complete discrete 2 d gabor transforms by neural networks for image analysis and compression a three layered neural network is described for transforming two dimensional discrete signals into generalized nonorthogonal 2 d gabor representations for image analysis segmentation and compression these transforms are conjoint spatial spectral representations which provide a complete image description in terms of locally windowed 2 d spectral coordinates embedded within global 2 d spatial coordinates in the present neural network approach based on interlaminar interactions involving two layers with fixed weights and one layer with adjustable weights the network finds coefficients for complete conjoint 2 d gabor transforms without restrictive conditions in wavelet expansions based on a biologically inspired log polar ensemble of dilations rotations and translations of a single underlying 2 d gabor wavelet template image compression is illustrated with ratios up to 20 1 also demonstrated is image segmentation based on the clustering of coefficients in the complete 2 d gabor transform

control of underactuated spacecraft with bounded inputs bounded feedback control laws are designed for stabilization and tracking of underactuated spacecraft the flat outputs of the system are computed and are used to generate reference trajectories for the tracking problem

isogeometric collocation neumann boundary conditions and contact abstract isogeometric collocation methods have been proposed recently and their accuracy and efficiency demonstrated for elastostatics and explicit dynamics this paper addresses two important aspects in the development of the isogeometric collocation technology namely the imposition of neumann boundary conditions and the enforcement of contact constraints which are both treated within the same framework it is shown that the strong imposition of neumann boundary conditions may lead to a significant loss of accuracy in some situations in particular when non uniform meshes are used two possible remedies are proposed to restore the desired level of accuracy while keeping the computational cost virtually unchanged i e a hybrid collocation galerkin approach and an enhanced collocation ec approach a frictionless contact formulation suitable for the collocation framework is further proposed and shown to pass the contact patch test to machine precision when combined with the ec approach the formulation is shown to deliver accurate results and to perform robustly also for highly non uniform meshes for all the collocation formulations contact pressures are greater than or equal to zero pointwise in contrast with standard lagrange finite elements

a fast learning algorithm for gabor transformation an adaptive learning approach for the computation of the coefficients of the generalized nonorthogonal 2 d gabor 1946 transform representation is introduced the algorithm uses a recursive least squares rls type algorithm the aim is to achieve minimum mean squared error for the reconstructed image from the set of the gabor coefficients the proposed rls learning offers better accuracy and faster convergence behavior when compared with the least mean squares lms based algorithms applications of this scheme in image data reduction are also demonstrated

the impact of surface higher order differentiability in two dimensional contact elements the aim of this work is to propose new contact elements of higher order of differentiability for analysing two dimensional frictionless contact problems several methods were proposed in the literature to solve the problem caused by the lack of continuity resulting from the discretization among them are bezier interpolation hermitian interpolation and splines one of the difficulties in using hermitian interpolation is to verify the partition of unity therefore new elements that satisfy the c 1 and c 2 continuity at the interface are presented in this paper these new contact elements are based on hermitian polynomials for ensuring a higher order of continuity the advantage is that this approach can be easily developed not only for linear elements but also for quadratic elements with higher order of differentiability the performance of different surface representations is assessed through a comparison with a c 0 surface discretization some numerical examples are used for assessing the accuracy and the convergence behaviour

the node to segment algorithm for 2d frictionless contact classical formulation and special cases the so called node to segment nts algorithm is probably the most widely used discretization technique for large deformation contact between surfaces with non matching meshes despite the classical nts contact element has been available in the literature for a long time its detailed description appears to be currently disseminated in several papers moreover the classical nts formulation presents some limitations which are well known but have been the subject of limited investigations in particular the algorithm presents severe problems in dealing with some special cases in which the identification of the master segment related to a slave node is either ambiguous or impossible the objectives of this paper are to provide a careful review of the classical formulation and to propose new techniques for the treatment of the aforementioned special cases the paper is composed of three parts in the first one the classical formulation of the nts algorithm in two dimensions and in the frictionless case is reviewed in detail the main geometric relationships are presented and the contact contributions to the stiffness matrix and to the residual vector are derived the second part is devoted to the treatment of the special cases some algorithms specially developed to deal with such cases are illustrated finally the third part presents some numerical examples which show the effectiveness of the proposed algorithms

algorithms for the analysis of 3d finite strain contact problems from the constraint imposition aspects in 3d to friction regularization various ideas are exposed in this paper a variation of the rockafellar lagrangian is proposed which results in continuous second order derivatives if lagrange multiplier estimates are greater or equal than one this fact allows the adoption of a full second order i e lagrange newton method avoiding sequential unconstrained minimization techniques an algorithm for global and local contact detection is presented which is developed for dealing with large step sizes typical of implicit methods a modified constraint definition to deal with non smooth situations is presented aspects of friction implementation including a regularization scheme which ensures stepwise objectivity are detailed finally several illustrative examples are carried out with success

a modified node to segment algorithm passing the contact patch test summary several investigations have shown that the classical one pass node to segment nts algorithms for the enforcement of contact constraints fail the contact patch test this implies that the algorithms may introduce solution errors at the contacting surfaces and these errors do not necessarily decrease with mesh refinement the previous research has mainly focused on the lagrange multiplier method to exactly enforce the contact geometry conditions the situation is even worse with the penalty method due to its inherent approximation that yields a solution affected by a non zero penetration the aim of this study is to analyze and improve the contact patch test behavior of the one pass nts algorithm used in conjunction with the penalty method for 2d frictionless contact the paper deals with the case of linear elements for this purpose several sequential modifications of the basic formulation have been considered which yield incremental improvements in results of the contact patch test the final proposed formulation is a modified one pass nts algorithm which is able to pass the contact patch test also if used in conjunction with the penalty method in other words this algorithm is able to correctly reproduce the transfer of a constant contact pressure with a constant proportional penetration copyright q 2009 john wiley sons ltd

a point to segment contact formulation for isogeometric nurbs based finite elements formulation of isogeometric finite elements has received a great deal of attention in the recent past the present study deals with the treatment of problems in structural mechanics including large elastic deformations and contact one decisive difference between isogeometric finite elements based on nurbs functions and standard finite elements fe based on lagrange polynomials is higher inter element continuity this is a promising characteristics to model contact problems as all issues associated with kinks between elements are naturally avoided particularly in cases with large sliding this has the potential to be an attractive feature we present a bilateral isogeometric collocation contact formulation for geometrically non linear two dimensional problems using greville and botella points to collocate the contact integrals different methods to obtain accurate and physically meaningful stress distributions are investigated and compared the results show that the higher inter element continuity in context of non smooth problems may imply undesired effects in the numerical solution such as unphysical stress oscillations similar effects have been observed in standard p fem numerical experiments indicate that these oscillations may be avoided if the basis functions of contact and non contact zones are separated by knot relocation and knot repetition

adaptive gabor transformation for image processing an algorithm that computes the gabor coefficients of an image is presented an adaptive filter that uses the complex least mean square algorithm for their computation is proposed and its numerical characteristics are discussed it is shown that the filter is stable under certain conditions because the gabor transformation seems to be an excellent tool for image compression the efficiency of information coding using the gabor coefficients is investigated and compared with coding that uses the coefficients of the discrete cosine transformation dct properties of both transformations are discussed

a new computational approach to contact mechanics using variable node finite elements in this paper a new computational strategy for two dimensional contact problems is developed with the aid of variable node finite elements within the range of infinitesimal deformations the variable node elements which are among mls moving least square based finite elements enable us to transform node to surface contact problems into node to node contact problems this contact formulation with variable node elements leads to an accurate and effective solution procedure needless to mention that the contact patch test is passed without any additional treatment through several numerical examples we demonstrate its simplicity and the effectiveness of the proposed scheme

multirate based fast parallel algorithms for 2 d dht based real valued discrete gabor transform novel algorithms for the multirate and fast parallel implementation of the 2 d discrete hartley transform dht based real valued discrete gabor transform rdgt and its inverse transform are presented in this paper a 2 d multirate based analysis convolver bank is designed for the 2 d rdgt and a 2 d multirate based synthesis convolver bank is designed for the 2 d inverse rdgt the parallel channels in each of the two convolver banks have a unified structure and can apply the 2 d fast dht algorithm to speed up their computations the computational complexity of each parallel channel is low and is independent of the gabor oversampling rate all the 2 d rdgt coefficients of an image are computed in parallel during the analysis process and can be reconstructed in parallel during the synthesis process the computational complexity and time of the proposed parallel algorithms are analyzed and compared with those of the existing fastest algorithms for 2 d discrete gabor transforms the results indicate that the proposed algorithms are the fastest which make them attractive for real time image processing

attitude control without angular velocity measurement a passivity approach it is well known that the linear feedback of the quaternion of the attitude error and the angular velocity globally stabilizes the attitude of a rigid body in this note we show that the angular velocity feedback can be replaced by a nonlinear filter of the quaternion thus removing the need for direct angular velocity measurement in contrast to other approaches this design exploits the inherent passivity of the system a model based observer reconstructing the velocity is not needed an application of the proposed scheme is illustrated for the robot control problem simulation results are included to illustrate the theoretical results

n dimensional controllability with n 1 controls let m be a connected real analytic n dimensional manifold f g 1 g n 1 be complete real analytic vector fields on m which are linearly independent at some point of m and u 1 u n 1 be real valued controls consider the controllability of the system dot x t f x t sum min i 1 max n 1 u i t g i x t x 0 x 0 in m necessary and sufficient conditions are given so that this system is controllable on any simply connected domain d contained in m on which g 1 g n 1 are linearly independent these conditions depend on the computation of lie brackets at those points where f g 1 g n 1 are linearly dependent

exact nonlinear control of large angle rotational maneuvers the rigid body attitude control problem with external torques is transformed into an equivalent linear form implementable by three double integrators the linearizing transformations themselves are formulated in vector algebra requiring no integrators for implementation it is thereby shown that optimal command generation for fast slewing maneuvers can be carried out exactly in the transformed system together with regulator design without gain scheduling for correction of unmodeled disturbances in particular a general rest to rest maneuver is computed in closed form and coupled with a previously obtained exact detumbling maneuver so that arbitrary initial conditions can be accommodated an illustrative simulation is appended

convergence analysis of lms filters with uncorrelated gaussian data statistical analysis of the least mean squares lms adaptive algorithm with uncorrelated gaussian data is presented exact analytical expressions for the steady state mean square error mse and the performance degradation due to weight vector misadjustment are derived necessary and sufficient conditions for the convergence of the algorithm to the optimal wiener solution within a finite variance are derived it is found that the adaptive coefficient which controls the rate of convergence of the algorithm must be restricted to an interval significantly smaller than the domain commonly stated in the literature the outcome of this paper therefore places fundamental limitations on the mse performance and rate of convergence of the lms adaptive scheme

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

isogeometric collocation for large deformation elasticity and frictional contact problems abstract isogeometric collocation methods have been recently proposed as an alternative to standard galerkin approaches as they provide a significant reduction in computational cost for higher order discretizations in this work we explore the application of isogeometric collocation to large deformation elasticity and frictional contact problems we first derive the non linear governing equations for the elasticity problem with finite deformation kinematics and provide details on their consistent linearization some numerical examples demonstrate the performance of collocation in its basic and enhanced versions differing by the enforcement of neumann boundary conditions for problems with strong singularities enhanced collocation is shown to outperform basic collocation and to lead to a spatial convergence behavior very similar to galerkin whereas for weaker or no singularities enhanced and basic collocation may give very similar results a large deformation contact formulation is subsequently developed and tested in the frictional setting where collocation confirms the excellent performance already obtained for the frictionless case finally it is shown that the contact formulation in the collocation framework passes the contact patch test to machine precision in a three dimensional setting with arbitrarily inclined non matching discretizations thus outperforming most of the available contact formulations and all those with pointwise enforcement of the contact constraints

a computational contact formulation based on surface potentials this work presents the theory and numerical implementation of a contact formulation based on surface potentials the new theory formulates contact based on distance dependent surface interaction potentials and distinguishes between three interaction classes point interaction short range surface interaction and long range surface interaction here the focus is placed on frictionless contact although the first class readily admits frictional sticking contact as is also shown the proposed contact theory provides a unified framework for various contact formulations ranging from numerical constraint formulations like penalty barrier cross constrained and augmented lagrange multiplier methods to physical interaction formulations like cohesive zone models as well as electrostatic gravitational and van der waals interaction apart from recovering classical penalty and barrier formulations the new theory also naturally leads to a modified penalty and barrier method the formulation also recovers classical one pass contact algorithms however the real advantages lie in a novel two pass contact algorithm denoted the two half pass contact algorithm since each pass only accounts for the contact forces acting on the slave body this implies that traction continuity is only satisfied in theory but not imposed a priori in the algorithm instead it is obtained naturally to high accuracy as is demonstrated by several 2d and 3d numerical examples these include sliding contact peeling contact and electrostatic attraction between deformable solids among the examples is a detailed comparison between the new formulation and classical one pass approaches it is further shown that the new contact formulation passes the contact patch test

geometrically exact theory for contact interactions of 1d manifolds algorithmic implementation with various finite element models abstract the intuitive understanding of contact between bodies is based on the geometry of adjoining bodies a more sophisticated approach of an advanced analysis including the application of various numerical methods is to take advantage of the geometry of an analyzed object and describe the problem in the best coordinate system the best coordinate system to describe contact interaction in all its geometrical details is a coordinate system attached to the geometrical features of contacting bodies this leads to a systematical analysis of geometrical situations leading to contact pairs surface to surface line to surface point to surface line to line point to line each contact pair is inherited with a special coordinate system based on its geometrical properties the current contribution is concentrating on contact between 1d manifolds in 3d space this is the majority of edge to edge beam to beam cable to edge etc contact cases the geometrically exact curve to curve contact approach is then systematically combined together with various finite element approaches classical finite elements isogeometric beam finite elements and also with a new developed solid beam approach examples illustrating the diversity of various finite element combinations e g within knot mechanics are shown

volumetric coupling approaches for multiphysics simulations on non matching meshes summary in finite element analysis of volume coupled multiphysics different meshes for the involved physical fields are often highly desirable in terms of solution accuracy and computational costs we present a general methodology for volumetric coupling of different meshes within a monolithic solution scheme a straightforward collocation approach is compared to a mortar based method for nodal information transfer for the latter dual shape functions based on the biorthogonality concept are used to build the projection matrices thus further reducing the evaluation costs we give a detailed explanation of the integration scheme and the construction of dual shape functions for general first order and second order langrangian finite elements within the mortar method as well as an analysis of the conservation properties of the projection operators moreover possible incompatibilities due to different geometric approximations of curved boundaries are discussed numerical examples demonstrate the flexibility of the presented mortar approach for arbitrary finite element combinations in two and three dimensions and its applicability to different multiphysics coupling scenarios copyright 2016 john wiley sons ltd

linearization of attitude control error dynamics some useful properties of direction cosine and quaternion attitude formulations that include specification of attitude error and the inversion of rigid body rotational dynamics are reviewed the inversion procedure is then applied to a measure of attitude error to realize a new model follower control system that exhibits linear attitude error dynamics error analyses and simulation results for spacecraft attitude control systems are presented to demonstrate the more robust performance obtainable from an exact linear error formulation over that obtained from either direction cosine or quaternion formulations with simple linear feedback control laws

node to node scheme for three dimensional contact mechanics using polyhedral type variable node elements abstract a node to node contact scheme which is applicable for three dimensional contact analyses involving large deformations is developed with the aid of polyhedral elements the key issue is to transform nonmatching meshes into matching meshes in a seamless manner because polyhedral elements are allowed to have arbitrary numbers of polygonal faces and nodes they can be used as transition elements for coupling nonmatching meshes in this paper the polyhedral elements make it possible to always maintain node to node contact during the contact deformation the present approach guarantees that the patch test is passed and the nonpenetration condition is satisfied and hence it yields smoother contact pressure with faster convergence than the conventional node to surface or surface to surface contact scheme

a simple algorithm for localized construction of non matching structural interfaces a simple and effective algorithm for the modular construction of non matched interfaces is presented for the partitioned solution of large scale structural problems the formulation is based on a recently developed four field variational principle which introduces a connection frame between the interfaced partitions a key result of the present study is a frame nodal placement criterion that uniquely determines the frame discretization into piecewise linear elements so that the interface patch test condition is satisfied a priori the method is demonstrated with several 2d and 3d example problems

isogeometric large deformation frictionless contact using t splines t spline based isogeometric analysis is applied to frictionless contact problems between deformable bodies in the context of large deformations the continuum is discretized with cubic t splines and cubic nurbs a gauss point to surface formulation is combined with the penalty method to treat the contact constraints in the discretized setting it is demonstrated that analysis suitable t splines coupled with local refinement accurately approximate contact pressures with far fewer degrees of freedom than nurbs both two and three dimensional examples are presented additionally all t spline analysis models are generated using commercially available t spline modeling software without intermediate mesh generation or geometry clean up steps