detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

multiplicative markov decision chains previous treatments of multiplicative markov decision chains eg bellman bellman r 1957 dynamic programming princeton university press princeton new jersey mandl mandl p 1967 an iterative method for maximizing the characteristic root of positive matrices rev roumaine math pures appl xii 1317 1322 and howard and matheson howard r a matheson j e 1972 risk sensitive markov decision processes management sci 8 356 369 restricted attention to stationary policies and assumed that all transition matrices are irreducible and aperiodic they also used a first term optimality criterion namely maximizing the spectral radius of the associated transition matrix we give a constructive proof of the existence of optimal policies among all policies under new cumulative average optimality criteria which are more sensitive than the maximization of the spectral radius the algorithm for finding an optimal policy first searches for a stationary policy with a nonnilpotent transition matrix provided such a rule exists otherwise the method still finds an optimal policy though in this case the set of optimal policies usually does not contain a stationary policy if a stationary policy with a nonnilpotent transition matrix exists then we develop a policy improvement algorithm which finds a stationary optimal policy

on blind identifiability of fir mimo systems with cyclostationary inputs using second order statistics we consider a general n spl times n multiple input multiple output mimo system excited by unobservable inputs that are spatially independent cyclostationary with unknown statistics such a mimo scenario appears in many applications such as multiuser communications and separation of competing speakers in speech processing a special case of this problem i e a 2 spl times 2 system case was previously addressed in another work using frequency domain correlations of the system output in this paper we provide a set of conditions under which a general n spl times n system is uniquely identifiable based on the second order frequency domain correlations of the system output we provide a constructive proof for the uniqueness of the system solution which could also serve as a basis for a practical algorithm for system identification

modelling of wave propagation in composite plates using the time domain spectral element method abstract this paper presents results of numerical simulation of the propagation of transverse elastic waves corresponding to the a0 mode of lamb waves in a composite plate the problem is solved by the spectral element method spectral plate finite elements with 36 nodes defined at gauss lobatto legendre points are used as a consequence of the selection of lagrange polynomials for element shape functions discrete orthogonality is obtained leading to the diagonal form of the element mass matrix this results in a crucial reduction of numerical operations required for the solution of the equation of motion by time integration numerical calculations have been carried out for various orientations and relative volume fractions of reinforcing fibres within the plate the paper shows how the velocities of transverse elastic waves in composite materials depend on the orientation and the relative volume fraction of the reinforcement

blind identification of fir systems driven by markov like input signals we propose a new algorithm for the blind identification and equalization of finite impulse response fir systems using the second order statistics of the received signal the new algorithm is set in the same context as the algorithms of tong et al 1994 and moulines et al 1995 however unlike those earlier approaches it is designed to allow correlated input signals specifically the algorithm accommodates finite memory sources and sources whose autocorrelation function decays exponentially numerical simulations compare the equalization performance of the new algorithm to those of tong and moulines it is shown that our algorithm yields consistently lower bit error rates at a wide variety of signal to noise ratios and at various equalizer lengths moreover the algorithm maintains this advantage even if it has no a priori information of source correlation or if source symbols are uncorrelated

optimal steady states excessive functions and deterministic dynamic programs this paper studies the relationship between optimal steady states and excessive functions in undiscounted deterministic dynamic programming models optimal steady states arise in the turnpike theorems of optimal economic growth and the steady state policies of 3 4 81 excessive functions which play a critical role in constructing bounds on the performance of steady state policies in 3 81 are generalizations of lagrangian saddlepoints section 2 presents the dynamic programming model section 3 defines optimal steady states and discusses their importance section 4 characterizes the relationship between them and lagrangian saddle points section 5 introduces excessive functions and uses them to derive bounds on the optimal finite stage costs section 6 shows that the set of excessive functions associated with an oss contains a greatest element and a least element and proves that for s to be an optimal steady state it is necessary and sufficient that s be associated with an excessive function that is bounded above note that our model is quite general and does not assume convexity

closed form correlative coding cfc sub 2 blind identification of mimo channels isometry fitting to second order statistics we present a blind closed form consistent channel estimator for multiple input multiple output mimo systems that uses only second order statistics we spectrally modulate the output of each source by correlative coding it with a distinct filter the correlative filters are designed to meet the following desirable characteristics no additional power or bandwidth is required no synchronization between the sources is needed the original data rate is maintained we first prove an identifiability theorem under a simple spectral condition on the transmitted random processes the mimo channel is uniquely determined up to a phase offset per user from the second order statistics of the received data we then develop the closed form algorithm that attains this identifiability bound we show that minimum phase finite impulse response filters with arbitrary memory satisfy our sufficient spectral identifiability condition this results in a computationally attractive scheme for retrieving the data information sequences after the mimo channel has been identified we assess the performance of the proposed algorithms by computer simulations in particular the results show that our technique outperforms the previously introduced transmitter induced conjugate cyclostationarity approach when there are carrier frequency misadjustments

on a whitening approach to partial channel estimation and blind equalization of fir iir multiple input multiple output channels channel estimation and blind equalization of multiple input multiple output mimo communications channels is considered using primarily the second order statistics of the data such models arise when a single receiver data from multiple sources is fractionally sampled assuming that there is excess bandwidth or when an antenna array is used with or without fractional sampling we consider estimation of partial channel impulse response and design of finite length minimum mean square error mmse blind equalizers the basis of the approach is the design of a zero forcing equalizer that whitens the noise free data we allow infinite impulse response iir channels moreover the multichannel transfer function need not be column reduced our approaches also work when the subchannel transfer functions have common zeros as long as the common zeros are minimum phase zeros the channel length or model orders need not be known the sources are recovered up to a unitary mixing matrix and are further unmixed using higher order statistics of the data a linear prediction approach is also considered under the above conditions of possibly iir channels common subchannel zeros factors and not necessarily column reduced channels four illustrative simulation examples are provided

an algorithm for a dynamic programming model of fractional flows in an earlier paper the author introduced an n dimensional dynamic programming model of fractional flows characterized its solutions under general conditions and developed methods for their computation the latter which resemble algorithms for n state markovian decision processes break down when the costs are undiscounted and the flow matrices are nontransient here an algorithm is presented that computes many of the quantities of interest more efficiently under milder assumptions in addition some of our earlier results for the undiscounted case are extended to models with nontransient flow matrices

3 d large scale wave propagation modeling by spectral element method on cray t3e multiprocessor highly efficient algorithms and massively parallel computers are needed for acoustic full wave modeling in large scale 3 d realistic unbounded media in this work a spectral element method in conjunction with a new iterative solution technique is presented the very high spatial accuracy of the algorithm allows for increased computational efficiency when compared to standard finite element method in addition the use of an iterative solver based on a local element by element formulation and a matrix vector product which is factored and converted to a faster matrix matrix product allows for a significant reduction both in storage requirements and in the computational complexity the resulting algorithm can easily be implemented on high performance vector and or parallel processors the numerical scheme has been tested on a cray t3e supercomputer our experimental results show that efficiency is very high and that good load balancing can be obtained at run time because relevant blocks of computations are performed at the element level and are totally independent

the dynamic analysis of a cracked timoshenko beam by the spectral element method the aim of this paper is to introduce a new finite spectral element of a cracked timoshenko beam for modal and elastic wave propagation analysis the proposed approach deals with the spectral element method this method is suitable for analyzing wave propagation problems as well as for calculating modal parameters of the structure in the paper the results of the change in modal parameters due to crack appearance are presented the influence of the crack parameters especially of the changing location of the crack on the wave propagation is examined responses obtained at different points of the beam are presented proper analysis of these responses allows one to indicate the crack location in a very precise way this fact is very promising for the future work in the damage detection field

a two stage algorithm for mimo blind deconvolution of nonstationary colored signals a new two stage algorithm is proposed for the deconvolution of multi input multi output mimo systems with colored input signals while many blind deconvolution algorithms in the literature utilize high order statistics of the output signal for white input signals the additional information contained in colored input signals allows the design of second order statistical algorithms in fact practical signal sources such as speech signals do have distinct nonstationary colored power spectral densities we present a two stage signal separation approach in which the first step utilizes a matrix pencil between output auto correlation matrices at different delays whereas the second stage adopts a subspace method to identify and deconvolve mimo systems

blind mimo system identification based on cumulant subspace decomposition blind identification of multiple input multiple output mimo linear systems can be achieved by utilizing higher order statistics of the output signals we study the blind identification of mimo systems whose inputs are mutually independent temporally white non gaussian source signals based on sub space analysis we develop a new linear batch algorithm to identify mimo systems from the common nullspace of a set of fourth order cumulant matrices of the channel outputs given knowledge of the channel orders the identifiability conditions required by the proposed algorithm are properly established like most subspace based approaches this new algorithm remains sensitive to channel order overestimation simulation results illustrate its performance for various channel models

blind mimo fir channel identification based on second order spectra correlations we consider a problem of identifying a multiple input multiple output mimo finite impulse response fir system excited by colored inputs with known statistics we propose a new nonlinear optimization based method that involves the power spectra and cross spectra of the system output the proposed algorithm is tested for the case of cyclostationary inputs cdma scenario and stationary inputs sdma scenario simulation results indicate that the proposed scheme works well even for large order systems and is robust to noise and channel length mismatch

on fractional flow models and equivalent finite state processes this paper studies the relationships between a dynamic programming model of fractional flows in an n sector system and certain finite state processes the former which is described in section 2 is a nonstationary version of 4 under conditions given in section 3 the flow model is equivalent to an n state markovian decision process allowing for simpler computation in certain cases where that equivalence fails a partial solution to the flow model follows from the solution to an n l state semi markovian decision process this result which appears in section 6 helps to explain why the algorithms of 4 51 resemble ones for finite state processes it does not substantially reduce computation

prediction error method for second order blind identification blind channel identification methods based on the oversampled channel output are a problem of current theoretical and practical interest in this paper we introduce a second order blind identification technique based on a linear prediction approach in contrast to eigenstructure based methods it will be shown that the linear prediction error method is robust to order overdetermination an asymptotic performance analysis of the proposed estimation method is carried out consistency and asymptotic normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are finally presented to demonstrate the potential and the robustness of the proposed method

a subspace algorithm for certain blind identification problems the problem of blind identification of p inputs q outputs fir transfer functions is addressed existing subspace identification methods derived for p 1 are first reformulated in particular the links between the noise subspace of a certain covariance matrix of the output signals on which subspace methods build on and certain rational subspaces associated with the transfer function to be identified are elucidated based on these relations we study the behavior of the subspace method in the case where the order of the transfer function is overestimated next an asymptotic performance analysis of this estimation method is carried out consistency and asymptotical normality of the estimates is established a closed form expression for the asymptotic covariance of the estimates is given numerical simulations and investigations are presented to demonstrate the potential of the subspace method finally we take advantage of our new reformulation to discuss the extension of the subspace method to the case p 1 we show where the difficulties lie and we briefly indicate how to solve the corresponding problems the possible connections with classical approaches for ma model estimations are also outlined

blind channel equalization with colored sources based on second order statistics a linear prediction approach we consider the blind equalization and estimation of single user multichannel models from the second order statistics of the channel output when the channel input statistics are colored but known by exploiting certain results from linear prediction theory we generalize the algorithm of tong et al 1994 which was derived under the assumption of a white transmitted sequence in particular we show that all one needs to estimate the channel to within an unitary scaling constant and thus to find its equalizers is a that a standard channel matrix have full column rank and b a vector of the input signal and its delays have positive definite lag zero autocorrelation an algorithm is provided to determine the equalizer under these conditions we argue that because this algorithm makes explicit use of the input statistics the equalizers thus obtained should outperform those obtained by other methods that neither require nor exploit the knowledge of the input statistics simulation results are provided to verify this fact

blind equalization of nonlinear channels from second order statistics this paper addresses the blind equalization problem for single input multiple output nonlinear channels based on the second order statistics sos of the received signal we consider the class of linear in the parameters channels which can be seen as multiple input systems in which the additional inputs are nonlinear functions of the signal of interest these models include but are not limited to polynomial approximations of nonlinear systems although any sos based method can only identify the channel to within a mixing matrix at best sufficient conditions are given to ensure that the ambiguity is at a level that still allows for the computation of linear fir equalizers from the received signal sos should such equalizers exist these conditions involve only statistical characteristics of the input signal and the channel nonlinearities and can therefore be checked a priori based on these conditions blind algorithms are developed for the computation of the linear equalizers simulation results show that these algorithms compare favorably with previous deterministic methods

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

a spectrally formulated plate element for wave propagation analysis in anisotropic material a new spectrally formulated plate element is developed to study wave propagation in composite structures the element is based on the classical lamination plate theory recently developed method based on singular value decomposition svd is used in the element formulation along with this a new strategy based on the method of solving polynomial eigenvalue problem pep is proposed in this paper which significantly reduces human intervention and thus human error in the element formulation the developed element has an exact dynamic stiffness matrix as it uses the exact solution of the governing elastodynamic equation of plate in frequency wavenumber domain as the interpolating functions due to this the mass distribution is modeled exactly and as a result a single element captures the exact frequency response of a regular structure and it suffices to model a plate of any dimension thus the cost of computation is dramatically reduced compared to the cost of conventional finite element analysis the fast fourier transform fft and fourier series are used for inversion to time space domain this element is used to model plate with ply drops and to capture the propagation of lamb waves

unstructured grid method for stress wave propagation in elastic media a new numerical method named unstructured grid method is presented to calculate two dimensional stress wave propagation problems in elastic media this method is based on the dynamic equilibrium equations of the investigated lumps that are formed among the auxiliary unstructured grids the approach to the solution is obtained by calculating the node displacements and the central point stresses of the spatial grids alternately the stability criterion of the method is given and tested numerically analysis of dispersion for numerical phase velocity is studied the rule is provided to determine the spatial step size of discretization mesh so as to ensure the numerical accuracy of the unstructured grid method numerical results are compared with the available exact solutions and with the solutions of central difference method for demonstrating the good accuracy of the new method the unstructured grid method possesses higher calculating speed than the central difference method finally the dynamic behavior of a square plate with a hole under an impact loading is researched

simulation of anisotropic wave propagation based upon a spectral element method we introduce a numerical approach for modeling elastic wave propagation in 2 d and 3 d fully anisotropic media based upon a spectral element method the technique solves a weak formulation of the wave equation which is discretized using a high order polynomial representation on a finite element mesh for isotropic media the spectral element method is known for its high degree of accuracy its ability to handle complex model geometries and its low computational cost we show that the method can be extended to fully anisotropic media the mass matrix obtained is diagonal by construction which leads to a very efficient fully explicit solver we demonstrate the accuracy of the method by comparing it against a known analytical solution for a 2 d transversely isotropic test case and by comparing its predictions against those based upon a finite difference method for a 2 d heterogeneous anisotropic medium we show its generality and its flexibility by modeling wave propagation in a 3 d transversely isotropic medium with a symmetry axis tilted relative to the axes of the grid

reducing spurious oscillations in discontinuous wave propagation simulation using high order finite elements in this paper a modified explicit time integration scheme is proposed for simulating the propagation of discontinuous waves the spatial domain is discretized by the finite element method to obtain accurate results the standard finite element method requires a very fine mesh which is why the computational effort can be very time consuming the use of high order finite element methods such as the spectral element method based on lagrange polynomials through gauss lobatto legendre points or the iso geometric analysis using non uniform rational b splines can reduce the enormous computational costs significantly compared to the standard finite element method however explicit time integration schemes such as the central difference method cannot eliminate the spurious oscillation near the front wave the procedure proposed here is basically similar to the explicit method of noh and bathe but the semi discrete equation of motion is modified by introducing a damping parameter to suit the high order fem analysis of the discontinuous wave propagation the performance due to this modification is tested for one dimensional wave propagation problems using both lumped and consistent mass matrices then the idea of a combination of the consistent and row sum lumped mass matrices is evaluated the proposed method is studied also in two dimensions by considering the lamb problem of wave propagation the results are promising enough to provide a better simulation of the discontinuous wave propagation problem

blind channel identification with colored sources by exploiting properties of companion matrices this paper proposes a new second order statistics based method for blind multiple input multiple output mimo finite impulse response fir channel estimation driven by colored sources it is assumed that the second order statistics sos of the input sources are known a priori by exploiting the new derived properties of the companion matrices an original proof for the uniqueness of the system solution is provided which serves as a theoretical basis for the proposed new method that admits a closed form solution the corresponding identifiability conditions and the computational complexity of the proposed method are discussed and compared with other existing method numerical simulation results are presented to illustrate the performance of the proposed algorithm

a spectral element method for fluid dynamics laminar flow in a channel expansion a spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible navier stokes equations in the spectral element discretization the computational domain is broken into a series of elements and the velocity in each element is represented as a high order lagrangian interpolant through chebyshev collocation points the hyperbolic piece of the governing equations is then treated with an explicit collocation scheme while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle the implementation of the technique is demonstrated on a one dimensional inflow outflow advection diffusion equation and the method is then applied to laminar two dimensional separated flow in a channel expansion comparisons are made with experiment and previous numerical work

blind two input two output fir channel identification based on frequency domain second order statistics we present an analytical solution to the two input two output blind crosswise mixture identification based on eigenvalue decomposition of second order spectra correlations the sources are independent and non white but otherwise we consider their statistics to be unknown we show that the cross channels cannot be uniquely determined by the analysis of the frequency domain covariance alone due to the unknown eigenvector permutations however the problem can be attacked with the help of two invariant indices that are immune to these permutations using these indices together with standard reconstruction from phase techniques we show that the channels can be uniquely determined our theoretical results lead to a novel frequency domain second order algorithm that identifies the unknown channels

approximate spectral element for wave propagation analysis in inhomogenous layered media an approximate spectral element se is developed to model isotropic inhomogeneous layered media as opposed to the case of a homogeneous solid where the mass distribution is modeled exactly the se approach to the inhomogeneous material gives an approximate frequency response of the structure the element is formulated by approximating wave number over the domain this wave number has a nontrivial imaginary part justifying the notion of an inhomogeneous wave which is predominant in inhomogeneous materials material properties are made to vary linearly within the element although any other variation can be incorporated under the proposed scheme strains due to temperature are also taken into account which enables the analysis of a layered structure for thermal burst loading the formulated element is used to analyze the response of inhomogeneous layer structure subjected to high frequency mechanical and thermal loading furthermore the inherent advantage of the se in the solution of inverse problems is utilized to reconstruct the force history applied to an inhomogeneous layer from the measured responses the finite element responses are used as surrogate experimental data in particular a layered structure of functionally graded material fgm is taken for the case study where fgm smoothly blends two different material properties one of metal and the other of ceramic the fast fourier transform and fourier series are used for inversion to the time space domain