Equivalence of four-point and three-point rainflow cycle counting algorithms

Two forms of the rainflow cycle counting algorithm for fatigue damage prediction are shown to be equivalent, namely the three-point algorithm as presented by Bannantine et al. [Bannantine JA, Comer JJ, Handrock JL. Fundamentals of metal fatigue analysis. Englewood Cliffs, NJ: Prentice-Hall; 1990], and the four-point algorithm as presented by Amzallag et al. [Amzallag C, Gerey JP, Robert JL, Bahuaud J. Standardization of the rainflow counting method for fatigue analysis. Int J Fatigue 1994;16:287–293]. While it can be demonstrated by example that the same result is obtained by the two algorithms, no generalised proof of their equivalence has previously been presented. The proof is built on several identified properties of the four-point algorithm, including that certain modifications to the stress series being analysed do not alter the outcome.