Experimental test of asymmetrical cable-stayed bridges using MR-damper for vibration control

In this paper, a semi-active control by MR-damper is researched; its purpose is to effectively control vibration of asymmetrical cable-stayed bridges when earthquake is loaded on the type of bridge. For an experimental study, a model of 10.2 m high and 28 m long asymmetrical cable-stayed bridge structure was built being similar to a real one in size and function. A MR damper was also designed in proper size suitable for the control of the model. The experiment was performed in the way in which three piers were fixed on three shaking tables with 30% of El-centro earthquake wave, and a control device was placed on the lower part of its upper deck for horizontal control. As for control algorithms, Lyapunov and Clipped-optimal control algorithms were applied. The effectiveness of the semi-active control with MR damper for the asymmetrical cable-stayed bridge was measured under five control conditions: Un-control, Passive-off, Passive-on, Lyapunov Control, Clipped-optimal Control. The experiment showed that the semi-active control applying Lyapunov and Clipped-optimal algorithms effectively increased controllability almost in double, and decreased displacement 75% compared with the condition of passive-off. Therefore the semi-active method suggested in this paper is proven effective in controlling asymmetrical cable-stayed bridges.     

岩石声发射混沌特征分析

岩石等脆性材料在加载过程中,随着荷载的增加,材料内部的微裂纹产生、扩展并伴随着声发射现象的发生。声发射是研究脆性材料破坏的良好工具。对砂岩、细砂岩和高丽山砂岩3类岩石进行了声发射试验,记录了加载及破坏过程中产生的声发射信号,并且采用混沌动力学理论研究了3类岩石的声发射活动规律,计算了岩石的关联维数和最大Lyapunov指数。研究结果表明,岩石加载及破坏过程具有混沌特征,用相空间重构法可以较好地揭示岩石破坏过程的动力学特征,这为混沌理论在岩石、岩体声发射其他领域的研究及应用奠定了基础。     

Conditional Entropy

In this paper we show that the Conditional Entropy of nearby orbits may be a useful tool to explore the phase space associated to a given Hamiltonian. The arc length parameter along the orbits, instead of the time, is used as a random variable to compute the entropy. In the first part of this work we summarise the main analytical results to support this tool while, in the second part, we present numerical evidence that this technique is able to localise (stable) periodic and quasiperiodic orbits, 'aperiodic' orbits (chaotic motion) and unstable periodic orbits (the 'source' of chaotic motion). Besides, we show that this technique provides a measure of chaos which is similar to that given by the largest Lyapunov Characteristic Number. It is important to remark that this method is very simple to compute and does not require long time integrations, just realistic physical times. This revised version was published online in July 2006 with corrections to the Cover Date.     

多时滞系统的不稳定性

利用比较原理结合向量Lyapunov函数研究一类多滞后线性时变系统的不稳定性,并在此基础上进一步研究一类多滞后非线性系统及多滞后区间系数系统的不稳定性,给出相关定理,丰富已有文献的相应结果。     

一个正压和斜压不稳定的充要条件

提出一个新的李雅普诺夫函数，首次得到了正压和斜压不稳定的充要条件，大大改善了热知的Ｒａｙｌｅｉｇｈ－郭晓岚定理和Ｆｊｏｒｔｏｆｔ定理，解决了Ｒａｙｌｅｉｇｈ（１８８０）提出的无粘切变流正压稳定性问题。     

Lyapunov exponents of a simple stochastic model of the thermally and wind-driven ocean circulation

A reformulation of the simple model of the thermally and wind-driven ocean circulation introduced by Maas [Tellus 46A (1994) 671] is considered. Under a realistic range of forcing parameters, this model displays multiple attractors, corresponding to thermally direct and indirect circulations. The fixed point associated with the thermally direct circulation is unstable for a broad range of parameters, leading to limit cycles and chaotic behaviour. It is demonstrated that if weather variability is parameterised as stochastic perturbations to the mechanical and buoyancy fluxes, then the leading Lyapunov exponent of the circulation can become positive for sufficiently strong fluctuations in parameter ranges where it is deterministically zero. If the fluctuations are sufficiently small that the stochastic trajectories are not too far from the deterministic attractor, it is demonstrated that the sign of the leading Lyapunov exponent can have a substantial effect on the predictability of the system.     

误差非线性的增长理论及可预报性研究

对非线性系统的误差发展方程不作线性化近似,直接用原始的误差发展方程来研究初始误差的发展,提出了误差非线性的增长理论。首先,在相空间中定义一个非线性误差传播算子,初始误差在这个算子的作用下,可以非线性发展成任意时刻的误差;然后,在此基础上,引入了非线性局部Lyapunov指数的概念。由平均非线性局部Lyapunov指数可以得到误差平均相对增长随时间的演变情况;对于一个混沌系统,误差平均相对增长被证明将趋于一个饱和值,利用这个饱和值,混沌系统的可预报期限可以被定量地确定。误差非线性的增长理论可以应用于有限尺度大小初始扰动的可预报性研究,较误差的线性增长理论有明显的优越性。     

随机误差对混沌系统可预报性的影响

根据非线性局部Lyapunov指数的方法, 以Logistic映射和Lorenz系统的试验数据序列为例, 研究了在初始误差存在的情况下, 随机误差对混沌系统可预报性的影响。结果表明: 初始误差和随机误差对可预报期限影响所起的作用大小主要取决于两者的相对大小。当初始误差远大于随机误差时, 系统的可预报期限主要由初始误差决定, 可以不考虑随机误差对预报模式可预报性的影响; 反之, 当随机误差远大于初始误差时, 系统的可预报期限主要由随机误差决定; 当初始误差和随机误差量级相当时, 两者都对系统的可预报期限起重要作用。在后两种情况下, 在考虑初始误差对可预报性影响的同时还必须考虑随机误差的作用。此外, 我们在已知系统精确的控制方程和误差演化方程的条件下, 研究了随机误差对可预报性的影响, 理论所得结果与试验数据所得结果相似。这表明在随机误差较小的情况下, 对系统可预报期限的估计相对准确, 但在随机误差较大的情况下, 可预报期限的估计误差也较大。本文利用三种不同的滤波方法对序列进行了试验, 结果表明, Lanczos高通滤波得到的高频序列与原始加入的噪声序列无论是在强度上还是在演变趋势上都表现得相当一致, 其能有效地去除高频噪音继而提高对系统的可预报期限的估计, 这对实际气象观测资料如何有效地去除噪音具有一定的启发意义。     

数值天气预报和气候预测可预报性研究的若干动力学方法

简要回顾了数值天气预报和气候预测可预报性研究的若干动力学方法,包括用于研究第一类可预报性问题的线性奇异向量（LSV）和条件非线性最优初始扰动（CNOP-I）方法,以及Lyapunov指数和非线性局部Lyapunov指数方法。前两种方法用于研究预报或预测的预报误差问题,可以用于估计天气预报和气候预测的最大预报误差,而且根据导致最大预报误差的初始误差结构的信息,这两种方法可以用于确定预报或预测的初值敏感区。应该指出的是,LSV是基于线性化模式,对于描述非线性大气和海洋的运动具有局限性。因而,对于非线性模式,应该选择使用CNOP-I估计最大预报误差。Lyapunov指数和非线性局部Lyapunov指数可以用于研究第一类可预报性问题中的预报时限问题,前者是基于线性模式,不能解释非线性对预报时限的影响,而非线性局部Lyapunov指数方法则考虑了非线性的影响,能够较好地估计实际天气和气候的预报时限。第二类可预报性问题的研究方法相对较少,本文仅介绍了由我国科学家提出的关于模式参数扰动的条件非线性最优参数扰动（CNOP-P）方法,该方法可以用于寻找到对预报有最大影响的参数扰动,并可以进一步确定哪些参数最应该利用观测资料进行校准。另一方面,通过对比CNOP-I和CNOP-P对预报误差的影响,可以判断导致预报不确定性的主要误差因子,进而指导人们着力改进模式或者初始场。     

基于C-C方法的Lyapunov指数计算

识别混沌是对非线性时间序列进行分析，预测，控制的基础，克服已有文献用Lyapunov指数识别混沌时计算Lyapunov指数的不足，用C－C方法计算相空间重构的参数，然后利用混沌的遍历性及定义，提出计算最大Lyapunov指数的新方法，典型实例证明新算法的高效性与正确性。