- 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 a set of simple stress reversals. Its importance is that it allows the application of Miner's rule in order to assess the fatigue life of a structure subject to complex loading. Thealgorithm was developed byTatsuo Endo andM. Matsuiski in1968 ^{1}. Though there are a number of cycle-counting algorithms for such applications, the rainflow method is,as of 2004 , the most popular.Downing and Socie

^{2}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 E 1049-85^{3}. This algorithm is used inSandia National Laboratories LIFE2^{4}code for the fatigue analysis of wind turbine components.Igor Rychlik ^{5}gave a mathematical definition for the rainflow counting method, thus enabling closed-form computations from the statistical properties of the load signal.For simple periodic loadings, such as Figure 1, rainflow counting is unnecessary. That sequence clearly has 10 cycles of amplitude 20

MPa and a structure's life can be estimated from a simple application of the relevant S-N curve.Compare this with Figure 2 which cannot be assessed in terms of simply-described stress reversals.

**The algorithm**#Reduce the time history to a sequence of (tensile) peaks and (compressive) troughs.

#Imagine that the time history is a template for a rigid sheet (pagoda roof).

#Turn the sheet clockwise 90° (earliest time to the top).

#Each**"tensile peak**" is imagined as a source of water that "drips" down the pagoda.

#Count the number of half-cycles by looking for terminations in the flow occurring when either:

##It reaches the end of the time history;

##It merges with a flow that started at an earlier**"tensile peak**"; or

##It flows opposite a**"tensile peak**" of greater magnitude.

#Repeat step 5 for**"compressive troughs**".

#Assign a magnitude to each half-cycle equal to the stress difference between its start and termination.

#Pair up half-cycles of identical magnitude (but opposite sense) to count the number of complete cycles. Typically, there are some residual half-cycles.**Example***The stress history in Figure 2 is reduced to peaks and troughs in Figure 3.

*Half-cycle (A) starts at tensile peak (1) and terminates opposite a greater tensile stress, peak (2). Its amplitude is 16 MPa.

*Half-cycle (B) starts at tensile peak (4) and terminates where it is interrupted by a flow from an earlier peak, (3), Its amplitude is 17 MPa.

*Half-cycle (C) starts at tensile peak (5) and terminates at the end of the time history.

*Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched.**References**#Matsuiski, M. & Endo, T. (1969) Fatigue of metals subjected to varying stress, "Japan Soc. Mech. Engrg".

#Downing, S. D., Socie, D. F. (1982). Simple rainflow counting algorithms. International Journal of Fatigue, Volume 4, Issue 1, January, 31-40.

#ASTM E 1049-85. (Reapproved 2005). Standard practices for cycle counting in fatigue analysis. ASTM International.

#Schluter, L. (1991). Programmer's Guide for LIFE2's Rainflow Counting Algorithm. Sandia Report SAND90-2260.

#Rychlik, I. (1987) A New Definition of the Rainflow Cycle Counting Method, " Int. J. Fatigue 9:2, 119-121".

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Comptage Rainflow**— Le comptage rainflow est utilisé en analyse de fatigue dans le but de traduire le chargement en contraintes fonction du temps en cycles de contraintes simples caractérisés par une contrainte minimum et une contrainte maximum. Dans son principe,… … Wikipédia en Français**Comptage rainflow**— Le comptage rainflow est utilisé en analyse de fatigue des matériaux, dans le but de traduire le chargement en contraintes fonction du temps en cycles de contraintes simples caractérisés par une contrainte minimum et une contrainte maximum. Dans… … Wikipédia en Français**List of algorithms**— The following is a list of the algorithms described in Wikipedia. See also the list of data structures, list of algorithm general topics and list of terms relating to algorithms and data structures.If you intend to describe a new algorithm,… … Wikipedia**Fatigue (material)**— Metal fatigue redirects here. For the video game, see Metal Fatigue (disambiguation). v · d · e Materials failure modes … Wikipedia**Список алгоритмов**— Эта страница информационный список. Основная статья: Алгоритм Ниже приводится список алгоритмов, группированный по категориям. Более детальные сведения приводятся в списке структур данных и … Википедия**Tatsuo Endo**— (1925 1989) was a Japanese engineer who, in 1968 along with M. Matsuiski, developed the rainflow counting algorithm for fatigue analysis of structures while a visiting professor at the University of Illinois.Bibliography*Murakami, Y. (1992) The… … Wikipedia**FlexPro**— Infobox Software name = FlexPro developer = Weisang GmbH operating system = Windows genre = Numerical analysis, latest release version = 7.0 license = Proprietary website = [http://www.weisang.com/ http://www.weisang.com/] FlexPro is software… … Wikipedia