It is well known that dynamical systems that include devices based on shape memory alloys (SMA) can exhibit a wide spectrum of responses: periodic, quasi-periodic and chaotic motions. In view of the different types of possible applications, it is important to recognize the qualitative features of the system vibrations. To this end, various methods have been proposed in the literature and evaluated in different conditions. In this work, a comparison between some of the available methods is proposed, focusing attention on their ability to detect the regular–chaotic and chaotic–regular transitions. The specific system under consideration is a thermomechanical SMA oscillator with superelastic behavior subject to harmonic excitation. The diagnostic methods compared are 0–1 test, maximum Lyapunov exponent and the recurrence indicators. The obtained results show that each method used is suitable for distinguishing between the regular and non-regular response of the SMA oscillator, so one of them can be chosen, taking into account, for example, the length and a sampling of the collected data.

中文翻译：

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检测 SMA 振荡器中从规则运动到混沌运动的转变的不同方法的比较

众所周知，包括基于形状记忆合金 (SMA) 的设备的动力系统可以表现出广泛的响应：周期、准周期和混沌运动。鉴于可能应用的不同类型，识别系统振动的定性特征很重要。为此，文献中提出了各种方法，并在不同条件下进行了评估。在这项工作中，提出了一些可用方法之间的比较，重点关注它们检测规则-混沌和混沌-规则转换的能力。正在考虑的特定系统是具有超弹性行为的热机械 SMA 振荡器，受谐波激励。比较的诊断方法是0-1检验、最大Lyapunov指数和复发指标。