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

almost sure convergence of extremum seeking algorithm using stochastic perturbation abstract this paper presents an extremum seeking es algorithm where the perturbation signal is a martingale difference sequence m d s with a vanishing variance the measurement noise at the plant output is modeled by a superposition of deterministic component and a non stationary colored noise signal the optimizing set point of the uncertain reference to output equilibrium map is estimated by a stochastic approximation sa type algorithm the algorithm has a vanishing gain sequence dependent on the set point estimates by utilizing powerful tools of the martingale convergence theory it is proved that with probability one the set point estimates converge to the optimizing equilibrium point in spite of the presence of a measurement noise this result is derived without requiring boundedness or any prior condition on the set point estimates

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

brief stability of extremum seeking feedback for general nonlinear dynamic systems while the mainstream methods of adaptive control both linear and nonlinear deal only with regulation to known set points or reference trajectories in many applications the set point should be selected to achieve a maximum of an uncertain reference to output equilibrium map the techniques of the so called extremum control or self optimizing control developed for this problem in the 1950 1960s have long gone out of fashion in the theoretical control literature because of the difficulties that arise in a rigorous analytical treatment in this paper we provide the first proof of stability of an extremum seeking feedback scheme by employing the tools of averaging and singular perturbation analysis our scheme is much more general that the existing extremum control results which represent the plant as a static nonlinear map possibly cascaded with a linear dynamic block we allow the plant to be a general nonlinear dynamic system possibly non affine in control and open loop unstable whose reference to output equilibrium map has a maximum and whose equilibria are locally exponentially stabilizable

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

on the holographic reconstruction of vibroacoustic fields using equivalent sources and inverse boundary element method in using the near field acoustical holography based on the inverse boundary element method bem for the reconstruction of vibroacoustic source parameters an enormous number of measurements required in practice have limited the extended application of this method to obtain the sufficient field data with a small number of actual measured data the regeneration method of the radiated field using the multipoint equivalent sources is attempted in this paper in using the equivalent source method a vibrating source can be represented by distributed spherical sources inside the actual source surface in this paper the radiated field is expressed with a series of spherical hankel functions and spherical harmonics for suppressing the adverse effect of high order spherical functions spatial filtering of coefficients and wave vector components by a regularization scheme is adopted restored field data appended with actual measured data can be used as input for the inverse bem to reconstruct the source field

fast extremum seeking for wiener hammerstein plants this paper considers an observer based extremum seeking es scheme acting on a wiener hammerstein wh plant the es scheme utilises a high frequency sinusoidal dither in order to achieve fast minimisation of the plant s static nonlinearity unlike the prevailing analyses of fast es schemes acting on wh plants the presented result is semi global and applicable to plants with fairly general unknown nonlinearities design of the es scheme requires knowledge of the relative orders of both the input and output dynamics of the plant two different tunings of the es parameters are considered one which forces the es dynamics to be fast and one which is less restrictive it is shown that approximate knowledge of the phase of the plant s input dynamics is required if the es scheme is to use the less restrictive tuning for both tunings it is shown how the es scheme may be designed in order to simultaneously achieve arbitrarily fast and accurate minimisation of the static nonlinearity from an arbitrarily large set of initial conditions moreover the result shows that a wh plant with unstable input dynamics can in fact be stabilised by the es scheme

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

extremum seeking based perfect adaptive tracking of non pe references despite nonvanishing variance of perturbation abstract this paper presents a novel algorithm for adaptive stabilization of unstable discrete time systems with unknown control directions in a departure from commonly used recursive least squares and gradient type parameter estimators the proposed algorithm is based on extremum seeking es method the perturbation signal is a martingale difference sequence m d s with a non decaying bounded from below variance in spite of a non vanishing perturbation somewhat surprisingly it is shown that globally almost surely a s the tracking error converges to zero input and output signals are uniformly bounded and the parameter estimates are convergent sequences

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

entropy and distance of random graphs with application to structural pattern recognition the notion of a random graph is formally defined it deals with both the probabilistic and the structural aspects of relational data by interpreting an ensemble of attributed graphs as the outcomes of a random graph we can use its lower order distribution to characterize the ensemble to reflect the variability of a random graph shannon s entropy measure is used to synthesize an ensemble of attributed graphs into the distribution of a random graph or a set of distributions we propose a distance measure between random graphs based on the minimum change of entropy before and after their merging when the ensemble contains more than one class of pattern graphs the synthesis process yields distributions corresponding to various classes this process corresponds to unsupervised learning in pattern classification using the maximum likelihood rule and the probability computed for the pattern graph based on its matching with the random graph distributions of different classes we can classify the pattern graph to a class

estimation based approach for real time optimisation of uncertain nonlinear systems abstractin this paper the minimisation of an unknown but measurable cost function with uncertain dynamics is considered the drift term of the uncertain dynamical system and the gradient of the objective function are treated as unknown time varying parameters a novel estimation scheme based on almost invariant manifolds is proposed to estimate the time varying parameters a direct gradient based adaptive extremum seeking controller is designed to solve the uncertain optimisation problem this approach is shown to improve the transient performance of real time optimisation control systems

compositional segmentation and long range fractal correlations in dna sequences a segmentation algorithm based on the jensen shannon entropic divergence is used to decompose long range correlated dna sequences into statistically significant compositionally homogeneous patches by adequately setting the significance level for segmenting the sequence the underlying power law distribution of patch lengths can be revealed some of the identified dna domains were uncorrelated but most of them continued to display long range correlations even after several steps of recursive segmentation thus indicating a complex multi length scaled structure for the sequence on the other hand by separately shuffling each segment or by randomly rearranging the order in which the different segments occur in the sequence shuffled sequences preserving the original statistical distribution of patch lengths were generated both types of random sequences displayed the same correlation scaling exponents as the original dna sequence thus demonstrating that neither the internal structure of patches nor the order in which these are arranged in the sequence is critical therefore long range correlations in nucleotide sequences seem to rely only on the power law distribution of patch lengths textcopyright 1996 the american physical society

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

newton like extremum seeking for the control of thermoacoustic instability in practice the convergence rate and stability of perturbation based extremum seeking schemes can be very sensitive to the curvature of the plant map an example of this can be seen in the use of extremum seeking to reduce the amplitude of thermoacoustic oscillations in premixed gas turbine combustors this sensitivity to the plant map curvature arises from the use of a gradient descent adaptation algorithm such extremum seeking schemes may need to be conservatively tuned in order to maintain stability over a wide range of operating conditions resulting in slower optimization than could be achieved for a fixed operating condition this can severely reduce the effectiveness of perturbation based extremum seeking schemes in some applications in this paper a sinusoidally perturbed extremum seeking scheme using a newton like step is developed non local stability results for the scheme are formulated using a lyapunov analysis a local analysis of the scheme is given to investigate the influence of plant dynamics and to show that the local rate of convergence is independent of the plant map curvature the benefit of this plant map curvature independence is then experimentally demonstrated in minimizing the thermoacoustic oscillations in a model premixed combustor

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

extremum seeking with stochastic perturbations extremum seeking es using deterministic periodic perturbations has been an effective method for non model based real time optimization when only limited plant knowledge is available however periodicity can naturally lead to predictability which is undesirable in some tracking applications and unrepresentative of biological optimization processes such as bacterial chemotaxis with this in mind it is useful to investigate employing stochastic perturbations in the context of a typical es architecture and to compare the approach with existing stochastic optimization techniques in this work we show that convergence towards the extremum of a static map can be guaranteed with a stochastic es algorithm and quantify the behavior of a system with gaussian distributed perturbations at the extremum in terms of the es constants and map parameters we then examine the closed loop system when actuator dynamics are included as the separation of time scales between the perturbation signal and plant dynamics recommended in periodic es schemes cannot be guaranteed with stochastic perturbations consequently we investigate how actuator dynamics influence the allowable range of es parameters and necessitate changes in the closed loop structure finally simulation results are presented to demonstrate convergence and to validate predicted behavior about the extremum for the sake of analogy with the classical methods of stochastic approximation stochastic es in this technical note is pursued in discrete time

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

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

brief adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties we pose and solve an extremum seeking control problem for a class of nonlinear systems with unknown parameters extremum seeking controllers are developed to drive system states to the desired set points that extremize the value of an objective function the proposed adaptive extremum seeking controller is inverse optimal in the sense that it minimizes a meaningful cost function that incorporates penalty on both the performance error and control action simulation studies are provided to verify the effectiveness of the proposed approach

extremum seeking in singularly perturbed hybrid systems this technical note considers the stability of a class of singularly perturbed hybrid systems with a continuous slow subsystem this type of system encompasses many slowly varying adaptation schemes such as extremum seeking acting on hybrid systems such as urban traffic control and switching control conditions are given for semi global practical asymptotic stability of the closed loop system when the dynamics of the reduced system are also semi globally practically asymptotically stable this extends previous results which require global asymptotic stability of the reduced system furthermore the stability result is used to show convergence of an extremum seeking scheme acting upon a hybrid system

on non local stability properties of extremum seeking control in this paper we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted this non local stability result is proved by showing semi global practical stability of the closed loop system with respect to the design parameters we show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking simulation examples illustrate our results

stochastic adaptive stabilization via extremum seeking in case of unknown control directions this technical note presents a novel extremum seeking es based algorithm for global stabilization of unstable first order linear discrete time ldt stochastic systems with unknown control directions the probing signal is a martingale difference sequence with a vanishing variance the controller parameter estimate converges almost surely a s to the optimizing value the sample mean square value of the output converges a s to the minimal variance

semi global stability analysis of observer based extremum seeking for hammerstein plants this paper considers semi global stability of an observer based extremum seeking es scheme acting on a hammerstein plant unlike previous semi global analyses no restriction is placed on the speed of the es dynamics relative to the plant dynamics for any set of frequencies of a probing sinusoidal dither it is shown how the plant output can be made to converge to an arbitrarily small neighborhood of its minimum from an arbitrarily large set of initial conditions furthermore in the absence of noise it is shown how increasing the dither frequency can allow arbitrarily fast convergence of the plant input to a small neighborhood of its optimum practical application of the results requires no a priori knowledge of the plant nonlinearity however in order to design the es scheme to operate over a wide range of dither frequencies some knowledge of the plant dynamics is required simulation examples are used to demonstrate these results and to highlight practical considerations when using a high frequency dither

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

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

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

fast extremum seeking on hammerstein plants partial plant knowledge may be used to develop model based extremum seekers however existing results rely on a type of time scale separation which leads to slow optimization relative to the plant dynamics in this work a fast model based extremum seeking scheme is proposed for a hammerstein plant and semi global stability results are provided the structure of a hammerstein plant is used to advantage in designing filters that enable the extremum seeker to act on a faster time scale than the plant dynamics this leads to fast convergence while maintaining semi global stability

a perturbation based proportional integral extremum seeking control approach this paper proposes a proportional integral extremum seeking control technique the technique is a generalization of the standard perturbation based techniques which provides fast transient performance of the closed loop system to the optimum equilibrium of a measured cost function under the assumption that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown it is shown that for a class of minimum phase nonlinear system with a cost function of relative degree one the closed loop esc can practically stabilize the unknown equilibrium optimum the stabilization result provides an alternative approach to output feedback control of nonlinear systems the effectiveness of the proposed approach is demonstrated using simulation examples

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

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

quantitative linguistic study of dna sequences abstract a new family of compound poisson distribution functions from quantitative linguistics is used to study the linguistic features of dna sequences that go beyond the zipf s law the relative frequency distribution of n tuples and the compositional segmentation study can be fit reasonably well using this new family of distribution functions on the other hand the absolute values of the relative frequency come out naturally from the linguistic model without ambiguity it is suggesting that dna sequences have features that resemble natural language and it may be modeled by linguistic methodology

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

a framework for a class of hybrid extremum seeking controllers with dynamic inclusions abstract this paper presents a prescriptive framework for the design and analysis of a class of deterministic extremum seeking controllers escs based on hybrid dynamic inclusions this type of escs combines continuous and discrete time dynamics during the seeking process and its evolution in time is characterized by differential and difference inclusions rather than standard difference and differential equations examples of hybrid escs include but are not limited to purely continuous esc with optimizers described by set valued mappings esc with arbitrarily fast and slow switching modes esc with weakly jumping parameters as well as distributed escs for multi agent systems with time varying graphs since solutions of systems described by set valued mappings are usually not unique we do not insist on this property but rather we characterize the behavior of all possible solutions generated by the closed loop system making use of recent results in singular perturbations averaging and limit sets of sets for hybrid dynamical systems we establish a practical asymptotic stability result some examples of common classes of seeking dynamics described by hybrid systems are presented as well as some numerical simulations illustrating their application in standard maximization problems and nash seeking problems in game theoretical scenarios

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

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

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

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

analysis of symbolic sequences using the jensen shannon divergence we study statistical properties of the jensen shannon divergence d which quantifies the difference between probability distributions and which has been widely applied to analyses of symbolic sequences we present three interpretations of d in the framework of statistical physics information theory and mathematical statistics and obtain approximations of the mean the variance and the probability distribution of d in random uncorrelated sequences we present a segmentation method based on d that is able to segment a nonstationary symbolic sequence into stationary subsequences and apply this method to dna sequences which are known to be nonstationary on a wide range of different length scales

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

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