基于同伦延拓的冗余机械臂逆运动学优化算法研究

目的 针对偏置冗余机械臂的逆运动学,采用传统数值法存在依赖初始值、奇异位姿收敛性差等问题,提出一种改进数值法。方法 首先将非线性方程组转化为同伦方程组,引入同伦延拓算法能够有效避免依赖初始值的问题,同时能够获取逆运动学解空间。然后考虑奇异位姿,将同伦方程组转化为最小二乘问题,采用Levenberg Marquardt算法对同伦方程组进行路径追踪,以获取逆运动学解空间。最后将关节极限避免问题映射为解空间优化问题,引入二进制改进粒子群优化算法,获得最优逆运动学解。结果 实验结果表明,相较于传统数值法,文中所提数值法针对逆运动学求解具有更高的收敛率、更快的收敛速度,同时二进制改进粒子群算法能够有效避免关节极限问题。结论 采用文中所提数值法求解逆运动学的精度较高,能够满足实时性要求,对于机械臂用于包装作业具有一定的理论意义和工程应用价值。     

用同伦延拓算法模拟热偶精馏过程

讨论了考虑任意塔板可以存在交联流股的通用精馏过程的数学模型.以分离苯、甲苯、邻二甲苯物系的热偶精馏过程为计算实例,采用同伦延拓算法求解,在多种工况下均得到多解,并从中找出操作特性、经济效益均佳的设计条件.     

Thermal stresses induced by a remote uniform heat flow interacting with two circular inclusions

An analytical solution to two circular inclusions embedded in an infinite plate subjected to a remote uniform heat flux is provided in this article. Based on the method of analytical continuation and the technique of conformal mapping, the general expressions of the temperature and stresses are derived explicitly in a series form. Since our derived series solutions are expressed in terms of the material parameters, the present results are available for the case of even two circular inclusions are getting closer. For a limiting case, when two circular inclusions are set apart su?ciently, the derived analytical solutions are reduced to those of the corresponding single inclusion problem. Numerical results of interfacial stresses are performed and displayed in graphic form. It is interesting to see that both the normal and shear interfacial stresses experience a big jump across the point nearest to the neighboring inclusion, when the distance of two circular inclusions is su?ciently small.     

瓦斯抽采达标煤量的提出及其与矿井原“三量”的关系

为了全面分析多种因素影响下矿井开采接续的需求,改善采掘接替紧张及“三量”过剩造成的资源浪费,分析了瓦斯治理对煤炭开采过程的影响,提出了“瓦斯抽采达标煤量”以及“瓦斯抽采达标煤量合理可采期”的概念,建立了瓦斯抽采达标的计算公式,同时分析了矿井瓦斯抽采达标煤量与原“三量”的关系,对解决煤矿采掘接续紧张问题具有一定的指导意义。     

基于黎曼积分的连续最优潮流模型

在实际电力系统中,负荷在多种因素的综合影响下时刻变化着,一般将其看成是一个连续变化的函数,且目前智能电网的发展使连续时间的数据获取和发电机控制成为可能,所以对连续时间的负荷调度迫在眉睫。但是原先的静态、动态最优潮流仅能考虑离散函数的优化,其经济性和安全性受到了一定的局限。文中应用黎曼积分的思想对最优潮流进行拓展,考虑变量在时间上的连续性,从而建立基于黎曼积分的连续最优潮流模型。基于此理论对IEEE 5节点系统进行仿真,验证了此模型的准确性和实用性。最终结果表明了该模型能够解得一段连续时间内满足所有约束的连续调度时间方案,且发电机出力能很好地跟随负荷波动。     

基于连续潮流的配电网供电能力评估

随着非全相运行的分布式电源大量接入配电网,配电网固有的三相不平衡特征更加突出,传统配电网供电能力评估因忽略配电网三相不平衡特征导致结果不准确。为了准确分析三相不平衡特征对配电网最大供电能力评估的影响,建立了以配电网供电负荷参数最大为目标函数,考虑了支路热约束和节点电压等状态变量和分布式电源的有功和无功功率等控制变量的含分布式电源三相不平衡配电网供电能力评估模型。选择电压跌落情况最严重的相作为连续参数,确保预测-校正过程的的连续潮流法求解的结果更加精确。最后,采用拓展的IEEE33节点配电系统进行仿真验证,表明文中所提的模型和求解方法是有效的。     

A novel predictive homotopic path tracking algorithm to solve non-linear algebraic equations

In chemical engineering and other areas of mathematics and engineering sciences, systems of non-linear algebraic equations often must be solved, and a problem is that these types of systems often cannot be solved analytically. Homotopic continuation methods are globally convergent and can find several solutions to the analyzed algebraic system and consist of a predictive step followed by a corrective step, which can cause reversion of homotopic path tracking. Therefore, in this work, the use of a homotopy continuation method (HCM) based on a purely predictive methodology is proposed; that is, it only makes use of predictor vectors (without correction vectors) to find the solution to several systems of non-linear algebraic equations with a multiplicity of solutions, employing lower central proccessing unit (CPU) time in comparison with standard homotopic tracking algorithms.