Stochastic Finite Element Method for Mechanical Vibration Based on Conjugate Gradient(CG)

When material properties, geometry parameters and applied loads are assumed to be stochastic, the vibration equation of a system is transformed to static problem by using Newmark method. In order to improve the computational efficiency and to save storage, the Conjugate Gradient （CG） method is presented. The CG is an effective method for solving a large system of linear equations and belongs to the method of iteration with rapid convergence and high precision. An example is given and calculated results are compared to validate the proposed methods.

A New Class of Nonlinear Conjugate Gradient Methods with Global Convergence Properties

非线性共轭梯度法由于其迭代简单和储存量小,且搜索方向不需要满足正割条件,在求解大规模无约束优化问题时占据及其重要的地位.提出了一类新的共轭梯度法,其搜索方向是目标函数的下降方向.若假设目标函数连续可微且梯度满足Lipschitz条件,线性搜索满足Wolfe原则,讨论了所设计算法的全局收敛性.

H-CRAN中IRS辅助的D2D系统资源分配与RCG波束成形优化

以异构云无线电接入网(heterogeneous cloud radio access network,H-CRAN)中智能反射面(intelli‐gent reflecting surface,IRS)辅助的端到端(device-to-device,D2D)通信系统为背景,研究了该系统中以和速率最大化为目标的资源分配与黎曼共轭梯度(Riemannian conjugate gradient,RCG)波束成形优化方法。以最大化系统和速率为优化目标,构造子信道复用系数、发射功率门限以及IRS反射系数模约束等多约束优化问题。对于该非线性混合整数规划问题,提出了一种基于相对信道强度的延迟接受算法,以获得信道复用系数。随后将目标优化问题分解为两个子问题进行交替优化。对于发射功率优化子问题,使用逐次凸逼近(successive convex approximation,SCA)方法进行求解。对于IRS波束成形子问题,将IRS相移约束转化为复圆流形后,采用RCG算法进行求解。仿真结果表明,当IRS反射阵源数为50、基站最大发射功率为46 dBm时,与现有信道分配方案和随机信道分配方案相比,所提信道分配方案的和速率性能分别提高了5.2 bit/(s·Hz)和14.6 bit/(s·Hz)。与无IRS通信场景相比,部署IRS的和速率性能显著提高约31.2 bit/(s·Hz)。

NEW HYBRID CONJUGATE GRADIENT METHOD AS A CONVEX COMBINATION OF LS AND FR METHODS

In this paper, we present a new hybrid conjugate gradient algorithm for unconstrained optimization. This method is a convex combination of Liu-Storey conjugate gradient method and Fletcher-Reeves conjugate gradient method. We also prove that the search direction of any hybrid conjugate gradient method, which is a convex combination of two conjugate gradient methods, satisfies the famous D-L conjugacy condition and in the same time accords with the Newton direction with the suitable condition. Furthermore, this property doesn't depend on any line search. Next, we also prove that, moduling the value of the parameter t,the Newton direction condition is equivalent to Dai-Liao conjugacy condition.The strong Wolfe line search conditions are used.The global convergence of this new method is proved.Numerical comparisons show that the present hybrid conjugate gradient algorithm is the efficient one.

A SUBSPACE PROJECTED CONJUGATE GRADIENT ALGORITHM FOR LARGE BOUND CONSTRAINED QUADRATIC PROGRAMMING

A subspace projected conjugate gradient method is proposed for solving large bound constrained quadratic programming. The conjugate gradient method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At every iterative level, the search direction consists of two parts, one of which is a subspace trumcated Newton direction, another is a modified gradient direction. With the projected search the algorithm is suitable to large problems. The convergence of the method is proved and same numerical tests with dimensions ranging from 5000 to 20000 are given.

Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization

Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criticized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimization problems,but they have difficulties in finding diverse solutions for LSMOPs.Currently,how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored.In this paper,a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method.On the one hand,conjugate gradients and differential evolution are used to update different decision variables of a set of solutions,where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front.On the other hand,objective decomposition strategy of evolutionary multi-objective optimization is used to differentiate the conjugate gradients of solutions,and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent.In comparison with state-of-the-art evolutionary algorithms,mathematical programming methods,and hybrid algorithms,the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Three-dimensional conjugate gradient inversion of magnetotelluric full information data

基于阻抗张肌数据， tipper 数据，和conjugate 坡度算法的分析，我们发展一三维( 3D )为转换结合坡度算法完整的信息数据决定了从的 magnetotelluric 五电并且磁场部件并且讨论方法为 3D 倒置结果的量的解释使用完整的信息数据。从合成数据的 3D 倒置的结果显示从转换的结果更好联合张肌和 tipper 数据是的阻抗比的完整的信息数据源于转换仅仅阻抗张肌数据(或 tipper 数据) 在改进分辨率和可靠性。合成例子也表明这个 3D 倒置算法的有效性和稳定性。

A modified three–term conjugate gradient method with sufficient descent property

A hybridization of the three–term conjugate gradient method proposed by Zhang et al. and the nonlinear conjugate gradient method proposed by Polak and Ribi`ere, and Polyak is suggested. Based on an eigenvalue analysis, it is shown that search directions of the proposed method satisfy the sufficient descent condition, independent of the line search and the objective function convexity. Global convergence of the method is established under an Armijo–type line search condition. Numerical experiments show practical efficiency of the proposed method.

A Globally Convergent Polak-Ribiere-Polyak Conjugate Gradient Method with Armijo-Type Line Search

In this paper, we propose a globally convergent Polak-Ribiere-Polyak (PRP) conjugate gradient method for nonconvex minimization of differentiable functions by employing an Armijo-type line search which is simpler and less demanding than those defined in [4,10]. A favorite property of this method is that we can choose the initial stepsize as the one-dimensional minimizer of a quadratic modelΦ(t):= f(xk)+tgkTdk+(1/2) t2dkTQkdk, where Qk is a positive definite matrix that carries some second order information of the objective function f. So, this line search may make the stepsize tk more easily accepted. Preliminary numerical results show that this method is efficient.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

Subspace Minimization Conjugate Gradient Method Based on Cubic Regularization Model for Unconstrained Optimization

Many methods have been put forward to solve unconstrained optimization problems,among which conjugate gradient method(CG)is very important.With the increasing emergence of large⁃scale problems,the subspace technology has become particularly important and widely used in the field of optimization.In this study,a new CG method was put forward,which combined subspace technology and a cubic regularization model.Besides,a special scaled norm in a cubic regularization model was analyzed.Under certain conditions,some significant characteristics of the search direction were given and the convergence of the algorithm was built.Numerical comparisons show that for the 145 test functions under the CUTEr library,the proposed method is better than two classical CG methods and two new subspaces conjugate gradient methods.

One Step Positive Approach for Sheet Metal Forming Simulation Based on Quasi-conjugate-gradient Method

In one step inverse finite element approach, an initial blank shape is normally predicted from the final deformed shape. The final deformed shape needs to be trimmed into a final part after stamping, the trimmed area, therefore, needs to be compensated manually before using one step inverse approach, which causes low efficiency and in consistency with the real situation. To solve this problem, one step positive approach is proposed to simulate the sheet metal stamping process. Firstly the spatial initial solution of one step positive method is preliminarily obtained by using the mapping relationship and area coordinates, then based on the deformation theory the iterative solving is carried out in three-dimensional coordinate system by using quasi-conjugate-gradient method. During iterative process the contact judgment method is introduced to ensure that the nodes on the spatial initial solution are not separated from die surface. The predicted results of sheet metal forming process that include the shape and thickness of the stamped part can be obtained after the iterative solving process. The validity of the proposed approach is verified by comparing the predicted results obtained through the proposed approach with those obtained through the module of one step inverse approach in Autoform and the real stamped part. In one step positive method, the stamped shape of regular sheet can be calculated fast and effectively. During the iterative solution, the quasi-conjugate-gradient method is proposed to take the place of solving system of equations, and it can improve the stability and precision of the algorithm.

Convergence Analysis on a Class of Nonmonotone Conjugate Gradient Methods without Sufficient Decrease Condition

In [3] Liu et al. investigated global convergence of conjugate gradient methods.In that paper they allowed βk to be selected in a wider range and the global convergence of the corresponding algorithm without sufficient decrease condition was proved. This paper investigates global convergence of nonmonotone conjugate gradient method under the same conditions.

Super-resolution processing of passive millimeter-wave images based on conjugate-gradient algorithm

This paper designs a 3 mm radiometer and validate with experiments based on the principle of passive millimeter wave （PMMW） imaging. The poor spatial resolution, which is limited by antenna size, should be improved by post data processing. A conjugate-gradient （CG） algorithm is adopted to circumvent this drawback. Simulation and real data collected in laboratory environment are given, and the results show that the CG algorithm improves the spatial resolution and convergent rate. Further, it can reduce the ringing effects which are caused by regularizing the image restoration. Thus, the CG algorithm is easily implemented for PMMW imaging.

基于非结构网格的直流电法三维NLCG反演研究

直流电阻率法是矿产勘查、环境调查、工程勘察等领域应用广泛的地球物理勘探方法之一,目前反演方法仍以二维反演为主,而实际地电勘探目标体均为三维结构,二维反演容易受旁侧效应影响。基于上述问题,本文展开了三维电阻率反演研究,实现了非结构化独立网格的三维非线性共轭梯度反演算法。非结构独立正反演网格既能适用于三维非平坦地形,可以实现网格的局部加密,又能克服正反演嵌套网格和同套网格的弊端;非线性共轭梯度法运用伴随原理不需要计算灵敏度矩阵,节约了计算资源和计算时间。程序对双立方体模型进行反演,经过100次迭代,misfit达到8%,反演重构异常体形态、位置与模型较为吻合,最后程序对某高速隧道塌陷区实测数据进行反演,通过与BERT2.0反演结果进行对比,证明了反演解释效果具有实际应用价值。

基于SCG优化SSAE-FFNN的电能质量复合扰动深度特征提取与分类

随着智能电网的发展,电能质量问题已遍布电网并威胁着电网的安全稳定,且电能质量监测数据日渐庞大,因此实现大规模系统中电能质量扰动(power quality disturbances,PQDs)的深度特征提取及智能分类识别对电力系统污染检测与管理具有重要意义。为此,文中提出一种基于堆叠稀疏自编码器(stacked sparse auto encoder,SSAE)和前馈神经网络(feedforward neural network,FFNN)的电能质量复合扰动分类方法。首先,基于IEEE标准构建PQDs仿真模型。然后,建立基于SSAE-FFNN的PQDs分类模型,并引入缩放共轭梯度(scaled conjugate gradient,SCG)算法对模型进行优化,以提高梯度下降速度和网络训练效率。接着,为有效降低堆叠网络的重构损失同时提取出深度的低维特征,构建SSAE的逐层训练集及微调策略。最后,通过算例分析验证文中方法的分类效果、鲁棒性、泛化性和适用场景规模。结果表明,文中方法能够有效识别电能质量复合扰动,对含误差扰动和某地市电网的21组实测扰动录波数据也有较高的分类准确率。

A Hybrid Conjugate Gradient Algorithm for Solving Relative Orientation of Big Rotation Angle Stereo Pair

The fast convergence without initial value dependence is the key to solving large angle relative orientation.Therefore,a hybrid conjugate gradient algorithm is proposed in this paper.The concrete process is:①stochastic hill climbing(SHC)algorithm is used to make a random disturbance to the given initial value of the relative orientation element,and the new value to guarantee the optimization direction is generated.②In local optimization,a super-linear convergent conjugate gradient method is used to replace the steepest descent method in relative orientation to improve its convergence rate.③The global convergence condition is that the calculation error is less than the prescribed limit error.The comparison experiment shows that the method proposed in this paper is independent of the initial value,and has higher accuracy and fewer iterations.

Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations

Conjugate gradient optimization algorithms depend on the search directions.with different choices for the parameters in the search directions.In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved .Firstly,it is shown that,using reverse modulus of continuity funciton and forcing function,the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman's step size rule and a bounded level set .Secondly,by using comparing technique,some general convergence propecties of the new method with other kind of step size rule are established,Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.

The Irregular Weighted Wavelet Frame Conjugate Gradient Algorithm

The dropping off of data during information transmission and the storage device’s damage etc.often leads the sampled data to be non-uniform.The paper, based on the stability theory of irregular wavelet frame and the irregular weighted wavelet frame operator,proposed an irregular weighted wavelet fame conjugate gradient iterative algorithm for the reconstruction of non-uniformly sampling signal. Compared the experiment results with the iterative algorithm of the Ref.[5],the new algorithm has remarkable advantages in approximation error,running time and so on.