Solar Weather Event Modelling and Prediction

Key drivers of solar weather and mid-term solar weather are reviewed by considering a selection of relevant physics- and statistics-based scientific models as well as a selection of related prediction models, in order to provide an updated operational scenario for space weather applications. The characteristics and outcomes of the considered scientific and prediction models indicate that they only partially cope with the complex nature of solar activity for the lack of a detailed knowledge of the underlying physics. This is indicated by the fact that, on one hand, scientific models based on chaos theory and non-linear dynamics reproduce better the observed features, and, on the other hand, that prediction models based on statistics and artificial neural networks perform better. To date, the solar weather prediction success at most time and spatial scales is far from being satisfactory, but the forthcoming ground- and space-based high-resolution observations can add fundamental tiles to the modelling and predicting frameworks as well as the application of advanced mathematical approaches in the analysis of diachronic solar observations, that are a must to provide comprehensive and homogeneous data sets.     

Dynamical Systems Approach to Space Environment Turbulence

Space plasmas are dominated by waves, instabilities and turbulence. Dynamical systems approach offers powerful mathematical and computational techniques to probe the origin and nature of space environment turbulence. Using the nonlinear dynamics tools such as the bifurcation diagram and Poincaré maps, we study the transition from order to chaos, from weak to strong chaos, and the destruction of a chaotic attractor. The characterization of the complex system dynamics of the space environment, such as the Alfvén turbulence, can improve the capability of monitoring Sun-Earth connections and prediction of space weather. This revised version was published online in August 2006 with corrections to the Cover Date.     

基于径向基函数的变量预测模型模式识别方法

针对变量预测模型模式识别方法中4种数学模型不足以反映特征值之间复杂关系的缺陷.因此,提出了一种基于径向基函数的变量预测模型(VPMRBF)模式识别方法,把提取的特征值输入到VPMRBF分类器中,然后通过训练样本建立反映特征值之间复杂关系的径向基函数预测模型,最后把测试样本的特征值作为径向基函数预测模型的输入,以预测误差平方和为依据完成分类.该方法充分有效地利用并且结合径向基函数和变量预测模式识别方法的优点,实现了故障特征提取到故障识别的全程诊断. 滚动轴承故障诊断实验分析结果表明:与径向基神经网络、支持向量机和变量预测模式识别方法相比,VPMRBF的识别率分别提高了4.75%,1.75%和5.25%.      

混合神经网络和混沌理论的股票价格预测研究

针对股票时间序列的非线性特点,结合混沌理论和神经网络理论,提出了基于混沌理论的股票价格神经网络预测方法。同时利用重构相空间的嵌入维数确定神经网络的结构,对实际的股票时间序列预测结果表明,该方法能有效地进行短期预测,在股票时间序列预测中有广泛的实用价值。     

非线性时间序列的动力学混沌特征自动提取技术

提出了一种非线性时间序列混沌特征的自动提取方法.该方法直接根据非线性时间序列, 依次计算出延迟时间、嵌入维数、相关维数、最大李雅普诺夫指数、相轨迹特征以及Poincare特征等混沌特征, 整个特征的提取过程自动完成, 毋须人工干预.最后用算例表明了该方法的有效性和正确性.该方法对于利用非线性混沌特征进行非线性系统故障诊断和趋势预测具有重要意义.      

Reference Models of Nations

This paper describes several reference models of a nation such that the development of these models will facilitate the understanding of such models of nations and assist in their use by decision-makers for the purpose of achieving a more stable and peaceful set of relationships among countries. Through the development and understanding of these reference models of nations, and the understanding of their use in national decision-making, it should be possible to use more effectively the methodology of systems, man, and cybernetics to help bring about a more peaceful world in which cooperative security among nations is possible.     

球轴承内圈剥落缺陷双冲击特征动力学建模

基于Hertz接触理论,以内圈滚道表面存在局部剥落的球轴承为研究对象,对球轴承局部剥落故障所激起的非线性激励机理进行研究,分析球轴承双冲击现象激励机理。将滚动体与球轴承内外圈非线性接触特性纳入考虑,提出时变位移激励与时变接触力激励相耦合的球轴承局部剥落双冲击现象动力学模型。研究中采用Runge-Kutta数值积分法求解该二阶非线性动力学微分方程,并对故障球轴承仿真信号进行双冲击时间间隔特征验证。在不同转速和内圈剥落尺寸条件下开展仿真与实验研究,通过仿真和实测信号的双冲击时间间隔与理论双冲击时间间隔对比分析,仿真信号的双冲击时间间隔与理论值对比的误差结果皆小于2%,与实测信号的双冲击时间间隔值对比的误差结果皆小于12%;同时,仿真信号与实测信号具有很好的相似性,从而验证了该动力学模型的有效性。      

全流量补燃循环发动机系统的响应特性

以全流量补燃循环氢氧发动机系统为研究对象,对其的动态响应特性进行了研究。建立了描述全流量补燃循环发动机动态特性的非线性数学模型,将免疫策略算法同龙格-库塔法结合起来,提出了求解含有隐式项的常微分方程组的变步长龙格-库塔方法,并应用该方法对全流量补燃循环发动机系统的动态响应特性进行了仿真计算。计算结果表明,当发动机在某一个稳定工况工作时,发动机入口推进剂压强的变化对发动机性能参数的影响不大,发动机的参数都能比较平稳的过渡到一个新的稳定工况;当发动机在短时间内进行小范围的推力调节时,发动机参数的过渡过程的曲线也比较平稳,但是当在短时间内进行大范围推力调节时,参数的过渡过程的曲线振动比较剧烈,因此应当在进行大范围推力调节时,应当对调节时间进行适当延长,或者分级进行推力调节。      

证券投资组合的优化分析

在日趋发达的商品经济社会,证券投资在各类经济活动中有着重要的地位.如何从几种证券中选择最优投资组合,这就是证券投资组合分析的内容.主要介绍从建立数学模型,选用非线性分析的数值计算方法,到在微机上实现的过程和最终的分析结果.     

Chaotic zero dynamics in kinematically redundant robots

The authors attempt to integrate two areas in robotics that are maturing rapidly: the control of kinematically redundant rigid robots and feedback linearization. Kinematically redundant robots have several advantages over nonredundant robot arms. The extra degrees of freedom are used to reach around or between obstacles. Unlike nonredundant rigid link robots that do not exhibit zero dynamics, the self motions of kinematically redundant robots can be used for torque optimization or avoiding obstacles. It is shown that induced self motions can be chaotic. The main contribution is to demonstrate chaos in cases of feedback linearization when the decoupling matrix is nonsquare and there are less outputs than inputs     

Observing Chaos in External Spiral Galaxies

The feasibility of observing chaotic behavior in the stellar component of spiral galaxies is discussed. Three sources for development of chaos are considered namely: steep potential gradients, resonances and growing spiral perturbations. Several regions where chaos could be expected are identified such as the very central region, the end of the bar, the start of the main spiral pattern and the termination of strong spiral arms.The main observational signature is likely to be an increased velocity dispersion while multiple peaks in the velocity profile due to bifurcation of the main family of periodic orbits near resonances could be viewed as an indicator of increased stochasticity. It is non-trivial to distinguish between a higher velocity dispersion due to chaotic motions and non-periodic orbits trapped around the central family of stable periodic orbits. This requires a good dynamic model which can be obtained by combining near-infrared K surface photometry maps and kinematic information.The ESO VLT 8m unit telescopes were taken as a reference to judge if it is feasible to observe chaos in disk galaxies with current state-of-the-art equipment. Whereas surface photometry map easily can be obtained with smaller telescopes, detailed line-of-sight velocity profiles from absorption lines are difficult to observed below an isophotal level of I20 mag/ even with an 8m class telescope. This suggests that it would be possible to observe chaotic behavior in spiral galaxies out to the end of the bar or start of the main spiral pattern but not further out in the spiral arms.     

基于极大代数的离港航班优化调度

改变以往采用的排队论和线性规划等方法，用极大代数理论研究了航班调度优化问题，将进离港系统的非线性转化为极大代数意义下的线性，结合离散事件动态系统理论(DES)的摄动分析法、鲁棒分析法，论证了不同机型排列对系统性能的影响?运用这一方法，实现了对机型排列的寻优，为科学的航班调度提供了定量的参考：     

民用涡扇发动机预测控制器设计

对一定包线范围内的稳态预测控制器和加速减速过渡态控制器设计展开研究.针对某大涵道比民用涡扇发动机,根据发动机进口参数的相对变化指标对控制区域进行划分,以标称点处发动机线性模型为对象设计了相应的预测控制器,利用提出的多层参数调度方案实现了不同飞行条件及不同发动机状态下预测控制器参数的自适应调整.仿真结果表明:所设计的发动机预测控制系统在控制区域内的设计点和非设计点均具有良好的性能,为全包线设计提供了有效方法.     

金属橡胶隔振器产生混沌的解析预测

在考虑金属橡胶隔振系统的非线性刚度和非线性迟滞恢复力的基础上,建立了金属橡胶隔振器的非线性动力学方程.根据非线性振动理论,得出了系统在弱非线性情况下的一次谐波慢变参数的平均化方程;推出了谐波慢变参数状态方程的离散化映射,获得了金属橡胶隔振器出现混沌的解析条件.      

结合不确定度的发动机模型辨识气路诊断

针对航空发动机气路诊断中测量参数个数小于待诊断参数个数的不适定问题,利用了发动机平衡技术,结合非线性的发动机数学模型,并综合考虑了测量参数的不确定度和理论模型部件性能的不确定度,建立了一种结合不确定度的发动机气路故障诊断辨识算法——变分加权最小二乘法,并将该算法应用于某发动机的诊断分析中.结果表明:运用该方法可分析出测量数据和模型计算数据之间的差别,同时,利用所得的故障参数修正量修正原发动机数学模型,使模型计算推力与试验测量推力最大偏差由8.25%减小到1.66%,耗油率最大偏差由6.25%减小到1.50%.      

考虑表面波纹度的滚动轴承-转子系统非线性动力特性

提出了考虑滚动轴承内外圈滚道表面波纹度、Hertzian弹性接触力和径向游隙等非线性因素的滚动轴承模型,建立了滚动轴承-转子系统的动力学微分方程,并用Runge-Kutta-Felhberg算法对其求解.利用分岔图、Poincaré映射图和频谱图,分析了参数变化时的滚动轴承-转子系统的分岔、混沌等非线性动力特性.结果表明:外圈波纹度波数与滚动轴承滚珠数目相等时,转子系统会产生强烈振动;转子系统进入混沌的主要途径是倍周期分岔;内圈波纹度引起的振动频率与波数有明确的函数关系.      

共轴式直升机线性系统建模

应用小扰动理论和数值法,对共轴式直升机飞行动力学非线性数学模型进行线性化,获得了用于操稳特性分析和控制系统设计的共轴式直升机线性化模型.以某型共轴式直升机为研究对象,计算其稳定性导数和控制导数,结果与俄罗斯计算结果基本一致,并对研究对象的稳定性进行了初步分析.     

Optimal assimilation for ionospheric weather – Theoretical aspect

Observation, specification and prediction of ionospheric weather are the key scientific pursuits of space physicists, which largely based on an optimal assimilation system. The optimal assimilation system, or commonly called data assimilation system, consists of dynamic process, observation system and optimal estimation procedure. We attempt to give a complete framework in this paper under which the data assimilation procedure carries through. We discuss some crucial issues of data assimilation as follows: modeling a dynamic system for ionospheric weather; state estimation for static or steady system in sense of optimization and likelihood; state and its uncertainty estimation for dynamic process. Meanwhile we also discuss briefly the observability of an observation system; system parameter identification. Some data assimilation procedures existed at present are reviewed in the framework of this paper. As an example, a second order dynamic system is discussed in more detail to illustrate the specific optimal assimilation procedure, ranging from modeling the system, state and its uncertainty calculation, to the quantitatively integration of dynamic law, measurement to significantly reduce the estimation error. The analysis shows that the optimal assimilation model, with mathematical core of optimal estimation, differs from the theoretical, empirical and semi-empirical models in assimilating measured data, being constrained by physical law and being optimized respectively. The data assimilation technique, due to its optimization and integration feature, could obtain better accurate results than those obtained by dynamic process, measurement or their statistical analysis alone. The model based on optimal assimilation meets well with the criterion of the model or algorithm assessment by ‘space weather metrics’. More attention for optimal assimilation procedure creation should be paid to transition matrix finding, which is usually not easy for practical space weather system. High performance computing hardware and software studies should be promoted further so as to meet the requirement of large storage and extensive computation in the optimal estimation. The discussion in this paper is appropriate for the static or steady state or transition process of dynamic system. Many phenomena in space environment are unstable and chaos. So space environment study should include and integrate these two branches of learning. This revised version was published online in August 2006 with corrections to the Cover Date.     

水平盘旋下裂纹转子的非线性响应

研究了裂纹转子在平飞和水平盘旋状态下的非线性响应, 建立了水平盘旋下裂纹转子的数学模型, 推导了转子运动方程.由结果发现:响应进入混沌的道路有拟周期环面破裂、周期3运动失稳和阵发性混沌进入混沌3条.水平盘旋一般会对系统的非线性响应起到抑制作用, 但是系统响应的振幅明显增大, 因此增大了转轴发生断裂和转子碰摩的可能性;并且, 水平盘旋会激起转子摆振临界转速分频附近的非线性振动.      

不可压缩平板边界层转捩中突变过程的数值模拟

采用时间模式对不可压平板边界层从层流到湍流的转捩过程进行了直接数值模拟.分析结果表明:在层流-湍流转捩的突变过程开始之前,已经产生非线性作用;二维波与三维波的幅值实际增长率也偏离线性状态,而且在二者之间存在能量转移的迹象.在突变过程中,速度变形率对总应力的影响较大,在转捩结束后雷诺应力对总应力的影响比较显著.研究表明:正是由于大量谐波被快速激发并增大,导致了雷诺应力及其法向梯度也快速增大.这使得平均流剖面快速被修正,流动快速转为湍流.