Dynamic Modeling of Spatial Cooperation Between Dual-Arm Mobile Manipulators北大核心CSCD

移动机械臂进行空间协作时会产生复杂的非线性耦合,使得采用Lagrange方程或Newton-Euler法直接进行建模极为繁琐。针对双移动机械臂空间协作问题,提出了一种结合Udwadia-Kalaba (U-K)方法与Lagrange方程建立动力学模型的方法。在建模过程中,将负载简化为连杆,选择负载中心断开的方式对系统进行分解,从而避免了机械臂末端关节断开导致的末端关节转角与连杆转角的约束信息缺失问题;将分割形成的两个子系统通过Lagrange方程进行建模,得到了子系统的动力学模型;再将协作系统的固有几何关系通过约束形式引入,应用U-K方法得到了协作系统动力学模型,减少了建立动力学模型所需要的计算量;最后通过数值仿真验证了该方法所得到的动力学模型的准确性。     

可计算建模

可计算建模(computable modeling) 指根据所研究问题对计算精度的要求, 综合运用相关领域知识建立或简化模型, 减少计算量, 提高计算效率, 使得模型在现有计算机条件下可计算. 可计算建模是科学与工程计算研究的一个重要方面. 本文主要通过若干例子介绍可计算建模研究的内涵.     

西南边境作战某军减员率的ARIMA分析

为研究战役卫生减员的统计分布,建立模型,提供计算机模拟研究的基础。本收集了我军西南边境作战某军的经验数据,计算每天减员率,采用柯尔莫哥洛夫—斯米尔诺夫方法进行拟合优度检验,运用博克斯—詹金斯方法建立时间序列模型。结果表明该军减员率分布符合对数正态分布,可用ARIMA(0,1,1)建模。     

托克托准格尔特大桥48m跨长引桥静动力分析

以托克托准格尔特大桥48 m跨长引桥为研究对象,采用ANSYS建立有限元模型,并对其自振特性和静力特性进行了计算分析。结果表明,该桥主梁和桥墩均具有较高的刚度和强度,结构安全。     

北京市水资源利用建模分析研究

以北京市为例,分别应用无偏灰色GM(1,1)模型和非线性模型对北京市2001年-2010年的用水量进行了建模,利用最优化方法,计算了上述两种模型的最优组合模型,通过三种模型分别计算了北京市2001年-2010年的水资源利用量,并与北京市2001年-2010年的实际用水量进行了对比,采用精度检验方法,分别对无偏灰色模型,非线性模型和组合模型进行了精度检验,计算结果表明,加权组合模型是三种模型中精度最高的模型,通过组合模型计算得出的用水量值与实际水资源利用量相比误差最小,由此得出,可以利用组合模型对北京市未来的水资源利用量进行预测,预测结果可为其他相关研究提供参考.     

灰色预测模型算法的改进研究

为了解决固定模型预测时变系统容易出现较大误差的问题,提出模型更新算法,即采用将移动窗算法与传统灰色预测模型相结合的方法.通过在建模序列中删除一部分旧数据、纳入一部分新数据的方式递推更新预测模型,并分解数学模型所涉及的关键量ab从而简化递推数学公式;利用国家统计年鉴的统计数据验证上述方法的有效性.为了解决传统灰色预测模型建模长度选择的问题,而递推算法能在已知模型参数基础上通过简单计算获得新模型的各项参数,文章给出了详细的递推数学公式;另外对于最小建模长度L_(min)也进行讨论,认为L_(min)≥3,并给出证明.所改进算法提高灰色模型的预测精度,同时也为最优序列长度计算提供理论依据.     

飞行器结构噪声致振试验及声振耦合响应分析

以高超声速飞行器X-43A为研究对象,建立其有限元结构模型,在动力学实验室进行飞行器结构模型的固有频率测试,通过固有频率计算与试验结果对比,二者误差在1%左右,这表明所建立的结构有限元模型是比较准确的．在高声强混响室进行飞行器结构噪声致振试验,得到飞行器结构测点加速度功率谱密度(power spectral density, PSD)和舱内声场噪声声压级,通过声振耦合数值模拟计算结果与试验值对比,结果表明:数值模拟计算方法对振动噪声环境预测是比较可靠的,结构振动响应与舱内噪声响应的有限元分析与试验结果趋势上较为一致,低频段吻合较好;高频外噪声场引起的飞行器弹性腔体结构振动占据结构振动响应的主要成分,尤其是以结构低阶振动为主,而外噪声场传递到封闭腔体内的噪声也主要是通过结构腔体弹性壁板的低阶振动传播,即使外噪声激励是宽频的,封闭舱内响应噪声的频率主分量仍然是结构的低阶模态振动．     

引气方式对轴流压气机性能影响研究

航空发动机空气系统需要从多级轴流压气机中间级引气,不同引气方式将对轴流压气机性能和流场产生不同影响.以一带进口导叶的单级轴流压气机为研究对象,采用数值模拟方法研究了全周开缝、均布开孔以及不同开孔角度等引气方式对压气机性能的影响.结果表明,引气可不同程度地提高压气机性能,沿流向倾斜开设引气孔使喘振裕度提升最大,达到8.2%,反流向开设引气孔使压气机效率、压比有较大提高.     

基于信息再利用的灰色系统GM(1.1)模型建模方法及应用

目的:寻找新的灰色系统GM(1.1)模型建模方法,建立拟合精度与预测精度较高的GM(1.1)模型.方法:在邓聚龙教授建模方法的基础上,用基于信息再利用的方法,建立新的灰色系统GM(1.1)模型.结果:用基于信息再利用的灰色系统GM(1.1)模型建模方法建立的GM(1.1)模型,其拟合精度与预测精度不但优于传统方法建立的GM(1.1)模型,而且优于其他改进方法建立的GM(1.1)模型.结论:基于信息再利用的灰色系统GM(1.1)模型建模方法不但建模过程简单适用,而且其建立的GM(1.1)模型拟合精度与预测精度优于其他改进方法建立的GM(1.1)模型,因而具有广泛的应用价值.     

蜘蛛网结构性能研究

以蛛网捕丝与放射丝结点为研究对象,首先应用达朗贝尔原理对结点进行受力分析,运用动力松弛法将猎物作用于结点的动态力变为静力建模;然后考虑不同捕食策略对蛛网结构的影响,将捕食策略变为约束条件,蛛丝上的最小残余力作为优化目标,建立基于捕食策略的单目标规划模型;最后提出将环境影响因子转化为目标函数的约束条件的模型改进方法。     

Heterogeneous multiscale methods for stiff ordinary differential equations

The heterogeneous multiscale methods (HMM) is a general framework for the numerical approximation of multiscale problems. It is here developed for ordinary differential equations containing different time scales. Stability and convergence results for the proposed HMM methods are presented together with numerical tests. The analysis covers some existing methods and the new algorithms that are based on higher-order estimates of the effective force by kernels satisfying certain moment conditions and regularity properties. These new methods have superior computational complexity compared to traditional methods for stiff problems with oscillatory solutions.

     

Partitioned adaptive Runge-Kutta methods and their stability

Summary This paper deals with the solution of partitioned systems of nonlinear stiff differential equations. Given a differential system, the user may specify some equations to be stiff and others to be nonstiff. For the numerical solution of such a system partitioned adaptive Runge-Kutta methods are studied. Nonstiff equations are integrated by an explicit Runge-Kutta method while an adaptive Runge-Kutta method is used for the stiff part of the system.The paper discusses numerical stability and contractivity as well as the implementation and usage of such compound methods. Test results for three partitioned stiff initial value problems for different tolerances are presented.     

刚性多滞量积分微分方程的Runge-Kutta 方法

本文研究了求解刚性多滞量积分微分方程的Runge-Kutta方法的非线性稳定性和计算有效性.经典Runge—Kutta方法连同复合求积公式和Pouzet求积公式被改造用于求解一类刚性多滞量Volterra型积分微分方程.其分析导出了:在适当条件下,扩展的Runge-Kutta方法是渐近稳定和整体稳定的.此外,数值试验表明所给出的方法是高度有效的.     

Numerical Methods for Stiff Index-3 DAEs

Space semidiscretization of PDAEs, i.e. coupled systems of PDEs and algebraic equations, give raise to stiff DAEs and thus the standard theory of numerical methods for DAEs is not valid. As the study of numerical methods for stiff ODEs is done in terms of logarithmic norms, it seems natural to use also logarithmic norms for stiff DAEs. In this paper we show how the standard conditions imposed on the PDAE and the semidiscretized problem are formally the same if they are expressed in terms of logarithmic norms. To study the mathematical problem and their numerical approximations, this link between the standard conditions and logarithmic norms allow us to use for stiff DAEs techniques similar to the ones used for stiff ODEs. The analysis is done for problems which appear in the context of elastic multibody systems, but once the tools, i.e., logarithmic norms, are developed, they can also be used for the analysis of other PDAEs/DAEs.     

Variable-Order ESIRK Methods for Stiff Differential Equations

ESIRK methods (Effective order Singly-Implicit Runge–Kutta methods) have been shown to be efficient for the numerical solution of stiff differential equations. In this paper, we consider a new implementation of these methods with a variable order strategy. We show that the efficiency of the ESIRK method for stiff problems is improved by using the proposed variable order schemes.     

A new family of A-stable Runge-Kutta methods with equation-dependent coefficients for stiff problems

Numerical Algorithms - A new family of A-stable Runge-Kutta methods with equation-dependent (EDRK) coefficients for the numerical solution of stiff differential equations is investigated. The newly...     

New splitting methods for two-dimensional evolutionary equations

New second- and third-order splitting methods are proposed for evolutionary-type partial differential equations in a two-dimensional space. These methods are derived on the basis of diagonally implicit methods applied to the numerical analysis of stiff ordinary differential equations. The splitting methods are found to be absolutely unconditionally stable. Test calculations are presented.     

Unconditionally stable explicit methods for parabolic equations

Summary This paper discussesrational Runge-Kutta methods for stiff differential equations of high dimensions. These methods are explicit and in addition do not require the computation or storage of the Jacobian. A stability analysis (based onn-dimensional linear equations) is given. A second orderA ₀-stable method with embedded error control is constructed and numerical results of stiff problems originating from linear and nonlinear parabolic equations are presented.     

Comparing the contractivity properties of semi-implicit methods

Contractivity is a desirable property of numerical integration methods for stiff systems of ordinary differential equations. In this paper, numerical parameters are used to allow a direct and quantitative comparison of the contractivity properties of various methods for non-linear stiff problems. Results are provided for popular Rosenbrock methods and some more recently developed semi-implicit methods.     

Exponentially fitted variants of Euler's method for ODEs

A new class of Euler's method for the numerical solution of ordinary differential equations is presented in this article. The methods are iterative in nature and admit their geometric derivation from an exponentially fitted osculating straight line. They are single-step methods and do not require evaluation of any derivatives. The accuracy and stability of the proposed methods are considered and their applicability to stiff problems is also discussed.