矿山事故时序分形特征研究

矿山属于高危行业,其事故致因和演化机理十分复杂,分形理论为解决复杂性问题提供了可能。通过对我国近年来矿山行业事故时序进行研究发现,矿山事故时间序列具有明显的分形特征,其饱和关联维数为6.390,说明要恰当描述其变化特征进行动力系统建模至少需要6～7个状态变量;该时间序列的Kolmogorov熵近似为0.0586,说明该混沌动力系统的平均可预测时间尺度为17个月。该研究结果可为建立矿山事故的时序预测预报模型提供依据。

THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS

The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.

多自由度非线性随机系统的响应与稳定性

响应与稳定性分析一直是随机动力学研究的热点,发展预测随机响应及判定系统响应性态的方法具有重要的科学意义与广阔的应用前景.本文综述了有关多自由度非线性随机系统的响应与稳定性的研究.首先简介用于随机系统响应预测的Fokker–Planck–Kolmogorov方程法、随机平均法、等效线性化法、等效非线性系统法和MonteCarlo模拟法,评述其优缺点,进而讨论了多自由度非线性随机系统响应的精确平稳解、近似瞬态解的研究现状.然后介绍了随机系统稳定性分析的两类方法,即Lyapunov函数法及Lyapunov指数法,并综述了多自由度非线性随机系统稳定性分析的研究现状.最后给出几点发展建议.

Determining chaotic invariant properties of short-circuiting gas metal arc welding from an observed time series

The experimental time series of welding current produced by carbon dioxide gas metal arc welding with shortcircuiting transfer were recorded and subsequently evaluated. Based on phase space reconstruction, the correlation dimeusions and Kolmogorov entropies of the corresponding system have been numerically calculated using the Grassberger-Procaccia algorithm at different time delays. It was found out that the time delay has little effect on the estimation of correlation dimension; conversely, it plays a key role in producing precise results on the estimation of Kolmogorov entropy.

一类Kolmogorov系统的动力性质

用定性分析的方法对一类Kolmogorov系统(dx)/(dt)=x(a_0-a_11x+a_2x^(n-1)-a3x^n+ a_4xy^m),(dy)/(dt)=y(b_1x^n-b_2),进行了研究．讨论了系统平衡点的性态,给出了系统无闭轨的充分条件以及存在唯一稳定极限环的条件．包含并推广了文献[3]的相关结果．

广义Kolmogorov矩阵的遍历性

在本文中,我们证明了广义Kolmogorov矩阵所对应的Markov链的强遍历性与指数遍历性,并且给出它的最大指数遍历常数的一个下界。