基于未知输入观测器的非线性动态系统故障估计

针对一类受扰非线性动态系统的执行器故障估计问题,提出一种未知输入观测器来实现故障估计。首先,通过坐标变换将原系统转化为合适的形式;其次,采用线性矩阵不等式与Lyapunov泛函分别设计H_∞输出反馈控制器和未知输入观测器,在此基础上实现对系统中执行器故障的渐近估计;最后,通过机械臂系统仿真分析并验证了所提方法的有效性。与已有方法相比,所提方法不要求故障可导,也不要求故障或干扰上界已知,因此易于在工程实际中实现对非线性系统执行器故障的估计。     

高超声速内收缩进气道分步优化设计方法

提出了基准流场与唇口平面形状分步优化的高超声速内收缩进气道设计方法。基准流场以反射激波不均匀性最小和总压恢复最大进行多目标优化设计,使用结合Tayler-Maccoll方程的有旋特征线方法(MOC)进行流场计算,获得双拐点母线内收缩锥基准流场。进气道唇口形状以沿流线积分(Streamline Integral Method, SIM)获得的进气道无黏阻力最小为目标进行优化设计,获得类椭圆形唇口平面形状。针对优化设计结果进行数值模拟,与传统直母线基准流场相比,双拐点母线基准流场反射激波后流动不均匀性下降40%左右,总压损失减少35%左右,总体性能提升明显。类椭圆唇口进气道在设计点的单位质量流量无黏阻力相较于圆形唇口降低6%,具有良好的压缩特性和气动效率,能够减弱进气系统对飞行器气动性能的不利影响。研究结果表明该方法是一种高效且实用的高超声速内收缩进气道设计方法。     

固定翼双旋弹动力学分岔特性分析

针对一种滚转稳定的固定翼双旋弹,对其非线性动力学进行了分岔特性分析,并在此基础上研究了各系统参数对其动力学分岔特性的影响。根据固定翼双旋弹非对称的特点,通过数值计算方法研究其飞行过程中平衡点随同向鸭翼安装角的变化规律,通过系统的分岔图得知系统具有三组稳定平衡点,其中只有一组平衡点为理想可行的稳定平衡点,因此需限定同向鸭翼安装角的范围以使固定翼双旋弹保持稳定飞行。在此基础上针对固定翼双旋弹弹道修正组件周期旋转和转角固定两种工作模式,通过各系统参数下的系统分岔图总结了固定翼双旋弹结构及气动力参数对其动力学系统分岔特性的影响。仿真结果表明,固定翼双旋弹的各气动力参数及飞行速度均对系统的分岔特性具有较大影响,应合理选定这些系统参数以使其具有良好的气动特性。     

考虑摩擦的多间隙直齿弯扭振动建模和分岔特性

采用集中质量法,建立了齿轮-转子-轴承系统的六自由度的多间隙弯扭耦合的非线性振动模型,模型中考虑了齿面摩擦、时变啮合刚度、齿侧间隙和支承间隙等因素.根据系统在转速、齿侧间隙、齿面摩擦以及啮合阻尼等参数下的全局分岔图和Poincare截面图,研究了各参数对系统分岔特性的影响.分析可知:在一定的齿侧间隙、啮合阻尼和低齿面摩擦因数下,随着转速的逐渐增加,系统通过拟周期分岔进入混沌.当齿面摩擦因数逐渐增加时,系统由良好润滑状态进入干摩擦,系统的混沌运动区域也因此在一临界点产生裂变,且通过激变的途径二次进入混沌;在一定的转速、啮合阻尼和齿面摩擦因数下,随着齿侧间隙的增加,系统通过激变进入混沌,同时可以发现,系统产生混沌和分岔主要发生在量纲一齿侧间隙小于3和大于7的区域,且最终通过倒分岔锁相为周期1运动;在一定的转速、啮合阻尼和齿侧间隙的条件下,随着齿面摩擦因数的增加,系统通过激变进入混沌.同时发现,随着啮合阻尼的增加,混沌区域逐渐裂变成2个、3个和4个混沌窗口,但最终都经由拟周期锁相为周期1运动.      

自适应高阶容积卡尔曼滤波在目标跟踪中的应用

针对传统容积卡尔曼滤波(CKF)在系统状态发生突变时估计精度下降的问题,将强跟踪滤波(STF)算法与高阶容积卡尔曼滤波(HCKF)算法相结合,提出了一种自适应高阶容积卡尔曼滤波(AHCKF)方法。该算法采用高阶球面-相径容积规则,可获得高于传统CKF的估计精度,同时在HCKF算法中引入STF,通过渐消因子在线修正预测误差协方差阵,强迫残差序列正交,提高了算法的鲁棒性,增强了算法应对系统状态突变等不确定因素的能力。将提出的AHCKF算法应用于具有状态突变的机动目标跟踪问题并进行数值仿真,仿真结果表明,AHCKF算法在系统状态发生突变的情况下表现出良好的滤波性能,有效地避免了状态突变造成的滤波精度下降,较传统的CKF、HCKF、交互式多模型-容积滤波(IMM-CKF)和自适应容积卡尔曼滤波(ACKF)算法有更强的鲁棒性和系统自适应能力。     

Evolution and History in a new “Mathematical SETI” model

In a recent paper (Maccone, 2011 [15]) and in a recent book (Maccone, 2012 [17]), this author proposed a new mathematical model capable of merging SETI and Darwinian Evolution into a single mathematical scheme. This model is based on exponentials and lognormal probability distributions, called “b-lognormals” if they start at any positive time b (“birth”) larger than zero. Indeed:

• 1.Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f_l in the Drake equation represents the fraction of planets suitable for life on which life actually arose, as it happened on Earth.
• 2.In 2008 (Maccone, 2008 [9]) this author firstly provided a statistical generalization of the Drake equation where the number N of communicating ET civilizations in the Galaxy was shown to follow the lognormal probability distribution. This fact is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution if the number of factors is increased at will, i.e. it approaches infinity.
• 3.Also, in Maccone (2011 [15]), it was shown that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of b-lognormal distributions constrained between the time axis and the exponential growth curve. This was a brand-new result. And one more new and far-reaching idea was to define Darwinian Evolution as a particular realization of a stochastic process called Geometric Brownian Motion (GBM) having the above exponential as its own mean value curve.
• 4.The b-lognormals may be also be interpreted as the lifespan of any living being, let it be a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization. In Maccone, (2012 [17, Chapters 6, 7, 8 and 11]), as well as in the present paper, we give important exact equations yielding the b-lognormal when its birth time, senility-time (descending inflexion point) and death time (where the tangent at senility intercepts the time axis) are known. These also are brand-new results. In particular, the σ=1 b-lognormals are shown to be related to the golden ratio, so famous in the arts and in architecture, and these special b-lognormals we call “golden b-lognormals”.
• 5.Applying this new mathematical apparatus to Human History leads to the discovery of the exponential trend of progress between Ancient Greece and the current USA Empire as the envelope of the b-lognormals of all Western Civilizations over a period of 2500 years.
• 6.We then invoke Shannon's Information Theory. The entropy of the obtained b-lognormals turns out to be the index of “development level” reached by each historic civilization. As a consequence, we get a numerical estimate of the entropy difference (i.e. the difference in the evolution levels) between any two civilizations. In particular, this was the case when Spaniards first met with Aztecs in 1519, and we find the relevant entropy difference between Spaniards an Aztecs to be 3.84 bits/individual over a period of about 50 centuries of technological difference. In a similar calculation, the entropy difference between the first living organism on Earth (RNA?) and Humans turns out to equal 25.57 bits/individual over a period of 3.5 billion years of Darwinian Evolution.
• 7.Finally, we extrapolate our exponentials into the future, which is of course arbitrary, but is the best Humans can do before they get in touch with any alien civilization. The results are appalling: the entropy difference between aliens 1 million years more advanced than Humans is of the order of 1000 bits/individual, while 10,000 bits/individual would be requested to any Civilization wishing to colonize the whole Galaxy (Fermi Paradox).
• 8.In conclusion, we have derived a mathematical model capable of estimating how much more advanced than humans an alien civilization will be when SETI succeeds.

     

3D复合材料中非线性纤维搭桥下脱层的屈曲和初始后屈曲

建立了缝纫层合板和编织复合材料等3D复合材料中非线性纤维搭桥下脱层屈曲的计算模型,根据最小总势能原理分析了脱层屈曲和初始后屈曲问题,得出了非线性纤维搭桥下脱层屈曲的一些重要特征,预报了强化型非线性搭桥脱层初始后屈曲的稳定性和软化型搭桥初始后屈曲的不稳定性。     

考虑杆臂效应与挠曲变形的全自动着舰技术

联合精确进近和着陆系统（JPALS）舰载组件旨在为最终进近阶段的舰载机提供自动着舰能力。针对由于舰船杆臂效应与挠曲变形的存在导致舰载机着舰定位精度下降的问题,开发了一种基于卫星引导的全自动着舰非线性化参数误差模型,结合舰船甲板运动及舰载机纵向飞行控制模型,评估舰船结构挠曲和姿态不确定性对着舰落点精度的影响。结果表明,杆臂效应与挠曲变形对着舰落点精度有显著影响,利用建立的误差模型以及飞行控制模型,能够将着舰落点精度有效控制在着舰标准之内。     

剪切气流中无黏液体横向射流破碎机理

航空发动机燃烧室中,液体燃料的雾化过程、特别是初始雾化过程非常复杂,至今无法建立准确的初始雾化模型。忽略液体射流黏性,采用线性不稳定性分析法对无黏液体（工质为水）在二维剪切横向气流中的破碎机理进行研究。通过建立射流的色散方程,根据其表面波的增长率及波数的发展情况对射流破碎进行预测。当气体韦伯数或液体韦伯数增大时,射流表面波增长率显著增加,最佳波长明显减小。液气动量比大于临界值时,Kelvin-Helmholtz （K-H）不稳定性占主导作用;反之,Rayleigh-Taylor （R-T）不稳定性占主导作用。二维剪切气流在射流方向上具有速度梯度,只改变横向气动力对射流表面波的作用。气体韦伯数与液体韦伯数对射流破碎的作用与均匀气流相似;保持气流流量相同时,负梯度剪切气流可以加速射流的破碎。     

奇异积分方程方法在接触压力分析中的应用

总结回顾了奇异积分方程的数值解法,对于第二类奇异积分方程使用分段连续函数法进行了求解;对于两个弹性体接触问题,通过接触体之间的滑移函数和间隙函数,建立求解接触压力的奇异积分方程.分别针对圆柱体与弹性半空间体、抛物线型压头与弹性半空间体、榫头与榫槽3类接触问题,确立奇异积分方程的具体表达式,而后使用分段连续函数方法进行求解,获得接触面上的接触压力.最后将计算所得的接触压力分别与理论解和有限元解进行了对比.对于圆柱体与弹性半空间体接触问题,奇异积分方程法的最大接触压力与理论解和有限元解的相对误差分别为0.3%和0.5%;对于榫头与榫槽接触问题,奇异积分方程方法计算所得的最大接触压力与有限元解的相对误差为1.8%,验证了奇异积分方程方法的有效性.