近似熵在欠驱动五杆机构混沌边缘分析中的应用

Application of Approximate Entropy to Analyzing the Edge of Chaos for Underactuated Five-bar Mechanism

熵是一种衡量数据不规则性的方法,也是少有的混沌现象的定量分析的指标之一。利用熵的方法找出机构运动的混沌边缘,并且确定出熵计算中阈值选取的有效方法为目的。以欠驱动五杆机构为研究对象,利用SimMechanics对其机构进行建模和仿真,提取随杆长变化的时间序列、计算近似熵的熵值并绘出熵变化线图的方法,找出系统从周期运动进入混沌的杆长取值范围。以李雅普诺夫指数与机构运动的相图为依据,确定了在近似熵计算时合适的阈值取值范围。为近似熵的计算提出了一种新的阈值取值方法。

Entropy is an approach to measure the irregularity of a set of data and one of rare quantitative analysis indicators for chaos. By using the method of entropy the edge of chaos for a mechanism is found and the threshold for the calculation of approximate entropy is selected. The chaotic motion arising from a planar closed--chain underactuated five--bar mechanism is studied. SimMechanics is employed to model the mechanism. By the time series extracted from the results of simulation, the approximate entropy is calculated and the variation chart of entropy is plotted, the range of rod length corresponding to the system changing from periodic motion to chaotic motion is found. Based on the Lyapunov exponents and the phase diagrams, the range of appropriate threshold value is fixed. A new approach to determine threshold value for the calculation of approximate entropy is proposed.