A comparison of different approaches to detect the transitions from regular to chaotic motions in SMA oscillator

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.