A new approach is proposed for diagnosing the nonlinear characteristics of vibratory systems in engineering applications. The correlation coefficient of two periods’ response wave is used in this approach and a new concept named similarity degree of waveform (SDW) is proposed to describe the correlations of the responses and therefore the characteristics of the nonlinear dynamic systems. A Duffing system is used in this research as an example to demonstrate the application and efficiency of the proposed approach. The approach has shown effectiveness in diagnosing periodic, multi-periodic, quasi-periodic and chaotic motions. The characterization with implementing the proposed approach is compared with that of the Lyapunov exponent method. The advantages of the proposed approach are demonstrated.

中文翻译：

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一种诊断振动系统非线性行为的波形相似性方法

提出了一种在工程应用中诊断振动系统非线性特性的新方法。该方法利用两个周期响应波的相关系数，提出了波形相似度（SDW）的新概念来描述响应的相关性，从而描述非线性动力系统的特性。本研究中使用 Duffing 系统作为示例来展示所提出方法的应用和效率。该方法在诊断周期性、多周期、准周期和混沌运动方面显示出有效性。将实施所提出方法的特征与 Lyapunov 指数方法的特征进行比较。证明了所提出方法的优点。