线性矩阵方程AXB=C的中心对称解及其最佳逼近

利用矩阵的广义异值分解，得到了线性矩阵方程AXB=C有中心对称解的充分必要条件，且有解时，给出了其解的一般表达式。另外，给出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。     

埃尔米特广义汉密尔顿矩阵的广义逆特征值问题

本文利用埃尔米特广义汉密尔顿矩阵的性质与矩阵的分解理论,导出了埃尔米特广义汉密尔顿矩阵的广义逆特征值问题解的一般表达式。进而运用希尔伯特空间的逼近理论,对任意给定的n阶复矩阵对,证明相关最佳逼近解的存在性与惟一性,得到了最佳逼近解的表达式。     

自由曲面的自适应跟踪测量方法研究

 激光传感器在测量自由曲面中有着非接触、精度高等优点，其应用越来越广泛． 但是激光测头的线性测量
范围较小，难以测量起伏变化较大的曲面． 针对这一问题，提出了激光测头的跟踪测量方法，使激光测头随曲面的
高度变化作上下调整，从而可以测量任一表面起伏的曲面，且能根据当前曲面的曲率大小自适应选择跟踪方式，实
现测点的自适应分布．最后，对一个工件分别进行了等间距测量和自适应跟踪测量，并对两种方法的测量结果做了
比较，证明了自适应跟踪测量方法的可行性和有效性，为自由曲面的测量提供了一种新的方法．     

反自反矩阵的二次特征值反问题及其最佳逼近

二次特征值反问题是二次特征值问题的一个逆过程,在结构动力模型修正领域中应用非常广泛．本文由给定的部分特征值和特征向量,利用矩阵分块法、奇异值分解和Moore-Penrose广义逆,分析了二次特征值反问题反自反解的存在性,得出了解的一般表达式．然后讨论了任意给定矩阵在解集中最佳逼近解的存在性和唯一性．最后给出解的表达式和数值算法,由算例验证了结果的正确性．     

矩阵方程AXB=C的中心对称最小二乘解及其最佳逼近的迭代算法

本文建立了求矩阵方程AXB=C的中心对称最小二乘解的迭代算法。在不考虑舍入误差时,对任意给定的初始中心对称矩阵,该算法能够在有限步迭代后得到此方程的中心对称最小二乘解。当选取特殊的初始矩阵时,可得到极小范数中心对称最小二乘解。另外,在上述解集合中也可得到给定矩阵的最佳逼近矩阵的表达式。     

多重循环矩阵的特征值形式及有关算法的复杂性

本文导出了多重循环矩阵的特征值和特征向量的显式表达式、并且证明了求N阶k重循环矩阵的全部特征值、做两个N除k重循环矩阵的乘积、求N阶k重循环矩阵的逆矩阵、求解系数阵为N阶k重循环矩阵的线代数方程组、求N阶k重循环矩阵的行列式值等问题的计算时间复杂性不超过O(Nlog_2N)。这些结果将为多元多项式、多项式的循环卷积、多维数列循环卷积的计算提供有力的工具。     

用多项式逼近理论的时变权重组合预测方法及其应用

提出一种基于一元多项式逼近和二元多项式逼近的时变权重组合预测方法,并将之应用于飞行器结构响应序列的建模与预测。充分考虑权重的无偏性和非负性,通过引入松弛变量将不等式约束转化为等式约束并基于惩罚函数构造新的组合预测目标函数;最后采用遗传算法获得未知变量的数值解及组合预测时变权重表达式。应用结果表明预测方法有效。     

设计与计算的双向集成

 在CAD系统与计算程序协同工作中发生的数据交换，应理想地沿两个方向进行，以支持产品开发过程，
这通常称为“双向数据交换”．然而，如何对此概念准确理解，学术界在表述上都不尽相同．原本意义上的单向数据
交换，可以按序反向地进行，而被说成是“双向”的．这样，在一种事实上每时每刻都沿双向进行的数据交换之外，还
存在一个相同的提法． 然而，这两种方案有根本区别的． 由此，对概念进行区分，并指出其差别．     

一类线性矩阵方程的最佳逼近解

本文利用投影定理、广义奇异值分解和标准相关分解技巧给出了一种求矩阵方程AXB=C的最小二乘反对称解的方法,得到了通解表达式。进而利用此表达式,导出了通解集做为一个矩阵集与任意给定矩阵的最小距离元素。     

汽车金属带式无级变速传动技术

 无级变速器是汽车传动技术的重要发展领域之一．介绍了金属带式无级变速传动技术的发展概况，阐述了
金属带式无级变速器的基本结构、传动原理，比较分析了其性能、可靠性、寿命与成本等一些技术特性．对金属带式
无级变速传动中的电液控制技术进行了分析，指出具有电液控制技术的无级变速综合控制系统才能满足现代汽车
发展的要求．     

Efficient non‐linear model reduction via a least‐squares Petrov–Galerkin projection and compressive tensor approximations

A Petrov–Galerkin projection method is proposed for reducing the dimension of a discrete non‐linear static or dynamic computational model in view of enabling its processing in real time. The right reduced‐order basis is chosen to be invariant and is constructed using the Proper Orthogonal Decomposition method. The left reduced‐order basis is selected to minimize the two‐norm of the residual arising at each Newton iteration. Thus, this basis is iteration‐dependent, enables capturing of non‐linearities, and leads to the globally convergent Gauss–Newton method. To avoid the significant computational cost of assembling the reduced‐order operators, the residual and action of the Jacobian on the right reduced‐order basis are each approximated by the product of an invariant, large‐scale matrix, and an iteration‐dependent, smaller one. The invariant matrix is computed using a data compression procedure that meets proposed consistency requirements. The iteration‐dependent matrix is computed to enable the least‐squares reconstruction of some entries of the approximated quantities. The results obtained for the solution of a turbulent flow problem and several non‐linear structural dynamics problems highlight the merit of the proposed consistency requirements. They also demonstrate the potential of this method to significantly reduce the computational cost associated with high‐dimensional non‐linear models while retaining their accuracy. Copyright © 2010 John Wiley & Sons, Ltd.     

An Improved Computational Method for the Calculation of Mixture Liquid–Vapor Critical Points

Knowledge of critical points is important to determine the phase behavior of a mixture. This work proposes a reliable and accurate method in order to locate the liquid–vapor critical point of a given mixture. The theoretical model is developed from the rigorous definition of critical points, based on the SRK equation of state (SRK EoS) or alternatively, on the PR EoS. In order to solve the resulting system of \(C+2\) nonlinear equations, an improved method is introduced into an existing Newton–Raphson algorithm, which can calculate all the variables simultaneously in each iteration step. The improvements mainly focus on the derivatives of the Jacobian matrix, on the convergence criteria, and on the damping coefficient. As a result, all equations and related conditions required for the computation of the scheme are illustrated in this paper. Finally, experimental data for the critical points of 44 mixtures are adopted in order to validate the method. For the SRK EoS, average absolute errors of the predicted critical-pressure and critical-temperature values are 123.82 kPa and 3.11 K, respectively, whereas the commercial software package Calsep PVTSIM’s prediction errors are 131.02 kPa and 3.24 K. For the PR EoS, the two above mentioned average absolute errors are 129.32 kPa and 2.45 K, while the PVTSIM’s errors are 137.24 kPa and 2.55 K, respectively.     

Dynamical Newton-Like Methods with Adaptive Stepsize for Solving Nonlinear Algebraic Equations

In this paper, a dynamical Newton-like method with the adaptive stepsize based on the construction of a scalar homotopy function to transform a vector function of non-linear algebraic equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of the fictitious time-like function, we derived the adaptive stepsize using the dynamics of the residual vector. Based on the proposed dynamical Newton-like method, we can also derive the dynamical Newton method (DNM) and the dynamical Jacobian-inverse free method (DJIFM) with the transformation matrix as the inverse of the Jacobian and the identity matrix, respectively. These two dynamical Newton-like methods are then adopted for the solution of NAEs. Numerical illustrations demonstrate that taking advantages of the dynamical Newton-like method with the adaptive stepsize the proposed two dynamical Newton-like methods can release limitations of the conventional Newton method such as root jumping, the divergence at inflection points, root oscillations, and the divergence of the root. Results reveal that with the use of the fictitious time-like function the proposed method presents exponential convergence. In addition, taking the advantages of the transformation matrix, the proposed method does not need to calculate the inverse of the Jacobian matrix and thus has great numerical stability.     

冗余度机器人的最优轨迹生成器

设计出了较为通用的冗余度机器人的最优轨迹规划器，将空间分离法和扩展雅可比矩阵法应用到冗余度机器人的逆运动学求解过程中，得出了较为简便的公式，该规划器回顾了雅可比矩阵的伪逆的计算，为冗余度机器人最优轨迹规划的实时应用奠定了基础。仿真结果表明，该规划器是可行的。     

On a high‐order Newton linearization method for solving the incompressible Navier–Stokes equations

The present study aims to accelerate the non‐linear convergence to incompressible Navier–Stokes solution by developing a high‐order Newton linearization method in non‐staggered grids. For the sake of accuracy, the linearized convection–diffusion–reaction finite‐difference equation is solved line‐by‐line using the nodally exact one‐dimensional scheme. The matrix size is reduced and, at the same time, the CPU time is considerably saved owing to the reduction of stencil points. This Newton linearization method is computationally efficient and is demonstrated to outperform the classical Newton method through computational exercises. Copyright © 2005 John Wiley & Sons, Ltd.     

刚柔协作3CD/2RPU-SPR搅拌摩擦焊机器人研究

为满足搅拌摩擦焊技术的要求,解决搅拌摩擦焊机器人在顶锻力承受以及焊接灵活性方面存在的不足,在三自由度2RPU-SPR搅拌摩擦焊机器人基础上增加了3根绳索,设计了一种刚柔协作3CD/2RPU-SPR搅拌摩擦焊机器人。基于运动学建模,运用封闭矢量法分别计算了3CD/2RPU-SPR搅拌摩擦焊机器人刚性部分与绳索部分的位置逆解;运用求导法求得了机器人刚性部分与绳索部分的速度雅克比矩阵,并运用特征长度法将雅克比矩阵无量纲化,基于求得的速度无量纲雅克比矩阵,利用MATLAB软件分别对添加绳索前后的搅拌摩擦焊机器人的各项运动学性能指标进行编程求解;应用遗传算法对3CD/2RPU-SPR搅拌摩擦焊机器人的性能指标进行优化,通过设定最优个体系数、种群数目、遗传进化次数,对满足3CD/2RPU-SPR搅拌摩擦焊接机器人全域刚度以及全域灵巧性的结构参数进行寻优求解。结果表明:3CD/2RPU-SPR搅拌摩擦焊机器人的承载力、灵巧性、全域灵巧性、刚度、全域刚度等性能指标均有所提高,且在综合考虑灵巧性以及刚度的优质工作空间内运动连续,说明3CD/2RPU-SPR搅拌摩擦焊机器人相较于2RPU-SPR搅拌摩擦焊机器人能够承受更大的顶锻力,且运动灵活性有所提高。通过遗传算法优化后找到符合3CD/2RPU-SPR搅拌摩擦焊机器人全域灵巧性以及全域刚度的10组结构参数,在综合考虑搅拌摩擦焊接工况下,从10组结构参数中选取最优的一组作为搅拌摩擦焊机器人的结构参数,在该结构参数下,机器人性能指标有所提高,更适合完成搅拌摩擦焊接工作。研究为提高机器人搅拌摩擦焊接质量提供了理论依据。     

Time integration of mechanical systems with elastohydrodynamic lubricated joints using Quasi‐Newton method and projection formulations

This work deals with the efficient time integration of mechanical systems with elastohydrodynamic (EHD) lubricated joints. Two novel approaches are presented. First, a projection function is used to formulate the well‐known Swift–Stieber cavitation condition and the mass‐conservative cavitation condition of Elrod as an unconstrained problem. Based on this formulation, the pressure variable from the EHD problem is added to the dynamic equations of a multi‐body system in a monolithic manner so that cavitation is solved within a global iteration. Compared with a partitioned state‐of‐the‐art formulation, where the pressure is solved locally in a nonlinear force element, this global search reduces simulation time. Second, a Quasi‐Newton method of DeGroote is applied during time integration to solve the nonlinear relation between pressure and deformation. Compared with a simplified Newton method, the calculation of the time‐consuming parts of the Jacobian are avoided, and therefore, simulation time is reduced significantly, when the Jacobian is calculated numerically. Solution strategies with the Quasi‐Newton method are presented for the partitioned formulation as well as for the new DAE formulations with projection function. Results are given for a simulation example of a rigid shaft in a flexible bearing. Copyright © 2016 John Wiley & Sons, Ltd.     

An efficient high-precision recursive dynamic algorithm for closed-loop multibody systems

As most closed-loop multibody systems do not have independent generalized coordinates, their dynamic equations are differential/algebraic equations (DAEs). In order to accurately solve DAEs, a usual method is using generalized α-class numerical methods to convert DAEs into difference equations by differential discretization and solve them by the Newton iteration method. However, the complexity of this method is O(n²) or more in each iteration, since it requires calculating the complex Jacobian matrix. Therefore, how to improve computational efficiency is an urgent problem. In this paper, we modify this method to make it more efficient. The first change is in the phase of building dynamic equations. We use the spatial vector note and the recursive method to establish dynamic equations (DAEs) of closed-loop multibody systems, which makes the Jacobian matrix have a special sparse structure. The second change is in the phase of solving difference equations. On the basis of the topology information of the system, we simplify this Jacobian matrix by proper matrix processing and solve the difference equations recursively. After these changes, the algorithm complexity can reach O(n) in each iteration. The algorithm proposed in this paper is not only accurate, which can control well the position/velocity constraint errors, but also efficient. It is suitable for chain systems, tree systems, and closed-loop systems.     

Comparison of fully implicit and IMPES formulations for simulation of water injection in fractured and unfractured media

In this work, we compare the fully implicit (FI) and implicit pressure‐explicit saturation (IMPES) formulations for the simulation of water injection in fractured media. The system of partial differential equations is discretized within the discrete‐fracture framework using a control‐volume method. A unique feature of the methodology is that there is no need for the computation of matrix–fracture transfer terms. The non‐linear system of equations resulting from the FI formulation is solved with state‐of‐the‐art Newton and tensor methods. Direct and Krylov iterative methods are employed to solve the system resulting from the Newton linearization. The performance of the FI and IMPES formulations is compared with numerical testing. Results show that the contrast between matrix and fracture properties affects the performance of both IMPES and FI formulations and that the tensor method outperforms all the Newton solvers for the near‐singular Jacobian matrix. Copyright © 2006 John Wiley & Sons, Ltd.     

一类刚柔协作混联机器人机构的绳索数量和位置分布研究

随着抛光、打磨工艺自动化水平的不断提高,并、混联机器人机构广泛应用于抛光、打磨工艺。为满足抛光、打磨等连续接触式作业的要求,将一类三自由度刚柔协作混联机器人机构作为抛光、打磨设备的主进给机构。通过建立3种绳索数量和位置分布不同的刚柔协作混联机器人机构的运动学模型,运用封闭矢量法分别求得其刚性部分和绳索部分的位置逆解,运用对位置逆解求导的方法得到了3UPS和绳索部分的速度雅克比矩阵;建立了UP支链的D-H坐标系,并运用微分变换法求得UP支链的速度雅克比矩阵,进而求得了3种刚柔协作混联机器人机构的量纲统一速度雅可比矩阵。利用MATLAB软件对该类刚柔协作混联机器人机构的各项性能指标进行求解,通过对比分析各项性能指标,得到了能够满足不同抛光、打磨工况要求的刚柔协作混联机器人机构的绳索数量及位置分布。研究结果为不同工况下刚柔协作混联机器人机构的绳索数量选取和布置提供了理论依据。