continuation of acoustic near fields this paper deals with the analytic continuation of a coherent pressure field specified on a finite sheet located close to and conformal to the surface of a vibrator this analytic continuation is an extension or extrapolation of the given measured field into a region outside and tangential to the original finite sheet and is based on the green s function the transfer function relating acoustic quantities on the two conformal surfaces the continuation of the measured pressure field is an inverse problem that requires the use or regularization theory especially when noise is present in the data an iteration algorithm is presented that is successful in continuing the pressure field into the tangential sheet the results are accurate close to the original boundary and taper decay toward zero with distance away from it the algorithm is tested on numerical and experimental data from a point driven rectangular plate results show the successful extrapolation continuation of this data into an area nearly double that of the original pressure field this algorithm is not limited to planar surfaces and can be applied to arbitrarily shaped surfaces

tensor algebras overc correspondences representations dilations andc envelopes tensor algebras overc correspondences are noncommutative generalizations of the disk algebra they contain as special cases analytic crossed products semi crossed products and popescu s noncommutative disk algebras in this paper a dilation theorem and a commutant lifting theorem for representations of tensor algebras is proved these are used to show that for certainc correspondences thec envelopes in the sense of arveson of the tensor algebras are the cuntz pimsner algebras of the correspondences

pullback and pushout constructions in c algebra theory abstract a systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of c algebras particular emphasis is given to the relations with tensor products both with the minimal and the maximal c tensor norm thus it is shown that pullback and pushout diagrams are stable under tensoring with a fixed algebra and stable under crossed products with a fixed group general tensor products between diagrams are also investigated the relations between the theory of extensions and pullback and pushout diagrams are explored in some detail the crowning result is that if three short exact sequences of c algebras are given with appropriate morphisms between the sequences allowing for pullback or pushout constructions at the levels of ideals algebras and quotients then the three new c algebras will again form a short exact sequence under some mild extra conditions as a generalization of a theorem of t a loring it is shown that each morphism between a pair of c algebras combined with its extension to the stabilized algebras gives rise to a pushout diagram this result has applications to corona extendibility and conditional projectivity finally the pullback and pushout constructions are applied to the class of noncommutative cw complexes defined by s eilers t a loring and g k pedersen j reine angew math 1998 499 101 143 to show that this category is stable under tensor products and under restricted direct sums

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

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

morphisms of extensions of c algebras pushing forward the busby invariant abstract we study completions of diagrams of extensions of c algebras in which all three c algebras in one of the rows and either the ideal or the quotient in the other are given along with the three morphisms between them we find universal solutions to all four of these problems under restrictions of varying severity on the given vertical maps and describe the solutions in terms of push outs and pull backs of certain diagrams our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products this leads to new results about the k theory of amalgamated free products verifying the cuntz conjecture in certain cases we also obtain new results about extensions of matricial field c algebras verifying partially a conjecture of blackadar and kirchberg finally we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes

spherical harmonics singular value decomposition and the head related transfer function abstract the singular value decomposition svd can be used to analyze the matrix of green functions relating the acoustic pressure at a number of field points to the strengths of a number of point sources on the surface of a body which radiates or scatters sound the left and right singular vectors of the resulting decomposition yield at a given frequency two sets of orthogonal basis functions describing field mode shapes and source mode shapes respectively this paper attempts to make the connection between this decomposition and the basis functions of classical acoustics in particular it is found that for a spherical co ordinate system when the source points and field points are chosen in order to sample the source and field appropriately then the matrices of left and right singular vectors are related to the sampled spherical harmonics by a unitary transformation preliminary investigations are presented of the sensitivity of this relationship to the manner in which the source and field are sampled in addition the great utility of the method is illustrated with some new results of numerical analysis of the scattering of sound by the outer ear pinna resonances and their associated mode shapes are identified at certain frequencies where high values of the dominant singular values indicate a strong coupling between source and field

a two step explicit p stable method of high phase lag order for linear periodic ivps in this paper we present a nonlinear two step explicit p stable method of fourth algebraic order and 12th phase lag order for solving one dimensional second order linear periodic initial value problems ivps of ordinary differential equations based on a special vector arithmetic with respect to an analytic function the method can be extended to be vector applicable for multi dimensional problems directly some numerical results are reported to illustrate the efficiency of the method

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

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

two low accuracy methods for stiff systems two low accuracy explicit one step methods for stiff ordinary differential equations are extended directly to solve systems of equations some defects of the component form of these methods are avoided to perform these a new set of vector computations are introduced some numerical experiments are presented to show the superiority of the new methods

analytic solutions of the radiation modes problem and the active control of sound power this paper explores the common mathematical foundation of two different problems the first one arises in electrical engineering for the detection and the spectral estimation of signals in noise and the second one appears in acoustics for the calculation of the acoustic radiation modes of rectangular structures although apparently unrelated it is found that both applications draw on the so called concentration problem of determining which functions that are band limited in one domain have maximal energy concentration within a region of the transform domain the analytic solutions to problems of this form are seen to involve prolate spheroidal wave functions in particular exact expressions are given for the radiation efficiencies and shapes of the radiation modes of a baffled beam as well as their asymptotics it is shown that a generalization of the concentration problem to the two dimensional case provides analytic solutions that solve with a good accuracy although approximately the radiation problem the properties of these special functions provide a rigorous basis of understanding some previously observed features of these applications namely the grouping property of the radiation modes of a baffled panel and the physical limitations for the active control of sound from a panel

the use of partially measured source data in near field acoustical holography based on the bem in applying the conformal near field acoustical holography nah to actual source identification problems it is often possible to determine the velocity at certain points of the source surface in advance this partially known velocity data would reduce the problem size and permit better reconstruction accuracy in this paper the effectiveness of using partially measured source data in the conformal nah is investigated which uses the boundary element method a vibro acoustic transfer matrix and measured field pressure data which is involved with the boundary integral equation are reorganized in order to deal with the partially measured surface velocities for a baffled vibrating panel simulations were performed by varying the number of velocity known nodes in addition the effect of measurement error is investigated for two extreme positioning methods of velocity known nodes without regularization the reconstructed error can be reduced considerably by employing some of the source data and this err

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

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

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

sensor scheme design for active structural acoustic control efficient sensing schemes for the active reduction of sound radiation from plates are presented based on error signals derived from spatially weighted plate velocity or near field pressure the schemes result in near optimal reductions as compared to weighting procedures derived from eigenvector or singular vector analysis of the radiation operator efficient control configurations are suggested using a possibly analog front end implementing a bank of spatial weighting functions and a digital controller with a minimized number of input and output channels the performance of different weighting functions is compared as well as the performance of different frequency dependent filtering functions design rules are given for the sensor spacing the number of weighting functions the number of actuators and the corresponding controller dimensionality

use of nonsingular boundary integral formulation for reducing errors due to near field measurements in the boundary element method based near field acoustic holography in the conformal near field acoustic holography nah using the boundary element method bem the transfer matrix relating the vibro acoustic properties of source and field depends solely on the geometrical condition of the problem this kind of nah is known to be very powerful in dealing with the sources having irregular shaped boundaries when the vibro acoustic source field is reconstructed by using this conformal nah one tends to position the sensors as close as possible to the source surface in order to get rich information on the nonpropagating wave components the conventional acoustic bem based on the kirchhoff helmholtz integral equation has the singularity problem in the close near field of the source surface this problem stems from the singular kernel of the green function of the boundary integral equation bie and the singularity can influence the reconstruction accuracy greatly in this paper the nonsingular bie is introduced to the nah calculation and the holographic bie is reformulated the effectiveness of nonsingular bem has been investigated for the reduction of reconstruction error through interior and exterior examples it is shown that the resolution of predicted field pressure could be improved in the close near field by employing the nonsingular bie because the bem based nah inevitably requires the field pressure measured in the close proximity to the source surface the present approach is recommended for improving the resolution of the reconstructed source field

new vector forms of elemental functions with taylor series in many practical applications one often need to use different elementary function in order to approximate the solution of the problem under consideration in this paper some new vector forms of elemental functions with taylor series are developed with the aid of a new set of vector calculations

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

the forward projection of harmonic pressure fields using the generalized internal source density method a previously developed generalized internal source density gisd method is extended to address the forward projection of harmonic pressure fields from normal velocity fields on a closed surface of revolution in a fluid the gisd approach is based on decomposing the normal velocity field on the closed surface into a summation of circumferential orders where the pressure field for each order is associated with an internal linear source distribution of ring sources on the axis of revolution of the surface the linear source distributions are formulated as integral equations of the first kind which are then solved using singular value decomposition methods far field pressures are simply related to the fourier transforms of the linear source distributions numerical results are presented to illustrate the forward projection of harmonic fields using the gisd method for both dirichlet and neumann problems the numerical results for spherical and finite cylindrical vibrators illustrate the usefulness of the gisd method over a wide range of frequencies for both acoustic radiation and scattering problems

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

the relationship of singular value decomposition to wave vector filtering in sound radiation problems singular value decomposition svd has recently been suggested as a filtering tool to analyze acoustic radiation the relationship between this filtering technique and the more familiar wave vector filtering is examined for a geometry with a preferred axis the source modes are found to consist approximately of a single wave number and the accompanying radiation modes are thus beams some simple examples are worked out to illustrate the general behavior of the filtering and some of the properties of the beams are given

esprit a subspace rotation approach to estimation of parameters of cisoids in noise the application of a subspace invariance approach esprit to the estimation of parameters frequencies and powers of cisoids in noise is described esprit exploits an underlying rotational invariance of signal subspaces spanned by two temporally displaced data sets the new approach has several advantages including improved resolution over pisarenko s technique for harmonic retrieval

exponential integrators for large systems of differential equations we study the numerical integration of large stiff systems of differential equations by methods that use matrix vector products with the exponential or a related function of the jacobian for large problems these can be approximated by krylov subspace methods which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators the exponential methods also offer favorable properties in the integration of differential equations whose jacobian has large imaginary eigenvalues we derive methods up to order 4 which are exact for linear constant coefficient equations the implementation of the methods is discussed numerical experiments with reaction diffusion problems and a time dependent schrodinger equation are included

phase mapping of acoustic sources by beamforming and iterative far field monopole substitution the first aim of this paper is to give emphasis to the importance of assessing phase information when reconstructing and mapping a sound field in fact in acoustic analysis phase distribution is frequently simply either not considered or ignored even though it can supply very useful information for the understanding of the mapping itself or for further analyses in this paper a procedure to carry out phase mapping of acoustic sources in beamforming measurement is illustrated the second aim of this paper is to propose a straightforward iterative optimization algorithm based on the monopole substitution starting from beamforming results it allows for the reconstruction of sound field without the use of any matrix inversion both numerical and experimental validations of the method are presented results shown hereafter prove the effectiveness of the approach

extensions of operator algebras i abstract we transcribe a portion of the theory of extensions of c algebras to general operator algebras we also include several new general facts about approximately unital ideals in operator algebras and the c algebras which they generate

tensor algebras of c correspondences and their c envelopes abstract we show that the c envelope of the tensor algebra of an arbitrary c correspondence x coincides with the cuntz pimsner algebra o x as defined by katsura t katsura on c algebras associated with c correspondences j funct anal 217 2004 366 401 this improves earlier results of muhly and solel p s muhly b solel tensor algebras over c correspondences representations dilations and c envelopes j funct anal 158 1998 389 457 and fowler muhly and raeburn n fowler p muhly i raeburn representations of cuntz pimsner algebras indiana univ math j 52 2003 569 605 who came to the same conclusion under the additional hypothesis that x is strict and faithful

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

sound power radiation from a vibrating structure in terms of structure dependent radiation modes abstract as a good supplement of conventional acoustic radiation modes a modes a set of so called structure dependent radiation modes s modes is introduced to describe the sound power radiation from a vibrating structure differing from a modes s modes are determined by not only the acoustic resistance matrix of the structure but also the frequency independent normal modes of the structure such a new definition has the following main advantages over the conventional one 1 it can reflect directly the influences of dynamic properties e g boundary conditions of the structures on its sound power radiation 2 the number of s modes generated is generally less than that of a modes since the former depends on the number of structural modes involved in the vibration while the latter depends on the number of segmented elemental radiators of the structure and consequently the demand for large data storage can be greatly alleviated especially for large structures and or higher frequency vibrations 3 the set of s modes possesses a better convergence than that of a modes because the higher ordered s modes can decay more rapidly than the same ordered a modes two baffled finite models i e a simple beam and a thin plate are employed to investigate numerically the acoustic properties of s modes and then compared with those of a modes it has been shown that the two sets of radiation modes share a very similar frequency dependent behavior in that the radiation efficiency falls off very rapidly with increasing mode order at low frequency range typically with kl

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

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

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

numerical modelling of the spatial acoustic response of the human pinna abstract this paper is concerned with the spatial acoustic response of the human pinna modelled with the boundary element method bem accurate geometric models of five pinnae are captured by using state of the art 3 d laser scanners and digitisers these computer models are converted to valid bem models and analysed acoustically up to 20 khz using baffled pinnae models we first repeat and validate numerically the normal concha modes as measured in the classical experiments made by e a g shaw in the 1970s we then study the spatial mode shapes of a baffled cylinder as a simplified model of the concha and accurate pinnae by applying the singular value decomposition svd technique the method is used to analyse at discrete frequencies a matrix of green functions relating the acoustic pressure at field points and source points in space we demonstrate how the singular vectors which appear as spatial mode shapes couple to the singular vectors of the sound field the relationship between these basis functions found with the svd and the normal concha mode shapes is demonstrated the method is also used in producing reduced order transfer functions by taking into account only the most dominant features of the singular vectors for the cases of a baffled cylinder and accurate baffled pinnae

subspace algorithms for error localization with quantized dft codes recently a class of real number bose chaudhuri hocquengem codes known as discrete fourier transform dft codes have been considered as joint source and channel codes for providing robustness to erasures and errors over wireless networks we propose three subspace algorithms for error localization with quantized dft codes the algorithms are similar to the music the minimum norm and the esprit algorithms used in array signal processing for direction of arrival estimation they provide different but related formulations of the error localizations by first partitioning a vector space into the channel error subspace and its orthogonal complement the noise subspace the locations of the errors are determined from either the error subspace eigenvectors or the noise subspace eigenvectors we also present a brief performance analysis of the localization error in terms of the perturbation of the error subspace due to quantization simulation results show that their localization performances are similar and they perform better than the coding theoretic approach over a broad range of channel error to quantization noise ratios

a method to compute the radiated sound power based on mapped acoustic radiation modes application of modal expansion approach for the exterior acoustic field has drawn wide research interests in recent years this is primarily due to the acoustic radiation modes arm that can diagonalize the impedance matrix hence significantly simplifying the computation of radiated sound power the orthogonal arm are typically calculated via a standard eigenvalue analysis of the impedance matrix which normally leads to numerical difficulties especially for wideband frequency and large scale problems in this paper a theory of mapped arm is proposed to avoid the cumbersome computation of arm for convex structures a mapping relationship between the arm on the surface of an equivalent spherical source and the mapped arm on the surface of a convex structure is obtained based on the equivalent source method multipole expansion method and boundary integral method furthermore analytical expressions for the radiated sound power of structures vibrating in its mapped arm as well as that of spheres are derived finally a simple method is proposed to approximate the radiated sound power based on the modal decomposition method and the mapping relationship numerical simulations are conducted to validate the accuracy and efficiency of the proposed approach and different vibrating structures with various geometries are considered results demonstrate that the proposed methodology for calculating the radiated sound power of convex structures is very efficient and accurate as compared with the traditional approach

crossed products of operator systems abstract in this paper we introduce the crossed product construction for a discrete group action on an operator system in analogy to the work of e katsoulis and c ramsey we describe three canonical crossed products arising from such a dynamical system we describe how these crossed product constructions behave under g equivariant maps tensor products and the canonical c covers we show that hyperrigidity is preserved under two of the three crossed products finally using a kavruk s notion of an operator system that detects c nuclearity we give a negative answer to a question on operator algebra crossed products posed by katsoulis and ramsey

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

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

the vector form of a sixth order a stable explicit one step method for stiff problems abstract a sixth order a stable explicit one step method for stiff ordinary differential equations is extended directly to solve systems of equations some defects of the component form of this method are avoided to perform these a new set of vector computations are introduced some numerical experiments are presented to show its superiority

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

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 method for computing acoustic fields based on the principle of wave superposition a method for computing the acoustic fields of arbitrarily shaped radiators is described that uses the principle of wave superposition the superposition integral which is shown to be equivalent to the helmholtz integral is based on the idea that the combined fields of an array of sources interior to a radiator can be made to reproduce a velocity prescribed on the surface of the radiator the strengths of the sources that produce this condition can in turn be used to compute the corresponding surface pressures the results of several numerical experiments are presented that demonstrate the simplicity of the method also the advantages that the superposition method has over the more commonly used boundary element methods are discussed these include simplicity of generating the matrix elements used in the numerical formulation and improved accuracy and speed the latter two being due to the avoidance of uniqueness and singularity problems inherent in the boundary element formulation

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

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

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

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

regularization in global sound equalization based on effort variation sound equalization in closed spaces can be significantly improved by generating propagating waves that are naturally associated with the geometry as for example plane waves in rectangular enclosures this paper presents a control approach termed effort variation regularization based on this idea effort variation equalization involves modifying the conventional cost function in sound equalization which is based on minimizing least squares reproduction errors by adding a term that is proportional to the squared deviations between complex source strengths calculated independently for the sources at each of the two walls perpendicular to the direction of propagation simulation results in a two dimensional room of irregular shape and in a rectangular room with sources randomly distributed on two opposite walls demonstrate that the proposed technique leads to smaller global reproduction errors and better equalization performance at listening positions outside of the control region compared to effort regularization and compared to a simple technique that involves driving groups of sources identically

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

a class of two step explicit methods for periodic ivps in this paper we present a class of non linear explicit second order methods for solving one dimensional periodic initial value problems ivps which are p stable in the sense of lambert and watson and of high order phase lag error for multi dimensional problems we introduce a special vector operation such that our methods can be extended to be vector applicable directly however it is not sufficient to investigate the stability behavior of the vector form of the methods based on the scalar test equation y l 2y after introducing a new test system and extending the definitions of the interval of periodicity and the phase lag order we discuss the stability property and the phase lag of the vector applicable methods the methods are p stable and of high phase lag for one frequency problems for multi frequency problems methods are of only second phase lag order and may have not a primary interval of periodicity some numerical results illustrate the conclusions

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

operator algebras with contractive approximate identities ii abstract we make several contributions to our recent program investigating structural properties of algebras of operators on a hilbert space for example we make substantial contributions to the noncommutative peak interpolation program begun by hay and the first author hay and neal another sample result an operator algebra has a contractive approximate identity iff the linear span of the elements with positive real part is dense we also extend the theory of compact projections to the most general case despite the title our algebras are often allowed to have no approximate identity

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

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

interior sound field control using generalized singular value decomposition in the frequency domain the problem of controlling a sound field inside a region surrounded by acoustic control sources is considered inspired by the kirchhoff helmholtz integral the use of double layer source arrays allows such a control and avoids the modification of the external sound field by the control sources by the approximation of the sources as monopole and radial dipole transducers however the practical implementation of the kirchhoff helmholtz integral in physical space leads to large numbers of control sources and error sensors along with excessive controller complexity in three dimensions the present study investigates the potential of the generalized singular value decomposition gsvd to reduce the controller complexity and separate the effect of control sources on the interior and exterior sound fields respectively a proper truncation of the singular basis provided by the gsvd factorization is shown to lead to effective cancellation of the interior sound field at frequencies below the spatial nyquist freq

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

l1 generalized inverse beam forming algorithm resolving coherent incoherent distributed and multipole sources abstract to resolve coherent incoherent distributed compact and multipole aerodynamic sound sources with phased array pressure data a new source detection algorithm is developed based on l1 generalized inverse techniques to extract each coherent signal a cross spectral matrix is decomposed into eigenmodes subsequently the complex source amplitude distribution that recovers each eigenmode is solved using generalized inverse techniques with reference solutions which include multipoles as well as a monopole namely the source distribution consisting of pre defined source types is solved as an l1 norm problem using iteratively re weighted least squares irls the capabilities of the proposed algorithm are demonstrated using various benchmark problems to compare the results with several existing beam forming algorithms and it is found that distributed sources as well as dipoles with arbitrary orientation can be identified regardless of coherency with another source the resolution is comparable to existing deconvolution techniques such as damas or clean and the computational cost is only several times more than that of damas2 the proposed algorithm is also examined using previous model scale test data taken in an open jet wind tunnel for a study on jet flap interaction and some indication of dipole radiation is discerned near the flap edge

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

analytical performance assessment of multi dimensional matrix and tensor based esprit type algorithms in this paper we present a generic framework for the asymptotic performance analysis of subspace based parameter estimation schemes it is based on earlier results on an explicit first order expansion of the estimation error in the signal subspace obtained via an svd of the noisy observation matrix we extend these results in a number of aspects firstly we demonstrate that an explicit first order expansion of the higher order svd hosvd based subspace estimate can be derived secondly we show how to obtain explicit first order expansions of the estimation error of arbitrary esprit type algorithms and provide the expressions for r d standard esprit r d unitary esprit r d standard tensor esprit as well as r d unitary tensor esprit thirdly we derive closed form expressions for the mean square error mse and show that they only depend on the second order moments of the noise hence to apply this framework we only need the noise to be zero mean and possess finite second order moments additional assumptions such as gaussianity or circular symmetry are not needed

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

far field acoustic holography onto cylindrical surfaces using pressure measured on semicircles a simple formula was recently proposed by williams j acoust soc am 99 2022 2032 1996 for imaging pressure and velocity on a vibrating circular cylindrical shell using the far field pressure measured along a meridional semicircle the method is discussed and some new results are presented the procedure is generalized to handle cylindrical surfaces of a noncircular but convex cross section it is demonstrated that williams formula predicts a supersonic surface intensity which gives the same meridional energy flux as the exact radiated far field pressure a modification of williams formula is suggested which uses pressure data from several neighboring semicircles although complete spherical coverage is not required the modified imaging formula is based upon the first two terms in an asymptotic expansion in the dimensionless wave number the leading order term yields the original formula and the second term results in a boundary layer type of correction in the circumferential direction numer