impact force sparse reconstruction from highly incomplete and inaccurate measurements abstract the classical l2 norm based regularization methods applied for force reconstruction inverse problem require that the number of measurements should not be less than the number of unknown sources taking into account the sparse nature of impact force in time domain we develop a general sparse methodology based on minimizing l1 norm for solving the highly underdetermined model of impact force reconstruction a monotonic two step iterative shrinkage thresholding mtwist algorithm is proposed to find the sparse solution to such an underdetermined model from highly incomplete and inaccurate measurements which can be problematic with tikhonov regularization mtwist is highly efficient for large scale ill posed problems since it mainly involves matrix vector multiplies without matrix factorization in sparsity frame the proposed sparse regularization method can not only determine the actual impact location from many candidate sources but also simultaneously reconstruct the time history of impact force simulation and experiment including single source and two source impact force reconstruction are conducted on a simply supported rectangular plate and a shell structure to illustrate the effectiveness and applicability of mtwist respectively both the locations and force time histories of the single source and two source cases are accurately reconstructed from a single accelerometer where the high noise level is considered in simulation and the primary noise in experiment is supposed to be colored noise meanwhile the consecutive impact forces reconstruction in a large scale greater than 104 sparse frame illustrates that mtwist has advantages of computational efficiency and identification accuracy over tikhonov regularization

two level method based on finite element and crank nicolson extrapolation for the time dependent navier stokes equations a fully discrete two level finite element method the two level method is presented for solving the two dimensional time dependent navier stokes problem the method requires a crank nicolson extrapolation solution u h tau 0 p h tau 0 on a spatial time coarse grid j h tau 0 and a backward euler solution u h tau p h tau on a space time fine grid j h tau the error estimates of optimal order of the discrete solution for the two level method are derived compared with the standard crank nicolson extrapolation method the one level method based on a space time fine grid j h tau the two level method is of the error estimates of the same order as the one level method in the h1 norm for velocity and the l2 norm for pressure however the two level method involves much less work than the one level method

on error estimates of the projection methods for the navier stokes equations second order schemes we present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible navier stokes equations the error analysis is accomplished by interpreting the respective projection schemes as second order time discretizations of a perturbed system which approximates the navier stokes equations numerical results in agreement with the error analysis are also presented

on error estimates of some higher order projection and penalty projection methods for navier stokes equations this paper is a continuation of our previous work 10 on projection methods we study first existing higher order projection schemes in the semidiscretized form for the navier stokes equations one error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent neumann boundary condition satisfied by the pressure approximations we then propose a penalty projection scheme for which we obtain improved error estimates

a force identification method using cubic b spline scaling functions for force identification the solution may differ from the desired force seriously due to the unknown noise included in the measured data as well as the ill posedness of inverse problem in this paper an efficient basis function expansion method based on wavelet multi resolution analysis using cubic b spline scaling functions as basis functions is proposed for identifying force history with high accuracy which can overcome the deficiency of the ill posed problem the unknown force is approximated by a set of translated cubic b spline scaling functions at a certain level and thereby the original governing equation of force identification is reformulated to find the coefficients of scaling functions which yields a well posed problem the proposed method based on wavelet multi resolution analysis has inherent numerical regularization for inverse problem by changing the level of scaling functions the number of basis functions employed to approximate the identified force depends on the level of scaling functions a regularization method for selecting the optimal level of cubic b spline scaling functions by virtue of condition number of matrix is proposed in this paper the validity and applicability of the proposed method are illustrated by two typical examples of volterra fredholm integral equations that are both typical ill posed problems force identification experiments including impact and harmonic forces are conducted on a cantilever beam to compare the accuracy and efficiency of the proposed method with that of the truncated singular value decomposition tsvd technique

on pressure approximation via projection methods for nonstationary incompressible navier stokes equations projection methods are an efficient tool to approximate strong solutions of the incompressible navier stokes equations as a major deficiency these methods often suffer from reduced accuracy for pressure iterates caused by nonphysical boundary data going along with suboptimal error estimates for pressure iterates we verify a rigorous bound for arising boundary layers in chorin s scheme under realistic regularity assumptions in a second step the new chorin penalty method is proposed where optimal rate of convergence for pressure iterates is shown

time domain galerkin method for dynamic load identification summary this paper proposes a new method called time domain galerkin method tdgm for investigating the structural dynamic load identification problems firstly the shape functions are adopted to approximate three parameters such as the dynamic load kernel function response and measured structural response secondly defining a residual function could be expressed as the difference of the measured response and the computational response thirdly select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero finally when the shape functions are chosen as the weighting function it establishes the forward model called tdgm furthermore the regularization method could have effectiveness in solving the ill posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load compared with the traditional green kernel function method gkfm tdgm can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification three numerical examples are provided to demonstrate the correctness and advantages of tdgm copyright 2015 john wiley sons ltd

force reconstruction analysis and regularization of a deconvolution problem the reconstruction of force is considered by means of indirect measurements this necessitates taking measurements from the impacted structure and then to deconvolve those signals from the impulse response function more precisely the purpose of the work described here is to analyze a deconvolution technique and to solve the problems which occur thus it is highlighted that the associated deconvolution problem depends on the location of the measurement points is it possible or not to reconstruct the impact force versus the location of this point numerical predictions are compared and validated with experiment but the deconvolution is a well known ill posed problem the results are often unstable this is why it is necessary to regularize the problem which consists of adding a condition to the solution which does not appear in the initial problem some regularization methods are presented nevertheless they necessitate the determination of a parameter the difficulty is to calculate an appropriate value of this regularization parameter the methods are successfully used to recover an experimental force

numerical construction of impulse response functions and input signal reconstruction abstract a new method for input signal reconstruction is presented this approach utilizes the convolution relationship of inputs and outputs of linear systems a linear discretization of sampled points was assumed in formulating the discrete convolution integral subsequently the resulting equation was modified via a linear constraint to facilitate solution by the least square method this improves the conditioning of discrete deconvolution the method was validated numerically on a single degree of freedom dynamic system inputs reconstructed matched the applied input very well for a low noise case a methodology for multiple inputs and outputs was developed the single input multiple output formulation was validated using experimental strain measurements of hammer pulse tests pulse areas and peak magnitudes were reconstructed with good accuracy

convergence analysis of a residual local projection finite element method for the navier stokes equations this work presents and analyzes a new residual local projection stabilized finite element method relp for the nonlinear incompressible navier stokes equations stokes problems defined elementwise drive the construction of the residual based terms which make the present method stable for the finite element pairs mathbb p 1 mathbb p l l 0 1 numerical upwinding is incorporated through an extra control on the advective derivative and on the residual of the divergence equation well posedness of the discrete problem as well as optimal error estimates in natural norms are proved under standard assumptions next a divergence free velocity field is provided by a simple postprocessing of the computed velocity and pressure using the lowest order raviart thomas basis functions this updated velocity is proved to converge optimally to the exact solution numerics assess the theoretical results and validate the relp method

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

derivation of a new parametric impulse response matrix utilized for nodal wind load identification by response measurement this paper provides new formulations to derive the impulse response matrix which is then used in the problem of load identification with application to wind induced vibration the applied loads are inversely identified based on the measured structural responses by solving the associated discrete ill posed problem to this end based on an existing parametric structural model the impulse response functions of acceleration velocity and displacement have been computed time discretization of convolution integral has been implemented according to an existing and a newly proposed procedure which differ in the numerical integration methods the former was evaluated based on a constant rectangular approximation of the sampled data and impulse response function in a number of steps corresponding to the sampling rate while the latter interpolates the sampled data in an arbitrary number of sub steps and then integrates over the sub steps and steps the identification procedure was implemented for a simulation example as well as an experimental laboratory case the ill conditioning of the impulse response matrix made it necessary to use tikhonov regularization to recover the applied force from noise polluted measured response the optimal regularization parameter has been obtained by l curve and gcv method the results of simulation represent good agreement between identified and measured force in the experiments the identification results based on the measured displacement as well as acceleration are provided further it is shown that the accuracy of experimentally identified load depends on the sensitivity of measurement instruments over the different frequency ranges

perron frobenius theory over real closed fields and fractional power series expansions abstract some of the main results of the perron frobenius theory of square nonnegative matrices over the reals are extended to matrices with elements in a real closed field we use the results to prove the existence of a fractional power series expansion for the perron frobenius eigenvalue and normalized eigenvector of real square nonnegative irreducible matrices which are obtained by perturbing a possibly reducible nonnegative matrix further we identify a system of equations and inequalities whose solution yields the coefficients of these expansions for irreducible matrices our analysis assures that any solution of this system yields a fractional power series with a positive radius of convergence

on a linearized backward euler method for the equations of motion of oldroyd fluids of order one in this paper a linearized backward euler method is discussed for the equations of motion arising in the oldroyd model of viscoelastic fluids some new a priori bounds are obtained for the solution under realistically assumed conditions on the data further the exponential decay properties for the exact as well as the discrete solutions are established finally a priori error estimates in bh 1 and bl 2 norms are derived for the the discrete problem which are valid uniformly for all time t 0

first second and third order fractional step methods for the three field viscoelastic flow problem in this paper three different fractional step methods are designed for the three field viscoelastic flow problem whose variables are velocity pressure and elastic stress the starting point of our methods is the same as for classical pressure segregation algorithms used in the newtonian incompressible navier stokes problem these methods can be understood as an inexact lu block factorization of the original system matrix of the fully discrete problem and are designed at the pure algebraic level the final schemes allow one to solve the problem in a fully decoupled form where each equation for velocity pressure and elastic stress is solved separately the first order scheme is obtained from a straightforward segregation of pressure and elastic stress in the momentum equation whereas the key point for the second order scheme is a first order extrapolation of these variables the third order fractional step method relies on yosida s scheme referring to the spatial discretization either the galerkin method or a stabilized finite element formulation can be used we describe the fractional step methods first assuming the former and then we explain the modifications introduced by the stabilized formulation we employ and that has been proposed in a previous work this discretization in space shows very good stability permitting in particular the use of equal interpolation for all variables

on error estimates of projection methods for navier stokes equations first order schemes in this paper projection methods or fractional step methods are studied in the semi discretized form for the navier stokes equations in a two or three dimensional bounded domain error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method a modified projection scheme which leads to improved error estimates is also proposed

smooth construction of impulse response functions and applied loads using a time domain deconvolution method abstract a time domain deconvolution method is developed to allow for continuous and differentiable impulse response function irf constructions and applied force reconstructions this is a two stage method where 1 the irf is constructed using measured outputs and applied dynamic loads and 2 a dynamic applied load is reconstructed using measured outputs and the constructed irf a generalized formulation is presented which would allow for any assumed form of the unknown irf subsequently linear and cubic example cases are presented the latter allows for continuous and differentiable solutions due to the ability to match time derivatives at each node the problem of ill conditioning in the deconvolution formulation is alleviated by assuming a distribution of the unknown irf or applied force over many sampling intervals where only the nodal values are of interest this results in a matrix equation with many more rows than columns and is subsequently solved using a least squares pseudo inverse the third order reconstructions are shown to more accurately reconstruct unknown irf and applied load when the sampling rate is small or when the constraint parameters are large the condition number is reduced for both the linear and cubic cases as the constraint parameters are increased meaning both methods are effective at reducing ill conditioning

a solution of a nonlinear system arising in spectral perturbation theory of nonnegative matrices abstract let p and e be two n n complex matrices such that for sufficiently small positive e p ee is nonnegative and irreducible it is known that the spectral radius of p ee and corresponding normalized eigenvector have fractional power series expansions the goal of the paper is to develop an algorithm for computing the coefficients of these expansions under two restrictive assumptions namely that p has a single jordan block corresponding to its spectral radius and that the unique up to scalar multiples left and right eigenvectors of p corresponding to its spectral radius say v and w satisfy v t ew 0 our approach is to consider an associated countable system of nonlinear equations and solve this system recursively at each step we consider the coefficients of the expansion of the spectral radius of p ee as parameters and solve a related linear system parametrically the next coefficient of the expansion of the spectral radius is then determined from feasibility considerations for a linear system this solution method is novel and seems useful for computing coefficients of corresponding expansions when the two restrictive assumptions are relaxed also interestingly the coefficients we compute yield a preferred basis of the generalized eigenspace corresponding to the spectral radius of the unperturbed matrix p

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

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

stability and convergence of second order time discrete projection method for the linearized oldroyd model abstract in this paper we consider the second order time discrete projection method for the linearized oldroyd model based on the time iterative discrete scheme by the projection method the original problem is decoupled into two linear subproblems and each subproblem can be solved easily unconditional stability and the corresponding convergence results of the numerical solutions are derived our main results are that the convergence orders in time for the velocity in l 2 norm is second order and for the pressure in h 1 norm is first order finally some numerical examples are provided to verify the performances of the developed numerical method