Fractional Order Signal Processing of Electrochemical Noises

Abstract

The corrosion processes of stainless steel under different solutions were examined using electrochemical noise (ECN). Using rescaled range analysis, we demonstrated that ECN signals produced by corrosion processes have non-stationary and self-similar properties. The comparison and analysis of ECN signals in both the time and frequency domains showed that conventional methods failed to sufficiently distinguish between the ECN signals obtained under different solutions. Therefore, we introduced the use of fractional Fourier transforms, a powerful tool for the time-frequency analysis of self-similar signals, to process ECN signals that can better describe the corrosion behaviours of the electrode in different solutions.

Vibrational resonance in Duffing systems with fractional-order damping

“…It is because one has F ð1Þ VR ¼ F ð2Þ VR ¼ F c in Eqs. (19) and (20) for the case a ¼ 1. The new resonance behavior induced by the fractional-order damping is the highlight of this paper.…”

“…The fractional-order derivative was raised by Leibniz more than 300 years ago, but it has become a hot topic in recent years. The fractional-order calculus is widely used in many scientific and engineering fields such as rheology, 16 viscoelasticity, 17,18 electrochemistry, 19,20 bioengineering, 21,22 mechanics, 23-26 automatic control, [27][28][29] signal processing, 30,31 quantum evolution of complex systems, 32 etc. So far, there are huge volumes of literatures in this area.…”