Discrete gradient methods and linear projection methods for preserving a conserved quantity of stochastic differential equations

Numerical methods preserving a conserved quantity for stochastic differential equations are considered. A class of discrete gradient methods based on the skew-gradient form is constructed, and the sufficient condition of convergence order 1 in the mean-square sense is given. Then a class of linear projection methods is constructed. The relationship of the two classes of methods for preserving a conserved quantity is proved, which is, the constructed linear projection methods can be considered as a subset of the constructed discrete gradient methods. Numerical experiments verify our theory and show the efficiency of proposed numerical methods.     

On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems

Gradient-based topology optimization typically involves thousands or millions of design variables. This makes efficient sensitivity analysis essential and for this the adjoint variable method (AVM) is indispensable. For transient problems it has been observed that the traditional AVM, based on a differentiate-then-discretize approach, may lead to inconsistent sensitivities. Herein this effect is explicitly demonstrated for a single dof system and the source of inconsistency is identified. Additionally, we outline an alternative discretize-then-differentiate AVM that inherently produces consistent sensitivities.     

Discrete Walsh operational matrices for analysis and optimal control of linear digital systems

By the introduction of the shift transformation matrix, direct product matrix and summation matrix of the discrete Walsh series, the analysis of time-varying digital control systems is facilitated and the approximate solution of time-invariant digital optimal control problems is achieved of this study. The design algorithms of digital optimal control are based on the discrete variational principle combined with the idea of penalty functions to obtain the conveniently computational formulations for evaluating the optimal control and trajectory. Three examples are illustrated by using the discrete Walsh approach.     

Discrete gradient algorithms of high order for one-dimensional systems

We show how to increase the order of one-dimensional discrete gradient numerical integrator without losing its advantages, such as exceptional stability, exact conservation of the energy integral and exact preservation of the trajectories in the phase space. The accuracy of our integrators is higher by several orders of magnitude as compared with the standard discrete gradient scheme (modified midpoint rule) and, what is more, our schemes have very high accuracy even for large time steps.     

Discrete analysis method for random vibration of structures subjected to spatially correlated filtered white noises

Random vibration analysis of large-span space structures or high-rise structures which are subjected to spatially correlated filtered white noise excitations such as wind load and earthquake motion, has been a difficult problem in engineering computation. Based on the idea of the discrete analysis method of random vibration, this paper attempts to solve this problem. The formulae of calculating structural mean and mean square responses are given. As an example, the wind-induced vibration of a cable roof structure is analysed by using these formulae.     

Dynamics and vibration analysis of suspended microchannel resonators based on strain gradient theory

Microsystem Technologies - In this paper, dynamics of a suspended microchannel resonator (SMR) will be derived using the strain gradient theory. Accordingly, the size dependent governing equation...     

Discrete linear recursive smoothing for systems with uncertain observations

The least-squares smoothing estimate for discrete linear systems with uncertain observations is investigated. The observations may contain noise alone, and the uncertainty in the observations is governed by a binary switching sequencegammak, wheregammakmay be regarded as a mixture process and is specified by a conditional probability distribution. Examples of such systems are found in multichannel data links with random interruptions, and such mixture sequences can also serve as models for a communication channel with multiplicative noise.     

Discrete pulse orthogonal functions for the analysis,parameter estimation and optimal control of linear digital systems

Discrete pulse orthogonal functions (DPOFs) are introduced, and their operational matrix is proposed to solve various control problems. The applications of DPOFs in digital control systems are analogous to those of block pulse functions (BPFs) in continuous systems. Applying the DPOFs, the approximate solutions of digital time-invariant systems can be easily obtained by a convenient algorithm. Three examples are presented to demonstrate the applications of DPOFs.     

Discrete pulse orthogonal functions for the analysis,parameter estimation and optimal control of linear time-varying digital systems

The analysis, parameter estimation and optimal control of linear time-varying digital systems are facilitated in this study. The discrete pulse orthogonal functions (DPOFs) and their operational matrices are taken as a sharp tool. The applications of DPOFs to digital control systems are analogous to those of the known block pulse functions (BPFs) in continuous systems. By applying the DPOFs, approximate solutions of digital time-varying systems can easily be obtained by convenient algorithms. Three examples are illustrated to demonstrate the proposed DPOF technique, and the approximate results are very accurate and satisfactory.     

融合子块梯度与线性预测的单高斯背景建模

针对单高斯背景模型不能适应非平稳场景且对初期保持静止后期运动的物体造成"鬼影"现象的问题,提出了融合子块梯度与线性预测的单高斯背景建模方法。首先,对每个像素点进行单高斯背景建模,并实现像素级的自适应更新,运用子块梯度算法将梯度在阈值内的子块作为背景以消除"鬼影";然后,将子块梯度法获得的前景与单高斯模型确定的前景做与运算,提高在非平稳场景下对背景的判断能力;最后,运用线性预测方法处理获得的前景点,将面积小于阈值的连通区域还原为背景。采用CDNET 2012 Dataset和Wallflower Dataset进行仿真实验:当场景变化幅度较大时,所提算法与混合高斯模型(GMM)相比,虽然检测率稍有下降,但检测精度提高了40%;在其他场景中检测率虽只提高约10%,检测精度却能提高25%以上。实验结果表明,融合子块梯度与线性预测的单高斯背景建模能够适应非平稳场景并消除"鬼影"现象,获得的背景比混合高斯模型更精确,提取的前景细节更丰富。     

含表面裂纹简支梁的非线性振动分析

对含表面裂纹简支梁在大幅振动下的几何非线性进行了理论分析,从建立了梁的非线性振动的半解析解.用Rayleigh方法将振型函数表示为线性模型振型函数的组合,建立了梁非线性振动的第一阶振型函数的显式表达式,数值模拟计算了不同的裂纹深度和给定不同第一函数系数a1对梁最大位移的影响.建立的显式方程简单,易于工程应用.     

RANDOM: A program for the stationary random vibration analysis of linear structures with hereditary characteristics

The paper describes a general framework for the spectral analysis of linear structures under stationary random excitation. The method can be implemented as a post-processor to a Finite Element programme.The formulation is made in the frequency domain in a way which includes structures with hereditary characteristics. It uses the coupled equations of the normal mode components.The method is illustrated by two examples. The first is used to show that the off-diagonal terms in the modal equations may sometimes be significant and that the damping must be treated carefully in the formulation. The second is concerned with the along wind response of buildings and is used as a benchmark. It is shown that in this case, which involves a fairly complicated excitation mechanism, the algorithm is very fast, and can reproduce previously published results.     

An efficient implementation of adjoint sensitivity analysis for optimal control problems

In this paper an efficient implementation of design sensitivity analysis techniques is presented for nonlinear optimal control problems using the adjoint variable method. Techniques for functionals (integrals) and dynamic response (or pointwise) constraints are developed. Emphasis is placed on the proper choice of numerical techniques which exploit the structure of the problem to achieve efficiency. Numerical results for two optimal control examples show great improvement over previous implementations. Unlike previous results the computational effort required for DSA is shown to increase only linearly with the number of discretization points used and is a much smaller percentage of total CPU time.     

基于GPU的稀疏线性系统的预条件共轭梯度法

研究了基于GPU的稀疏线性方程组的预条件共轭梯度法加速求解问题,并基于统一计算设备架构(CUDA)平台编制了程序,在NVIDIAGT430 GPU平台上进行了程序性能测试和分析。稀疏矩阵采用压缩稀疏行(CSR)格式压缩存储,针对预条件共轭梯度法的算法特性,研究了基于GPU的稀疏矩阵与向量相乘的性能优化、数据从CPU端传到GPU端的加速传输措施。将编制的稀疏矩阵与向量相乘的kernel函数和CUSPARSE函数库中的cusparseDcsrmv函数性能进行了对比,最优得到了2.1倍的加速效果。对于整个预条件共轭梯度法,通过自编kernel函数来实现的算法较之采用CUBLAS库和CUSPARSE库实现的算法稍具优势,与CPU端的预条件共轭梯度法相比,最优可以得到7.4倍的加速效果。     

Learning curves for stochastic gradient descent in linear feedforward networks

Gradient-following learning methods can encounter problems of implementation in many applications, and stochastic variants are sometimes used to overcome these difficulties. We analyze three online training methods used with a linear perceptron: direct gradient descent, node perturbation, and weight perturbation. Learning speed is defined as the rate of exponential decay in the learning curves. When the scalar parameter that controls the size of weight updates is chosen to maximize learning speed, node perturbation is slower than direct gradient descent by a factor equal to the number of output units; weight perturbation is slower still by an additional factor equal to the number of input units. Parallel perturbation allows faster learning than sequential perturbation, by a factor that does not depend on network size. We also characterize how uncertainty in quantities used in the stochastic updates affects the learning curves. This study suggests that in practice, weight perturbation may be slow for large networks, and node perturbation can have performance comparable to that of direct gradient descent when there are few output units. However, these statements depend on the specifics of the learning problem, such as the input distribution and the target function, and are not universally applicable.     

Efficient linear transverse normal stress analysis of layered composite plates

Based on the first order shear deformation theory (FSDT) a method is developed for calculating the transverse normal stress (in thickness direction) in layered composite plate structures. Two steps are necessary. First, the transverse shear stress calculation, and second, relying on the results of the first step, the transverse normal stress evaluation.In the first step strain derivatives are substituted with transverse shear forces which in turn are obtained from the corresponding material law. This leads to a derivative-free process which is numerically more accurate than a pure equilibrium approach. As a second step the transverse normal stress is equilibrated to the derivatives of the transverse shear stresses with respect to the in-plane coordinates. As compared to the standard equilibrium approach, the proposed procedure reduces the order of differentiation by one. Thus, only quadratic shape functions are necessary for evaluating the required derivatives on the element level.Numerical examples for symmetric cross-ply and antisymmetric angle-ply laminates show that the exact three-dimensional elasticity solution is very closely approximated. This holds for thin as well as rather thick plates with a slenderness ratio down to five. In contrast to many recently established methods, either higher order lamination theories or layerwise theories, the approach is easily applicable to finite elements, since only C⁰-continuity is necessary and the numerical effort is low.     

车削加工中的振动原因分析及消振措施探讨

受机床床身、主轴结构、刀具安装、工件装夹等组成的工艺系统的影响,在机械加工过程中无可避免的会产生受迫振动和自激振动。本文从现有机械加工过程中产生了哪几种振动,这些振动为什么会产生,以及振动产生的影响这三方面人手,提出通过改善机械工艺来解决振动问题。     

Iteration-fusing conjugate gradient for sparse linear systems with MPI + OmpSs

The Journal of Supercomputing - In this paper, we target the parallel solution of sparse linear systems via iterative Krylov subspace-based method enhanced with a block-Jacobi preconditioner on a...