基于Vega Prime的高空飞艇视景仿真设计

针对高空飞艇在飞行控制半物理仿真实验中实时数据可视化的问题,基于虚拟仿真技术,提出了一种高空飞艇视景仿真系统设计方案。建立了高空飞艇三维模型,并使用细节层次等高级建模技术对三维模型数据库进行了优化。提出了通过反射内存网与半物理仿真系统进行实时数据传输的方式,在Vega Prime环境下完成了基于控制台的视景仿真程序开发。在硬件系统支持下,实现了高空飞艇飞行过程仿真场景的立体渲染,仿真效果能够满足半物理仿真实验数据的实时逼真显示要求。     

快速有效的摄像机标定方法

提出了一种快速有效的基于径向约束的两步算法.该算法综合了线性模型和非线性模型的优点,在求解摄像机参数的过程中,采用线性模型标定摄像机中的一部分参数,进一步考虑非线性畸变,通过条件化简将非线性方程转化成线性方程求解其余摄像机参数,有效避免了直接求解非线性方程带来的计算繁琐和结果不稳定的缺陷.最后对标定结果采取最优化算法求精.实验结果表明,优化后的两步算法提高了摄像机标定的效率和准确性.     

不确定线性系统混合H_2 /H_∞ 鲁棒输出反馈控制

解决了在系统状态空间模型的状态与输出矩阵中含有范数有界参数不确定线性系统的混合H2 /H∞ 鲁棒输出反馈控制问题 .所推导的满阶控制器对于所有可容许的参数不确定都能满足给定的H∞ 干扰衰减水平 ,且为最坏情形H2 代价函数提供了一个最优的上界 .所得的结果需要求解一个含有尺度参数的修正代数Riccati方程以及三个含有尺度参数的交叉耦合非线性方程 .而且 ,也给出了一个求解这些含有尺度参数非线性方程的数值算法 .     

TOA定位算法非线性优化问题研究

无线传感器网络中基于到达时间TOA（time of arrival）的定位算法需要建立关于未知节点与锚节点距离的非线性方程。牛顿迭代法是求解非线性线方程数值解的有效方法。分析了一种基于牛顿迭代法求解TOA定位非线性方程的算法,提出了对应的牛顿迭代式。仿真结果表明,此算法可以满足定位的需求,且具有比经典CHAN算法更高的定位精度。     

求解非线性方程及方程组的人工蜂群算法

提出了用蜂群算法求解非线性方程和方程组。通过计算几个非线性方程和方程组问题,将结果与其他算法进行比较与分析,验证了算法的有效性。     

非线性方程求解在程序中的应用

本文借助应用极为广泛的求解非线性方程为例,通过对牛顿迭代法和弦截法求解过程分析,提出了一种新的求解非线性方程根的迭代公式及计算程序。用这种公式收敛速度快、精度高,具有一定的推广实用价值。     

Redhawk平台下飞机制动系统仿真研究

飞机制动系统的半物理仿真研究是提高飞机总体设计极为重要和有效的环节之一.以Redhawk并行仿真计算机为硬件平台,将刹车控制单元和液压模拟系统作为实物模型,在先进的SimulationWorkbench(SWB)仿真环境下对飞机制动系统进行了半物理仿真研究.经仿真测试,该仿真系统设计合理、有效,能够满足飞机防滑制动系统性能的要求.该系统对构建高性能飞机防滑制动系统的研究具有工程实际意义.     

非线性方程和方程组求解的安全两方计算协议

以实系数一元二次方程为研究对象,给出针对非线性方程的安全计算协议。在半诚实模型下,协议能够完成求解的计算任务,并且协议的正确性和保密性也得到了论述。在求解一元二次方程安全两方协议的基础上,对两种类型的二次方程组进行了研究,进一步给出相应情形下的安全两方计算协议。     

基于模型的虚拟温度传感器设计

针对航空发动机控制系统的半物理仿真过程中实时温度场难以模拟、接口电路的温度通道不能检验等问题,提出了一种基于模型的虚拟温度传感器设计思路。在Matlab/Simulink平台上建立传感器的变时间常数算法模型,使用RTW-EC的自动生成代码工具基于数字信号处理器(DSP)C2000微控制器设计了虚拟温度传感器,进一步结合CCS集成开发环境(IDE)对所生成的温度传感器代码进行了处理器在环(PIL)验证。仿真结果表明:所构建的虚拟传感器能够高精度模拟真实温度传感器的特性,可以满足航空发动机控制系统半物理仿真试验的要求。     

排爆机器人机械臂定位精度误差自动补偿方法研究

针对于排爆机器人在进行排除爆破物质时,机械臂不能满足绝对准确的定位要求,位置检测精度与实际距离之间存在一定的误差。为了解决这一问题,提出排爆机器人机械臂定位精度误差自动补偿方法。基于D-H运动模型和微分变换法创建排爆机器人机械臂位姿误差模型,对误差模型进行重复参数分析,去除重复参数获得可辨识的线性方程;在可辨识的运动学参数误差模型线性方程中加入一个增量进行误差补偿。最后通过仿真实验结果表明,所提方法通过对机械臂位姿误差模型进行有效补偿,使排爆机器人机械臂绝对定位精度均值提升1.3mm。     

Reduction of stable differential–algebraic equation systems via projections and system identification

Most large-scale process models derived from first principles are represented by nonlinear differential–algebraic equation (DAE) systems. Since such models are often computationally too expensive for real-time control, techniques for model reduction of these systems need to be investigated. However, models of DAE type have received little attention in the literature on nonlinear model reduction. In order to address this, a new technique for reducing nonlinear DAE systems is presented in this work. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. Additionally, the algebraic equations of the resulting system can be replaced by an explicit expression for the algebraic variables such as a feedforward neural network. This last property is important insofar as the reduced model does not require a DAE solver for its solution but system trajectories can instead be computed with regular ODE solvers. This technique is illustrated with a case study where responses of several different reduced-order models of a distillation column with 32 differential equations and 32 algebraic equations are compared.     

A method and a software package for numerical solution of the systems of nonlinear ordinary integro-differential-algebraic equations

A method, an algorithm and a software package for automatically solving the ordinary nonlinear integro-differential-algebraic equations (IDAEs) of a sufficiently general form are described. The author understands an automatic solution as obtaining a result without carrying out the stages of selecting a method, programming, and program checking. Both initial and boundary value problems for such equations are solved. It is assumed that the complete set of boundary and initial conditions at the beginning of the integration interval are given. By performing differentiation, the system of IDAEs can be modified, in general, into a system of ordinary nonlinear differential equations (IDEs). The problem of finding the solution of the above-mentioned system on the uniform grid on the integration interval is posed in two forms: as solving the system of IDAEs and as solving the appropriate system of IDEs, where the developed program is to be used. In order to reduce the system of IDAEs and the system of IDEs to the systems of ordinary nonlinear algebraic equations, at every stage of the algorithm the integration and differentiation formulas obtained earlier by N.G. Bandurin are used. Systems similar to those test systems of both nonlinear IDAEs and IDEs considered in this investigation are solved by using the computer programs. It is evident that the coincidence of the results for one and the same system of equations in its different forms can serve as good evidence of the correctness of the obtained results.     

无条件稳定的显式降维非线性有限元

针对传统降维非线性有限元计算速度与精确度难以兼顾的问题,提出了一种无条件稳定的显式迭代算法。基于泰勒展开式得到速度、加速度的三阶精度差分表达式从而获得新的有限元显式迭代方程,并分析其单自由度系统下的传递矩阵谱半径。改进迭代方程使谱半径始终小于1从而满足无条件稳定的要求。实验表明,改进后的显式迭代算法在等效阻尼比的精度上优于中心差分法和隐式迭代法;在降维非线性有限元模型计算中的计算耗时优于隐式迭代方法,提高了降维非线性有限元的迭代计算速度。模型在降维后维度数值较高时,仍能维持良好的计算耗时和帧率,保证了模型的精确度。     

New analytical method for solving Burgers' and nonlinear heat transfer equations and comparison with HAM

In this study, we present a numerical comparison between the differential transform method (DTM) and the homotopy analysis method (HAM) for solving Burgers' and nonlinear heat transfer problems. The first differential equation is the Burgers' equation serves as a useful model for many interesting problems in applied mathematics. The second one is the modeling equation of a straight fin with a temperature dependent thermal conductivity. In order to show the effectiveness of the DTM, the results obtained from the DTM is compared with available solutions obtained using the HAM [M.M. Rashidi, G. Domairry, S. Dinarvand, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 708-717; G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 489-499] and whit exact solutions. The method can easily be applied to many linear and nonlinear problems. It illustrates the validity and the great potential of the differential transform method in solving nonlinear partial differential equations. The obtained results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations and nonlinear ordinary differential equations that we are found to be in good agreement with the exact solutions.     

A modification of Davidenko''s method for nonlinear systems

In 1953 Davidenko showed how to reduce the solving of a system of nonlinear equations to the integration of a system or ordinary differential equations. This method also required the solution of linear algebraic equations at each integration step, which is computationally undesirable. We show how to reduce the solving of a system of nonlinear equations solely to the integration of a system of ordinary differential equations, avoiding entirely the solution of linear algebraic equations. A numerical example shows interesting differences between the two approaches in the neighborhood of a bifurcation point.     

Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs

The methods for the dynamical simulation of multi-body systems in real-time applications have to guarantee that the time integration of the equations of motion is always successfully completed within an a priori fixed sampling time interval, typically in the range of 1.0–10.0 ms. Model structure, model complexity and numerical solution methods have to be adapted to the needs of real-time simulation. Standard solvers for stiff and for constrained mechanical systems are implicit and cannot be used straightforwardly in real-time applications because of their iterative strategies to solve the nonlinear corrector equations and because of adaptive strategies for stepsize and order selection. As an alternative, we consider in the present paper noniterative fixed stepsize time integration methods for stiff ordinary differential equations (ODEs) resulting from tree-structured multi-body system models and for differential algebraic equations (DAEs) that result from multi-body system models with loop-closing constraints.     

新型GPS罗经系统的设计与动态仿真实现

关于优化船体导航的快速性,在船姿态测量问题的研究中,现有导航GPS对船体姿态测量运算量大,动态实时性差的特点。为解决上述问题,提出先建立卫星与基线间的空间基本模型,然后将基本模型在实际应用框架中进行讨论,在充分利用其几何关系传递与三角函数运算后,将二元非线性方程组化简为类一元高阶方程的形式,然后结合计算机对一元高阶方程求解的快速捕捉能力,以最短的时间获得方程组的函数解,而后确定对姿态求解。解决了以往无法直接求取解析解的难题,使方程的转化与计算机处理有机结合在一起。仿真结果表明,在同样精度要求下方法更快速、有效。     

Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations

In this paper, we study the simulation of nonlinear Schrödinger equation in one, two and three dimensions. The proposed method is based on a time-splitting method that decomposes the original problem into two parts, a linear equation and a nonlinear equation. The linear equation in one dimension is approximated with the Chebyshev pseudo-spectral collocation method in space variable and the Crank–Nicolson method in time; while the nonlinear equation with constant coefficients can be solved exactly. As the goal of the present paper is to study the nonlinear Schrödinger equation in the large finite domain, we propose a domain decomposition method. In comparison with the single-domain, the multi-domain methods can produce a sparse differentiation matrix with fewer memory space and less computations. In this study, we choose an overlapping multi-domain scheme. By applying the alternating direction implicit technique, we extend this efficient method to solve the nonlinear Schrödinger equation both in two and three dimensions, while for the solution at each time step, it only needs to solve a sequence of linear partial differential equations in one dimension, respectively. Several examples for one- and multi-dimensional nonlinear Schrödinger equations are presented to demonstrate high accuracy and capability of the proposed method. Some numerical experiments are reported which show that this scheme preserves the conservation laws of charge and energy.     

Fast Fourier-Galerkin Methods for Nonlinear Boundary Integral Equations

We develop in this paper a fast Fourier-Galerkin method for solving the nonlinear integral equation which is reformulated from a class of nonlinear boundary value problems. By projecting the nonlinear term onto the approximation subspaces, we make the Fourier-Galerkin method more efficient for solving the nonlinear integral equations. A fast algorithm for solving the resulting discrete nonlinear system is designed by integrating together the techniques of matrix compressing, numerical quadrature for oscillatory integrals, and the multilevel augmentation method. We prove that the proposed method enjoys an optimal convergence order and a nearly linear computational complexity. Numerical experiments are presented to confirm the theoretical estimates and to demonstrate the efficiency and accuracy of the proposed method.     

Exponential difference schemes with double integral transformation for solving convection-diffusion equations

Convection-diffusion equations are studied. These equations are used for describing many nonlinear processes in solids, liquids, and gases. Although many works deal with solving them, they are still challenging in terms of theoretical and numerical analysis. In this work, the grid approach based on the method of finite differences for solving equations of this kind is considered. In order to make it easier, the one-dimensional version of such an equation was chosen. However, the equation preserves its principal properties; i.e., it is non-monotonic and non-linear. To solve boundary-value problems for such equations, a special variant of the non-monotonic sweep procedure is proposed.