated by point sources and using experimental data from a cylindrical fuselage excited by a point force

instantaneous bayesian regularization applied to real time near field acoustic holography real time near field acoustic holography rt nah is used to recover non stationary sound sources using a planar microphone array direct propagation is described by the convolution of the wavenumber spectrum of the source under study with a known impulse response the deconvolution operation is achieved by a singular value decomposition of the propagator and tikhonov regularization is performed to stabilize the solution the inverse problem has an innate ill posed characteristic and the regularization process is the key factor in obtaining acceptable results the purpose of this paper is to present the instantaneous regularization process applied to rt nah method bayesian estimation of the regularization parameter is introduced from prior knowledge of the problem the computation of the regularization parameter is updated for each block of constant time interval allowing one to take into account the fluctuating properties of the sound field the superiority of bayesian regularization compared to state of the art methods is observed numerically and experimentally for reconstruction of non stationary sources rt nah is also enhanced to allow the reconstruction of long signals updating the regularization parameter accordingly to the fluctuations of the snr is revealed to be a necessary effort to reconstruct highly non stationary sources

porous media upscaling in terms of mathematical epistemic cognition in this work we revisit the meaning of the term solution with respect to a mathematical model representing a physical media upscaling system a central aim is to combine the science of mind with human mathematical ideas to solve real world upscaling problems we propose that in certain cases a nonconventional epistemic cognition solution which assumes that the model describes incomplete knowledge about nature and focuses on conceptual mechanisms and thinking processes can lead to a more realistic upscaling analysis than a conventional ontologic approach which assumes that the model describes nature as is and focuses on form manipulations in the present work we apply the epistemic cognition approach to the solution of the two dimensional bounded porous media upscaling problem a formal framework is presented and implementation issues related to the epistemic cognition methodology are considered numerical experiments are presented involving effective conductivities in bounded two dimensional sp

a receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate abstract in this paper we consider the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half space when the two bodies are pressed together the graded layer is modeled as a nonhomogeneous medium with an isotropic stress strain law and is subjected over a part of its top surface to normal tractions while the rest of it is free of tractions since the contact between the two bodies is assumed to be frictionless then only compressive normal tractions can be transmitted in the contact area using hankel transform the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius the global equilibrium condition of the layer is supplemented to solve the problem the singular integral equation is solved numerically using orthogonal chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact length that satisfies the global equilibrium condition the main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact

estimation of acoustic source strength by inverse methods part ii experimental investigation of methods for choosing regularization parameters two regularization methods tikhonov regularization and singular value discarding are used to improve the accuracy of reconstruction of acoustic source strength by inverse techniques in this paper some methods are investigated for choosing the tikhonov regularization parameter and the singular values to be discarded of these we concentrate on the use of ordinary cross validation and generalized cross validation these methods can provide an appropriate regularization parameter without prior knowledge of either the acoustic source strength or the contaminating measurement noise some experimental results obtained using a randomly vibrating simply supported plate mounted in a baffle are presented to illustrate the performance of the methods for choosing the regularization parameters

design of an optimal wave vector filter for enhancing the resolution of reconstructed source field by near field acoustical holography nah 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

block sparse beamforming for spatially extended sources in a bayesian formulation direction of arrival doa estimation refers to the localization of sound sources on an angular grid from noisy measurements of the associated wavefield with an array of sensors for accurate localization the number of angular look directions is much larger than the number of sensors hence the problem is underdetermined and requires regularization traditional methods use an l2 norm regularizer which promotes minimum power smooth solutions while regularizing with l1 norm promotes sparsity sparse signal reconstruction improves the resolution in doa estimation in the presence of a few point sources but cannot capture spatially extended sources the doa estimation problem is formulated in a bayesian framework where regularization is imposed through prior information on the source spatial distribution which is then reconstructed as the maximum a posteriori estimate a composite prior is introduced which simultaneously promotes a piecewise constant profile and sparsity in the solution simulations and experimental measurements show that this choice of regularization provides high resolution doa estimation in a general framework i e in the presence of spatially extended sources

source visualization by using statistically optimized near field acoustical holography in cylindrical coordinates nearfield acoustical holography nah is a useful tool for visualizing noise sources however to avoid spatial fourier transform related truncation effects the measurement or hologram surface must extend beyond the source to a region where the sound pressure drops to a level significantly lower than the peak level within the measurement aperture statistically optimized nearfield acoustical holography sonah first derived by steiner and hald in planar geometry is based on a formulation similar to that of nah however in sonah surface to surface projection of the sound field is performed by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy i e no spatial fourier transforms are performed thus the requirement that the measurement surface be extended is eliminated without compromising the accuracy of the procedure in the present work sonah was re formulated in cylindrical coordinates and wa

homogenization based interval analysis for structural acoustic problem involving periodical composites and multi scale uncertain but bounded parameters this paper presents a homogenization based interval analysis method for the prediction of coupled structural acoustic systems involving periodical composites and multi scale uncertain but bounded parameters in the structural acoustic system the macro plate structure is assumed to be composed of a periodically uniform microstructure the equivalent macro material properties of the microstructure are computed using the homogenization method by integrating the first order taylor expansion interval analysis method with the homogenization based finite element method a homogenization based interval finite element method hifem is developed to solve a periodical composite structural acoustic system with multi scale uncertain but bounded parameters the corresponding formulations of the hifem are deduced a subinterval technique is also introduced into the hifem for higher accuracy numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented method for a periodical composite structural acoustic system with multi scale uncertain but bounded parameters

sound field reconstruction within an entire cavity by plane wave expansions using a spherical microphone array a spherical microphone array has proved effective in reconstructing an enclosed sound field by a superposition of spherical wave functions in fourier domain it allows successful reconstructions surrounding the array but the accuracy will be degraded at a distance in order to extend the effective reconstruction to the entire cavity a plane wave basis in space domain is used owing to its non decaying propagating characteristic and compared with the conventional spherical wave function method in a low frequency sound field within a cylindrical cavity the sensitivity to measurement noise the effects of the numbers of plane waves and measurement positions are discussed simulations show that under the same measurement conditions the plane wave function method is superior in terms of reconstruction accuracy and data processing efficiency that is the entire sound field imaging can be achieved by only one time calculation instead of translations of local sets of coefficients with respect to every measur

reconstructing interior acoustic pressure fields via helmholtz equation least squares method this paper extends the helmholtz equation least squares hels method previously developed by wang and wu j acoust soc am 102 2020 2032 1997 to reconstruction of acoustic pressure fields inside the cavity of a vibrating object the acoustic pressures are reconstructed through an expansion of the acoustic modes generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation such an expansion is uniformly convergent because the selected acoustic modes consist of a uniformly convergent series of legendre functions the coefficients associated with these acoustic modes are determined by requiring the assumed form solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method numerical examples of partially vibrating spheres and cylinders with various half length to radius aspect ratios subject to different frequency excitations are demonstrated the recon

method of superposition applied to patch near field acoustic holography the method of superposition may be applied to reconstruct the field on a partial surface on a radiating structure from measurements made on a nearby limited surface unlike conformal near field holography where the measurement surface surrounds the entire structure in patch holography the measurement surface need only be approximately as large as the patch on the structure surface where the reconstruction is required using the method of superposition the field on and near the measurement surface may be approximated by the field produced by a source distribution placed on a surface inside the structure the source strengths are evaluated by applying boundary conditions on the measurement surface the algorithm requires the inversion of the green s function matrix which may be ill conditioned truncated singular value decomposition is used to invert it the field on the structure surface is then approximated by the field produced by the source distribution the algorithm is easier to implement than the

hybrid uncertain analysis of acoustic field with interval random parameters abstract for the acoustic field prediction without sufficient information an interval random model is introduced to treat with the uncertain parameters in which the probability distribution parameters of random variables are modeled as interval variables instead of given precise values based on the interval random model the hybrid uncertain acoustic dynamic equilibrium equation is constructed and a hybrid uncertain analysis method is proposed in the proposed method the interval random matrix and vector are expanded by the first order taylor series and the sound pressure response vector is obtained by the matrix perturbation technique a monotonic analysis is conducted for the sound pressure response vector and based on it the lower and upper bounds of the sound pressure response vector are obtained by the vertex method according to the response bounds the intervals of expectation and variance of the sound pressure response vector are calculated by the random interval moment method two numerical examples which include a simple problem with explicit expression and a complex engineering application are presented to demonstrate the effectiveness of the present method

exact solutions to the acoustic source reconstruction problem in this paper we generalize the recently developed analytical solutions of the radiation modes problem to the determination of closed form expressions for the singular value expansion of a number of integral operators that map the boundary velocity of a baffled planar structure onto the acoustic pressure radiated in far field or intermediate regions exact solutions to this problem involve prolate spheroidal wave functions that correspond to a set of independent distributions with finite spatial support and maximal energy concentration in a given bandwidth of the transform domain a stable solution to the inverse source reconstruction problem is obtained by decomposing the unknown boundary velocity into a number of efficiently radiating singular velocity patterns that correspond to the number of degrees of freedom of the radiated field it is found that the degree of ill posedness of the inverse problem is significantly reduced when considering a hemi circular observation arc with respect to a linear array of sensors by a factor scaling on the small angular aperture subtended by the observation line estimates are derived from the spatial resolution limits that can be achieved in the source reconstruction problem from the dimension of the efficiently radiating subspace

estimation of acoustic source strength within a cylindrical duct by inverse methods one method for deducing the strength of an acoustic source distribution from measurements of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution this method uses the singular value decomposition svd as the primary analysis tool and has shown some promise in the transformation process associated with the svd the strength of the discretized point source can be simply represented by the pressure field and the inversion of corresponding matrix of the frequency response function and the transformed pressures and source distribution are related by single real numbers only i e the singular values therefore the resolution and the accuracy of the reconstruction produced by such inversion methods will be highly dependent on how these small singular values are treated during the inversion process in the present work the emphasis is placed on the description of the inverse method for the investigation of the characteristics of acoustic sources within a circular duct firstly an analytical model is developed of the internal field from a finite duct with open ends an examination is presented of the capability of the inverse method in dealing with in duct sound source problems these guide the design of an optimal sensor array which can make the condition number as small as possible for the assumed source distribution also a series of experimental demonstrations are given of the proposed in duct sensor array for producing high resolution information regarding in duct sources

basic theory and properties of statistically optimized near field acoustical holography to avoid the requirement set by standard near field acoustical holography nah to measure an area that fully covers the source a set of so called patch nah methods has been introduced one such method is the statistically optimized nah sonah in this method the acoustic quantities on a mapping surface near the measurement surface are calculated by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy the present paper gives an overview of the basic theory of sonah including a description of phenomena such as spatial aliasing and wave number domain leakage a revised and generalized mathematical formulation is given covering the calculation of all three components of particle velocity and the use of up to six virtual source planes a set of formulas for the inherent estimation error level of the method is derived and used to visualize the regions of validity of the sonah predictions for some typical microphone array geometries the sensitivity of the inherent error level distribution to changes in the parameters of the sonah algorithm is also investigated

a receding contact plane problem between a functionally graded layer and a homogeneous substrate abstract in this paper we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half space when the two bodies are pressed together the graded layer is modeled as a nonhomogeneous medium with an isotropic stress strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions since the contact between the two bodies is assumed to be frictionless then only compressive normal tractions can be transmitted in the contact area using integral transforms the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half length the global equilibrium condition of the layer is supplemented to solve the problem the singular integral equation is solved numerically using chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half length that satisfies the global equilibrium condition the main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact

on reconstruction of acoustic pressure fields using the helmholtz equation least squares method this paper presents analyses and implementation of the reconstruction of acoustic pressure fields radiated from a general three dimensional complex vibrating structure using the helmholtz equation least squares hels method the structure under consideration emulates a full size four cylinder engine to simulate sound radiation from a vibrating structure harmonic excitations are assumed to act on arbitrarily selected surfaces the resulting vibration responses are solved by the commercial fem finite element method software i deas once the normal component of the surface velocity distribution is determined the surface acoustic pressures are calculated using standard boundary element method bem codes the radiated acoustic pressures over several planar surfaces at certain distances from the source are calculated by the helmholtz integral formulation these field pressures are taken as the input to the hels formulation to reconstruct acoustic pressures on the entire source surface as well as in the field the reconstructed acoustic pressures thus obtained are then compared with benchmark values numerical results demonstrate that good agreements can be obtained with relatively few expansion functions the hels method is shown to be very effective in the low to mid frequency regime and can potentially become a powerful noise diagnostic tool

estimation of acoustic source strength by inverse methods part i conditioning of the inverse problem this paper deals with the discrete inverse problem in acoustics it is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field the transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known in principle the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions the accuracy of source strength reconstruction in the presence of noise which contaminates the measured pressures is crucially dependent on the conditioning of the matrix to be inverted this paper examines the conditioning of this inverse problem particularly with regard to the geometry and number of sources and measurement positions and the non dimensional frequency a preliminary investigation is also presented of methods such as tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time stationary random processes and the spectra and cross spectra are measured at a number of positions in the radiated field the paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements

fast fourier transform and singular value decomposition formulations for patch nearfield acoustical holography nearfield acoustical holography nah requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby concentric surface the latter generally coincident with a vibrator patch nah provides a major simplification by eliminating the need for complete surface pressure scans only a small area needs to be scanned to determine the normal velocity on the corresponding small area concentric patch on the vibrator the theory of patch nah is based on 1 an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field and 2 a decomposition of the transfer function pressure to velocity and or pressure to pressure between the two surfaces using the singular value decomposition svd for general shapes and the fast fourier transform fft for planar surfaces inversion of the transfer function is stabilized using tikhonov regularization and the morozov discrepancy principle experimental results show that root mean square errors of the normal velocity reconstruction for a point driven vibrator over 200 2700 hz average less than 20 for two small concentric patch surfaces 0 4 cm apart reconstruction of the active normal acoustic intensity was also successful with less than 30 error over the frequency band

solving singular integral equations using gaussian quadrature and overdetermined system abstract gauss chebyshev quadrature and collocation at the zeros of the chebyshev polynomial of the first kind t n x and second kind u n x leads to an overdetermined system of linear algebraic equations the size of the coefficient matrix for the overdetermined system depends on the degrees of chebyshev polynomials used we show that we can get more accurate solution using t 4 n 4 x than other t n x the regularization method using generalized singular value decomposition is described and compared to gauss newton method for solving the overdetermined system of equations computational tests show that gsvd with an appropriate choice of regularization parameter gives better solution in solving singular integral equations

reconstruction of distributed dynamic loads on an euler beam via mode selection and consistent spatial expression this paper presents a convenient and efficient approach to reconstruct two dimensional distributed dynamic loads on a damped thin elastic plate from its steady state dynamic response the approach is based on a mode selection method which comes from an idea that an optimal range of frequency and mode exists for dynamic load reconstruction as well as on the consistent spatial expression of the distributed dynamic loads the criterion for mode selection is derived theoretically a comparison between the method of truncated singular value decomposition tsvd and the method of mode selection demonstrates that the former is unstable while the latter is not only stable but robust with the proposed criterion the method of mode selection enables one to find an optimal range for load reconstruction provided that the error bounds of both parameters and objective are given or estimated and hence to make a balance between the reconstruction range and the error control

stochastic diagrammatic analysis of groundwater flow in heterogeneous porous media the diagrammatic approach is an alternative to standard analytical methods for solving stochastic differential equations governing groundwater flow with spatially variable hydraulic conductivity this approach uses diagrams instead of abstract symbols to visualize complex multifold integrals that appear in the perturbative expansion of the stochastic flow solution and reduces the original flow problem to a closed set of equations for the mean and the covariance functions diagrammatic analysis provides an improved formulation of the flow problem over conventional first order series approximations which are based on assumptions such as constant mean hydraulic gradient infinite flow domain and neglect of cross correlation terms this formulation includes simple schemes like finite order diagrammatic perturbations that account for mean gradient trends and boundary condition effects as well as more advanced schemes like diagrammatic porous media description operators which contain infinite order correlations in other words diagrammatic analysis covers not only the cases where low order diagrams lead to good approximations of flow but also those situations where low order perturbation is insufficient and a more sophisticated analysis is needed diagrams lead to a nonlocal equation for the mean hydraulic gradient in terms of which necessary conditions are formulated for the existence of an effective hydraulic conductivity three dimensional flow in an isotropic bounded domain with dirichlet boundary conditions is considered and an integral equation for the mean hydraulic head is derived by means of diagrams this formulation provides an explicit expression for the boundary effects within the three dimensional flow domain in addition to these theoretical results the numerical performance of the diagrammatic approach is tested and useful insight is obtained by means of one dimensional flow examples where the exact stochastic solutions are available

bayesian focalization quantifying source localization with environmental uncertainty this paper applies a bayesian formulation to study ocean acoustic source localization as a function of uncertainty in environmental properties water column and seabed and of data information content signal to noise ratio snr and number of frequencies the approach follows that of the optimum uncertain field processor a m richardson and l w nolte j acoust soc am 89 2280 2284 1991 in that localization uncertainty is quantified by joint marginal probability distributions for source range and depth integrated over uncertain environmental properties the integration is carried out here using metropolis gibbs sampling for environmental parameters and heat bath gibbs sampling for source location to provide efficient sampling over complicated parameter spaces the approach is applied to acoustic data from a shallow water site in the mediterranean sea where previous geoacoustic studies have been carried out it is found that reliable localization requires a sufficient combination of prior e

application of bem boundary element method based acoustic holography to radiation analysis of sound sources with arbitrarily shaped geometries a method employing holograms that conform with arbitrarily shaped sources has been developed for enhancing conventional near field acoustic holography which has been limited to sources with simple geometries e g planar or cylindrical surfaces four holography transformation algorithms have been developed based on acoustic holography theory and the boundary element method bem singular value decomposition svd has been incorporated into the algorithms in order to alleviate the ill posed nature frequently encountered in backward reconstruction of a field a pulsating sphere a cylinder with spherical endcaps and a vibrating piston set in a rigid sphere have been adopted in a numerical simulation for verifying the algorithms satisfactory agreement has been achieved between the holographically transformed results and the analytical solutions

a mapping relationship based near field acoustic holography with spherical fundamental solutions for helmholtz equation abstract in the procedure of the near field acoustic holography nah based on the fundamental solutions for helmholtz equation fs the number of fs and the measurement setup to obtain their coefficients are two crucial issues to the successful reconstruction the current work is motivated to develop a framework for the nah which supplies a guideline to the determination of the number of fs as well as an optimized measurement setup a mapping relationship between modes on surfaces of boundary and hologram is analytically derived by adopting the modes as fs in spherical coordinates thus reconstruction is converted to obtain the coefficients of participant modes on holograms in addition an integral identity is firstly to be derived for the modes on convex surfaces which is useful in determining the inefficient or evanescent modes for acoustic radiation in free space to determine the number of fs adopted in the mapping relationship based nah mrs based nah two approaches are proposed to supply reasonable estimations with criteria of point wise pressure and energy respectively a technique to approximate a specific degree of mode on patches by a set of locally orthogonal patterns is explored for three widely used holograms such as planar cylindrical and spherical holograms which results in an automatic determinations of the number and position of experimental setup for a given tolerance numerical examples are set up to validate the theory and techniques in the mrs based nah reconstructions of a cubic model demonstrate the potential of the proposed method for regular models even with corners and shapers worse results for the elongated cylinder with two spherical caps reveal the deficiency of the mrs based nah for irregular models which is largely due to the adopted modes are fs in spherical coordinates the nah framework pursued in the current work provides a new insight to the reconstruction procedure based on the fs in spherical coordinates

helmholtz equation least squares method for reconstructing the acoustic pressure field a method using spherical wave expansion theory to reconstruct acoustic pressure field from a vibrating object is developed the radiated acoustic pressures are obtained by means of an expansion of independent functions generated by the gram schmidt orthonormalization with respect to the particular solutions to the helmholtz equation on the vibrating surface under consideration the coefficients associated with these independent functions are determined by requiring the assumed form of solution to satisfy the pressure boundary condition at the measurement points the errors incurred in this process are minimized by the least squares method once these coefficients are specified the acoustic pressure at any point including the source surface is completely determined in this paper this method is used to reconstruct the surface acoustic pressures based on the measured acoustic pressure signals in the field it is shown that this method can be applied to both separable and nonseparable geometries and the

reconstruction of nonstationary sound fields based on the time domain plane wave superposition method a time domain plane wave superposition method is proposed to reconstruct nonstationary sound fields in this method the sound field is expressed as a superposition of time convolutions between the estimated time wavenumber spectrum of the sound pressure on a virtual source plane and the time domain propagation kernel at each wavenumber by discretizing the time convolutions directly the reconstruction can be carried out iteratively in the time domain thus providing the advantage of continuously reconstructing time dependent pressure signals in the reconstruction process the tikhonov regularization is introduced at each time step to obtain a relevant estimate of the time wavenumber spectrum on the virtual source plane because the double infinite integral of the two dimensional spatial fourier transform is discretized directly in the wavenumber domain in the proposed method it does not need to perform the two dimensional spatial fast fourier transform that is generally used in time domain holography and real time near field acoustic holography and therefore it avoids some errors associated with the two dimensional spatial fast fourier transform in theory and makes possible to use an irregular microphone array the feasibility of the proposed method is demonstrated by numerical simulations and an experiment with two speakers

beamforming regularization matrix and inverse problems applied to sound field measurement and extrapolation using microphone array for sound field reproduction using multichannel spatial sound systems such as wave field synthesis and ambisonics sound field extrapolation is a useful tool for the measurement description and characterization of a sound environment to be reproduced in a listening area in this paper the inverse problem theory is adapted to sound field extrapolation around a microphone array for further spatial sound and sound environment reproduction a general review of inverse problem theory and analysis tools is given and used for the comparative evaluation of various microphone array configurations classical direct regularization methods such as truncated singular value decomposition and tikhonov regularization are recalled on the basis of the reviewed background a new regularization method adapted to the problem at hand is introduced this method involves the use of an a priori beamforming measurement to define a data dependent discrete smoothing norm for the regularization of the inverse problem this method which represents the main contribution of this paper shows promising results and opens new research avenues

comparison of methods for parameter selection in tikhonov regularization with application to inverse force determination in performing transfer path analysis of structure borne sound transmission the operational forces at the excitation points and or at the connections within the structure borne paths are required these forces can be obtained by using inverse techniques but the measured data used will contain some unknown errors therefore the reconstructed forces may include large errors due to the inversion of an ill conditioned matrix of these measured data in this study tikhonov regularization is used in order to improve the conditioning of the matrix inversion several methods are available to select the optimal regularization parameter the purpose of this paper is to compare the performance of the ordinary and generalized cross validation methods and the l curve criterion simulations are carried out representing measurements on a rectangular plate for different noise levels in measured data also the robustness of the conclusions is investigated by varying the shape of the plates the force positions and the noise levels included in the measured data the l curve method is found to perform better than ocv or gcv particularly for high noise levels in the operational responses but less well when these noise levels are low it is therefore found to be less susceptible to producing large reconstruction errors but it tends to over regularize the solution in the presence of low noise leading to under estimates of the forces in practice measurements of operational responses may be susceptible to noise contamination which suggests that the l curve method is likely to be the most appropriate method in practical situations nevertheless it is important to obtain good estimates of the likely noise in the signals before determining the most appropriate regularization technique ordinary cross validation method is generally found to have a better performance than generalized cross validation method if the matrix condition numbers are high since the need for regularization is greater with high condition numbers it is consequently found that the ordinary cross validation method gives more reliable results overall than the generalized cross validation method

structural source identification using a generalized tikhonov regularization abstract this paper addresses the problem of identifying mechanical exciting forces from vibration measurements the proposed approach is based on a generalized tikhonov regularization that allows taking into account prior information on the measurement noise as well as on the main characteristics of sources to identify like its sparsity or regularity to solve such a regularization problem efficiently a generalized iteratively reweighted least squares girls algorithm is introduced proposed numerical and experimental validations reveal the crucial role of prior information in the quality of the source identification and the performance of the girls algorithm

the helmholtz equation least squares method and rayleigh hypothesis in near field acoustical holography in this paper we present a numerical investigation of reconstructing time harmonic acoustic pressure field in two dimensional space by using a series expansion the so called helmholtz equation least squares hels method series expansion methods or the rayleigh methods have been widely used in predicting the scattered acoustic pressure with regularization they can also be applied to reconstruction of acoustic pressure on the source surface from the measurements taken in the field and hels is the first such attempt for these problems in this paper we establish hels in the framework of the rayleigh methods and reveal its interrelationship with the rayleigh hypothesis in particular to regularize a reconstruction problem we use the method of quasisolutions i e a tikhonov regularization with an a posteriori choice of the regularization parameter it is shown that without regularization hels can still yield a satisfactory reconstruction of acoustic radiation from an arbitrary object when enough me

impact force sparse reconstruction from highly incomplete and inaccurate measurements abstract the classical l2 norm based regularization methods applied for force reconstruction inverse problem require that the number of measurements should not be less than the number of unknown sources taking into account the sparse nature of impact force in time domain we develop a general sparse methodology based on minimizing l1 norm for solving the highly underdetermined model of impact force reconstruction a monotonic two step iterative shrinkage thresholding mtwist algorithm is proposed to find the sparse solution to such an underdetermined model from highly incomplete and inaccurate measurements which can be problematic with tikhonov regularization mtwist is highly efficient for large scale ill posed problems since it mainly involves matrix vector multiplies without matrix factorization in sparsity frame the proposed sparse regularization method can not only determine the actual impact location from many candidate sources but also simultaneously reconstruct the time history of impact force simulation and experiment including single source and two source impact force reconstruction are conducted on a simply supported rectangular plate and a shell structure to illustrate the effectiveness and applicability of mtwist respectively both the locations and force time histories of the single source and two source cases are accurately reconstructed from a single accelerometer where the high noise level is considered in simulation and the primary noise in experiment is supposed to be colored noise meanwhile the consecutive impact forces reconstruction in a large scale greater than 104 sparse frame illustrates that mtwist has advantages of computational efficiency and identification accuracy over tikhonov regularization

analytic solutions to the acoustic source reconstruction problem in this paper we generalize the recently developed analytical solutions of the radiation modes problem to the determination of closed form expressions for the singular value expansion of a number

conformal generalized near field acoustic holography for axisymmetric geometries the normal velocity field on the boundary of a radiating source is reconstructed with high resolution by using pressure data measured in the very near field to include evanescent components fast decaying with the distance the measurement points belong to a surface conformal to the reconstruction is performed by identifying the boundary normal velocity distribution generating the pressure field best mean square fitting the measurement data the ensuing normal equations are solved by resorting to the singular value decomposition svd of the transformation from the boundary normal velocity to the pressure at the measurement points the reconstructed boundary normal velocity is represented as a linear combination of basis functions each associated with a singular value sv the errors in the estimation of the coefficients of the linear combination are proportional to the inverses of the corresponding svs to achieve robustness the svd is truncated to retain the terms corresponding to a limited dynamic range in turn related to the dynamic range of the measurement system for axisymmetric but otherwise general surfaces the numerical complexity is reduced because separate svds of greatly reduced dimensionality must be performed on a number of matrices each associated with one of the harmonics of the fourier expansion of the field around the symmetry axis in a numerical experiment making use of an available computer model by processing very near field pressure samples the normal velocity was reconstructed with excellent accuracy on the surface of a finite compliant cylinder with flat endcaps excited by point forces the viability of the method was then confirmed in a measurement tank experiment in which the distribution of the boundary normal velocity was reconstructed on a finite compliant cylinder driven by point shakers comparison with accelerometer data shows good agreement on a wide frequency band

iterative regularization method in generalized inverse beamforming abstract beamforming based on microphone array is a method to identify sound sources it can visualize the sound field of the source plane and reveal interesting acoustic information generalized inverse beamforming gib is one important branch of beamforming techniques due to its high identification accuracy and computational efficiency however in real testing situation errors caused by measurement noise and configuration problems may seriously reduce the beamforming accuracy as an inverse problem the stability of gib can be improved with regularization methods we proposed a new iterative regularization method for gib by iteratively redefining the form of regularization matrix and calculating the corresponding solution moreover the new method is applied to functional beamforming and double layer antenna beamforming respectively numerical simulations and experiments are implemented the results show that the proposed regularization method leads to more robust beamforming output and higher accuracy in both the two applications

bayesian space frequency separation of wide band sound sources by a hierarchical approach this paper proposes an efficient solution to the separation of uncorrelated wide band sound sources which overlap each other in both space and frequency domains the space frequency separation is solved in a hierarchical way by 1 expanding the sound sources onto a set of spatial basis functions whose coefficients become the unknowns of the problem backpropagation step and 2 blindly demixing the coefficients of the spatial basis into uncorrelated components relating to sources of distinct physical origins separation step the backpropagation and separation steps are both investigated from a bayesian perspective in particular markov chain monte carlo sampling is advocated to obtain bayesian estimates of the separated sources separation is guaranteed for sound sources having different power spectra and sufficiently smooth spatial modes with respect to frequency the validity and efficiency of the proposed separation procedure are demonstrated on laboratory experiments

reconstruction of vibro acoustic fields using hybrid nearfield acoustic holography hybrid nearfield acoustical holography is utilized to reconstruct the vibro acoustic fields generated by an arbitrary structure vibrating in an unbounded fluid medium this hybrid nah is based on the modified helmholtz equation least squares method that expresses the field acoustic pressure in terms of expansions of outgoing and incoming waves the expansion coefficients are determined by solving an over determined linear system of equations obtained by matching the assumed form solution to a finite number of acoustic pressures measured in the field via least squares the measurements are taken over a conformal surface around the source at close range so that the evanescent waves can be captured once the expansion coefficients are specified enough field acoustic pressures are regenerated on a conformal surface around the source and are taken as input to the helmholtz integral formulation implemented numerically by the boundary element method the acoustic pressure and normal velocity on the source surface are reconstructed using singular value decomposition modified tikhonov regularization and generalized cross validation method this hybrid nah enables one to obtain a satisfactory reconstruction cost effectively because the majority of the input data are calculated but not measured numerical examples of reconstructing the vibro acoustic quantities on the surfaces of an engine block and a highly elongated cylinder are demonstrated

estimation of plate material properties by means of a complex wavenumber fit using hankel s functions and the image source method abstract this paper presents a new wave fitting approach to estimate the frequency dependent material properties of thin isotropic plate structures from an experimentally obtained vibrational field exciting the plate at a single point the method projects the measurement data on to an analytical image source model in which hankel s functions are used for a description of the wave fields emanating from the point of excitation including the reflected wave fields from the edges of the finite plate by minimizing the error between the projected field and the measured field varying the complex wave number and the source strengths of the image sources an optimum fit is searched for thus the source strengths of the image sources do not need to be determined theoretically but are estimated from the fit on to the experimental data instead thus avoiding difficulties in theoretically assessing the reflection coefficient of the edges of the plate the approach uses a complex wavenumber fit enabling the determination of the dynamic stiffness of the plate structure and its damping properties as function of frequency the method is especially suited for plates with a sufficient amount of damping excited at high frequencies

the quantification of structure borne transmission paths by inverse methods part 1 improved singular value rejection methods structure borne sound from installed machinery is often transmitted into a receiver structure via many connection points and several co ordinate directions at each of them in order to quantify the contributions from the various connection points the operational forces at the interfaces or an equivalent set of forces at some other locations should be determined these forces may be combined with measured transfer functions to determine their contributions to the sound at the receiver locations inverse methods are becoming widely used in which a matrix of measured accelerances is inverted at each frequency and used with operational acceleration data to find the forces due to poor conditioning of this matrix however the results can often be unreliable in this paper using both simulations and measurements an assessment is made of the success and failure of various strategies for dealing with the problems of ill conditioning in particular over determination and singular value rejection in each case the test structure is a rectangular plate and a wide frequency range is covered to include regions of both low and high modal overlap critical for the rejection of singular values is a suitable threshold it is established that previously used thresholds based on estimates of error in either accelerances or operational responses cannot be used universally an alternative approach is developed in which the accelerance matrix is perturbed by a different amount for each sample of the operational responses based on this approach a more robust strategy is proposed which takes account simultaneously of the effect of errors in both the accelerances and operational responses

application of lp norm regularisation techniques in the synthesis of indoor tyre pass by noise with the inverse method abstract pass by noise measurements can nowadays be realised in a laboratory environment with a microphone array and a stationary vehicle on a rolling road according to iso 362 1 2016 within this indoor testing procedure the contributions from the various noise sources in a car can be estimated with a set of microphones close to the various sources and the pass by noise then synthesised the methods described in this paper use measured near field pressure data close to a rolling tyre at 50 km h to estimate virtual source strength using the inverse method and the synthesised far field tyre noise is then compared with the one measured directly at a far field microphone array a combination of l1 norm and l2 norm regularisation methods are investigated to optimise the equivalent source position and strength and subsequently the far field pass by noise pressure estimates through the frequency range of interest it is shown that by optimising the positions of 4 equivalent sources acceptable representations of the measured far field spectra can be synthesised

transducer sensitivity compensation using diagonal preconditioning for time reversal and tikhonov inverse filtering in acoustic systems filters are commonly used in sound reproduction and communication systems as a means of compensating for the response of the electro acoustic plant two commonly used filter designs in the field of acoustics are the time reversal filter and the tikhonov inverse filter in this paper the influence of transducer sensitivities on the performance of these filters is examined it is shown that the sensitivity of the transducers can negatively affect the performance of the resulting filter to compensate for the decrease in performance diagonal preconditioning can be implemented in the system it is shown that by using diagonal matrices which minimize the condition number of the system the loss in performance arising from unbalanced sensitivities is minimized this paper proposes an algorithm to find such a set of diagonal matrices and results are presented showing the improvements in performance arising from the modified filter design

a parameterized background data weak approach to variational data assimilation formulation analysis and application to acoustics summary we present a parameterized background data weak pbdw formulation of the variational data assimilation state estimation problem for systems modeled by partial differential equations the main contributions are a constrained optimization weak framework informed by the notion of experimentally observable spaces a priori and a posteriori error estimates for the field and associated linear functional outputs weak greedy construction of prior background spaces associated with an underlying potentially high dimensional parametric manifold stability informed choice of observation functionals and related sensor locations and finally output prediction from the optimality saddle in o m3 operations where m is the number of experimental observations we present results for a synthetic helmholtz acoustics model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory to conclude we consider a physical raised box acoustic resonator chamber we integrate the pbdw methodology and a robotic observation platform to achieve real time in situ state estimation of the time harmonic pressure field we demonstrate the considerable improvement in prediction provided by the integration of a best knowledge model and experimental observations we extract even from these results with real data the numerical trends indicated by the theoretical convergence and stability analyses copyright 2014 john wiley sons ltd

acoustical inverse problems regularization direct definition of filter factors using signal to noise ratio abstract acoustic imaging aims at localization and characterization of sound sources using microphone arrays in this paper a new regularization method for acoustic imaging by inverse approach is proposed the method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors in place of regularization using classical methods such as truncated singular value decomposition and tikhonov regularization the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation defined from the estimated measurement noise the thresholding operation is achieved using modified filter functions the originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the tikhonov filter this has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems theoretical results show that this method is comparatively more accurate than tikhonov regularization and truncated singular value decomposition

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

compressive sensing based spherical harmonics decomposition of a low frequency sound field within a cylindrical cavity a low frequency sound field within a cylindrical cavity can be well approximated by a sparse set of fourier bessel series in a spherical coordinate system the approximation accuracy can be guaranteed as long as the series coefficients are well estimated by use of spherical microphone arrays sma conventional methods like spherical fourier transform and helmholtz equation least square require a large number of sensors and it is difficult to estimate the high order coefficients in the presence of sensor noise to cope with these issues compressive sensing cs is utilized and compared with the conventional methods in this study the estimate of the high order coefficients from contaminated measurements is examined and the effect of modal behavior is analyzed numerical simulations show that sensors can be significantly saved especially for high order cavity modes due to the low sparsity of coefficients which is also stable as the modal frequency increases and the overall accuracy is also improved the optimal sma configuration for the use of cs is studied a large sma with omni microphone deployed by the fliege sampling scheme is suggested the cs results are finally validated through the good simulated reconstructions of cylindrical cavity modes

a probability density function discretization and approximation method for the dynamic load identification of stochastic structures abstract aiming at structures containing random parameters with multi peak probability density functions pdfs or great variable coefficients an analytical method of probability density function discretization and approximation pdfda is proposed for dynamic load identification dynamic loads are expressed as the functions of time and random parameters in time domain and the forward model is established through the discretized convolution integral of loads and the corresponding unit pulse response functions the pdf of each random parameter is discretized into several subintervals and in each subinterval the original pdf curve is approximated via uniform distribution pdf with equal probability value then the joint distribution model is built and hence the equivalent deterministic equations are solved to identify unknown loads inverse analysis is operated separately at each variable in the joint distribution model through regularization because of noise contaminated measured responses in order to assess the accuracy of identified results pdf curves and statistical properties of loads are achieved based on the specially assumed distributions of identified loads numerical simulations demonstrate the efficiency and superiority of the presented method

reconstruction of vibroacoustic responses of a highly nonspherical structure using helmholtz equation least squares method the vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using helmholtz equation least squares hels method the objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using hels the test object is a simply supported and baffled thin plate the reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical hankel functions and spherical harmonics which are taken as the basis functions in the hels formulation yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately the input field acoustic pressures for reconstruction are generated by the rayleigh integral the reconstructed normal surface velocities are validated against the benchmark values and the out of plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate the impacts of various parameters such as number of measurement points measurement distance location of the origin of the coordinate system microphone spacing and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined

extension of measurement surface in near field acoustic holography in near field acoustic holography when measurements are made over a limited surface there has been recent interest in numerically enlarging the measurement surface tangentially current algorithms use iterative methods to extrapolate the field tangentially outward an algorithm based on the method of superposition is applied here which may be used to either extrapolate the field to enlarge the measurement surface or to interpolate in case there is a hole in the measurement surface where data are not available

on the holographic reconstruction of vibroacoustic fields using equivalent sources and inverse boundary element method 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

hybrid uncertain analysis for structural acoustic problem with random and interval parameters abstract in this paper hybrid perturbation monte carlo method hpmcm and hybrid perturbation vertex method hpvm are developed for the hybrid uncertain structural acoustic problem with random and interval variables the random variables are used to treat the uncertain parameters with sufficient information whereas the interval variables are used to treat the uncertain parameters with limited information in hpmcm the intervals of expectation and variance of the frequency response vector are calculated by a combination of random interval matrix perturbation method random interval moment method and monte carlo method in hpvm a monotonicity analysis is conducted for the frequency response vector based on the random interval matrix perturbation method and then the intervals of expectation and variance of the frequency response vector are calculated by employing the random interval moment method and the vertex method numerical results on a shell structural acoustic problem verify the effectiveness and high efficiency of hpvm compared with hpmcm

acoustic imaging using under determined inverse approaches frequency limitations and optimal regularization this paper presents an acoustic imaging technique based on an under determined inverse approach the principle is to quantify an elementary source distribution on a source surface from acoustic pressure measurements the acoustic transfer system between elementary sources and microphone positions very under determined is then reduced to a square system using singular value decomposition the high frequency limitation of this method is studied as well as the regularization techniques that have to be used at low frequency a monte carlo simulation is carried out to compare the efficiency of generalized cross validation and l curve validation to choose the tikhonov regularization parameter a combined validation criterion is finally proposed to take advantage of both approaches

bayesian approach of nearfield acoustic reconstruction with particle filters this paper demonstrates that inverse source reconstruction can be performed using a methodology of particle filters that relies primarily on the bayesian approach of parameter estimation in particular the proposed approach is applied in the context of nearfield acoustic holography based on the equivalent source method esm a state space model is formulated in light of the esm the parameters to estimate are amplitudes and locations of the equivalent sources the parameters constitute the state vector which follows a first order markov process with the transition matrix being the identity for every frequency domain data frame filtered estimates of the state vector obtained are assigned weights adaptively the implementation of recursive bayesian filters involves a sequential monte carlo sampling procedure that treats the estimates as point masses with a discrete probability mass function pmf which evolves with iteration the weight update equation governs the evolution of this pmf and depends primarily on the likelihood function and the prior distribution it is evident from the simulation results that the inclusion of the appropriate prior distribution is crucial in the parameter estimation

solving singular integral equations using gaussian quadrature and overdetermined systems abstract for singular integral equations of the cauchy type on an open interval a bounded solution exists only if an additional condition is satisfied in direct methods of solution when the integrals are replaced by quadratures it is not obvious that the resulting discrete system of equations will be consistent it is shown that for gauss chebyshev quadrature the overdetermined system of equations is consistent if and only if the discrete analog of the compatibility condition is satisfied the behavior of solutions to inconsistent systems is examined

reconstruction of vibroacoustic fields in half space by using hybrid near field acoustical holography in this paper we examine the accuracy and efficiency of reconstructing the vibroacoustic quantities generated by a vibrating structure in half space by using hybrid near field acoustic holography nah and modified helmholtz equation least squares hels formulations in hybrid nah we combine modified hels with an inverse boundary element method ibem to reconstruct a vibroacoustic field the main advantage of this approach is that the majority of the input data can be regenerated but not measured thus the efficiency is greatly enhanced in modified hels we expand the field acoustic pressure in terms of outgoing and incoming spherical waves and specify the corresponding expansion coefficients by solving a system of equations obtained by matching the assumed form solution to the measured acoustic pressure here the system of equations is ill conditioned and tikhonov regularization is implemented through singular value decomposition svd and the generalized cross validation gcv method numerical examples of a dilating and oscillating spheres and finite cylinder are demonstrated test results show that hybrid nah can yield a more accurate reconstruction than does a modified hels but a modified hels is more efficient than is hybrid nah work supported by nsf

the generalized cattaneo partial slip plane contact problem i theory the cattaneo problem is considered for a general plane contact between elastically similar materials i e a monotonically increasing tangential load starting from zero with normal loading held fixed instead of the classical argument on the displacement field in the stick zone of cattaneo solution we attack the problem implicitly from the governing integral equations in the stick zones after discussing and solving the full stick case we move to the more realistic for finite friction case of partial slip we show that upon isolating the effect of full sliding the equalities and inequalities governing the corrective solution for the corrective shearing tractions in the stick zone are exactly the same as those governing the solution of the normal contact problem with a lower load but the same rotation as the actual one this analogy permits us to deduce several general properties and gives a general procedures for solving partial slip cattaneo problems as frictionless normal indentation ones therefore the general solutions for single multiple and periodic contacts is given a comprehensive set of explicit results is given in the part ii of the paper

acoustical source reconstruction from non synchronous sequential measurements by fast iterative shrinkage thresholding algorithm abstract acoustical source reconstruction is a typical inverse problem whose minimum frequency of reconstruction hinges on the size of the array and maximum frequency depends on the spacing distance between the microphones for the sake of enlarging the frequency of reconstruction and reducing the cost of an acquisition system cyclic projection cp a method of sequential measurements without reference was recently investigated jsv 2016 372 31 49 in this paper the propagation based fast iterative shrinkage thresholding algorithm propagation fista is introduced which improves cp in two aspects 1 the number of acoustic sources is no longer needed and the only making assumption is that of a weakly sparse eigenvalue spectrum 2 the construction of the spatial basis is much easier and adaptive to practical scenarios of acoustical measurements benefiting from the introduction of propagation based spatial basis the proposed propagation fista is first investigated with different simulations and experimental setups and is next illustrated with an industrial case

experimental study of the mapping relationship based near field acoustic holography with spherical fundamental solutions abstract this paper is a consequent work of the previously proposed mapping relationship based near field acoustic holography mrs based nah h j wu w k jiang and h b zhang jsv 373 66 88 2016 it is devoted to the performance study of its practical application with error analysis and experimental validation two types of errors the truncation errors due to the limited number of participant modes and the inevitable measurement errors caused by uncertainties in the experiment are considered in the analysis the influences of the errors on the performance of mrs based nah are systematically investigated first of all expression of the relative reconstruction error of the pressure energy is derived based on the two types of errors an approach is developed to estimate the lower and upper bounds of the relative error it gives a guide to predict the error for a reconstruction under the condition that the truncation error and the signal to noise ratio are given then the condition number of the inverse operator is investigated to measure the sensitivity of the reconstruction to the input errors asymptotic expressions of the condition number for a special case conformal spherical model and hologram are obtained which indicates the condition number has a geometric growth with the number of participant modes numerical examples with different kinds of errors are elaborately designed to validate the stability as well as the correctness of the error analysis at last the mrs based nah is further examined and verified by a physical experiment a vibrating cubic model reconstructed from measurement on a spherical hologram a satisfied agreement with the directly measured pressure on a validation surface is observed for both quantity and distribution of the reconstructed pressure

on the choice of expansion functions in the helmholtz equation least squares method this paper examines the performance of helmholtz equation least squares hels method in reconstructing acoustic radiation from an arbitrary source by using three different expansions namely localized spherical waves lsw distributed spherical waves dsw and distributed point sources dps under the same set of measurements the reconstructed acoustic pressures are validated against the benchmark data measured at the same locations as reconstruction points for frequencies up to 3275 hz reconstruction is obtained by using tikhonov regularization or its modification with the regularization parameter selected by error free parameter choice methods the impact of the number of measurement points on the resultant reconstruction accuracy under different expansion functions is investigated results demonstrate that dsw leads to a better conditioned transfer matrix yields more accurate reconstruction than both lsw and dps and is not affected as much by the change in measurement points also it is possible to obtain optimal locations of the auxiliary sources for dsw lsw and dps by taking an independent layer of measurements use of these auxiliary sources and an optimal combination of regularization and error free parameter choice methods can yield a satisfactory reconstruction of acoustic quantities on the source surfaces as well as in the field in the most cost effective manner

bayesian force reconstruction with an uncertain model this paper presents a bayesian approach for force reconstruction which can deal with both measurement noise and model uncertainty in particular an uncertain model is considered for inversion in the form of a matrix of frequency response functions whose modal parameters originate from either measurements or a finite element model the model uncertainty and the regularization parameter are jointly determined with the unknown force through monte carlo markov chain methods bayesian credible intervals of the force are built from its posterior probability density function by taking into account the quantified model uncertainty and measurement noise the proposed approach is illustrated and validated on numerical and experimental examples

a study on regularization parameter choice in near field acoustical holography regularization plays an important role in near field acoustical holography nah and choosing the right amount of regularization is crucial in order to get a meaningful solution an automated method such as the l curve or generalized cross validation gcv is often used in nah to choose a regularization parameter these parameter choice methods pcms are attractive since they require no a priori knowledge about the noise however there seems to be no clear understanding of when one pcm is better than the other this paper presents comparisons of three pcms gcv l curve and normalized cumulative periodogram ncp the latter method is new within nah and it is based on the fourier transform of the residual vector the methods are used in connection with three nah methods statistically optimized near field acoustical holography sonah the inverse boundary element method ibem and the equivalent source method esm all combinations of the pcms and the nah methods are investigated using simulated measurements with different types of noise added to the input finally the comparisons are carried out for a practical experiment this aim of this work is to create a better understanding of which mechanisms that affect the performance of the different pcms

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal

reconstruction of sound quadratic properties from non synchronous measurements with insufficient or without references proof of concept in inverse acoustics the reconstruction of distant sound fields from microphone array measurements is fundamentally limited by the size of the array and by the microphone density one approach to simulate large arrays and or high microphone density is to scan the object of interest by sequentially moving a small prototype array this typically requires a sufficient number of high quality fixed references in order to preserve the phase relationships between consecutive snapshots or that measurements are made in the near field in order to allow the successive reconstruction of local patches of the source by deliberately neglecting waves not radiating through the array patch holography in the present work a solution is introduced to reconstruct the quadratic properties e g source power quadratic flux sound intensity of the radiating object from non synchronous sequential measurements when references are insufficient in quantity or in quality remarkably it also operates without any reference at all in certain conditions it relies on the assumptions that the sound field is i stationary and ii spatially correlated and boils down to the factorization of a structured covariance matrix this is undertaken within a bayesian probabilistic approach where the source field is encoded by unobservable latent variables which are iteratively reconstructed by using the expected maximization em algorithm the method is shown to return virtually similar results as if all data were captured simultaneously or sequentially with sufficient high quality references as a consequence it bears an advantage in terms of cost and simplicity in addition it is ultimately able to synthesize statistically equivalent realizations of the source field which may turn out useful for numerical simulation of sound propagation a solution is also provided within the bayesian framework for automatically setting the regularization parameter to its optimal value

hybrid near field acoustic holography hybrid near field acoustical holography nah is developed for reconstructing acoustic radiation from an arbitrary object in a cost effective manner this hybrid nah is derived from a modified helmholtz equation least squares hels formula that expands the acoustic pressure in terms of outgoing and incoming waves the expansion coefficients are determined by solving an overdetermined linear system of equations obtained by matching the assumed form solution to measured acoustic pressures through the least squares measurements are taken over a conformal surface around a source at close range so that the evanescent waves can be captured next the modified hels is utilized to regenerate as much acoustic pressures on the conformal surface as necessary and take them as input to the helmholtz integral formulation implemented numerically by boundary element method bem the acoustic pressures and normal velocities on the source surface are reconstructed by using a modified tikhnov regularization tr with its regularization parameter determined by generalized cross validation gcv method results demonstrate that this hybrid nah combines the advantages of hels and inverse bem this is because a majority of the input data are regenerated but not measured thus the efficiency of reconstruction is greatly enhanced meanwhile the accuracy of reconstruction is ensured by the helmholtz integral theory and modified tr together with gcv method provided that hels converges fast enough on the measurement surface numerical examples of reconstructing acoustic quantities on the surface of a simplified engine block are demonstrated work supported by nsf

a bayesian approach to sound source reconstruction optimal basis regularization and focusing the reconstruction of acoustical sources from discrete field measurements is a difficult inverse problem that has been approached in different ways classical methods beamforming near field acoustical holography inverse boundary elements wave superposition equivalent sources etc all consist implicitly or explicitly in interpolating the measurements onto some spatial functions whose propagation are known and in reconstructing the source field by retropropagation this raises the fundamental question as whether for a given source topology and array geometry there exists an optimal interpolation basis which minimizes the reconstruction error this paper provides a general answer to this question by proceeding from a bayesian formulation that is ideally suited to combining information of physical and probabilistic natures the main findings are the followings 1 the optimal basis functions are the m eigen functions of a specific continuous discrete propagation operator with m being the number of microphones in the array 2 the a priori inclusion of spatial information on the source field causes super resolution according to a phenomenon coined bayesian focusing 3 the approach is naturally endowed with an internal regularization mechanism and results in a robust regularization criterion with no more than one minimum 4 it admits classical methods as particular cases

a frictional receding contact plane problem between a functionally graded layer and a homogeneous substrate abstract this paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space when they are pressed against each other the graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant poisson s ratio a segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction the entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction it is assumed that the contact region is under sliding contact conditions with the coulomb s law used to relate the tangential traction to the normal component employing fourier integral transforms and applying the necessary boundary conditions the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem the gauss chebyshev quadrature collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations this system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously the main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region

the quantification of structure borne transmission paths by inverse methods part 2 use of regularization techniques the inversion of an ill conditioned matrix of measured data lies at the heart of procedures for the quantification of structure borne sources and transmission paths in an earlier paper the use of over determination singular value decomposition and the rejection of small singular values was discussed in the present paper alternative techniques for regularizing the matrix inversion are considered such techniques have been used in the field of digital image processing and more recently in relation to nearfield acoustic holography the application to structure borne sound transmission involves matrices which vary much more with frequency and from one element to another in this study tikhonov regularization is used with the ordinary cross validation method for selecting the regularization parameter an iterative inversion technique is also studied here a form of cross validation is developed allowing an optimum value of the iteration parameter to be selected simulations are carried out using a rectangular plate structure to assess the relative merits of these techniques experiments are also performed to validate the results both techniques are found to give considerably improved results compared to singular value rejection