multiscale simulation of transport in an open quantum system resonances and wkb interpolation a numerical scheme for the one dimensional stationary schrodinger poisson model is described the scheme is used to simulate a resonant tunneling diode and provides an important reduction of the simulation time the improvement is twofold first the grid spacing in the position variable is made coarser by using oscillating interpolation functions derived from the wkb asymptotics then the discretization of the energy variable which is a parameter for the schrodinger equation is improved by approaching the wavefunctions in the double barrier region by its projection on the resonant states following the work of presilla sjostrand and jona lasinio on schrodinger equations with concentrated non linearities ann phys 240 1995 1 21

high order multiscale discontinuous galerkin methods for the one dimensional stationary schrodinger equation abstract in this paper we extend our previous work on the second order multiscale discontinuous galerkin dg method for one dimensional stationary schrodinger equations with oscillating solutions dong et al 2016 to high order we propose two types of high order multiscale finite element spaces and prove that the resulting dg methods with these spaces converge optimally with respect to the mesh size h in l 2 norm when h is small enough numerically we observe that these two multiscale dg methods achieve at least the second order convergence without any resonance errors when h e and optimal high order convergence when h e where e is the scale of the wave length we also demonstrate their ability to capture highly oscillating solutions of the schrodinger equation in the application of the resonant tunneling diode rtd model

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

schrodinger poisson systems in dimension d 3 the whole space case after a study made for bounded domains and in the periodic case we investigate the variational formulation of schrodinger poisson systems set on the whole space d d 3 this variational formulation leads to a uniqueness result while the existence of a solution is proved only for small data because of the lack of coerciveness the end of this paper briefly presents the extension of this formalism to a physically relevant problem where the potential is periodic in one direction

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

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

uniform manifold sampling ums sampling the maximum entropy pdf maximum entropy pdf projection mepp is a way to construct generative models from feature transformations corresponding to each dimension reducing feature mapping such as a feed forward neural network or an algorithm to calculate linear prediction coefficients from time series and given a prior distribution for the features there exists a unique generative model for the input data which subject to mild requirements is maximum entropy maxent among all probability density functions pdfs that are consistent with the given feature prior in this paper we consider the problem of sampling from these maxent projected pdfs the sampling process consists of drawing a sample from the given feature prior distribution then drawing samples uniformly distributed on the inversion set set of input samples consistent with the drawn feature value usually a manifold the process is called uniform manifold sampling ums we describe ums for simple nonlinear and iterative feature transformations then focus on linear transformations with input data constraints x i 0 or 0 leq x i leq 1 which require mcmc based sampling we discover that the manifold centroid sample mean for a fixed feature value is useful as a deterministic maxent feature inversion solution we show how to predict the centroid efficiently without sampling and demonstrate its usefulness in speeding up mcmc by an order of magnitude and in spectral estimation and image reconstruction finally we provide an example of ums in a classification experiment in which we use monte carlo integration to create true generative models from arbitrary classifiers

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

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

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

an accelerated algorithm for 2d simulations of the quantum ballistic transport in nanoscale mosfets an accelerated algorithm for the resolution of the coupled schrodinger poisson system with open boundary conditions is presented this method improves the sub band decomposition method sdm introduced in n ben abdallah e polizzi subband decomposition approach for the simulation of quantum electron transport in nanostructures j comput phys 202 1 2005 150 180 the principal feature of the here presented model consists in an inexpensive and fast resolution of the schrodinger equation in the transport direction due to the application of wkb techniques oscillating wkb basis elements are constructed and replace the piecewise polynomial interpolation functions used in sdm this procedure is shown to reduce considerably the computational time while keeping a good accuracy

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

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

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

wkb based schemes for the oscillatory 1d schrodinger equation in the semiclassical limit an efficient and accurate numerical method is presented for the solution of highly oscillatory differential equations while standard methods would require a very fine grid to resolve the oscillations the presented approach uses first an analytic second order wkb type transformation which filters out the dominant oscillations the resulting ode is much smoother and can hence be discretized on a much coarser grid with significantly reduced numerical costs in many practically relevant examples the method is even asymptotically correct w r t the small parameter varepsilon that identifies the oscillation wavelength indeed in these cases the error then vanishes for varepsilon to0 even on a fixed spatial mesh applications to the stationary schrodinger equation are presented

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

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

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

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

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

a fast learning algorithm for deep belief nets we show how to use complementary priors to eliminate the explaining away effects that make inference difficult in densely connected belief nets that have many hidden layers using complementary priors we derive a fast greedy algorithm that can learn deep directed belief networks one layer at a time provided the top two layers form an undirected associative memory the fast greedy algorithm is used to initialize a slower learning procedure that fine tunes the weights using a contrastive version of the wake sleep algorithm after fine tuning a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels this generative model gives better digit classification than the best discriminative learning algorithms the low dimensional manifolds on which the digits lie are modeled by long ravines in the free energy landscape of the top level associative memory and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind

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

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

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

maximum entropy pdf design using feature density constraints applications in signal processing this paper revisits an existing method of constructing high dimensional probability density functions pdfs based on the pdf at the output of a dimension reducing feature transformation we show how to modify the method so that it can provide the pdf with the highest entropy among all pdfs that generate the given low dimensional pdf the method is completely general and applies to arbitrary feature transformations the chain rule is described for multi stage feature calculations typically used in signal processing examples are given including mfcc and auto regressive features experimental verification of the results using simulated data is provided including a comparison with competing generative methods

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

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

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

on time splitting spectral approximations for the schrodinger equation in the semiclassical regime in this paper we study time splitting spectral approximations for the linear schrodinger equation in the semiclassical regime where the planck constant e is small in this regime the equation propagates oscillations with a wavelength of o e and finite difference approximations require the spatial mesh size h o e and the time step k o e in order to obtain physically correct observables much sharper mesh size constraints are necessary for a uniform l2 approximation of the wave function the spectral time splitting approximation under study will be proved to be unconditionally stable time reversible and gauge invariant it conserves the position density and gives uniform l2 approximation of the wave function for k o e and h o e extensive numerical examples in both one and two space dimensions and analytical considerations based on the wigner transform even show that weaker constraints e g k independent of e and h o e are admissible for obtaining correct observables finally we address the application to nonlinear schrodinger equations and conduct some numerical experiments to predict the corresponding admissible meshing strategies

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

efficient monte carlo procedures for generating points uniformly distributed over bounded regions we consider the monte carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region the class of markovian methods considered generate points asymptotically uniformly distributed within the region computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions

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

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

the pdf projection theorem and the class specific method we present the theoretical foundation for optimal classification using class specific features and provide examples of its use a new probability density function pdf projection theorem makes it possible to project probability density functions from a low dimensional feature space back to the raw data space an m ary classifier is constructed by estimating the pdfs of class specific features then transforming each pdf back to the raw data space where they can be fairly compared although statistical sufficiency is not a requirement the classifier thus constructed becomes equivalent to the optimal bayes classifier if the features meet sufficiency requirements individually for each class this classifier is completely modular and avoids the dimensionality curse associated with large complex problems by recursive application of the projection theorem it is possible to analyze complex signal processing chains we apply the method to feature sets including linear functions of independent random variables cepstrum and mel cepstrum in addition we demonstrate how it is possible to automate the feature and model selection process by direct comparison of log likelihood values on the common raw data domain

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

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

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

a two level domain decomposition method for the iterative solution of high frequency exterior helmholtz problems summary we present a lagrange multiplier based two level domain decomposition method for solving iteratively large scale systems of equations arising from the finite element discretization of high frequency exterior helmholtz problems the proposed method is essentially an extension of the regularized feti finite element tearing and interconnecting method to indefinite problems its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves we show numerically that the proposed method is scalable with respect to the mesh size the subdomain size and the wavenumber we report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements

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

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

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

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

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

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

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

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

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