an exact finite rotation shell theory its mixed variational formulation and its finite element implementation a non linear shell theory including transverse shear strains with exact description of the kinematical fields is developed the strain measures are derived via the polar decomposition theorem allowing for an explicit use of a three parametric rotation tensor thus in plane rotations also called drilling degrees of freedom are included in a natural way various alternatives of the theory are derived for a special version of the theory with altogether six kinematical fields different mixed variational principles are given a hybrid finite element formulation which does not exhibit locking phenomena is developed numerical examples of shell deformation at finite rotations with excellent element performance are presented comparison with results reported in the literature demonstrates the features of the theory as well as the proposed finite element formulation

moving horizon state estimation for nonlinear systems using neural networks moving horizon mh state estimation is addressed for nonlinear discrete time systems affected by bounded noises acting on system and measurement equations by minimizing a sliding window least squares cost function such a problem is solved by searching for suboptimal solutions for which a certain error is allowed in the minimization of the cost function nonlinear parameterized approximating functions such as feedforward neural networks are employed for the purpose of design thanks to the offline optimization of the parameters the resulting mh estimation scheme requires a reduced online computational effort simulation results are presented to show the effectiveness of the proposed approach in comparison with other estimation techniques

wall pressure and shear stress spectra from direct simulations of channel flow wall pressure and shear stress spectra from direct numerical simulations of turbulent plane channel flow are presented in this paper simulations have been carried out at a series of reynolds numbers up to re 1440 which corresponds to re 6 92 x 10 4 based on channel width and centerline velocity single point and two point statistics for velocity pressure and their derivatives have been collected including velocity moments up to fourth order the results have been used to study the reynolds number dependence of wall pressure and shear stress spectra it is found that the point spectrum of wall pressure collapses for re 360 under a mixed scaling for frequencies lower than the peak frequency of the frequency weighted spectrum and under viscous scaling for frequencies higher than the peak point spectra of wall shear stress components are found to collapse for re 360 under viscous scaling the normalized mean square wall pressure increases linearly with the logarithm of reynolds number the rms wall shear stresses also increase with reynolds number over the present range but suggest some leveling off at high reynolds number

finite surface discretization for incompressible navier stokes equations and coupled conservation laws abstract we present a new finite surface discretization fsd aiming at the incompressible navier stokes equations nse and other coupled conservation laws this discretization defines the velocities as surfaced averaged values living on the faces of the pressure volumes in which the mass is set to be conserved consequently the calculation of the mass balance on these control volumes is exact which allows more accurate information to be kept in the velocity field and produces a very accurate prediction of the pressure in the next time step the proposed discretization reduces the stencil size of the poisson equation in the projection method compared to the finite volume and finite difference discretizations due to highly accurate mass conservation the compact sixth order approximation of fsd can be used with an explicit fourth order pressure treatment this property greatly reduces the cost and complexity of the implementation we present the discrete evolution equation of the surface averaged velocities together with the enforcement of mass conservation and the solution procedure for the pressure the approximation of the nse under this new discretization uses a combination of finite difference and finite volume methods the proposed method is validated using standard laminar test cases we identify the conditions under which a fourth order pressure treatment can support the sixth order and eighth order approximations of the convection term using fourier analysis the performance of the method is evaluated on turbulent channel flows up to friction reynolds number of 950 the quantitative relationships between the accuracy of the solution and grid size are identified we present two performance indices for comparison with other methods at the error level of 1 per mille the proposed method is 28 times faster than the classic second order scheme

on a stress resultant geometrically exact shell model part vii shell intersections with dof finite element formulations abstract if the mid surface of a shell is smooth the classical theory describes the orientation of the director field attached to the mid surface by two independent rotational degrees of freedom at a shell intersection where this smoothness assumption no longer holds it is shown that the director field in the full nonlinear continuum shell equations must be necessarily described by three degrees of freedom this added degree of freedom however is totally unrelated to the so called drill rotation widely used as a means of tackling the shell intersection problem a computational procedure involving a trivial modification of the global singularity free update procedure described in part iii of this work is described which completely resolves the shell intersection problem without introducing drill springs or related ad hoc devices the proposed approach leaves unchanged standard finite element formulations in terms of 5 dof node affects only the global update formulae and exhibits excellent performance as illustrated by representative numerical simulations

gaussian particle filtering sequential bayesian estimation for nonlinear dynamic state space models involves recursive estimation of filtering and predictive distributions of unobserved time varying signals based on noisy observations this paper introduces a new filter called the gaussian particle filter it is based on the particle filtering concept and it approximates the posterior distributions by single gaussians similar to gaussian filters like the extended kalman filter and its variants it is shown that under the gaussianity assumption the gaussian particle filter is asymptotically optimal in the number of particles and hence has much improved performance and versatility over other gaussian filters especially when nontrivial nonlinearities are present simulation results are presented to demonstrate the versatility and improved performance of the gaussian particle filter over conventional gaussian filters and the lower complexity than known particle filters

iterated posterior linearization smoother this note considers the problem of bayesian smoothing in nonlinear state space models with additive noise using gaussian approximations sigma point approximations to the general gaussian rauch tung striebel smoother are widely used methods to tackle this problem these algorithms perform statistical linear regression slr of the nonlinear functions considering only the previous measurements we argue that slr should be done taking all measurements into account we propose the iterated posterior linearization smoother ipls which is an iterated algorithm that performs slr of the nonlinear functions with respect to the current posterior approximation the algorithm is demonstrated to outperform conventional gaussian nonlinear smoothers in two numerical examples

a numerical integration perspective on gaussian filters this paper proposes a numerical integration perspective on the gaussian filters a gaussian filter is approximation of the bayesian inference with the gaussian posterior probability density assumption being valid there exists a variation of gaussian filters in the literature that derived themselves from very different backgrounds from the numerical integration viewpoint various versions of gaussian filters are only distinctive from each other in their specific treatments of approximating the multiple statistical integrations a common base is provided for the first time to analyze and compare gaussian filters with respect to accuracy efficiency and stability factor this study is expected to facilitate the selection of appropriate gaussian filters in practice and to help design more efficient filters by employing better numerical integration methods

series expansion approximations of brownian motion for non linear kalman filtering of diffusion processes in this paper we describe a novel application of sigma point methods to continuous discrete filtering the nonlinear continuous discrete filtering problem is often computationally intractable to solve assumed density filtering methods attempt to match statistics of the filtering distribution to some set of more tractable probability distributions filters such as these are usually decompose the problem into two sub problems the first of these is a prediction step in which one uses the known dynamics of the signal to predict its state at time tk 1 given observations up to time tk in the second step one updates the prediction upon arrival of the observation at time tk 1 the aim of this paper is to describe a novel method that improves the prediction step we decompose the brownian motion driving the signal in a generalised fourier series which is truncated after a number of terms this approximation to brownian motion can be described using a relatively small number of fourier coefficients and allows us to compute statistics of the filtering distribution with a single application of a sigma point method assumed density filters that exist in the literature usually rely on discretisation of the signal dynamics followed by iterated application of a sigma point transform or a limiting case thereof iterating the transform in this manner can lead to loss of information about the filtering distribution in highly non linear settings we demonstrate that our method is better equipped to cope with such problems

a third order multistep time discretization for a chebyshev tau spectral method a time discretization scheme based on the third order backward difference formula has been embedded into a chebyshev tau spectral method for the navier stokes equations the time discretization is a variant of the second order backward scheme proposed by krasnov et al 2008 3 high resolution direct numerical simulations of turbulent incompressible channel flow have been performed to compare the backward scheme to the runge kutta scheme proposed by spalart et al 1991 2 it is shown that the runge kutta scheme leads to a poor convergence of some third order spatial derivatives in the direct vicinity of the wall derivatives that represent the diffusion of wall tangential vorticity the convergence at the wall is shown to be significantly improved if the backward scheme is applied

gaussian filters for nonlinear filtering problems we develop and analyze real time and accurate filters for nonlinear filtering problems based on the gaussian distributions we present the systematic formulation of gaussian filters and develop efficient and accurate numerical integration of the optimal filter we also discuss the mixed gaussian filters in which the conditional probability density is approximated by the sum of gaussian distributions a new update rule of weights for gaussian sum filters is proposed our numerical tests demonstrate that new filters significantly improve the extended kalman filter with no additional cost and the new gaussian sum filter has a nearly optimal performance

evidence of nonlogarithmic behavior of turbulent channel and pipe flow employing data of peak position and peak values of reynolds shear stress provided by canonical channel flow direct numerical simulations and pipe and channel flow experiments three recent theories predicting the mean velocity profile of wall bounded turbulent flows are compared based on that analysis it is verified that the mean velocity profile of such internal flows is logarithmic only to leading order and that the higher order terms are proportional to reciprocal powers of the karman number this finding clearly indicates that higher order effects with respect to the karman number and the wall normal coordinate must be considered furthermore our results show that even the statistics of the flow region closest to the wall are affected by flow phenomena that scale with outer variables

the character of the turbulent wall pressure spectrum at subconvective wavenumbers and a suggested comprehensive model the likely character of the wavevector frequency spectrum of turbulent wall pressure on a smooth rigid plane is reexamined also modeling is extended for low mach numbers to the acoustic wavenumber domain from the relation of the wavevector frequency amplitude of wall pressure to amplitudes of fluctuating vorticity related velocity products reynolds stresses regarded as its sources the dependence of the wall pressure spectrum at subconvective wavenumbers is seen to depend essentially on the rate of decrease of the source cross spectra with wall distance y and on the identity of the wavenumber coefficient e g v or 1 that scales this profile a model wall pressure spectrum proposed earlier is generalized with respect to this rate of decrease and found to permit a range of possible dependences between k0 and k2 in that part of the subconvective domain where k 1 if a contribution to the source spectrum exists that is roughly independent of wall distance for v y k 1 it may dominate the wall pressure in the subconvective range and lead for k 1 to wavenumber independence of the spectrum in accord with the martin leehey wind tunnel measurement a comprehensive trial model for the wall pressure spectrum based on source models yielding this character is proposed and viewed as potentially satisfactory in all wavenumber domains from the acoustic to the convective for c k 1 it varies as k2 as follows for any source spectral profile that decreases at least as y 4 for y and accords with the phillips kraichnan theorem

skew t filter and smoother with improved covariance matrix approximation filtering and smoothing algorithms for linear discrete time state space models with skew t distributed measurement noise are proposed the algorithms use a variational bayes based posterior approximation with coupled location and skewness variables to reduce the error caused by the variational approximation although the variational update is done suboptimally using an expectation propagation algorithm our simulations show that the proposed method gives a more accurate approximation of the posterior covariance matrix than an earlier proposed variational algorithm consequently the novel filter and smoother outperform the earlier proposed robust filter and smoother and other existing low complexity alternatives in accuracy and speed we present both simulations and tests based on real world navigation data in particular the global positioning system data in an urban area to demonstrate the performance of the novel methods moreover the extension of the proposed algorithms to cover the case where the distribution of the measurement noise is multivariate skew t is outlined finally this paper presents a study of theoretical performance bounds for the proposed algorithms

probability distribution functions and coherent structures in a turbulent channel with the aid of a direct numerical simulation of an incompressible plane turbulent channel at h 162 we have determined the probability distribution functions pdf s of pressure and of the various velocity components from the wall to the channel center the pressure turns out to be symmetric with exponential tails at the wall as well as at y 2 5 at y 12 where the streamwise streaks intensity is maximum the pressure has become asymmetric this character intensifies with the distance away from the wall and the distribution obtained in the channel center resembles those determined in isotropic turbulence and free shear flows very close to the wall y 2 5 the pdf of u ensuremath is highly skewed with exponential and sub gaussian distributions at high and low values respectively this indicates that the high speed streaks are very intermittent at the wall the reverse occurs close to the channel center where intense negative u ensuremath prevail then we show that the most probable orientation of the fluctuating vorticity vector is perpendicular to the wall in the region 5l y l30 which is basically in the low and high speed regions while it is 45 ifmmode circ else textdegree fi with respect to the wall above

semi implicit runge kutta schemes development and application to compressible channel flow time stepconstraintdueto thefine meshnear thewall the explicitsubschemeis asix stage fourth order low storage runge kutta scheme based on analysis in fourier space and results obtained for propagation test cases the semiimplicitschemesareshowntobeoforder3and forwavesdiscretizedbyanumberofpointsperperiodbetween4and 16 tobeasaccurateas ormoreaccuratethan thestandardexplicitfourth orderrunge kuttaalgorithmintermsof dissipationanddispersion thelarge eddysimulationofacompressibleturbulentchannelflowatafrictionreynolds numberof360andamachnumberof0 1isthencarriedoutwithoneoftheproposedalgorithms thecomputational time is reduced by a factor 1 33 with respect to a large eddy simulation using the explicit subscheme in all directions wall pressure and velocity spectra from the large eddy simulation are presented to give insights into the flow turbulent structures in particular wave number frequency spectra are calculated acoustic components appear to be identified in these spectra

gaussian smoothers for nonlinear systems with one step randomly delayed measurements this technical note is concerned with the nonlinear state smoothing problem in the case that the measurements are randomly delayed by one sampling time under gaussian domain two general gaussian approximation ga and gaussian mixture approximation gma smoothers are proposed in minimum mean square error mmse sense the smoothing implementation is transformed into computing some special posterior covariances which triggers the development of the new unscented kalman smoother uks by applying unscented transformation ut simulation results demonstrate the superior performance of the proposed ga uks and gma uks algorithms

on gaussian optimal smoothing of non linear state space models in this note we shall present a new gaussian approximation based framework for approximate optimal smoothing of non linear stochastic state space models the approximation framework can be used for efficiently solving non linear fixed interval fixed point and fixed lag optimal smoothing problems we shall also numerically compare accuracies of approximations which are based on taylor series expansion unscented transformation central differences and gauss hermite quadrature

surface pressure fluctuations beneath two and three dimensional turbulent boundary layers surface pressure fluctuation measurements were made in two dimensional turbulent boundary layers at two reynolds numbers re 7 3 10 3 and 2 34 104 and pressure driven three dimensional turbulent boundary layers at two reynolds numbers approach re 5 94 x 10 3 and 2 32 104 the collapse of spectral levels at middle and high frequencies and the effects of inner and outer boundary layer scaling variables are shown for a wide range of reynolds numbers 1 4 x 10 3 2 34 104 for the two dimensional flows such scaling parameters do not collapse the pressure spectra beneath three dimensional flows which have a nearly constant or flat midfrequency range and at some measurement stations and spectral levels within the flat and high frequency spectral ranges that significantly raise p additionally dimensional spectral levels within the flat frequency range are independent of reynolds number analysis based on the poisson equation shows that the variation of the high frequency spectral levels is related to the variation in near wall mean velocity gradients and 2 structure due to the spanwise pressure gradient

an investigation of a finite rotation four node assumed strain shell element the paper presents a shell formulation based on the degenerated solid approach the theory employs covariant strains and performs explicit integration through the shell thickness the rigid body motion is exactly represented the consistent tangent stiffness matrix is evaluated for the four node quadrilateral it is shown in the final part that this type of element which distinguishes itself by a very simple and easily understandable theory gives good answers for linear as well as non linear applications

compact fourth order finite volume method for numerical solutions of navier stokes equations on staggered grids the development of a compact fourth order finite volume method for solutions of the navier stokes equations on staggered grids is presented a special attention is given to the conservation laws on momentum control volumes a higher order divergence free interpolation for convective velocities is developed which ensures a perfect conservation of mass and momentum on momentum control volumes three forms of the nonlinear correction for staggered grids are proposed and studied the accuracy of each approximation is assessed comparatively in fourier space the importance of higher order approximations of pressure is discussed and numerically demonstrated fourth order accuracy of the complete scheme is illustrated by the doubly periodic shear layer and the instability of plane channel flow the efficiency of the scheme is demonstrated by a grid dependency study of turbulent channel flows by means of direct numerical simulations the proposed scheme is highly accurate and efficient at the same level of accuracy the fourth order scheme can be ten times faster than the second order counterpart this gain in efficiency can be spent on a higher resolution for more accurate solutions at a lower cost

nonlinear gaussian smoothers with colored measurement noise this paper is concerned with the gaussian approximation ga smoothing estimation for the nonlinear system with the colored measurement noise modeled as an autoregressive process firstly based on measurement differencing scheme designing the ga smoothers with the colored measurement noise is transformed into deriving the ga ones with delayed state secondly the novel fixed interval fixed point and fixed lag ga smoothers are proposed via the recursive operation of analytical computation and nonlinear integrals as the general and unifying frameworks they are applicable for both linear and nonlinear systems by setting the noise correlation parameter as zero they can automatically reduce to the standard ga smoothers with uncorrelated white noises many implementations of the ga frameworks can be developed through utilizing different numerical technologies for computing such nonlinear integrals e g the cubature rule based cubature kalman smoothers ckss with the colored measurement noise finally the superior performance in estimation accuracy and computation efficiency of the proposed smoothing methods is demonstrated with a multi sensor target tracking example

unscented rauch tung striebel smoother this note considers the application of the unscented transform to optimal smoothing of nonlinear state space models in this note a new rauch tung striebel type form of the fixed interval unscented kalman smoother is derived the new smoother differs from the previously proposed two filter formulation based unscented kalman smoother in the sense that it is not based on running two independent filters forward and backward in time instead a separate backward smoothing pass is used which recursively computes corrections to the forward filtering result the smoother equations are derived as approximations to the formal bayesian optimal smoothing equations the performance of the new smoother is demonstrated with a simulation

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

cubature kalman smoothers the cubature kalman filter ckf is a relatively new addition to derivative free approximate bayesian filters built under the gaussian assumption this paper extends the ckf theory to address nonlinear smoothing problems the resulting state estimator is named the fixed interval cubature kalman smoother fi cks moreover the fi cks is reformulated to propagate the square root error covariances although algebraically equivalent to the fi cks the square root variant ensures reliable implementation when committed to embedded systems with fixed precision or when the inference problem itself is ill conditioned finally to validate the formulation the square root fi cks is applied to track a ballistic target on reentry

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

cubature kalman filters in this paper we present a new nonlinear filter for high dimensional state estimation which we have named the cubature kalman filter ckf the heart of the ckf is a spherical radial cubature rule which makes it possible to numerically compute multivariate moment integrals encountered in the nonlinear bayesian filter specifically we derive a third degree spherical radial cubature rule that provides a set of cubature points scaling linearly with the state vector dimension the ckf may therefore provide a systematic solution for high dimensional nonlinear filtering problems the paper also includes the derivation of a square root version of the ckf for improved numerical stability the ckf is tested experimentally in two nonlinear state estimation problems in the first problem the proposed cubature rule is used to compute the second order statistics of a nonlinearly transformed gaussian random variable the second problem addresses the use of the ckf for tracking a maneuvering aircraft the results of both experiments demonstrate the improved performance of the ckf over conventional nonlinear filters

on a stress resultant geometrically exact shell model part vi conserving algorithms for non linear dynamics in parts i to v of the present work the formulation and finite element implementation of a non linear stress resultant shell model are considered in detail this paper is concerned with the extension of these results to incorporate completely general non linear dynamic response of special interest here is the dynamics of very flexible shells undergoing large overall motion which conserves the total linear and angular momentum and for the hamiltonian case the total energy a main goal of this paper is the design of non linear time stepping algorithms and the construction of finite element interpolations which preserve exactly these fundamental constants of motion it is shown that only a very special class of algorithms namely a formulation of the mid point rule in conservation form exactly preserves the total linear and angular momentum for the hamiltonian case a somewhat surprising result is proved regardless of the degree of non linearity in the stored energy function a generalized mid point rule algorithm always exists which exactly conserves energy the conservation properties of a time stepping algorithm need not and in general will not be preserved by the spatial discretization precise conditions which ensure preservation of these conservation properties are derived a number of numerical simulations are presented which illustrate the exact conservation properties of the proposed methodology

the projection method for the incompressible navier stokes equations the pressure near a no slip wall an explicit staggered projection method for the incompressible navier stokes equations with no slip walls is analyzed and used in simulations to address several issues related to the pressure boundary condition required when the continuity equation is replaced by the standard pressure poisson equation ppe 2 p u u f first it is shown that a ppe system supplemented with a neumann pressure boundary condition derived from the momentum equation can be made consistent with the navier stokes equations if it is extended with the requirement that 2 u 0 is zero near the wall and the solution is sufficiently smooth this implies that it is possible to formulate a boundary condition for the standard ppe without the necessity to resort to green s functions which is interesting for theoretical reasons second the equivalence is shown between the staggered projection method and the staggered discretization of above ppe system the derivation of the equivalence sheds light upon the so called ppe paradox and leads to an approximation of the wall value of p n which is not required but implied by the staggered projection method third the near wall regularity of a solution of the navier stokes equations is numerically analyzed by means of direct numerical simulation of turbulent channel flow performed with the staggered projection method from the numerical inspection of all terms of the momentum equation in the near wall region it is concluded that the three components of the momentum equation are satisfied on the wall for t 0 for short times but also in the turbulent regime in the limit t 0 the pressure gradient is observed to converge to the initial pressure gradient in the l 2 norm which confirms a disputed theoretical result in literature even in the maximum norm the pressure gradient appears to converge to the initial pressure gradient the only discontinuities observed in the simulations are the discontinuities of the tangential viscous terms and the time derivatives of the tangential velocities on the wall at t 0 thus the numerical results indicate that the regularity of the solution for turbulent channel flow is stronger than claimed by existing theory