Rainflow-counting algorithm

The rainflow-counting algorithm (also known as the rain-flow counting method) is used in the analysis of fatigue data in order to reduce a spectrum of varying stress into an equivalent set of simple stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain hysterisis cycles. This simplification allows the fatigue life of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage, or in a crack growth equation to calculate the crack increment. The algorithm was developed by Tatsuo Endo and M. Matsuishi in 1968. The rainflow-counting algorithm (also known as the rain-flow counting method) is used in the analysis of fatigue data in order to reduce a spectrum of varying stress into an equivalent set of simple stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain hysterisis cycles. This simplification allows the fatigue life of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage, or in a crack growth equation to calculate the crack increment. The algorithm was developed by Tatsuo Endo and M. Matsuishi in 1968. A feature of cycle counting methods is that only the turning points of a cycle matters and not the number or rate of application of the intermediate points. For simple periodic loadings, such as Figure 1, rainflow counting is unnecessary. That sequence clearly has 10 cycles of amplitude 10 MPa and a structure's life can be estimated from a simple application of the relevant S-N curve. Compare this to the data in Figure 2, which cannot be assessed in terms of simple stress reversals. The rainflow method is compatible with the cycles obtained from examination of the stress-strain hysteresis cycles. When a material is cyclically strained, a plot of stress against strain shows loops forming from the smaller interruption cycles. At the end of the smaller cycle, the material resumes the stress-strain path of the original cycle, as if the interruption had not occurred. The closed loops represent the energy dissipated by the material. The rainflow algorithm was developed by T. Endo and M. Matsuishi (an M.S. student at the time) in 1968 and presented in a Japanese paper. The first english presentation by the authors was in 1974. They communicated the technique to N. E. Dowling and J. Morrow in the U.S. who verified the technique and further popularised its use. Downing and Socie created one of the more widely referenced and utilized rainflow cycle-counting algorithms in 1982, which was included as one of many cycle-counting algorithms in ASTM E1049-85. Igor Rychlik gave a mathematical definition for the rainflow counting method, thus enabling closed-form computations from the statistical properties of the load signal. There are a number of different algorithms for identifying the rainflow cycles within a sequence. They all find the closed cycles and may be left with half closed residual cycles at the end. All methods start with the process of eliminating non turning points from the sequence. A completely closed set of rainflow cycles can be obtained for a repeated load sequence such as used in fatigue testing by starting at the largest peak and continue to the end and wrapping around to the beginning. . This method evaluates each set of 4 adjacent turning points A-B-C-D in turn: