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

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

on a structural property in the state complexity of projected regular languages a transition is unobservable if it is labeled by a symbol removed by a projection the present paper investigates a new structural property of incomplete deterministic finite automata a number of states incident with an unobservable transition and its effect on the state complexity of projected regular languages we show that the known upper bound can be met only by automata with one unobservable transition up to unobservable multi transitions we improve this upper bound by taking into consideration the structural property of minimal incomplete automata and prove the tightness of new upper bounds special attention is focused on the case of finite languages the paper also presents and discusses several fundamental problems which are still open

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

3 d sound source reconstruction and field reprediction using the helmholtz integral equation abstract a method for reconstruction of the boundary conditions of an arbitrarily shaped three dimensional 3 d sound source from a finite number of field pressures is presented and the associated field is repredicted by using the helmholtz integral equation to minimize the reconstruction error due to noise in the field pressures a filtering method is proposed and it is verified that numerically singular values which correspond to the higher order modes of the evanescent like components of the source velocities are eliminated for arbitrarily shaped sources with complex boundary conditions the reconstruction is performed accurately when the size of each element is less than a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of a sphere in the vicinity of the source our technique can be used in computer aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from the finite number of field pressures and repredicts the variation of the sound field procuced by a redesigned loudspeaker cabinet on which the reconstructed diaphragm is mounted

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

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

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

krylov subspace iterative methods for boundary element method based near field acoustic holography the reconstruction of the acoustic field for general surfaces is obtained from the solution of a matrix system that results from a boundary integral equation discretized using boundary element methods the solution to the resultant matrix system is obtained using iterative regularization methods that counteract the effect of noise on the measurements these methods will not require the calculation of the singular value decomposition which can be expensive when the matrix system is considerably large krylov subspace methods are iterative methods that have the phenomena known as semi convergence i e the optimal regularization solution is obtained after a few iterations if the iteration is not stopped the method converges to a solution that generally is totally corrupted by errors on the measurements for these methods the number of iterations play the role of the regularization parameter we will focus our attention to the study of the regularizing properties from the krylov subspace methods like conjugate gradients least squares qr and the recently proposed hybrid method a discussion and comparison of the available stopping rules will be included a vibrating plate is considered as an example to validate our results

a one step patch near field acoustical holography procedure when performing holography measurements over a limited area of a source the hologram pressure typically remains finite at the edge of the measurement aperture patch near field acoustical holography nah has been developed specifically to mitigate the effects related to that windowing in iterative patch nah the source distribution is reconstructed in two steps first the partially measured sound field is extended iteratively and then the extended pressure is projected onto the source surface by using conventional nah procedures in the present work a one step procedure for performing that combined task is described in this approach the acoustical property to be reconstructed on a surface of interest is related to the partially measured pressure on the hologram surface in terms of sampling and bandlimiting matrices and the reconstructed result is obtained by finding the regularized least squares solution of the latter relation a procedure for determining the cutoff wave number of the bandlimiting matrix without a priori knowledge of the signal bandwidth is suggested the proposed procedure was validated by using a synthetic sound field created by a point driven simply supported plated

wavelet preprocessing for lessening truncation effects in nearfield acoustical holography the goal of planar nearfield acoustical holography nah is to recover the sound field at the sound source from pressure measurements made close to the source plane the theory requires the pressure to be measured over a complete plane because experimentation consists of acquiring only a finite measurement aperture of the pressure field it naturally causes erroneous values in the reconstructed field wavelet preprocessing applied to the pressure measurements in the nearfield provides a solution to lessen the effects due to the truncation of the hologram the approach is based on a multiresolution analysis of the field from different wave number bands followed by selective spatial filtering of effects highlighted by the first analysis experimental results show the relevance of the method by comparison to standard nah involving exponential filtering in the wave number domain the computation of objective indicators based on distance measurements between wave number spectra and comparisons between pattern

measurement of structural intensity using boundary element method based nearfield acoustical holography the regularization method for measurement of structural intensity si using boundary element method bem based nearfield acoustical holography nah is proposed spatial derivatives of normal displacement are necessary to obtain the structural intensity the derivative operations amplify high wavenumber component of measurement noise and contaminate the measurement result of si to overcome this difficulty regularization method for measurement of si using fast fourier transform based nah has been introduced in this paper this regularization method is modified for the bem based nah the bem based nah avoids the aperture replication problem therefore measurement aperture for bem based nah can be set smaller than that for fft based nah the effectiveness of the proposed method is demonstrated by experiments

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

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

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

poles and zeros of matrices of rational functions abstract this expository paper considers the problem of defining poles and zeros with multiplicity including those at infinity for a matrix of rational functions over a field the underlying theme question for the paper is does the number of poles of a matrix equal the number of zeros and what structural meaning underlies such an assertion our approach is motivated by ideas from linear system theory and control engineering control theoretic ideas are not a prerequisite and we hope to encourage specialists in classical linear and commutative algebra to investigate this promising source of new algebra problems

complexity of infimal observable superlanguages the infimal prefix closed controllable and observable superlanguage plays an essential role in the relationship between controllability observability and co observability the central notions of supervisory control theory existing algorithms for its computation are exponential and it is not known whether a polynomial algorithm exists we answer the question by studying the state complexity of this language state complexity of a language is the number of states of its minimal deterministic finite automaton dfa for a language with state complexity n we show that the upper bound state complexity on the infimal prefix closed and observable superlanguage is 2 n 1 and that this bound is asymptotically tight hence there is no algorithm computing a dfa of the infimal prefix closed and observable superlanguage in polynomial time our construction shows that such a dfa can be computed in time o 2 n the construction involves nondeterministic finite automata nfas and a computation of the supremal prefix closed sublanguage we study the computation of supremal prefix closed sublanguages and show that there is no polynomial time algorithm computing an nfa of the supremal prefix closed sublanguage of a language given as an nfa even if the language is unary

patch near field acoustical holography in cylindrical geometry spatial discrete fourier transform based near field acoustical holography is known to suffer from windowing effects since the measurement aperture is necessarily finite the latter effect can be mitigated by using patch holography in which the measured field is extended beyond the measurement aperture based on successive smoothing operations in this article the application of a patch holography algorithm to cylindrical geometries is described in planar geometry initial zero padding can be applied to the hologram pressure to an arbitrary degree in both in plane directions since the pressure magnitude is expected to limit ultimately towards zero in both directions in a cylindrical geometry zero padding can be implemented axially in the same way but the number of zeros added in the circumferential direction is necessarily determined by the angular sample spacing owing to the periodic nature of the field in this direction by using both numerical simulation and experimental results it is shown that the patch extrapolation procedure works well in the cylindrical case and a discussion of rigid reflecting boundaries is also included finally reconstruction results obtained by the combined use of pressures measured in the finite aperture and two different regularization parameter selection techniques are compared and the effect of projection distance is discussed

brief paper formulae relating controllability observability and co observability we present formulae relating controllability observability and co observability arising in the context of supervisory control of discrete event systems given a discrete event plant g with event set e uncontrollable event set e u i and observation mask m i of the ith supervisor we first show that the infimal prefix closed l g i e u i controllable and l g e u i m i co observable superlanguage equals the intersection taken over all i s of the infimal prefix closed l g e u i controllable and l g m i observable superlanguage next we show that the infimal prefix closed and e m observable superlanguage computation preserves e e u controllability these results can be used to compute individual supervisors in the decentralized control setting

patch near field acoustic holography regularized extension and statistically optimized methods the patch holography method allows one to make measurements on an extended structure using a small microphone array increased attention has been paid to the two techniques which are quite different at first glance one is to extrapolate the pressure field measured on the hologram plane while the other is to use statistically optimized processing a singular value decomposition formulation of the latter is proposed in this paper the similarity of the two techniques is shown here both use a convolution of the measured pressure patch to obtain a better estimate of the wavenumber spectrum backward propagated on the structure by using the morozov discrepancy principle to compute the regularization parameter the two methods lead to very close results

extended zeros and model matching the model matching equation t z p z m z induces constraints upon the multivariate zero structures of p z and m z the nature of the constraint is best explained by extending the usual notion of zero in particular the extended gamma zero module of p z must contain as a submodule the module z gamma of matching gamma zeros which depends only upon t z and m z and the extended omega zero module of m z must contain as a factor module the module z omega of matching omega zeros which depends only upon t z and p z essential solutions in which the constraint is by module isomorphism are possible if and only if the nullity of p z does not exceed the nullity of t z on the one hand or the co nullity of m z does not exceed the co nullity of t z on the other both the matching zero modules and their finitely generated torsion parts which have state space interpretation can be given concrete intuitive interpretation in terms of short exact seq

reduction methods of the reconstruction error for large scale implementation of near field acoustical holography new extrapolation methods in real and wave number spaces are proposed to extend near field acoustical holography nah toward a more quantitative technique applicable to the vibration measurement of actual large scale structures the finiteness of the measurement aperture is a serious impediment to such large scale implementation of nah because the measurement aperture sufficiently larger than the vibrating structure of interest is usually needed we should thus investigate how to reduce the reconstruction error when the measurement aperture is restricted to a fraction of the vibrating structure the following practical suggestions are derived from simulations and underwater experiments 1 a wave number space extrapolation method can reduce the reconstruction error to about 25 for the measurement aperture corresponding to 1 16th of the vibrating structure when 10 000 iterations of the extrapolation process are applied 2 a real space extrapolation method can reduce the reconstruction error to negligible degree 10 10 for the measurement aperture corresponding to four times as large as the vibration structure when ten iterations of the extrapolation process are applied 3 the former method may be widely and safely applied but many iterations are necessary the latter method can reduce the reconstruction error very quickly but a wider measurement aperture than that in the former is needed therefore when the measurement aperture cannot be larger than the vibrating structure the former method is recommended while when the measurement aperture is larger than the structure the latter method is recommended summing up the accuracy of our proposed methods which is attributed to the property of data extrapolation method that the data inside the measurement aperture is conserved after adequately extrapolating the data outside the aperture will be relevant to a more quantitative measurement and analysis of real large scale structures

further results on polynomial characterizations of f g invariant and reachability subspaces this paper is concerned with further development of the unification between polynomial matrix and geometric theories of linear systems following the work of emre and hautus equivalence between different polynomial characterizations of f g invariant and reachability subspaces is shown explicitly several new results are given which clarify the relations between the polynomial system matrix invariant subspaces and system zeros finally a polynomial characterization of and a constructive procedure to obtain the largest stabilizability subspace in ker h are given

on the causal factorization problem in this note the formalism of the infinite zero module and of the infinite pole module is used to analyze the causal factorization problem this allows us to express its solutions in terms of zeros and poles at infinity and to have a better understanding of both the problem and the techniques previously proposed by various authors to solve it moreover we obtain a characterization in terms of the existence of certain causal factorizations of the transfer functions having no infinite zeros

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

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

reconstruction of the acoustic field over a limited surface area on a vibrating cylinder the acoustic field on a small region on the surface of a radiating cylindrical shell is reconstructed from measurements of pressure made on a limited nearby surface the boundary element method is applied to compute an operator relating the pressure on a small measurement surface located near the structure to the normal velocity at all points on the structure surface since the inverse problem of the reconstruction of the surface field is ill posed singular value decomposition is applied to invert the operator it is demonstrated that the surface field may be reconstructed over the portion of the structure surface located under the measurement surface

strictly observable linear systems a theory of strictly observable linear systems is developed in a module theoretic framework which is consistent with the classical algebraic theory of linear time invariant realization the theory incorporates in a unified framework the reduction of linear systems through precompensation through state feedback and through dynamic output feedback

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

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

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

nearfield acoustic holography nah ii holographic reconstruction algorithms and computer implementation the basic theory treating steady state acoustic radiation problems in the nearfield has been presented in several articles on nearfield acoustic holography in this article the approximations and assumptions necessary to reduce the infinite and continuous convolution integrals encountered in these problems to a finite and discrete form suitable for high speed numerical processing are illuminated theoretically and tested numerically to evaluate the convolution integrals two assumptions are made first the boundary field may be replaced with a patchwise constant field for reasonably small patches and second the field is negligible outside of a finite region with these two assumptions the problem reduces to one of representing the green s functions six methods of sampling or representing the green s functions are developed and these are compared theoretically and numerically

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

on the zeros of a minimal realization in an earlier work the authors have introduced a coordinate free module theoretic definition of zeros for the transfer function g s of a linear multivariable system a b c the first contribution of this paper is the construction of an explicit k z module isomorphism from that zero module z g to v r where v is the supremal a b invariant subspace contained in kerc and r is the supremal a b controllable subspace contained in kerc and where a b c constitutes a minimal realization of g s the isomorphism is developed from an exact commutative diagram of k vector spaces the second contribution is the introduction of a zero signal generator and the establishment of a relation between this generator and the classic notion of blocked signal transmissions

minimization of bias error due to windows in planar acoustic holography using a minimum error window bias errors in the prediction of a sound field using planar acoustic holography are due to aliasing and window effects it is noteworthy that aliasing is negligible in the forward predictions if the sampling space is less than a quarter wavelength however bias error induced by a window is the major concern for accurate holographic prediction because of the small number of measurement points in the planar acoustic holography for the reduction of this error a new class of window the mew is proposed and compared with hann gaussian and kaiser bessel windows it is built by modifying the method that papoulis proposed by minimizing the second order moment of the window spectrum the characteristics of the mew vary with the number of weighting values and the number of higher order moment terms to be eliminated the applicability of the mew on planar acoustic holography is demonstrated

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

dynamical structures on pencils poles and fundamental subspaces abstract this paper provides a bridge between singular system representations module theory and the geometric theory of subspaces by means of a theorem the little pole space associated with a singular system is shown to be isomorphic to the global system pole space a module theoretic concept incorporating both finite and infinite system pole information these results hold true for any regular matrix pencil ze a and may be interpreted as special cases in terms of causal and anticausal systems moreover fundamental subspaces associated with matrix pencils are isomorphic to k z and o modules representing finite and infinite system poles as a result dynamical structures on these limit spaces may be determined

think globally act locally decentralized supervisory control decentralized supervisory control is investigated by considering problem formulations that model systems whose specifications are given as global constraints but whose solution is described by local controllers a necessary and sufficient condition is given for the existence of a solution to the problem of finding decentralized supervisors that ensure that the behavior of the closed loop system lies in a given range where the range of behavior can be described by regular languages it can be effectively tested whether the decentralized control problem is solvable in this case a procedure is given to compute the associated supervisors

surface decomposition method for near field acoustic holography near field acoustic holography reconstruction of the acoustic field at the surface of an arbitrarily shaped radiating structure from pressure measurements at a nearby conformal surface is obtained from the solution of a boundary integral equation this integral equation is discretized using the equivalent source method and transformed into a matrix system that can be solved using iterative regularization methods that counteract the effect of noise on the measurements this work considers the case when the resultant matrix system is so large that it cannot be explicitly formed and iterative methods of solution cannot be directly implemented in this case the method of surface decomposition is proposed where the measurement surface is divided into smaller nonoverlapping subsurfaces each subsurface is used to form a smaller matrix system that is solved and the result joined together to generate a global solution to the original matrix system numerically generated data are used to study the use of subsurface extensions to increase the continuity of the global solution and investigate the size of the subsurfaces as well as the distance between the measurement and the vibrating surface finally a vibrating ship hull structure is considered as a physical example to apply and validate the proposed methodology

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

a method for the efficient construction of acoustic pressure cross spectral matrices abstract a method is presented for constructing with the minimum number of physical measurements the full cross spectral matrix of acoustic pressures associated with a number of measurement positions it is necessary to evaluate the elements of the matrix in question when using inverse methods for the reconstruction of acoustic source strength spectra the method presented uses the concept of reference microphones the relation between the rank of the cross spectral matrix of acoustic pressures and the number of uncorrelated acoustic sources is discussed and used to determine the required number of reference microphones a method is proposed for selecting this number in the inverse problem in which information regarding acoustic sources is unknown the results of computer simulations are presented which explore the main features of the technique under various conditions experimental results are also presented which validate the technique

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

near field acoustic holography for an axisymmetric geometry a new formulation near field acoustic holography has recently been extended to nonseparable coordinate systems by applying the boundary elements method the formulation currently implemented applies singular value decomposition to treat the presence of evanescent waves in the near field of the structure a new method is introduced for an axisymmetric geometry that is better suited for broadband data than the singular value decomposition algorithm enabling reduced computation time and providing a new expansion for the surface field with a set of functions that can be expressed as real functions independent of frequency and independent of the choice of a measurement surface the method is tested on numerically generated data

duality in polynomial models with some applications to geometric control theory duality is studied in the context of polynomial models for linear systems the output injection group the dual of the feedback group is studied and a polynomial characterization of c a invariant subspaces as well as of the maximal reachability subspaces contained in ker c is given

reconstruction of source distributions from sound pressures measured over discontinuous regions multipatch holography and interpolation in the present work a method of alternating orthogonal projections is described in the context of near field acoustical holography it allows missing or not measured data to be recovered thus relieving the strictness of measurement requirements related to the use of the discrete fourier transform the method described here provides the detailed foundation for the patch holography procedure that has previously been introduced to mitigate finite measurement aperture effects by allowing the sound field to be iteratively extended beyond the measurement aperture it is also shown that the latter iterative algorithm can be used regardless of the spatial distribution of measured data i e patches can be discontinuous numerical simulations performed by using a synthetic sound field created by a point driven simply supported plate were used to demonstrate the latter point in particular a multipatch holography procedure is described that allows a source distribution to be reconstructed from the hologram

implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography two integral equation methods are considered which can be inverted to provide the surface velocity and or pressure given a measurement of the pressure on an imaginary surface in the nearfield of a vibrating or scattering body this problem is central to nearfield acoustical holography nah the integral equations are discretized using boundary element methods bems the integral equation methods considered are 1 an indirect formulation method based on the single layer integral equation and 2 a direct formulation method based on a system of equations derived from the helmholtz kirchhoff integral equation the formation of integral equations from the mentioned methods will not involve the explicit inversion of matrices but instead will require this inversion to be done implicitly since these methods back track the sound field from the measurement surface to the surface of the source vibrator they are ill posed in nature and tikhonov regularization are used to stabilize the reconstruction problems a

the infimal prefix closed and observable superlanguage of given language abstract the supervisory control of discrete event systems under partial observation is examined in particular the condition of observability needed to solve the two main existing problems is investigated a fixed point characterization of observability is given and is shown to yield an effective test for observability where the system under consideration is specified by regular languages a formula for the infimal prefix closed observable superlanguage of a given language is presented where the system is specified by regular languages the formula for the infimal observable language is effectively computable

a unified pole zero module for linear transfer functions abstract a new module theoretic tool is presented for the study of linear time invariant input output maps transfer functions for suitable subrings 0 of the field k s of rational functions an o module called the structure module can be attached to each transfer function this structure module naturally contains the classical kalman pole module as a submodule which gives the wyman sain multivariable zero module as the corresponding factor module a posteriori the resulting exact sequence splits and the structure module is isomorphic to the direct sum of the pole module and the zero module calculations over local rings echo valuation theoretic results obtained by kung and kailath

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

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

on the zeros and poles of a transfer function abstract the poles and zeros of a linear transfer function can be studied by means of the pole module and the transmission zero module these algebraic constructions yield finite dimensional vector spaces whose dimensions are the number of poles and the number of multivariable zeros of the transfer function in addition these spaces carry the structure of a module over a ring of polynomials which gives them a dynamical or state space structure the analogous theory at infinity gives finite dimensional spaces which are modules over the valuation ring of proper rational functions following ideas of wedderburn and forney we introduce new finite dimensional vector spaces which measure generic zeros which arise when a transfer function fails to be injective or surjective a new exact sequence relates the global spaces of zeros the global spaces of poles and the new generic zero spaces this sequence gives a structural result which can be summarized as follows the number of zeros of any transfer function is equal to the number of poles when everything is counted appropriately the same result unifies and extends a number of results of geometric control theory by relating global poles and zeros of general possibly improper transfer functions to controlled invariant and controllability subspaces including such spaces at infinity

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

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