an inverse method to compute equivalent forces on a structure based on sound power measurements when modelling the dynamic response of an existing structure to predict the effects of design modifications many types of forces are difficult to characterize e g those due to unsteady flows or acoustic excitation to model the forcing function in such cases a method is presented which solves for an equivalent forcing function based on sound power measurements the method assumes that the equivalent forcing function may be represented with a superposition of force distributions on a mode by mode basis i e there is one force distribution per eigenvalue with the shape of the eigenvector the method is applied to cases where the structure is lightly damped and has low modal density experimental results show that the method accurately predicts the effect of design changes on the structure s radiated sound power the accuracy of the method is sensitive to small differences between the experimental and theoretical natural frequencies and thus it is important to match the damped natural frequencies of the physical structure as accurately as possible

boundary states extended symmetry algebra and module structure for certain rational torus models the massless bosonic field compactified on the circle of rational r2 is reexamined in the presense of boundaries a particular class of models corresponding to r2 1 2k is distinguished by demanding the existence of a consistent set of neumann boundary states the boundary states are constructed explicitly for these models and the fusion rules are derived from them these are the ones prescribed by the verlinde formula from the s matrix of the theory in addition the extended symmetry algebra of these theories is constructed which is responsible for the rationality of these theories finally the chiral space of these models is shown to split into a direct sum of irreducible modules of the extended symmetry algebra

c 1 conformal field theories on riemann surfaces we study the theory ofc 1 torus and 2 orbifold models on general riemann surfaces the operator content and occurrence of multi critical points in this class of theories is discussed the partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered riemann surfaces it is shown that orbifold partition functions are sensitive to the torelli group we give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces modular transformations are naturally incorporated as canonical transformations in the hilbert space

finite element interval analysis of external loads identified by displacement input with uncertainty a finite element formulation is proposed for the interval estimation of the nodal forces identified by displacement input with uncertainty the stiffness matrix of the structural system in problem of linear elastic body under static loading is assumed to be known and determinate this assumption enables us to derive the governing equation of the nodal forces to be identified with respect to the nominal displacement input from the stiffness equation based on the moore penrose generalized inverse solution of the unknown remnant displacements we assume that the uncertain errors involved in the nodal displacements obtained somehow by measurement and used as input are confined in a convex hull the effect of the uncertainty on the identified nodal forces is evaluated by the sensitivity analysis of the forces with respect to the uncertain displacements how to estimate the scatter of the identified nodal forces corresponding to the uncertain displacements confined in the convex hull is devised by means of the lagrange multiplier method the validity of the proposed method for identification and interval estimation of the nodal forces is shown by the numerical example of an elastic square plate in the plane stress state and subject to in plane loading

filtered stochastic galerkin methods for hyperbolic equations abstract uncertainty quantification for nonlinear hyperbolic problems becomes a challenging task in the vicinity of shocks standard intrusive methods such as stochastic galerkin sg lead to oscillatory solutions and can result in non hyperbolic moment systems the intrusive polynomial moment ipm method guarantees hyperbolicity but comes at higher numerical costs in this paper we filter the generalized polynomial chaos gpc coefficients of the sg approximation which allows a numerically cheap reduction of oscillations the derived filter is based on lasso regression which sets small gpc coefficients of high order to zero we adaptively and automatically choose the filter strength to obtain a zero valued highest order moment the filtered sg method is tested for burgers and the euler equations results show a reduction of oscillations at shocks which leads to an improved approximation of expectation values and the variance compared to sg and ipm

a stochastic galerkin method for first order quasilinear hyperbolic systems with uncertainty this paper is concerned with generalized polynomial chaos gpc approximation for first order quasilinear hyperbolic systems with uncertainty the one dimensional 1d hyperbolic system is first symmetrized with the aid of left eigenvector matrix of the jacobian matrix then the gpc stochastic galerkin method is applied to derive a provably symmetrically hyperbolic equations for the gpc expansion coefficients the resulting deterministic gpc galerkin system is discretized by a path conservative finite volume weno scheme in space and a third order total variation diminishing runge kutta method in time the method is further extended to two dimensional 2d quasilinear hyperbolic system with uncertainty where the symmetric hyperbolicity of the one dimensional gpc galerkin system is carried over via an operator splitting technique several numerical experiments are conducted to demonstrate the accuracy and effectiveness of the proposed gpc stochastic galerkin method

time domain identification of loads on plate like structures using an array of acoustic velocity sensors the fat force analysis technique method has been developped to identify loads on beams or plates from the knowledge of their flexural displacements the method is based on a local discretisation of the differential operator of the studied structure all derivatives of the displacement field are assessed at a given point from a finite difference scheme the estimation of the operator gives as an output the value of the force distribution up to now applications of the fat method have been made in the frequency domain scanning the studied structure with accelerometers or with a laser vibrometer and using phase references to get the phase relation between different points the aim of the present study is to show that the fat method allows to identify loads in the time domain this operation requires the simultaneous measurement of at least 13 points on the plate that can be realized without contact using an array of acoustic velocity sensors in the very near field of the plate the method has been app

intrusive galerkin methods with upwinding for uncertain nonlinear hyperbolic systems this paper deals with stochastic spectral methods for uncertainty propagation and quantification in nonlinear hyperbolic systems of conservation laws we consider problems with parametric uncertainty in initial conditions and model coefficients whose solutions exhibit discontinuities in the spatial as well as in the stochastic variables the stochastic spectral method relies on multi resolution schemes where the stochastic domain is discretized using tensor product stochastic elements supporting local polynomial bases a galerkin projection is used to derive a system of deterministic equations for the stochastic modes of the solution hyperbolicity of the resulting galerkin system is analyzed a finite volume scheme with a roe type solver is used for discretization of the spatial and time variables an original technique is introduced for the fast evaluation of approximate upwind matrices which is particularly well adapted to local polynomial bases efficiency and robustness of the overall method are assessed on the burgers and euler equations with shocks

a fast and stable well balanced scheme with hydrostatic reconstruction for shallow water flows we consider the saint venant system for shallow water flows with nonflat bottom it is a hyperbolic system of conservation laws that approximately describes various geophysical flows such as rivers coastal areas and oceans when completed with a coriolis term or granular flows when completed with friction numerical approximate solutions to this system may be generated using conservative finite volume methods which are known to properly handle shocks and contact discontinuities however in general these schemes are known to be quite inaccurate for near steady states as the structure of their numerical truncation errors is generally not compatible with exact physical steady state conditions this difficulty can be overcome by using the so called well balanced schemes we describe a general strategy based on a local hydrostatic reconstruction that allows us to derive a well balanced scheme from any given numerical flux for the homogeneous problem whenever the initial solver satisfies some classical stability properties it yields a simple and fast well balanced scheme that preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality

high order collocation methods for differential equations with random inputs recently there has been a growing interest in designing efficient methods for the solution of ordinary partial differential equations with random inputs to this end stochastic galerkin methods appear to be superior to other nonsampling methods and in many cases to several sampling methods however when the governing equations take complicated forms numerical implementations of stochastic galerkin methods can become nontrivial and care is needed to design robust and efficient solvers for the resulting equations on the other hand the traditional sampling methods e g monte carlo methods are straightforward to implement but they do not offer convergence as fast as stochastic galerkin methods in this paper a high order stochastic collocation approach is proposed similar to stochastic galerkin methods the collocation methods take advantage of an assumption of smoothness of the solution in random space to achieve fast convergence however the numerical implementation of stochastic collocation is trivial as it requires only repetitive runs of an existing deterministic solver similar to monte carlo methods the computational cost of the collocation methods depends on the choice of the collocation points and we present several feasible constructions one particular choice based on sparse grids depends weakly on the dimensionality of the random space and is more suitable for highly accurate computations of practical applications with large dimensional random inputs numerical examples are presented to demonstrate the accuracy and efficiency of the stochastic collocation methods

multilevel monte carlo finite volume methods for shallow water equations with uncertain topography in multi dimensions the initial data and bottom topography used as inputs in shallow water models are prone to uncertainty due to measurement errors we model this uncertainty statistically in terms of random shallow water equations we extend the multilevel monte carlo mlmc algorithm to numerically approximate the random shallow water equations efficiently the mlmc algorithm is suitably modified to deal with uncertain and possibly uncorrelated data on each node of the underlying topography grid by the use of a hierarchical topography representation numerical experiments in one and two space dimensions are presented to demonstrate the efficiency of the mlmc algorithm

hyperbolicity preserving and well balanced stochastic galerkin method for shallow water equations a stochastic galerkin formulation for a stochastic system of balanced or conservation laws may fail to preserve the hyperbolicity of the original system in this work we develop a hyperbolicity pr

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

reconstruction of a distributed force applied on a thin cylindrical shell by an inverse method and spatial filtering the localization and the magnitude of acting steady states forces resulting from the dynamic response of a cylindrical shell are investigated the derivatives present in the equation of motion are expressed in terms of displacements using finite difference schemes displacements of the structure are introduced into the equation of motion in order to calculate the distribution of these forces numerical simulations show that when the force distribution is calculated using well defined displacements the exact position of the force is easily determined however when the displacements are mixed with uncertainties noise appears and the real force is relatively inaccurate in order to handle this instability in the inverse problem a regularization method based on signal processing techniques such as windowing and filtering in the spatial wavenumber domain should be performed numerical examples that illustrate the regularization process show that when the local filtering is applied to the force distribution calculated from noisy data reasonable results are obtained experiments are performed on a cylindrical shell in order to measure its velocities unfortunately using the displacements derived from measured velocities high sensitivity to the noise in the measurements is observed overall the experimental identification gives also good results when the same technique of filtering is applied to the force distribution

vibration source identification using corrected finite difference schemes abstract this paper addresses the problem of the location and identification of vibration excitations from the measurement of the displacement field of a vibrating structure it constitutes an improvement of the force analysis technique published several years ago the development is based on the use of the motion equation which is discretized by finite difference schemes approximating spatial derivatives of the displacement in a first instance the error due to this approximation is analytically calculated in the case of beams and the low pass filtering effect of the finite difference schemes in the wavenumber domain is shown this filter also contains singularities implying bias errors especially if the spacing between sensors is chosen in order to regularize the problem in a second instance a corrected value is applied to the classic schemes used in the force analysis technique which suppresses completely the singularities of the filter after the complete description of the corrected force analysis technique on beams the extension to plates is described where simulations with noisy data show the very good accuracy one can obtain without the requirement of an added regularization for the excitation identification

uncertainty quantification for systems of conservation laws uncertainty quantification through stochastic spectral methods has been recently applied to several kinds of non linear stochastic pdes in this paper we introduce a formalism based on kinetic theory to tackle uncertain hyperbolic systems of conservation laws with polynomial chaos pc methods the idea is to introduce a new variable the entropic variable in bijection with our vector of unknowns which we develop on the polynomial basis by performing a galerkin projection we obtain a deterministic system of conservation laws we state several properties of this deterministic system in the case of a general uncertain system of conservation laws we then apply the method to the case of the inviscid burgers equation with random initial conditions and we present some preliminary results for the euler system we systematically compare results from our new approach to results from the stochastic galerkin method in the vicinity of discontinuities the new method bounds the oscillations due to gibbs phenomenon to a certain range through the entropy of the system without the use of any adaptative random space discretizations it is found to be more precise than the stochastic galerkin method for smooth cases but above all for discontinuous cases

extraction of the acoustic component of a turbulent flow exciting a plate by inverting the vibration problem abstract an improvement of the force analysis technique fat an inverse method of vibration is proposed to identify the low wavenumbers including the acoustic component of a turbulent flow that excites a plate this method is a significant progress since the usual techniques of measurements with flush mounted sensors are not able to separate the acoustic and the aerodynamic energies of the excitation because the aerodynamic component is too high moreover the main cause of vibration or acoustic radiation of the structure might be due to the acoustic part by a phenomenon of spatial coincidence between the acoustic wavelengths and those of the plate this underlines the need to extract the acoustic part in this work numerical experiments are performed to solve both the direct and inverse problems of vibration the excitation is a turbulent boundary layer and combines the pressure field of the corcos model and a diffuse acoustic field these pressures are obtained by a synthesis method based on the cholesky decomposition of the cross spectra matrices and are used to excite a plate thus the application of the inverse problem fat that requires only the vibration data shows that the method is able to identify and to isolate the acoustic part of the excitation indeed the discretization of the inverse operator motion equation of the plate acts as a low pass wavenumber filter in addition this method is simple to implement because it can be applied locally no need to know the boundary conditions and measurements can be carried out on the opposite side of the plate without affecting the flow finally an improvement of fat is proposed it regularizes optimally and automatically the inverse problem by analyzing the mean quadratic pressure of the reconstructed force distribution this optimized fat in the case of the turbulent flow has the advantage of measuring the acoustic component up to higher frequencies even in the presence of noise

w algebras new rational models and completeness of the c 1 classification two series ofw with two generators are constructed from chiral vertex operators of a free field representation ifc 1 24k there exists aw 2 3k algebra for k 2 and aw 2 8k algebra for k 4 all possible lowest weight representations their characters and fusion rules are calculated proving that these theories are rational it is shown that these non unitary theories complete the classification of all rational theories with effective central chargeceff 1 the results are generalized to the case of extended supersymmetric conformal algebras

adaptive stochastic galerkin fem abstract a framework for residual based a posteriori error estimation and adaptive mesh refinement and polynomial chaos expansion for general second order linear elliptic pdes with random coefficients is presented a parametric deterministic elliptic boundary value problem on an infinite dimensional parameter space is discretized by means of a galerkin projection onto finite generalized polynomial chaos gpc expansions and by discretizing each gpc coefficient by a fem in the physical domain an anisotropic residual based a posteriori error estimator is developed it contains bounds for both contributions to the overall error the error due to gpc discretization and the error due to finite element discretization of the gpc coefficients in the expansion the reliability of the residual estimator is established based on the explicit form of the residual estimator an adaptive refinement strategy is presented which allows to steer the polynomial degree adaptation and the dimension adaptation in the stochastic galerkin discretization and embedded in the gpc adaptation loop also the finite element mesh refinement of the gpc coefficients in the physical domain asynchronous mesh adaptation for different gpc coefficients is permitted subject to a minimal compatibility requirement on meshes used for different gpc coefficients details on the implementation with the open source software framework alea are presented it is generic and is based on available stiffness and mass matrices of a fem for the deterministic nonparametric nominal problem evaluated in the fenics environment preconditioning of the resulting matrix equation and iterative solution are discussed numerical experiments in two spatial dimensions for membrane and plane stress boundary value problems on polygons are presented they indicate substantial savings in total computational complexity due to fe mesh coarsening in high gpc coefficients

identification of external structural loads from measured harmonic responses abstract in many practical situations it is difficult to perform direct measurements or calculations of the external forces acting on an existing vibrating structure instead the structural response may than be measured and the position and magnitude of the exciting forces be calculated from the measured response unfortunately the results from this inverse process are often highly sensitive to noise in the measurements of the response and errors in the model of the structure the present study is focussed on this sensitivity under the assumption of a linear relation between the unknown harmonic force amplitudes and the response at discrete measurement positions a scalar measure of the sensitivity is suggested numerical examples that illustrate the sensitivity and its correlation to the proposed sensitivity measure are given the present sensitivity measure can be calculated for different candidate experimental configurations prior to any actual measurements and hence assist in the experimental design

a stochastic galerkin method for the boltzmann equation with uncertainty we develop a stochastic galerkin method for the boltzmann equation with uncertainty the method is based on the generalized polynomial chaos gpc approximation in the stochastic galerkin framework and can handle random inputs from collision kernel initial data or boundary data we show that a simple singular value decomposition of gpc related coefficients combined with the fast fourier spectral method in velocity space allows one to compute the high dimensional collision operator very efficiently in the spatially homogeneous case we first prove that the analytical solution preserves the regularity of the initial data in the random space and then use it to establish the spectral accuracy of the proposed stochastic galerkin method several numerical examples are presented to illustrate the validity of the proposed scheme

flexural intensity measurement on finite plates using modal spectrum ideal filtering abstract flexural intensities on various plate like structures with arbitrary boundary conditions are calculated using measured and fem yielded mobility in doing so a two dimensional spatial fourier transform has been implemented along with a refined k spectral filtering concept intensity is decomposed into individual contributions from bending moments twisting moments and shear forces the source and energy sink localization and energy flow have been analyzed through these contributions the effect of reflections from the plate edges and that of the uncorrelated noise on the intensity are discussed it is shown that the width of the k filters may have a non negligible influence on the shape of the intensity field damping in the structure can efficiently control the edge reflections and therefore help to localize the energy sources and sinks a link has been found at certain excitation conditions between the radiated acoustic intensity and the active flexural intensity it is also observed that the classical method of studying the vibration transmission using vibration amplitude measurements does not reflect the transmitted vibration energy but rather provides information on non propagating reactive energy the fem study further explains some of the experimental observations and suggests the possibility of applying intensity to complex analytical models

a novel approach for distributed dynamic load reconstruction by space time domain decoupling abstract a novel inverse approach based on green s function method and orthogonal polynomial fitting technique is presented in this paper to reconstruct the distributed dynamic load acting on a structure this approach enables one to identify the time history and reconstruct the spatial distribution function separately it is first assumed in this paper that the distribution function and the time history of the distributed dynamic load are separable modal analysis proves the sameness of the form between the modal loads and the actual time history with the knowledge of corresponding green s functions and modal responses the modal loads are identified later approximating the spatial distribution function by a set of chebyshev orthogonal polynomials new distributed dynamic loads are constructed with each orthogonal polynomial performing as the spatial distribution function and the previously identified modal load acting as the time history fitting the modal loads the coefficients of each orthogonal polynomial are achieved and then the spatial distribution function recovered to overcome the intrinsic ill conditioned characteristic appropriate regularization methods are adopted in both the modal load identification and the distribution function reconstruction numerical examples demonstrate the validity and accuracy of the proposed method

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

vibratory source identification by using the finite element model of a subdomain of a flexural beam abstract this paper proposes the identification of vibration excitations by an inverse method the use of the local operator of a structure for which the vibration field is obtained by measurements is investigated this method has already been developed on analytically known structures but there are as yet few applications the goal of this paper is to adapt the same technique by using an operator obtained with the finite element method rather than a discretised differential motion equation the first difficulty is the measurement of rotational degrees of freedom a concept analogous to an observation matrix enabling only the measurement of displacements is then proposed the method of extracting the operator on a part of the structure is also discussed two variants are proposed an operator with free boundary conditions and a truncated operator without boundary conditions the first permits identifying internal forces at the boundaries of the subdomain whereas the second ignores them in order to regularise the inverse method a tikhonov approach is used an important point of this paper is the discussion of the effect of this regularisation which implies ambiguities between reconstructed forces and moments in the results the possibility of an a priori force only assumption is then demonstrated and recommended after illustrations obtained from numerical simulations on beams an experimental validation is provided for a beam excited by a shaker where several signals are used giving several signal to noise ratios the results are discussed and compared to the force measured directly by a piezoelectric sensor

a sparse grid stochastic collocation method for partial differential equations with random input data this work proposes and analyzes a smolyak type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms input data of the model to compute solution statistics the sparse grid stochastic collocation method uses approximate solutions produced here by finite elements corresponding to a deterministic set of points in the random input space this naturally requires solving uncoupled deterministic problems as in the monte carlo method if the number of random variables needed to describe the input data is moderately large full tensor product spaces are computationally expensive to use due to the curse of dimensionality in this case the sparse grid approach is still expected to be competitive with the classical monte carlo method therefore it is of major practical relevance to understand in which situations the sparse grid stochastic collocation method is more efficient than monte carlo this work provides error estimates for the fully discrete solution using l q norms and analyzes the computational efficiency of the proposed method in particular it demonstrates algebraic convergence with respect to the total number of collocation points and quantifies the effect of the dimension of the problem number of input random variables in the final estimates the derived estimates are then used to compare the method with monte carlo indicating for which problems the former is more efficient than the latter computational evidence complements the present theory and shows the effectiveness of the sparse grid stochastic collocation method compared to full tensor and monte carlo approaches

galerkin finite element approximations of stochastic elliptic partial differential equations we describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous dirichlet boundary conditions here the aim of the com putations is to approximate statistical moments of the solution and in particular we give a priori error estimates for the computation of the expected value of the solution the first method gener ates independent identically distributed approximations of the solution by sampling the coefficients of the equation and using a standard galerkin finite element variational formulation the monte carlo method then uses these approximations to compute corresponding sample averages the sec ond method is based on a finite dimensional approximation of the stochastic coefficients turning the original stochastic problem into a deterministic parametric elliptic problem a galerkin finite element method of either the h o rp version then approximates the corresponding deterministic solution yielding approximations of the desired statistics we present a priori error estimates and include a comparison of the computational work required by each numerical approximation to achieve a given accuracy this comparison suggests intuitive conditions for an optimal selection of the numerical approximation

efficient stochastic galerkin methods for random diffusion equations we discuss in this paper efficient solvers for stochastic diffusion equations in random media we employ generalized polynomial chaos gpc expansion to express the solution in a convergent series and obtain a set of deterministic equations for the expansion coefficients by galerkin projection although the resulting system of diffusion equations are coupled we show that one can construct fast numerical methods to solve them in a decoupled fashion the methods are based on separation of the diagonal terms and off diagonal terms in the matrix of the galerkin system we examine properties of this matrix and show that the proposed method is unconditionally stable for unsteady problems and convergent for steady problems with a convergent rate independent of discretization parameters numerical examples are provided for both steady and unsteady random diffusions to support the analysis

a hyperbolicity preserving stochastic galerkin approximation for uncertain hyperbolic systems of equations abstract uncertainty quantification through stochastic spectral methods is rising in popularity we derive a modification of the classical stochastic galerkin method that ensures the hyperbolicity of the underlying hyperbolic system of partial differential equations the modification is done using a suitable slope limiter based on similar ideas in the context of kinetic moment models we apply the resulting modified stochastic galerkin method to the compressible euler equations and the m 1 model of radiative transfer our numerical results show that it can compete with other uq methods like the intrusive polynomial moment method while being computationally inexpensive and easy to implement

review of force reconstruction techniques abstract an important engineering problem is the recovery of the input of a system given its output this is a difficult problem to solve in that it is often an ill defined problem such ill posedness is problematic since noise becomes very influential and results in inaccurate or non unique solutions to combat this ill posedness additional constraints are typically applied to redefine the problem leading to a well defined problem with a unique solution current input reconstruction methods span the spectrum of analysis and computation and we have grouped them into three categories direct regularization and probabilistic statistical each of these groups is divided into several subsets that offer different perspectives in which to view the reconstruction problem our primary interests lie in the behavior of mechanical systems and as such we have focused on the literature in these fields however applicability includes other fields with the same and similar governing equations

identification of stiffness and damping properties of plates by using the local equation of motion this paper deals with the identification of stiffness and damping properties of vibrating structures by an inverse method inspired from the force analysis technique fat the proposed approach uses a local equation of motion assumed a priori which provides a relative straightforward relationship between the displacement field and material properties the spatial derivatives of the displacement in the equation are calculated using finite differences as this operation amplifies measurement noise a regularization step is applied before solving the inverse problem a procedure is proposed to automatically adjust the level of regularization the method also allows one to identify local stiffness and damping on a heterogeneous structure illustrations for both homogeneous and heterogeneous cases are shown using simulated and measured displacement fields

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

a new regularization method for the dynamic load identification of stochastic structures for the dynamic load identification for stochastic structures ill posedness and randomness are main causes that lead to instability and low accuracy monte carlo simulation mcs method is a robust and effective random simulation technique for the dynamic load identification problems of stochastic structures however it needs large computational cost and is also inefficient for practical engineering applications because of the requirement of a large quantity of samples in order to improve its computational efficiency this paper proposes a novel computational algorithm for the dynamic load identification of stochastic structures first the newly developed algorithm transforms dynamic load identification problems for stochastic structures into equivalent deterministic dynamic load identification problems second a new regularization method is proposed to realize the deterministic dynamic load identification third the assessments of the statistics of identified loads are obtained based on statistical theory finally the stability and robustness of the proposed algorithm are well validated by two engineering examples it is demonstrated that the newly developed regularization method outperforms the traditional tikhonov regularization method in computational accuracy moreover the newly proposed algorithm can significantly improve the computational efficiency of mcs and is very stable and effective in solving the dynamic load identification for stochastic structures