脊骨线对于非线性系统的判断、描述和参数识别，具有重要的意义；而现有的脊骨线提取方法大多理论上较为复杂，且有局部线性化误差较大、数据波动剧烈等问题，限制了工程应用。提出一种新的非线性系统脊骨线提取方法，该方法利用非线性系统自由振动响应的一次谐波分量，计算谐波信号峰值点的瞬时频率，可以方便地提取脊骨线；这种新的非线性系统脊骨线提取方法理论明确、简单，计算方便，易于工程应用。通过三个数值算例说明了该方法的有效性，同时将此方法应用于非线性描述，并综合讨论了非线性描述的几何方法；并基于此方法进行了非线性系统参数识别，取得了良好的效果。
Abstract
Backbone curves are of great significance for nonlinear identification including detection, characterization, and parameters identification.However, existing methods to extract backbone curves are of complex theories, and there are some problems, such as linearization errors and data fluctuation.A first-order component is main part of harmonic signal, it is convenient to extract backbone curve from instantaneous frequencies of peak points based on the first-order component of free vibration response signal.The proposed method is with simple conception and easy computation, it is suitable to be applied in practice.Three numerical simulations were utilized to verify its effectiveness.Meanwhile, several geometric methods for nonlinear characterization were discussed.Finally, parameter identification of a nonlinear system based on the proposed method was conducted, and good identification results were achieved by comparing with existing method.
关键词
脊骨线 /
非线性识别 /
非线性描述 /
参数识别
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Key words
backbone curve /
nonlinear identification /
nonlinear characterization /
parameter identification
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