Poincaré截面法在混沌振动识别中的应用研究

Study on the Application of Poincaré Section Algorithm to Chaotic Vibration Identification

摘要: 针对混沌识别过程中，单变量时间序列相空间重构吸引子上Poincaré截面的位置难以选择以及当系统受到不可公约的准周期激励时Poincaré截面难以确定等问题，对Poincaré截面法进行了修正，即将不可约多频激励条件下满足近邻截面条件的点近似为同截面，且对穿越轨线中同点束进行归一化处理。仿真和试验结果表明，在不同激励频率以及当试验信号重构吸引子出现轨道簇时，该方法能够有效地确定Poincaré截面，观察到了包括多周期、混沌、拟周期振动在内的不同截面图，为实测非线性时间序列分析提供有益参考。

Abstract: In the process of Poincaré section extraction for chaotic vibration identification, there are many problems such as selection of the Poincaré section location on the phase space attractor reconstructed from single variable time series, determination of these sections when the system under quasi-periodic excitations, should be solved effectively. The improved Poincaré section is presented in this paper. The main idea is to consider these points which are satisfied with the neighborhood condition as the same section points, and a bunch of experimental trajectories which are derived from the signals are normalized. The simulation and experiment results show that when the cluster orbits of experimental attractor occur and the system is excited with different frequencies, the improved method is applied to determine the Poincaré section correctly. The interested phenomenon including multi-periodic behavior, chaos, and quasi-periodic vibration section are observed.