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南京航空航天大学学报

1999年8月 第31卷第4期

目 次

理论与试验研究

完全非线性近似逆及其在轨迹跟踪中的应用 贺也平 沈春林(367)

多时滞区间矩阵系统的H∞鲁棒控制 吴庆宪 王 源(373)

参数曲面的拟自适应三角化 沈庆云 周儒荣(381)

深冲钢W08A1热轧模拟试验研究 高 霖 王先进(388)

用遗传算法精确计算圆度误差 廖 平 陆敬舜(393)

矩形喷管内外喷流流场的数值模拟 李 博 梁德旺(398)

直升机“地面共振”的输出反馈最优控制 顾仲权 陈爱华(404)

压电结构的控制结构一体化设计 张俊华 张 方 朱德懋 等(410)

液压减震器动力特性的影响因素研究 汪通悦 曾 励 顾乾坤 等(416)

非对称广义特征值问题的拟Eberlein算法及其并行化 薛长峰 周树荃(422)

卷帘行存储下的一种并行Cholesky分解及其在PAR95上的实现 王顺绪 周树荃(428)

用ｎ表示第n个素数 王友菁 蒋华松(434)

综述

纤维增强树脂基复合材料结构的优化设计 温卫东 徐惠珍 顾玉明 等(436)

研究简报

带极端特征向量的重新开始GMRES算法 王正盛 钟宝江(447)

PID控制器参数的隶属函数自整定技术及其应用研究 张 琦 胡育文 朱剑英(452)

无人机回收气囊缓冲特性研究 戈嗣诚 施允涛(458)

镍钛形状记忆合金丝的性能测试分析 熊 克 陶宝祺 何存富(464)

含孔边裂纹各向异性有限板的二维问题 张志华 王林江 吕庆风(470)

轮辐式航线网的航班计划优化模型 吴桐水 余立华 宁宣熙(475)

几何质量特性的统计控制技术 赵逢余 马义中(480)

学术动态

我校设立校内特聘教授岗位 (427)

国防科工委领导来校视察调研 (484)

《国际航空宇航摘要》(IAA)1998年前3个季度收录我国8种航空航天期刊27期的情况 (380)

“舰面旋翼飞行器旋翼瞬态响应研究”通过技术鉴定 (397)

“GPS姿态及定位定向系统”通过技术鉴定 (433)

外事简讯 (451)

南京航空航天大学召开首届研究生学术会议 (463)

“开关磁阻起动/发电机研究”通过技术鉴定 (483)

　

JOURNAL OF NANJING UNIVERSITY OF AERONAUTICS ＆　ＡＳＴＲＯＮＡＵＴＩＣＳ

August １９９9 Ｖｏｌ．31　Ｎｏ．4

ＣＯＮＴＥＮＴＳ

ＴＨＥＯＲＥＴＩＣＡＬ　ＡＮＤ　ＥＸＰＥＲＩＭＥＮＴＡＬ　ＲＥＳＥＡＲＣＨ

Full Nonlinear Approximate Inversion and Application to Trajectory Track

ing He Yeping， Shen Chunlin(367)

H∞ Robust Control for Interval Matrix Systems with Multiple Time Delay

Wu Qingxian， Wang Yuan(373)

SemiAdaptive Triangulation of Parametric Surface Shen

Qingyun， Zhou Rurong(381)

Hot Deformation Simulation of W08Al DeepDrawingSteel

Gao Lin， Wang Xianjin(388)

A Calculating Metod of Circle Error Using Genetic Algorithms

Liao Ping， Lu Jingshun(393)

Numerical Simulation in Flow Fields of a Rectangular Nozzle

Li Bo， Liang Dewang(398)

Optimal Output Feedback Control for “Ground Resonance” of Helicopter

Gu Zhongquan， Chen Aihua(404)

ControlStructural Synthesis for PiezoelectricStructures

Zhang Junhua， Zhang Fang， Zhu Demao， et al(410)

Study on Influential Factors to Dynamic Characteristics of Hydraulic

Buffers Wang Tongyue， Zeng Li， Gu Qiankun， et al(416)

EberleinLike Algorithm and Parallel EberleinLike Algorithm for Nonsym

metricGeneralized Eigenvalue Problem

Xue Changfeng， Zhou Shuquan(422)

An Algorithm of Cholesky Decomposition at the Storage Pattern of Wrapped

Interleaved Row Storage and Its Implementation on PAR95

Wang Shunxu， Zhou Shuquan(428)

An Expression of the ｎth Prime Number Wang Youjing，

Jiang Huasong(434)

SUMMARIZATION

Optimum Design of FiberReinforced Graphite/Epoxy Composite Structures

Wen Weidong， Xu Huizhen， Gu Yuming， et al(436)

RESEARCH BULLETINS

A Restarted GMRES Method Augmented with Extreme Eigenvectors

Wang Zhengsheng， Zhong Baojiang(447)

Study on Membership Function SelfModify Technique and Application of PID

　

Controller Parameters Zhang Qi， Hu Yuwen， Zhu Jianying(452)

Study on Cushioning Characteristics of Air Bag for RPV Recovery

Ge Sicheng， Shi Yuntao(458)

Measurements and Analyses for Properties of NiTi Shape Memory Alloy Wires

Xiong Ke， Tao Baoqi， He Cunfu(464)

TwoDimensional Problem of Finite Anisotropic Plate with Cracks Emanating

froma Hole Zhang Zhihua， Wang Linjiang， Lｕ¨ Qingfeng(470)

Optimal Scheduling Model of Hub and Spokes Route Network

Wu Tongshui， Yu Lihua， Ning Xuanxi(475)

Statistical Control Technique for Geometrical Performance

　

　

完全非线性近似逆及其在轨迹跟踪中的应用

贺也平 沈春林

(南京航空航天大学自动控制系 南京，210016)

摘要 非线性系统输出跟踪问题在理论和实际中都具有十分重

要的意义。人们对此问题进行了大量地研究和广泛地应用。但是所有的研究对象一般都要求

仿射型非线性系统，以便容易解出相应的控制输入。对于一般的完全非线性系统，由于没有

控制输入的显性表达式，很难得到相应的结果。本文讨论了完全非线性系统的输出跟踪问题

，在理论上研究了完全非线性系统逆的存在性。利用神经网络可逼近任意L2函数的特

性，提出了求解完全非线性系统逆近似控制律的方法，并由此研究了完全非线性飞机模型的

轨迹跟踪问题。通过对飞机轨迹跟踪问题的仿真，表明该方法是切实可行的。

关键词：神经网络；轨迹；非线性逆；输出跟踪；完全非线性

中图分类号：V249；O231

Full Nonlinear Approximate Inversion and Application to Trajectory Tracking

He Yeping Shen Chunlin

(Department of Automatic Control, Nanjing University of Aeronautics & Astronauti

cs Nanjing,210016)

Abstract Output tracking problem for nonlinear systems is of importance to theo

retical and practical applications. There are many approaches and

applications in this field. But all the methods require that the system is affi

ne in the control so as to express tracking control law conveniently. There is l

ittle result for general nonlinear systems in which the control do not linearly

appear because the control input can not be directly solved. In this paper, the

output tracking for general nonlinear systems is discussed. Existence of the ful

l nonlinear inversion is proved. With the property that neural networks are able

to approximate any L2 function uniformly, a technique to approximate nonl

inear inverse is presented. Trajectory tracking of a full aircraft model is simu

lated and satisfactory results are obtained.

Key words: neural networks； trajectories； nonlinear inversion； output trackin

g； full nonlinearity

　

　

　

　

多时滞区间矩阵系统的H∞鲁棒控制

吴庆宪 王 源

(南京航空航天大学自动控制系 南京，210016)

摘要 研究了系统矩阵、时滞矩阵和输入矩阵均含有不确定性

的多时滞区间矩阵系统的Ｈ∞鲁棒控制问题。文中首先针对时滞系统ｘ·（ｔ）＝Ａｘ（ｔ

）＋ΔＡｘ（ｔ－τ）在A稳定条件下，运用根轨迹法，导出时滞系统

稳定的条件；接着运用该条件及Ｈ∞控制方法和实对称矩阵集合最小上界定理，设计了多

时滞区间矩阵系统的Ｈ∞鲁棒控制器。该设计方法把确定多个矩阵不等式共同解的复杂问

题简化为求解单子代数Riccati矩阵方程，所得多时滞区间矩阵系统的Ｈ∞控制律，对于

所有

允许的不确定性，可使闭环系统稳定，且使系统从扰动输入到控制输出的传递函数具有Ｈ

∞范数界。文中算例表明了该方法的有效性。

关键词：稳定性；鲁棒控制；时滞系统；区间矩阵系统；最小上界；H∞控制

中图分类号：TP273；TB114

H∞ Robust Control for Interval Matrix Systems with Multiple Time Delay

Wu Qingxian Wang Yuan

(Department of Automatic Control, Nanjing University of Aeronautics & Astronauti

cs Nanjing，210016)

Abstract The problem of Ｈ∞ robust control for multiple time

delay systems with system matrix， time delay matrix and input matrix being inte

rv

al is studied. First supposing that A is stable, the stability condition of

the time delay system ｘ·（ｔ）＝Ａｘ（ｔ）＋ΔＡｘ（ｔ－τ）　

is o

btained by using the method of root locus. Then based on the stability condition

, Ｈ∞　control theory and the method for determining the minimum upper bou

nd of the real symmetric matrix set, a design method of robust controller for in

terval matrix systems with multiple time delay is presented. In this method, the

co

mplex problem for determining the solution of matrix inequalities is simplified

to solving single algebraic Riccati equation. The Ｈ∞ linear feedback control

law obtained not only stabilizes the closedloop system but also makes the Ｈ

∞ norm of the system transfer function from the disturbance inputs to control

outputs below a given bound over all admissible uncertainties. An illustrative

example is given to demonstrate the effectiveness of the design method.

Key words： stability； robust control； timedelay systems； interval matrix s

ystems； minimum upper bound； Ｈ∞ control

　

　

　

　

　

　

参数曲面的拟自适应三角化

沈庆云

(佛山大学机电一体化研究所 佛山，528000)

周儒荣

(南京航空航天大学CAD/CAM工程研究中心 南京，210016)

摘要 提出了一种参数曲面的拟自适应三角化离散算法。该算

法通过对曲面的参数域进行预剖分，以及引入曲面上一点处的“最大绝对法曲率”的概念，

采用“分而治之”的方法分片对参数曲面的参数域进行三角形网格剖分。该方法基本上可以

像“自适应”方法一样，根据曲面的法曲率变化来控制三角化剖分的密度，生成的三角片数

量较少，并且可以避免在三维空间产生狭长的三角形、退化三角形与“裂缝”，运行速度明

显比自适应方法快。

关键词：参数；自适应性；三角形；参数曲面

中图分类号：TP121; TP391; TP746

SemiAdaptive Triangulation of Parametric Surface

Shen Qingyun

(Siyuan Mechatronics Institute, Foshan University Foshan，528000)

Zhou Rurong

(Research Center of CAD/CAM Engineering, Nanjing Un

iversity of Aeronautics & Astronautics Nanjing,210016)

Abstract A semiadaptive triangulation of parametrically define

d surface is presented. By predividing parametric region of the surface and in

troducing the concept “maximum absolute normal curvature” at a point on the s

urface, the method adopts “divide and conquer” approach triangulating the para

m

etric region of the surface piecewise. Basically like “adaptive approach”, the

method can control triangulation density with respect to the change of normal c

urvature of the surface generating a small number of triangular facets, and thin

y triangles, degenerate triangles and “cracks” in 3D space will not occur, but

the speed of the algorithm is higher than that of adaptive one.

Key words: parameters; adaptivity; triangles; parametric surface

　

　

　

　

深冲钢W08Al热轧模拟试验研究

高 霖

(南京航空航天大学机电工程学院 南京，210016)

王先进

（北京科技大学材料科学与工程学院 北京，100083）

　

摘要 在热模拟试验机上对W08Al深冲钢进行了热轧模拟试验，

测量了材料在不同情况下的相变温度，考察了不同热轧工艺参数对晶粒尺寸和织构的影响。

结果表明，铸坯经预先热变形后重新加热测量相变时，相变温度较低，而直接热变形后测量

相变温度升高；在Ar3温度以上采用大变形量可以使晶粒细化，但在两相区终轧

变形会造成混晶现象；Ar3温度以上热变形所得的变形织构是弱的，进入两相区

终轧变形则不利织构（100）成分很快发展起来，并且织构的取向密度沿板厚方向明显不均

匀。最后对W08Al热轧合理热轧工艺提出了建议。

关键词：热轧；深冲；相变；织构

中图分类号：TG3

Hot Deformation Simulation of W08Al DeepDrawingSteel

Gao Lin

(Department of Mechanical Engineering, Nanjing University of Aeronautics & Astro

nautics Nanjing, 210016)

Wang Xianjin

(College of Material Science and Engineering, Beijing University of Science and

Technology Beijing, 100083)

　

Abstract Hot deformation simulation of W08Al deepdrawingstee

l in a THERMACMASTORZ testing machine is carried out to find out the phase t

ransformation point, the microstructure and texture as influenced by different p

rocessing parameters. The results show that hot predeformation tends to lower

Ar3 while direct hot deformation in as cast condition tend to increase

　

Ar3, that a high deformation reduction reduces the grain size except in

(α＋γ) z

one, and that the unfavorable texture of (100) will rapidly develop as soon as t

emperature drops below Ar3. Modifications of the existing processing parameter

s for the production of W08Al hot rolled plate are suggested to ensure a better

deep drawing quality.

Key words: hot rolling; deep drawing; phase transformations; texture

　

　

　

　

用遗传算法精确计算圆度误差

廖 平

(中南工业大学机电工程学院 长沙，410083)

陆敬舜

(南京航空航天大学机电工程学院 南京，210016)

摘要 提出了一种应用遗传算法计算满足最小区域法的圆度

误差的新思路，并对传统的遗传算法提出了一些改进。采用实数值编码，其计算结果精确

度非常高，理论上可以获得全局最优解；保留上一代种群中适应度最好的个体到下一代，可

以确保解的收敛性；对基于实数值编码的繁殖算子、交叉算子、变异算子给出了具体的操作

方法。仿真结果表明，用改进的遗传算法求解圆度误差，简单明了，收敛速度快，在计算机

上容易实现。

关键词：遗传算法；测量；误差分析；圆度误差

中图分类号：TP2742

A Calculating Metod of Circle Error Using Genetic Algorithms

Liao Ping

(Department of Mechanical Engineering, Central South University of Technology C

hangsha,410083)

Lu Jingshun

(Department of Mechanical Engineering, Nanjing University of Aeronautics & Astro

nautics Nanjing,210016)

　

Abstract Genetic algorithms can effectively find out the optimal

solution but the traditional genetic algorithms has some defects, it exists the

problems of precocity, stagnancy and blind mutaion. Otherwise, its calculating

precision is limited by the length of binary encoding, sometimes it cann′t obta

in the global optimal solution. Some improving methods for the traditional

genet

ic algorithms are discussed and its application in calculating circle error is p

roposed. The realized methods of the reproduction operator, cross operator and m

utation operator on account of real numeric encoding are suggested. Simulation s

hows that real numeric encoding save the best individual into the next generatio

n can effectively improve the accuracy and searching speed for the global optimi

zation. It also shows that the improved genetic algorithms can effectively calcu

late the circle error and can be easily realized by computer.

Key words: genetic algorithms; measurement; error analysis; circle error

　

　

　

　

矩形喷管内外喷流流场的数值模拟

李 博 梁德旺

(南京航空航天大学动力工程系 南京，210016)

摘要 基于Frave平均的NS方程和B/L湍流模型，采用了Jameson

格式和MUSCL格式，对外流在亚声、超声和零Mach数三种状态时矩形喷管的喷流流场进行了

数值模拟，探讨了内外喷流及喷管内的流动特征，并与实验数据进行了比较，计算结果与实

验结果吻合较好，验证了计算所使用的NAPA软件的可靠性，从而为用计算流体力学的方法模

拟具有两股来流的三维湍流流场提供了一种有效的手段。

关键词：流体力学；计算流体力学；喷流；数值模拟

中图分类号：V211.11

Numerical Simulation in Flow Fields of a Rectangular Nozzle

Li Bo Liang Dewang

(Department of Power Engineering， Nanjing University of Aeronautics & Astronaut

ics Nanjing，210016)

Abstract Based on Fraveaveraged threedimensional compressibl

e NavierStokes equations and BaldwinLomax algebraic turbulence model, the je

t flow field of a rectangular nozzle under the state of subsonic, supersonic and

zero Mach number is simulated. The characteristics of the flow from inside and

outside nozzle and jet flow are discussed and the numerical results are compared

with experimental data. The comparison shows that they match well. It verified

the reliability of the NAPA software used in the simulation, and so an effective

method for simulating threedimensional turbulent flow field with two inflows

by computational fluid mechanics is achieved.

Key words: fluid mechanics；computation fluid mechanics； jet stream; numerical

simulation

　

　

　

　

　

直升机“地面共振”的输出反馈最优控制

顾仲权 陈爱华

(南京航空航天大学飞行器系 南京，210016)

摘要 在导出采用SAS的桨距控制的直升机“地面共振”空间模

型的状态方程和输出方程的基础上，研究抑制直升机“地面共振”的控制律综合设计方法。

鉴于工程实用性，宜采用可测得的输出作反馈控制；由于直升机旋翼工作转速范围宽，反馈

控制应保证旋翼从起动到最大工作转速范围内闭环系统全速稳定。因此，提出并研究满

足上述要求的基于输出反馈的次最优控制法与基于观测器的输出反馈最优控制法。仿真计算

表明了这些方法对抑制直升机“地面共振”的有效性。关键词：直

升机；动稳定性；主动控制；地面共振

中图分类号：V21442

Optimal Output Feedback Control for “Ground Resonance” of Helicopter

Gu Zhongquan Chen Aihua

(Department of Aircraft Engineering， Nanjing Unive

rsity of Aeronautics & Astronautics Nanjing, 210016)

Abstracts Based on the deduction of the state and output equat

ions for the space model of “ground resonance” of helicopter using SAS pitch c

ontrol the control law design method for suppressing “ground resonance” of hel

icopter is studied. It is preferable to use feedback control with measurable sta

tes for practical applications. Because of wide range of rotor operated speed, t

he feedback control should guarantee the system stability at the whole speed ran

ge of the rotor from zero to its maximum operated speed. Therefore the control l

aw design methods based on suboptimal control method and optimal observercontr

ol method with measurable states are presented and studied. Simulation calculati

ons show the effectiveness of suppressing “ground resonance” of helicopter by

the methods mentioned.

Key words: helicopters; dynamic stabilities; active control; ground resonance

　

　

　

　

压电结构的控制结构一体化设计

张俊华 张 方 朱德懋 李岳锋

(南京航空航天大学振动工程研究所 南京，210016)

摘要 对于离散分布、同位配置压电片驱动器和传感器的压电

耦合板，首先构造了四节点Kirchhoff矩形板弯单元，从而建立了有限元模型。在此

基础上，给出了主动阻尼振动控制模型。将系统的存留能量指标归结为一个Lyapunov方程的

解。以系统的存留能量指标为适应度函数，以作动器和传感器的位置及控制增益为优化参数

，利用基于共享函数机制小生境技术的遗传算法进行结构、控制设计。最后，对一悬臂

压电耦合板进行了实例分析。结果表明，该方法是解决控制结构一体化设计的一种有效途

径，可以得到多个最优解或次优解。

关键词：控制；结构；振动控制；遗传算法；控制结构一体化设计

中图分类号：TB535；TP206

ControlStructural Synthesis for PiezoelectricStructures

Zhang Junhua Zhang Fang Zhu Demao Li Yuefeng

(Research Institute of Vibration Engineering, Nanjing University of Aeronautics

& Astronautics Nanjing，210016)

　

Abstract A 4node Kirchhoff plate bending element for piezoco

upled plates with distributed collocated piezoelectric actuator and sensor coupl

es is firstly formulated. Thus the finite element model of the distributed syste

m is established. On this basis, the active damping vibration control model is p

resented. The reserved energy index of the thin plate system is reduced as the s

olution of a Lyapunov equation. Thus the reserved energy index is considered as

fitness function. The optimal design of placement and control gains of the piezo

electric actuator/sensor couples is investigated using genetic algorithm with ni

ching based share function. Finally, an example of a cantilever piezocoupled p

late is considered. The results show that the method is an effective technique f

or solving the problem on the control augmentedstructural synthesis, and multi

ple optimal or nearoptimal solutions can be obtained.

Key words: control； structures; vibration control; genetic algorithms; control

structural synthesis

　

　

　

　

液压减震器动力特性的影响因素研究

汪通悦

（淮阴工业专科学校机械工程系 淮阴，223001）

曾 励 顾乾坤 刘正埙

(南京航空航天大学机电工程学院 南京，210016)

摘要 介绍了摩托车液压减震器的结构及原理，建立了其动力

特性的理论模型。通过数字仿真计算研究了液压油的容性、感性等对减震器动力特性的影

响情况，得出了两者影响刚好相反的结论，并与实际测量结果对比，验证了模型的正确性

。这对减震器性能优化及结构改进具有指导价值，为建立基于几何尺寸参数的减震器动力特

性模型奠定了基础。

关键词：液压减震器；动力特性；容性；感性；影响曲线

中图分类号：TH137.9

Study on Influential Factors to Dynamic Characteristics of Hydraulic Buffer

s

Wang Tongyue

(Department of Mechanical Engineering, Huaiyin Industry College Huaiyin, 223001

)

Zeng Li Gu Qiankun Liu Zhengxun

(Department of Mechanical Engineering, Nanjing University of Aeronautics & Astro

nautics Nanjing, 210016)

Abstract Introduces the structure and principle on motorcycle

hydraulic buffers and builds a theoretical model of its dynamic characteristics.

This paper also investigates the influences on the dynamic characteristics of

hydraulic buffers cause

d by the capacity, inductive of hydraulic oil through digital simulative calcula

tion and draws a conclusion that the influences on these two parameters are ju

st contrary. The model′s correctness is verified by comparing with the real mea

surements. It is of guarding value to optimize property, to improve structure on

th

e hydraulic buffers and settles the basis for establishing dynamic characteris

tics model of absorber based on dimension parameter.

Key words： hydraulic buffers； dynamic characteristics； capacity； inducti

ve； influence curve

　

　

　

　

非对称广义特征值问题的拟Eberlein算法及其并行化

薛长峰

（盐城工学院基础部 盐城，224003）

周树荃

(南京航空航天大学理学院 南京，210016)

摘要 非对称广义特征值问题的并行计算，目前在国内外研究

得很少，G.W.Stewart和P.J

.Eberlein曾分别研究非Hermite 矩阵标准特征值的并行拟Jacobi算法，1989年J.P.Charl

ier和P.Van Dooren在G.W.Stewart 的工作基础上提出了求解非对称广义特征值问题的

拟Jacobi算法（简称CV算法）与并行拟Jacobi 算法。文中以J.P.Charlier等人的工

作为基础，提出求解大型非对称广义特征值问题的拟Eberlein算法与并行拟Eberlein算

法，Challenge L 并行系统上的数值试验表明，不仅并行效率很高，且敛速远优于CV算法

。

关键词：算法；广义特征值；并行计算；拟Jacobi型算法；并行拟Jacobi型算法

中图分类号：O241；O342

EberleinLike Algorithm and Parallel EberleinLike Algorithm for Nonsymmetric

Generalized Eigenvalue Problem

　

Xue Changfeng

(Department of Basic Science, Yancheng Institute of Technology Yancheng，224003

)

Zhou Shuquan

(College of Science, Nanjing University of Aeronautics & Astronautics Nanjing,2

10016)

Abstract So far the research of parallel computation for gen

ernalized eigenvalue problem is made to be very little in home and abroad.G.W.st

ewart and P.J.Eberlein made the research of parallel computation for eigenvalue

problem of nonhermitian matrix,respectively.J.P.charlier and P. Van Dooren put f

orward Jacobilike algorithm (CV algorithm) and parallel Jacobilike algorit

hm for nonsymmetric generalized eigenvalue problem. This paper puts forward Eber

leinlike algorithm and parallel Eberleinlike algorithm for solving large sca

le nonsym

metric generalized problem. The numerical results on Challenge L parallel system

show that its parallel efficiency is very high and its convergence speed is mu

ch faster than that of CV algorithm.

Key words:algorithm; generalized eigenvalue; parallel computing; Jacobilike ty

pe algorithm; parallel Jacobilike type algorithm

　

　

　

　

　

　

卷帘行存储下的一种并行Cholesky分解及其在PAR95上的实现

王顺绪 周树荃

(南京航空航天大学理学院 南京，210016)

摘要 Cholesky分解在科学与工程计算中占有重要的地位,串行

的Cholesky分解已有成熟的方法,但并行的Cholesky 分解方法要充分考虑机器体系的结构，

在拥有共享内存的MIMD型多处理机、SIMD型向量机系统上前人已有较好的工作，本文给出适

用于MPP大规模并行计算机的卷帘行存储行格式的并行Cholesky分解算法，该算法使用了优

先计算优先发送的策略，减少了结点机之间相互等待的时间，建立了结点机之间用于通讯的

通讯数组，避免了使用撒播这一通讯模式，减少了通讯时间，通过在PAR95上的数值试验表

明，随着问题规模的扩大，并行效率越来越高，并且该法容易推广到多行卷帘存储的形式。

关键词：对称矩阵；并行处理；Cholesky分解；卷帘存储；MPP处理机系统

中图分类号：O241；O342

An Algorithm of Cholesky Decomposition at the Storage Pattern of Wrapped Interl

eaved Row Storage and Its Implementation on PAR95

Wang Shunxu Zhou Shuquan

(College of Science, Nanjing University of Aeronautics & Astronautics

Nanjing,210016)

Abstract Cholesky method is in a high position in scientific and

engineering calculation. Sequential Cholesky decomposition has been fully deve

loped, but parallel Cholesky decomposition method must take the structure of the

computer into account. The former researchers have achieved satisfying result o

n MIMD with shared memory and SIMD vector computer. This paper gives a parallel

Cholesky method suitable to MPP parallel computer under the storage pattern of

wrapped interleaved row storage. With the strategy of compute ahead and send ahe

ad, the method reduces the waiting time, defines a communicating dimension used

for communication between node computer, avoid broadcasting, so the time need fo

r the communication has been reduced. The numerical experiment on PAR95 shows th

a

t the larger the scale, the higher the efficiency. The algorithm can be easily g

eneralized to the storage pattern of multiple rows wrapped interleaved storage.

　

Key words: symmetric matrices; parallel processing; Cholesky decomposition; wrap

ped interleaved storage; MPP processor system

　

　

　

　

　

用ｎ表示第n个素数

王友菁 蒋华松

(南京林业大学基础部 南京，210037)

摘要 给出一个用ｎ表示第n个素数的公式

ｐ１＝２

ｐｎ＝３＋∑∞ｋ＝１［１＋（ｎ－１/２）－∑ｋｉ＝１ｓｉｎ（２ｉ）２ｉ＋１π

ｓｉｎπ２ｉ＋１ｎ－１/２）－∑ｋｉ＝１ｓｉｎ（２ｉ）２ｉ＋１

πｓｉｎπ２ｉ＋１｜］ （ｎ＝２，３，４，…）

关键词：素数； Wilson定理； 第ｎ个素数

中图分类号：O1561

An Expression of the ｎth Prime Number

Wang Youjing Jiang Huasong

(Department of Basic Courses, Nanjing Forestry University Nanjing,21

0037)

Abstract An expression of the ｎth prime number is given

Key words: prime numbers; Wilson theorem; the ｎth prime number

　

　

　

　

纤维增强树脂基复合材料结构的优化设计

温卫东 徐惠珍 顾玉明 郝 勇

(南京航空航天大学动力工程系 南京，210016)

摘要 综述了国内外纤维增强树脂基复合材料

结构优化设计的研究成果与发展状况，内容涉及到层合板壳结构以及夹层结构的屈曲、振动

、可靠性、结构强度以及多级多目标等问题的优化设计。文中还涉及到发动机复合材料构件

优化方面的一些研究成果，给出了其优化设计的网络框图。论文最后对复合材料结构优

化设计当前存在的主要问题和今后发展方向作了分析，并指出今后的研究方向：（1）

多级多目标多学科的优化设计，不仅涉及到基本理论、建模和方法，而且更加强调工程实际

问题；（2）发展相应的软件专家系统，更加强调软件面向对象编程和CAD技术的应用；（3

）注重探究快速有效的优化算法以及探究随机优化和可靠性优化技术，从而快速有效地获得

对优化设计点的可靠评价等。

关键词：复合材料；振动；可靠性；屈曲；最优设计；多目标；结构强度；发动机

中图分类号：TB332; TH122; O34

Optimum Design of FiberReinforced Graphite/Epoxy Composite Structures

Wen Weidong Xu Huizhen Gu Yuming Hao Yong

(Department of Power Engineering, Nanjing University of Aeronautics & Astronauti

cs Nanjing,210016)

Abstract The optimum design of composite structures is not only

a basic theoretical research and appliedbasic research, but also a design

technology widely applied for engineering.The research results and development

are summarized. In the optimum designs of fiberreinforced graphite/epoxy compo

site structures, which deals with the bucking, vibration, reliabilitybased, st

rength, multilevel as well as multiobjective optimum designs of laminate pla

te, laminate shell and sandwich structures. Some researches on the optimum desig

ns of aeroengine composite structures are discussed as well. Finally, the main

existing problems and the future research in composite optimization designs are

analyzed. It is pointed out that: (1) the optimum design of multilevel and mult

iobjective as well as multidis′ciplinary problems not only deals with the basic

th

eory，modelling and optimum methods, but also emphasizes on solving engineering

problems; (2)the development of software expert systems will stress to use the t

e

chnology of orientated objective programming and CAD;(3) it will be taken much a

ttention to the development of fast and efficient optimum algorithm, as well as

th

e design technology of random optimum and reliabilitybased optimum so as to ob

tain quickly and efficiently the reliable evaluations of design values, and so

on.

Key words: composite materials; vibration; reliability; buckling; optimum desig

n; multiobject; structure strength; aeroengine

　

　

　

　

　

带极端特征向量的重新开始GMRES算法

王正盛 钟宝江

(南京航空航天大学理学院 南京，210016)

摘要 求解大型非对称线性方程组的GMRES算法通常以其重新开

始版本来减少存储量和计算量，而重新开始过程将影响残量的收敛速度。由此可以考虑在重

新开始时保留一些重要信息，如把极端特征值对应的近似特征向量加到新的Krylov子空间中

。这样可以大大加快其收敛速度，而且保持残量最小化性质。

关键词：线性系统；迭代法；Krylov子空间

中图分类号：O241.6

A Restarted GMRES Method Augmented with Extreme Eigenvectors

Wang Zhengsheng Zhong Baojiang

(College of Science, Nanjing University of Aeronautics & Astronautics Nanjing,

210016)

Abstract GMRES method for solving unsymmetric linear systems is

generally used with restarting to reduce storage and orthogonalization cost. Res

tarting slows down the convergence. However, it is possible to save some importa

nt information at the time of the restarting. It is suggested that approximate e

ige

nvectors corresponding to a few of the extreme eigenvalues are formed and are ad

ded t

o the subspace for GMRES. The convergence can be much faster, and the minimal re

sidual property is retained.

Key words： linear systems； iteration method；Krylov subspace

　

　

　

　

　

PID控制器参数的隶属函数自整定技术及其应用研究

张 琦 胡育文

(南京航空航天大学自动控制系 南京，210016)

朱剑英

(南京航空航天大学机电工程学院 南京，210016)

摘要 PID控制技术在工业过程控制中得到了广泛应用，但传统的PI

D控制器不具有参数的在线整定功能，当系统工作条件较差时，难以满足控制要求，从而影

响了控制品质的进一步提高。本文应用模糊数学中的隶属函数, 以工程施工机械中大量应用

的液压阀控油缸为被控对象，建立数学模型和试验系统，实现ＰＩＤ控制器参数的在线自整

定。文中对其理论方法、计算机仿真和应用研究进行了论述。

关键词：自动控制；隶属函数；参数整定

中图分类号：ＴＨ137.52；ＴＰ273

Study on Membership Function SelfModify Technique and Application of PID Contr

oller Parameters

Zhang Qi Hu Yuwen

(Department of Automatic Control, Nanjing University of Aeronautics & Astronauti

cs Nanjing,210016)

Zhu Jianying

(Department of Mechanical Engineering, Nanjing University of Aeronautics & Astro

nautics Nanjing, 210016)

Abstract PID control technique has been used in industrial proce

ss on a large scale. However, it is difficult to selftune the parameters of PI

D controller in the conventional PID technique ontime, so the control quality

is not satisfactory and is difficult to be improved if the operating condition i

s bad. This paper utilizes the membership function theory in dealing with the m

athematical model and experimental device of the valvecontrolcylinder system

which is often used in construction machinery, performs the investigation of th

e theoretic method, computer simulation and tests on the ontime membership fun

ction selfmodify technique of the PID controller parameters. Some results of t

he computer simulation and tests are given.

Key words: automatic control; membership functions; parameter modifying

　

　

　

　

无人机回收气囊缓冲特性研究

戈嗣诚 施允涛

(南京航空航天大学无人机研究所 南京，210016)

摘要 用缓冲气囊的缓冲特性对无人机伞降气囊回收方式进

行了研究，并以单个气囊为对象，分析了影响缓冲性能的主要因素，认为质量体积比m/v

ｉ和排气口面积An是决定缓冲效果的主要因素。在理论分析的基础上给出了质量体

积比m/v

ｉ的最优值，同时建立了排气口分析模型，推导出计算排气口面积的公式，实践证明其

结果是正确的，对工程应用具有特别重要的意义。

关键词：无人驾驶飞机；回收；气囊；缓冲；排气口

中图分类号：V279；V244.1

Study on Cushioning Characteristics of Air Bag for RPV Recovery

Ge Sicheng Shi Yuntao

(Research Institute of Pilotless Aircraft， Nanjing University of Aeronautics &

Astronautics Nanjing，210016)

　

Abstract Research on the cushioning characteristic of air bag fo

r the parachuteair bag recovery system for the remotely piloted vehicle (RPV)

is made. It finds out that the air bags can be used to absorb landing shocks at

normal par

achute sinking speeds with deceleration acceptable for RPVs. This paper analyzes

the main factors affecting the deceleration characteristic such as bag shape,in

itial pressure,initial bag height, masstovolume ratio　(m/vi) and the

area of the flow nozzle　(An) by using a oneair bagsystem,and it is co

ncludes that masstovolume ratio　(m/vi) and the area of the flow nozzl

e　(An) are the main factors.　From the standpoints of maximum deceleratio

n and required stroke,the vertical cylinder appears to be the best shape studied

. The optimal value of m/vi is given and the flow nozzle analysis model is

used to derive the formula of the area of the flow nozzle.The conclusions are p

roved to be true and practical in engineering use.

Key words: pilotless aircraft; recovery; air bag; flow nozzle; cushion

　

　

　

　

　

镍钛形状记忆合金丝的性能测试分析

熊 克 陶宝祺 何存富

(南京航空航天大学智能材料与结构航空科技重点实验室 南京，210016)

　

摘要 从形状记忆合金(SMA)的性能测试和智能材料与结构研究

的角度出发，论述了SMA驱动元件的应力、应变、温度和相变之间的测试关系，并通过分阶

段和不同的变量组合，对直径0.5　ｍｍ的NiTi SMA丝(Ni49.2% at Ti)的基本驱动特性进

行了系统的测试分析，测试内容主要集中于相变温度、自由状态下的最大回复应变、约束状

态下的回复应力等。结果表明，NiTi SMA丝的应力应变温度关系呈现出高度的非线性，

环境温度和外加应力是影响NiTi丝性能的主要因素，外载荷将使相变温度升高；约束回复中

，随着约束应变量的增大和温度的升高，NiTi丝的回复应力也增大。该测试结果为更好地监

测和控制NiTi SMA的驱动行为、设计SMA驱动元件提供了参考依据。

关键词：形状记忆合金；驱动器；测试分析；智能材料与结构

中图分类号：TG139.6; TG115.9; V250.3

Measurements and Analyses for Properties of NiTi Shape Memory Alloy Wires

Xiong Ke Tao Baoqi He Cunfu

(The Key Laboratory for Smart Materials and Structures, Nanjing University of Ae

ronautics & Astronautics Nanjing,210016)

　

Abstract The testing methods for shape memory alloy (SMA) are pr

oposed b

ased on material evaluation technology and requirement of smart materials and st

ructures.The important relationships among strain, stress, resistance and temper

ature of NiTi SMA wires (Ni49.2% at Ti , 0.5 mm in diameter) are synthetically

tested and analyzed by different combination of parameters.The research concentr

ates on primary actuating properties of NiTi wires, such as phase transformatio

n process, recovery strain in free condition, recovery stress at different restr

ained strains(2.14%, 2.87% and 3.6%) and stresstemperature factors at differen

t restrained stresses　(50 MPa,75 MPa and 100 MPa ), which are mainly affected b

y te

mperature and applied stress. Experimental results are very useful to monitor th

e actuating behaviors and to design actuators of NiTi SMA in smart materials and

structures.

Key words： shape memory alloys; actuators; measurement and analysis; smart mate

rials and structures

　

　

　

　

　

　

含孔边裂纹各向异性有限板的二维问题

张志华 王林江 吕庆风

(南京航空航天大学无人机研究所 南京，210016)

摘要 应用边界元法，并结合一种特殊的复变函数基本解，研

究了含孔边裂纹的各向异性有限板的应力强度因子修正系数的计算。这种特解边界元法避免

了在裂纹

附近划分单元，可以获得较好的数值计算精度。通过算例分析，结果表明本方法精度高，运

算量小，具有一定的工程应用价值。

关键词：应力集中；边界元法；各向异性有限板；孔边裂纹

中图分类号：TB123；TP3016；TB115

TwoDimensional Problem of Finite Anisotropic Plate with Cracks Emanating from

a Hole

Zhang Zhihua Wang Linjiang Lｕ Qingfeng

(Research Institute of Pilotless Aircraft, Nanjing

University of Aeronautics & Astronautics Nanjing，210016)

　

Abstract A boundary element formulation incorporating a derived

fundamental as its kernels is developed. The boundary element equation extends

only over the portion of boundary, not including the surface of elliptical hol

e or the crack. Thus numerical difficulties associated with modelling stress con

centration or singularity can be avoided and better numerical accuracy obtained.

Examples are given in which the stress concentration factors are obtained

with

the procedure compiled by this paper. The results show that the method has bett

er accuracy and less calculating time. This method is valuable in engineering ca

lculation.

Key words: stress concentration; boundary element methods; finite anisotropic pl

ate; crack emanating from a hole

　

　

　

　

轮辐式航线网的航班计划优化模型

吴桐水 余立华

（中国民航学院经管系 天津，300300）

宁宣熙

(南京航空航天大学工商学院 南京，210016)

摘要 分析了轮辐式航线网布局模式的特征，提出了在轮辐式

航线网上进行航班计划优化所要考虑的主要因素，进而独立研究了该种布局模式的航班计划

优化模型。并通过一个案例说明该种轮辐式航线网航班计划优化模型的应用。

关键词：最佳航线；数学模型；航线网；枢纽站；辐射航线；城市对的航线结构

中图分类号：O157.5;F562.1

Optimal Scheduling Model of Hub and Spokes Route Network

Wu Tongshui Yu Lihua

(Operation and Management Department, Civil Aviation Institute of Ch

ina Tianjing,300300)

Ning Xuanxi

(Business and Management College， Nanjing University of Aeronautics & Astronau

tics Nanjing,210016)

Abstract Analyses the features of Hub and Spokes route

network, presents the main factors which should be considered during the proces

s of optimizing the Hub and Spokes route network schedule, and firstly presents

the mathematics model of optimizing the schedule of Hub and Spokes route network

. Furthermore, this paper constructs a Hub and Spokes route network exampl, and

analyses the application of the optimal scheduling model on this route network

.

Key words: optimal routes; mathematical models; routes networks; hub; spoke rou

te; city pairs route structure

　

　

　

　

几何质量特性的统计控制技术

赵逢余 马义中

(郑州航空工业管理学院质量工程研究所 郑州，450005)

摘要 采用常规控制图的基本假设是生产过程的输出变量服从

正态分布。在实际生产中，虽然生产过程的某些质量特性(如形状与位置等几何质量特性)也

呈现正态分布，但由于测量工具及这些特性自身的特殊性，测量数据通常呈现出以目标值为

折叠点的折叠正态分布，这就无法应用常规的统计控制技术。为了解决这种情况下的质量控

制问题，本文分析了形状与位置等几何质量特性测量过程中的特殊性，以及测量数据的分布

规律，在此基础上，给出了评价工序能力的方法，构造了相应的控制图，并设计了相应的中

文软件。实证结果表明：该软件既简单又实用，能适用于大部分形状和位置质量特性的质量

控制问题。

关键词：几何；质量；统计；控制；折叠正态分布

中图分类号：TP39；F273；V2605

Statistical Control Technique for Geometrical Performance

Zhao Fengyu Ma Yizhong

(Quality Engineering Department, Zhengzhou Institute of Aeronautical Industrial

Management Zhengzhou,450005)

　

Abstract Traditionally, control charts are applied for assuming

that process observations follow normal distribution. Unfortunately, this assump

tion is frequently violated in practice. This is because most geometry errors of

mechanical parts are distributed foldednornally by virtue of measurement tool

s and methods. They make conventional control chart invalid.In order to deal wit

h this problem, this paper discusses the specific features in measuring geometr

ical performance and sets up the distribution function for this kind of measured

data. On the basis of that, the method of evaluating the process performance is

given, the related process control approach is presented and the software for f

eature of geometries performance analysis and control is introduced. The results

show that the software is both simple and useful, and can be used to monitor p

roduction process being of quality characteristics of gemetry errors.

Key words： geometry; quality; statistics; control; folded normal distributions