混沌激励下振动系统的非线性参数识别

Parametric identification of nonlinearity using chaotic excitation

对基于时-频相结合的非线性振动系统的参数识别问题进行了研究。首先建立含非线性参数单自由度振动系统的力学模型,将已知非线性系统产生的混沌响应作为该系统的激励,假定其响应有若干不稳定的周期轨道组成,从混沌响应的状态空间中提取出近似周期轨道,采用谐波平衡法识别出系统的参数,然后对识别出的参数进行误差分析。最后通过数值模拟,验证了混沌信号作为激励源对非线性系统进行参数识别的可行性。

The question about parametric identification of nonlinear vibration system based on time-frequency analysis was studied.The mechanical model of a single-degree-of-freedom vibration system with nonlinear parameters was established,and the chaotic response of a known nonlinear system was used as an excitation for parametric identification.It was assumed that the system consists of several unstable periodic orbits.The approximate periodic orbits were extracted from the state space of chaotic response based on recurrence property,and the harmonic balance identification method was used to identify the parameters of nonlinear system.Then the error of identified parameters were analysed.It is indicated that using chaotic signal as driving source for identifying the nonlinear system is feasible by numerical simulation.