采用分形示性数分析信号的混沌程度

研究了离散点集分形示性数的计算，提出了分析信号的混沌程度的方法。由分形信息理论出发，对离散采样的数字信号，通过变化采样频率，多次采样构造原始信号的分形点集；引入分形示性数的概念，得到了分形点集的分形示性数的计算方法，由分形示性数来区分运动的混沌程度。通过计算可以看出，该方法是可行的。

On Proposing a New Fractal Index More Helpful to Fault Diagnosis in Vibration Engineering

Abstract: Existing fractal dimensions, in our opinion, are not quite helpful to fault diagnosis. We propose a new fractal index (F7) that can distinguish the degree of chaos, which, to our best knowledge, existing fractal dimensions fail to do. For an incipient fault, chaos of sampling signal is very weak, but its strength increases rapidly with the development of chaos. Our F7 is based on definition of fractal sets. We derive eqs. (1) through (9), the more important ones of which are eqs. (7) and (9), and h(x) on the left-hand side of eq. (9) is the F7 we want. Figs. 2 and 3 show respectively Poincar'e maps of a rotor with incipient crack and one with developed crack, corresponding respectively to F7 = 0. 633 and F7 = 0. 851. Figs. 4 and 5 show respectively the time-domain phase diagrams of intermittent chaos and pure chaos of another cracked rotor, corresponding respectively to F7 = 0. 533 and F7 = 0. 801. Existing fractal dimension methods fail to distinguish between these two types of chaos.