adaptive sparse polynomial chaos expansion based on least angle regression polynomial chaos pc expansions are used in stochastic finite element analysis to represent the random model response by a set of coefficients in a suitable so called polynomial chaos basis the number of terms to be computed grows dramatically with the size of the input random vector which makes the computational cost of classical solution schemes may it be intrusive i e of galerkin type or non intrusive unaffordable when the deterministic finite element model is expensive to evaluate to address such problems the paper describes a non intrusive method that builds a sparse pc expansion first an original strategy for truncating the pc expansions based on hyperbolic index sets is proposed then an adaptive algorithm based on least angle regression lar is devised for automatically detecting the significant coefficients of the pc expansion beside the sparsity of the basis the experimental design used at each step of the algorithm is systematically complemented in order to avoid the overfitting phenomenon the accuracy of the pc metamodel is checked using an estimate inspired by statistical learning theory namely the corrected leave one out error as a consequence a rather small number of pc terms are eventually retained sparse representation which may be obtained at a reduced computational cost compared to the classical full pc approximation the convergence of the algorithm is shown on an analytical function then the method is illustrated on three stochastic finite element problems the first model features 10 input random variables whereas the two others involve an input random field which is discretized into 38 and 30 500 random variables respectively

modeling uncertainty in steady state diffusion problems via generalized polynomial chaos abstract we present a generalized polynomial chaos algorithm for the solution of stochastic elliptic partial differential equations subject to uncertain inputs in particular we focus on the solution of the poisson equation with random diffusivity forcing and boundary conditions the stochastic input and solution are represented spectrally by employing the orthogonal polynomial functionals from the askey scheme as a generalization of the original polynomial chaos idea of wiener amer j math 60 1938 897 a galerkin projection in random space is applied to derive the equations in the weak form the resulting set of deterministic equations for each random mode is solved iteratively by a block gauss seidel iteration technique both discrete and continuous random distributions are considered and convergence is verified in model problems and against monte carlo simulations

braided autoequivalences and the equivariant brauer group of a quasitriangular hopf algebra abstract let h r be a finite dimensional quasitriangular hopf algebra over a field k and m h the representation category of h in this paper we study the braided autoequivalences of the drinfeld center yd h h trivializable on m h we establish a group isomorphism between the group of those autoequivalences and the group of quantum commutative bi galois objects of the transmutation braided hopf algebra h r we then apply this isomorphism to obtain a categorical interpretation of the exact sequence of the equivariant brauer group bm k h r in 18 to this aim we have to develop the braided bi galois theory established by schauenburg in 14 15 which generalizes the hopf bi galois theory over usual hopf algebras to the one over braided hopf algebras in a braided monoidal category

an exact sequence for the brauer group of a finite quantum group abstract in this paper we give a general method to compute the brauer group of a finite quantum group i e a faithfully projective coquasitriangular hopf algebra over a commutative ring with unity let h r be a finite quantum group with an r matrix r on h h there exists a braided hopf algebra h r in the braided monoidal category of right h comodules s majid j pure appl algebra 86 1993 187 221 we construct a group gal h r consisting of quantum commutative h r bigalois objects and show that there is an exact sequence of group homomorphisms 1 br k bc k h r gal h r where br k is the usual brauer group of k and bc k h r is the brauer group of h r with respect to the r matrix r

digital analysis of rotated images the problem of estimating the relative rotations of two images taken from the same scene is considered and a numerical method for computing such rotations is presented the main features of the proposed method consist of the possibility of fast in place computations with no preliminary interpolation of the data and a considerable precision for moderate rotation angles the final estimate is performed with a least square criterion but in the present case even such computations can be substantially simplified a detailed analysis shows that for practical applications the influence of discretization errors does not affect in a relevant way the precision of the results that is also confirmed by numerical experiments

a data driven stochastic collocation approach for uncertainty quantification in mems this work presents a data driven stochastic collocation approach to include the effect of uncertain design parameters during complex multi physics simulation of micro electromechanical systems mems the proposed framework comprises of two key steps first probabilistic characterization of the input uncertain parameters based on available experimental information and second propagation of these uncertainties through the predictive model to relevant quantities of interest the uncertain input parameters are modeled as independent random variables for which the distributions are estimated based on available experimental observations using a nonparametric diffusion mixing based estimator botev nonparametric density estimation via diffusion mixing technical report 2007 the diffusion based estimator derives from the analogy between the kernel density estimation kde procedure and the heat dissipation equation and constructs density estimates that are smooth and asymptotically consistent the diffusion model allows for the incorporation of the prior density and leads to an improved density estimate in comparison with the standard kde approach as demonstrated through several numerical examples following the characterization step the uncertainties are propagated to the output variables using the stochastic collocation approach based on sparse grid interpolation smolyak soviet math dokl 1963 4 240 243 the developed framework is used to study the effect of variations in young s modulus induced as a result of variations in manufacturing process parameters or heterogeneous measurements on the performance of a mems switch copyright 2010 john wiley sons ltd

polynomial meta models with canonical low rank approximations the growing need for uncertainty analysis of complex computational models has led to an expanding use of meta models across engineering and sciences the efficiency of meta modeling techniques relies on their ability to provide statistically equivalent analytical representations based on relatively few evaluations of the original model polynomial chaos expansions pce have proven a powerful tool for developing meta models in a wide range of applications the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials the classical pce approach nevertheless faces the curse of dimensionality namely the exponential increase of the basis size with increasing input dimension to address this limitation the sparse pce technique has been proposed in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm an alternative for developing meta models with polynomial functions in high dimensional problems is offered by the newly emerged low rank approximations lra approach by exploiting the tensor product structure of the multivariate basis lra can provide polynomial representations in highly compressed formats through extensive numerical investigations we herein first shed light on issues relating to the construction of canonical lra with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions specifically we examine the selection of optimal rank stopping criteria in the updating of the polynomial coefficients and error estimation in the sequel we confront canonical lra to sparse pce in structural mechanics and heat conduction applications based on finite element solutions canonical lra exhibit smaller errors than sparse pce in cases when the number of available model evaluations is small with respect to the input dimension a situation that is often encountered in real life problems by introducing the conditional generalization error we further demonstrate that canonical lra tend to outperform sparse pce in the prediction of extreme model responses which is critical in reliability analysis

sequential subspace reliability method with univariate revolving integration a new computational framework called the sequential subspace reliability method ssrm is presented this method decomposes the multidimensional random space into multiple two dimensional subspaces in this manner ssrm is able to approximate bivariate interaction effects when the reliability estimate contribution is calculated subspace by subspace the final assessment is updated in a progressive manner the iterative history of sequential reliability assessment can be used to understand the complexity and convergence behavior of the limit state function of interest in a decision making situation the flexibility of the proposed ssrm to provide iterative updates on reliability estimation becomes especially valuable in dealing with large scale and complex problems under the constraints of limited time and resources to calculate the individual subspace contributions a novel univariate revolving integration uri method is proposed the uri method takes advantage of the axisymmetric nature of a joint pr

a robust and efficient stepwise regression method for building sparse polynomial chaos expansions abstract polynomial chaos pc expansions are widely used in various engineering fields for quantifying uncertainties arising from uncertain parameters the computational cost of classical pc solution schemes is unaffordable as the number of deterministic simulations to be calculated grows dramatically with the number of stochastic dimension this considerably restricts the practical use of pc at the industrial level a common approach to address such problems is to make use of sparse pc expansions this paper presents a non intrusive regression based method for building sparse pc expansions the most important pc contributions are detected sequentially through an automatic search procedure the variable selection criterion is based on efficient tools relevant to probabilistic method two benchmark analytical functions are used to validate the proposed algorithm the computational efficiency of the method is then illustrated by a more realistic cfd application consisting of the non deterministic flow around a transonic airfoil subject to geometrical uncertainties to assess the performance of the developed methodology a detailed comparison is made with the well established lar based selection technique the results show that the developed sparse regression technique is able to identify the most significant pc contributions describing the problem moreover the most important stochastic features are captured at a reduced computational cost compared to the lar method the results also demonstrate the superior robustness of the method by repeating the analyses using random experimental designs

on the registration of an object translating on a static background this work considers the determination of the relative movements between consecutive images taken from the same scene registration a problem arising in many application fields with the exception of specialized techniques for specific applications the most reliable registration algorithms are based on the use of 2 d fourier transforms they typically require a relevant computational effort the computational bulkiness typical of such methods can be overcome by 1 d techniques needless to say at the price of a degraded performance in presence of disturbances this paper proposes a new 1 d method which exploits the availability of several frames typical of practical contexts in order to determine the translation of an object moving between two endpoints on a static background the noise performance of the new technique is shown to be quite superior to that of the reported 1 d methods for sufficiently long sequences the noise performance favourably compares with that of 2 d techniques with considerable computational savings the possibilities of the method are exemplified by a number of practical examples

a posteriori error estimation and adaptivity in stochastic galerkin fem for parametric elliptic pdes beyond the affine case abstract we consider a linear elliptic partial differential equation pde with a generic uniformly bounded parametric coefficient the solution to this pde problem is approximated in the framework of stochastic galerkin finite element methods we perform a posteriori error analysis of galerkin approximations and derive a reliable and efficient estimate for the energy error in these approximations practical versions of this error estimate are discussed and tested numerically for a model problem with non affine parametric representation of the coefficient furthermore we use the error reduction indicators derived from spatial and parametric error estimators to guide an adaptive solution algorithm for the given parametric pde problem the performance of the adaptive algorithm is tested numerically for model problems with two different non affine parametric representations of the coefficient

probabilistic collocation for period 1 limit cycle oscillations in this paper probabilistic collocation for limit cycle oscillations pclco is proposed probabilistic collocation pc is a non intrusive approach to compute the polynomial chaos description of uncertainty numerically polynomial chaos can require impractical high orders to approximate long term time integration problems due to the fast increase of required polynomial chaos order with time pclco is a pc formulation for modeling the long term stochastic behavior of dynamical systems exhibiting a periodic response i e a limit cycle oscillation lco in the pc method deterministic time series are computed at collocation points in probability space in pclco pc is applied to a time independent parametrization of the periodic response of the deterministic solves instead of to the time dependent functions themselves due to the time independent parametrization the accuracy of pclco is independent of time the approach is applied to period 1 oscillations with one main frequency subject to a random parameter numerical results are presented for the harmonic oscillator a two dof airfoil flutter model and the fluid structure interaction of an elastically mounted cylinder

the brauer group of modified supergroup algebras abstract the computation of the brauer group bm of modified supergroup algebras over a field is performed yielding in particular the computation of the brauer group of all finite dimensional triangular hopf algebras when the base field is algebraically closed and of characteristic zero the used techniques are also applied for the computation of lazy cohomology of modified supergroup algebras we relate our construction with yinhuo zhang s exact sequence when the base ring is a field as an example we compute explicitly the brauer group and lazy cohomology for modified supergroup algebras with extensions of weyl groups of irreducible root systems as a group datum and their standard representation as a representation datum

algebraic aspects of the quantum yang baxter equation in this paper we examine a variety of algebraic contexts in which the quantum yang baxter equation arises and derive methods for generating new solutions from given ones the solutions we describe are encoded in objects which have a module and a comodule structure over a bialgebra our work here is based in part on the ideas of dr1 dr2 suppose that r m m m m is a solution to the quantum yang baxter equation where m is a finite dimensional vector space over a field k in dr2 it was shown that r can be derived from a left h module structure and a right h comodule structure on m for some bialgebra h over k also see yet maj1 maj2 frt2 the module and comodule structure satisfy a natural compatibility condition m together with these structures is called a left quantum yang baxter h module every left quantum yang baxter module gives rise to a solution to the quantum yang baxter equation in a natural way we study the category hyb of left quantum yang baxter h modules and show that many of the familiar constructions in the module category hm can be made in hyb through these constructions solutions to the quantum yang baxter equation can be combined in various ways to generate new ones we place particular emphasis on the tensor product of objects of hyb and ways in which the tensor algebra t m of an object m of hyb can be viewed as an object of hyb using the tensor algebra we are able to extend certain solutions when dim m 2 to the quantum plane we turn the tensor algebra t m of an object m of hyb into an object of hyb by giving it a module algebra and a comodule algebra structure module algebra and comodule algebra structures play a very important role in this paper in section 9 we develop a calculus for uq sl2 starting with a right k slq 2 comodule algebra structure on the quantum plane k x y q where k slq 2 is the coordinate ring of quantum slq 2 over k this calculus has been described in other ways m s sud the right comodule algebra structure on k x y q accounts for the left uq sl2 module algebra structure on k x y q described in m s we show how the basic irreducible representations of tak follow by the calculus a module algebra action or comodule algebra action is a natural vehicle for extending structure on a submodule or subcomodule respectively to the subalgebra it generates the calculus and the solutions to the quantum yang baxter equation we describe in this paper are determined in this manner on small structures two dimensional in this case we believe that many more results will follow from this circle of ideas in section 2 we discuss basic aspects of coalgebra and bialgebras used in the sequel a good general reference for this is sweedler s book sb on hopf algebras in section 3 we review the quantum yang baxter equation in connection with quantum yang baxter modules the a r construction of faddeev reshetikhin and takhtajan frt is considered in this light and examined in detail in when r arises from two commuting operators even though this particular r is rather simple the algebra structure of a r is surprisingly complex using the scratchpad computer algebra system we determine the algebra structure of a r in an interesting specific case showing that our particular example has a finite non commutative groeb

generalized spectral decomposition for stochastic nonlinear problems we present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems the method consists in the construction of a reduced basis approximation of the galerkin solution and is independent of the stochastic discretization selected polynomial chaos stochastic multi element or multi wavelets two algorithms are proposed for the sequential construction of the successive generalized spectral modes they involve decoupled resolutions of a series of deterministic and low dimensional stochastic problems compared to the classical galerkin method the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes the methodology is detailed and tested on two model problems the one dimensional steady viscous burgers equation and a two dimensional nonlinear diffusion problem these examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space

the brauer group of a braided monoidal category representation theory of finite groups prompted the introduction of the brauer group of a field and also of its schur subgroups the theory of quadratic forms and spaces introduced the zr2z graded variant of the brauer group together with the typical clifford algebras and related w x representations cf the work of wall 29 the extension of the zr2zgraded theory to gradings by other cyclic groups and consequently to abelian groups replacing the usual clifford algebras by the so called generalized clifford algebras is then natural from the algebraic point of view however extension to nonabelian groups did not seem to be possible at least not by simple modifications of the abelian theory at the same time the generalization of the brauer group of graded algebras obtained w x by long 12 13 made use of hopf algebras but again cocommutativity conditions were present the recent interest in quantum groups motivated the authors to introduce the brauer group of a quantum group as the brauer group of crossed module algebras also called quantum yang w x baxter module algebras in 4 5 the use of the category of crossed w x modules originated in the case of group algebras cf whitehead 30 module algebras or coalgebras of this crossed type were introduced by w x radford in 24 and used by majid in the description of modules over drinfel d quantum doubles the noncocommutativity aspects of the theory concerning the brauer group in terms of crossed module algebras do not have a counterpart in classical theory note that a first unifying categorical theory has been w x obtained by pareigis in 23 this theory deals with the brauer group of a

a comparison of three methods for selecting values of input variables in the analysis of output from a computer code two types of sampling plans are examined as alternatives to simple random sampling in monte carlo studies these plans are shown to be improvements over simple random sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function

strain and stress computations in stochastic finite element methods this paper focuses on the computation of statistical moments of strains and stresses in a random system model where uncertainty is modeled by a stochastic finite element method based on the polynomial chaos expansion it identifies the cases where this objective can be achieved by analytical means using the orthogonality property of the chaos polynomials and those where it requires a numerical integration technique to this effect the applicability and efficiency of several numerical integration schemes are considered these include the gauss hermite quadrature with the direct tensor product also known as the kronecker product smolyak s approximation of such a tensor product monte carlo sampling and the latin hypercube sampling method an algorithm for reducing the dimensionality of integration under a direct tensor product is also explored for optimizing the computational cost and complexity the convergence rate and algorithmic complexity of all of these methods are discussed and illustrated with the non deterministic linear stress analysis of a plate copyright 2007 john wiley sons ltd

adaptive surrogate modeling by anova and sparse polynomial dimensional decomposition for global sensitivity analysis in fluid simulation the polynomial dimensional decomposition pdd is employed in this work for the global sensitivity analysis and uncertainty quantification uq of stochastic systems subject to a moderate to large number of input random variables due to the intimate connection between the pdd and the analysis of variance anova approaches pdd is able to provide a simpler and more direct evaluation of the sobol sensitivity indices when compared to the polynomial chaos expansion pc unfortunately the number of pdd terms grows exponentially with respect to the size of the input random vector which makes the computational cost of standard methods unaffordable for real engineering applications in order to address the problem of the curse of dimensionality this work proposes essentially variance based adaptive strategies aiming to build a cheap meta model i e surrogate model by employing the sparse pdd approach with its coefficients computed by regression three levels of adaptivity are carried out in this paper 1 the truncated dimensionality for anova component functions 2 the active dimension technique especially for second and higher order parameter interactions and 3 the stepwise regression approach designed to retain only the most influential polynomials in the pdd expansion during this adaptive procedure featuring stepwise regressions the surrogate model representation keeps containing few terms so that the cost to resolve repeatedly the linear systems of the least squares regression problem is negligible the size of the finally obtained sparse pdd representation is much smaller than the one of the full expansion since only significant terms are eventually retained consequently a much smaller number of calls to the deterministic model is required to compute the final pdd coefficients

ingredients for a general purpose stochastic finite elements implementation abstract the stochastic finite element method has seen a number of incarnations over the past few years ranging from perturbation based methods and neumann expansion based methods to methods for evaluating bounds on the response variability and more recent functional expansions combined with error minimization techniques of these only the last class of methods provides an explicit expression to the solution of the problem as opposed to evaluating a global norm of this solution and can thus be viewed as a rational extension of concepts developed for the deterministic finite element method the main obstacle in developing a substantial user community of various stochastic finite element methods has been the lack of a general purpose formalism for addressing issues of general engineering interest this paper presents the main ingredients for developing a general purpose version of the spectral stochastic finite element method

modeling uncertainty in flow simulations via generalized polynomial chaos we present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations the stochastic input is represented spectrally by employing orthogonal polynomial functionals from the askey scheme as trial basis to represent the random space a standard galerkin projection is applied in the random dimension to obtain the equations in the weak form the resulting system of deterministic equations is then solved with standard methods to obtain the solution for each random mode this approach can be considered as a generalization of the original polynomial chaos expansion first introduced by wiener am j math 60 1938 897 the original method employs the hermite polynomials one of the 13 members of the askey scheme as the basis in random space the algorithm is applied to micro channel flows with random wall boundary conditions and to external flows with random freestream efficiency and convergence are studied by comparing with exact solutions as well as numerical solutions obtained by monte carlo simulations it is shown that the generalized polynomial chaos method promises a substantial speed up compared with the monte carlo method the utilization of different type orthogonal polynomials from the askey scheme also provides a more efficient way to represent general non gaussian processes compared with the original wiener hermite expansions

an adaptive least squares global sensitivity method and application to a plasma coupled combustion prediction with parametric correlation abstract we introduce an efficient non intrusive surrogate based methodology for global sensitivity analysis and uncertainty quantification modified covariance based sensitivity indices mcov si are defined for outputs that reflect correlated effects the overall approach is applied to simulations of a complex plasma coupled combustion system with disparate uncertain parameters in sub models for chemical kinetics and a laser induced breakdown ignition seed the surrogate is based on an analysis of variance anova expansion such as widely used in statistics with orthogonal polynomials representing the anova subspaces and a polynomial dimensional decomposition pdd representing its multi dimensional components the coefficients of the pdd expansion are obtained using a least squares regression which both avoids the direct computation of high dimensional integrals and affords an attractive flexibility in choosing sampling points this facilitates importance sampling using a bayesian calibrated posterior distribution which is fast and thus particularly advantageous in common practical cases such as our large scale demonstration for which the asymptotic convergence properties of polynomial expansions cannot be realized due to computation expense effort instead is focused on efficient finite resolution sampling standard covariance based sensitivity indices cov si are employed to account for correlation of the uncertain parameters magnitude of cov si is unfortunately unbounded which can produce extremely large indices that limit their utility alternatively mcov si are then proposed in order to bound this magnitude 0 1 the polynomial expansion is coupled with an adaptive anova strategy to provide an accurate surrogate as the union of several low dimensional spaces avoiding the typical computational cost of a high dimensional expansion it is also adaptively simplified according to the relative contribution of the different polynomials to the total variance the approach is demonstrated for a laser induced turbulent combustion simulation model which includes parameters with correlated effects

nonuniform image motion estimation from noisy data image motion estimation is viewed as a problem in nonlinear demodulation the motion d x modulates the intensity of the previous frame s x to result in the intensity of the present frame s x d x an iterative algorithm based on the generalized maximum likelihood criterion is developed and implemented to demodulate d x an advantage of this scheme is the incorporation of the covariance function matrix which is specifically useful in the stationary case to determine the integration region alpha sub x simulation demonstrated the ability of the algorithm to deal with cases such as markov 2 motion

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

a polynomial dimensional decomposition for stochastic computing this article presents a new polynomial dimensional decomposition method for solving stochastic problems commonly encountered in engineering disciplines and applied sciences the method involves a hierarchical decomposition of a multivariate response function in terms of variables with increasing dimensions a broad range of orthonormal polynomial bases consistent with the probability measure for fourier polynomial expansion of component functions and an innovative dimension reduction integration for calculating the coefficients of the expansion the new decomposition method does not require sample points as in the previous version yet it generates a convergent sequence of lower variate estimates of the probabilistic characteristics of a generic stochastic response the results of five numerical examples indicate that the proposed decomposition method provides accurate convergent and computationally efficient estimates of the tail probability of random mathematical functions or the reliability of mechanical systems

relative yetter drinfeld modules and comodules over braided groups let h1 be a quantum group and f h1 h2 a hopf algebra homomorphism assume that b is some braided group obtained by majid s transmutation process we first show that there is a tensor equivalence between the category of comodules over the braided group b and that of relative yetter drinfeld modules next we prove that the drinfeld centers of the two categories mentioned above are equivalent to the category of modules over some quantum double namely the category of ordinary yetter drinfeld modules over some radford s biproduct hopf algebra importantly the above results not only hold for a finite dimensional quantum group but also for an infinite dimensional one

four dimensional yetter drinfeld module algebras over h4 abstract in this paper we classify four dimensional yetter drinfeld module algebras over sweedler s 4 dimensional hopf algebra h 4 all h 4 azumaya algebras of dimension 4 have been given in particular all yetter drinfeld h 4 module algebra structures on the matrix algebra m 2 k are classified

towards essential improvement for the parareal tr and parareal gauss4 algorithms parareal is an iterative algorithm and is characterized by two propagators g and f which are respectively associated with large step size t and small step size t where t j t and j 2 is an integer for symmetric positive definite spd system u t a u t g t arising from semi discretizing time dependent pdes if we fix the g propagator to the backward euler method and choose for f some l stable time integrator it can be proven that the convergence factors of the corresponding parareal algorithms satisfy 1 3 j 2 and a 0 where a is the spectrum of the matrix a however this result does not hold when time integrators that lack l stability such as the trapezoidal rule and the 4th order gauss rk method are chosen as the f propagator the parareal algorithms using these two methods for the f propagator are denoted by parareal tr and parareal gauss4 in this paper we propose a strategy to let these two parareal algorithms possess such a uniform convergence property the idea is to choose an l stable propagator f and on each coarse time interval t n t n 1 we perform first two steps of f then followed by j 2 steps of f precisely for the trapezoidal rule we select the 2nd order sdirk method as the f propagator and for the 4th order gauss rk method we select the 4th order lobatto iii c method as the f propagator numerical results are given to support our theoretical conclusions

recursive image registration with application to motion estimation an algorithm for real time recursive estimation of the two dimensional shift between successive images in an image sequence occurring e g in a down looking airborne tv sensor is presented the shift which is linearly related to ground velocity is adaptively tracked by means of the gradient of a similarity function relating the two successive images an implementation is presented in which substantial memory capacity and computational complexity are saved by using only a single line in the image frame and by binary quantization of the video signal a detailed analysis of the algorithm is presented using stochastic mathematical models for the terrain texture image noise and velocity variations under some simplifying assumptions closed form solutions for the error statistics including temporal power spectral density are derived the probability of loss of lock in tracking and the expected time for its reacquisition are evaluated and are found to be low at typical operating conditions the analysis also indicates considerable robustness of the algorithm to widely different image statistics numerical examples indicate very good performance in autonomous navigation applications

an exact maximum likelihood registration algorithm for data fusion data fusion is a process dealing with the association correlation and combination of data and information from multiple sources to achieve refined position and identity estimates we consider the registration problem which is a prerequisite process of a data fusion system to accurately estimate and correct systematic errors an exact maximum likelihood eml algorithm for registration is presented the algorithm is implemented using a recursive two step optimization that involves a modified gauss newton procedure to ensure fast convergence statistical performance of the algorithm is also investigated including its consistency and efficiency discussions in particular the explicit formulas for both the asymptotic covariance and the cramer rao bound crb are derived finally simulated and real life multiple radar data are used to evaluate the performance of the proposed algorithm

polynomial chaos expansion with latin hypercube sampling for estimating response variability a computationally efficient procedure for quantifying uncertainty and finding significant parameters of uncertainty models is presented to deal with the random nature of input parameters of structural models several efficient probabilistic methods are investigated specifically the polynomial chaos expansion with latin hypercube sampling is used to represent the response of an uncertain system latin hypercube sampling is employed for evaluating the generalized fourier coefficients of the polynomial chaos expansion because the key challenge in uncertainty analysis is to find the most significant components that drive response variability analysis of variance is employed to find the significant parameters of the approximation model several analytical examples and a large finite element model of a joined wing are used to verify the effectiveness of this procedure

weighted discrete least squares polynomial approximation using randomized quadratures we discuss the problem of polynomial approximation of multivariate functions using discrete least squares collocation the problem stems from uncertainty quantification uq where the independent variables of the functions are random variables with specified probability measure we propose to construct the least squares approximation on points randomly and uniformly sampled from tensor product gaussian quadrature points we analyze the stability properties of this method and prove that the method is asymptotically stable provided that the number of points scales linearly up to a logarithmic factor with the cardinality of the polynomial space specific results in both bounded and unbounded domains are obtained along with a convergence result for chebyshev measure numerical examples are provided to verify the theoretical results

comparative study of projection schemes for stochastic finite element analysis we present a comparison of subspace projection schemes for stochastic finite element analysis in terms of accuracy and computational efficiency more specifically we compare the polynomial chaos projection scheme with reduced basis projection schemes based on the preconditioned stochastic krylov subspace numerical studies are presented for two problems 1 static analysis of a plate with random young s modulus and 2 settlement of a foundation supported on a randomly heterogeneous soil monte carlo simulation results based on exact structural analysis are used to generate benchmark results against which the projection schemes are compared we show that stochastic reduced basis methods require significantly less computer memory and execution time compared to the polynomial chaos approach particularly for large scale problems with many random variables for the class of problems considered we find that stochastic reduced basis methods can be up to orders of magnitude faster while providing results of comparable or better accuracy

least squares polynomial chaos expansion a review of sampling strategies abstract as non intrusive polynomial chaos expansion pce techniques have gained growing popularity among researchers we here provide a comprehensive review of major sampling strategies for the least squares based pce traditional sampling methods such as monte carlo latin hypercube quasi monte carlo optimal design of experiments ode gaussian quadratures as well as more recent techniques such as coherence optimal and randomized quadratures are discussed we also propose a hybrid sampling method dubbed alphabetic coherence optimal that employs the so called alphabetic optimality criteria used in the context of ode in conjunction with coherence optimal samples a comparison between the empirical performance of the selected sampling methods applied to three numerical examples including high order pce s high dimensional problems and low oversampling ratios is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand we observed that the alphabetic coherence optimal technique outperforms other sampling methods specially when high order ode are employed and or the oversampling ratio is low

computational uncertainty analysis in multiresolution materials via stochastic constitutive theory abstract a stochastic constitutive theory is proposed in this work to propagate microstructure uncertainties in computational multiscale continuum models to bulk multiresolution material behavior ubiquitous fine resolution uncertainty sources influencing prediction of material properties based on their structures are categorized in detail and this research transmits these uncertainties to coarser material resolutions by introducing a stochastic constitutive theory deduced from volume element simulations to implement the stochastic upscaling process two advanced uncertainty quantification methods are examined statistical copula functions and random process polynomial chaos expansion both methods confront the mathematical difficulty in randomizing constitutive laws by capturing the marked correlation among constitutive parameters seen in complex materials thus the results proffer a more accurate probabilistic estimation of constitutive material behavior the contribution of this work is twofold uncertainty is propagated from heterogeneous material structure to material property via the stochastic constitutive theory and rigorous data driven mathematics are formalized to represent complicated dependence structures in multivariate statistical distributions to the authors knowledge this is the first work in multiresolution mechanics that presents an approach to computationally derive correlation functions from numerical experiments as opposed for instance to assuming one a priori the method put forth in this research though quite general is applied to a mathematical example and plastic high strength steel alloy for demonstration results include stochastic constitutive curve confidence intervals for the material stress strain response and qualitative comparisons of the two stochastic methods detailed herein

a maximum likelihood approach for image registration using control point and intensity registration of multidate or multisensor images is an essential process in many image processing applications including remote sensing medical image analysis and computer vision control point cp and intensity are the two basic features used separately for image registration in the literature in this paper an exact maximum likelihood eml registration method which combines both cp and intensity is proposed for image alignment the eml registration method maximizes the likelihood function based on cp and intensity to estimate the registration parameters including affine transformation and cp coordinates the explicit formulas of the cramer rao bound crb are also derived for the proposed eml and conventional image registration algorithms the performances of these image registration techniques are evaluated with the crbs

prediction of uncertain frequency response function bounds using polynomial chaos expansion a probabilistic method is developed to predict the uncertainty bounds on frequency response functions frfs developed from finite element models a non intrusive polynomial chaos expansion pce method is used to predict uncertainty regression models of the various parameters that make up a curvefit of the frf natural frequencies damping ratios complex amplitudes mass and stiffness residuals by making use of an efficient latin hypercube technique these uncertainty models are then combined to efficiently determine pdfs of the parameters and also the uncertainty bounds of the frfs the approach is demonstrated using two examples a simple beam containing uncertainty in young s modulus and a full scale aircraft composite wing model containing uncertainties in both young s modulus and the shear modulus the results were compared with monte carlo simulation mcs and it was found that the parameter pdfs and frf error bounds obtained using a 2nd order pce model agreed very well whilst requiring significantly less computation