基于自适应最稀疏时频分析的非线性系统识别

Identification of nonlinear vibration system by adaptive and sparsest time-frequency analysis

研究了基于自适应最稀疏时频分析方法的非线性系统识别方法。通过自适应最稀疏时频分析方法识别了Duffing非线性系统和Van der Pol非线性系统的自由振动响应以及这两种系统在简谐激励下的响应,得到了响应的瞬时振幅和瞬时频率,并用最小二乘曲线拟合了非线性系统识别参数及简谐激励的大小和频率。分析了识别精度的影响因素,与基于小波分析方法和希尔伯特-黄变换方法的非线性系统识别方法进行了比较,研究表明自适应最稀疏时频分析方法可以有效地识别典型非线性系统参数。

A nonlinear system identification method based on Adaptive and Sparsest Time-Frequency Analysis(ASTFA)is studied.The free vibration responses and harmonic vibration responses of Duffing nonlinear vibration system and Van der Pol nonlinear vibration system are analyzed by ASTFA to obtain the instantaneous amplitude and frequency and the nonlinear system parameters and the magnitude and frequency of harmonic excitation are identified by least square curve fitting.Factors affecting the accuracy of identification are analyzed and the identified results are compared with the result from wavelet analysis and Hilbert-Huang.The proposed method is proven to be effective to identify parameters of typical nonlinear vibration system.