Rainflow-counting algorithm - Revision history

NeedsGlasses: Undid revision 1282514477 by NiTCvasu (talk) remove largely off topic low quality ai slop. So sad that people would include this.

2025-03-26T22:44:32Z

Undid revision 1282514477 by NiTCvasu (talk) remove largely off topic low quality ai slop. So sad that people would include this.

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 Igor Rychlik gave a mathematical definition for the rainflow counting method,<ref>{{cite journal |last=Rychlik |first=I. |year=1987 |title=A New Definition of the Rainflow Cycle Counting Method |journal=International Journal of Fatigue |volume=9 |number=2 |pages=119–121|doi=10.1016/0142-1123(87)90054-5 }}</ref> thus enabling closed-form computations from the statistical properties of the load signal.
 == Algorithms ==
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 ==References==

NiTCvasu: ADDED content on Fatigue, Classification of Fatigue, Steps Involved ,Advantages and Limitations.

2025-03-26T22:02:52Z

ADDED content on Fatigue, Classification of Fatigue, Steps Involved ,Advantages and Limitations.

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 Igor Rychlik gave a mathematical definition for the rainflow counting method,<ref>{{cite journal |last=Rychlik |first=I. |year=1987 |title=A New Definition of the Rainflow Cycle Counting Method |journal=International Journal of Fatigue |volume=9 |number=2 |pages=119–121|doi=10.1016/0142-1123(87)90054-5 }}</ref> thus enabling closed-form computations from the statistical properties of the load signal.
 == Algorithms ==
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 |1
 |}
 ==References==

GoingBatty: -, typo(s) fixed: english → English

2025-01-03T03:13:31Z

-, typo(s) fixed: english → English

NeedsGlasses: removed 'uniaxial' since not limited to that type of loading and expanded meaning of equivalent

2024-03-21T12:34:13Z

removed 'uniaxial' since not limited to that type of loading and expanded meaning of equivalent

← Previous revision		Revision as of 12:34, 21 March 2024
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	[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]		[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]

	The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a ~~uniaxial~~ loading sequence of varying [[stress (physics)\|stress]] into ~~an equivalent~~ set of constant amplitude stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. In cases of multiaxial loading, [[critical plane analysis]] can be used together with rainflow counting to identify the uniaxial history associated with the plane that maximizes damage. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>		The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a loading sequence of varying [[stress (physics)\|stress]] into a set of constant amplitude stress reversals with equivalent fatigue damage. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. In cases of multiaxial loading, [[critical plane analysis]] can be used together with rainflow counting to identify the uniaxial history associated with the plane that maximizes damage. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>

	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.<ref name="endo74"/>		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.<ref name="endo74"/>

Uhai: Adding short description: "Materials science algorithm"

2024-03-18T17:27:44Z

Adding short description: "Materials science algorithm"

← Previous revision		Revision as of 17:27, 18 March 2024
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			{{Short description\|Materials science algorithm}}
	[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]		[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]

Citation bot: Add: isbn, pages. | Use this bot. Report bugs. | Suggested by BorgQueen | Category:Materials science | #UCB_Category 199/421

2022-11-16T05:19:34Z

Add: isbn, pages. | Use this bot. Report bugs. | Suggested by BorgQueen | Category:Materials science | #UCB_Category 199/421

← Previous revision		Revision as of 05:19, 16 November 2022
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	=== Four point method ===		=== Four point method ===
	[[File:Rainflow-4point-method.png\|thumb\|Rainflow counting using the four point method. Any pair of turning points B,C that lie between adjacent points A and D is a rainflow cycle. Count and eliminate the pair B,C and continue processing the sequence until no more cycles can be extracted.]]		[[File:Rainflow-4point-method.png\|thumb\|Rainflow counting using the four point method. Any pair of turning points B,C that lie between adjacent points A and D is a rainflow cycle. Count and eliminate the pair B,C and continue processing the sequence until no more cycles can be extracted.]]
	This method evaluates each set of 4 adjacent turning points A-B-C-D in turn:<ref name="lee12"> {{cite book \|title=Metal Fatigue Analysis Handbook\|chapter=Rainflow Cycle Counting Techniques \|first1=Yung-Li \|last1=Lee \|first2=Tana \|last2=Tjhung \|year=2012 \|doi=10.1016/B978-0-12-385204-5.00003-3}} </ref>		This method evaluates each set of 4 adjacent turning points A-B-C-D in turn:<ref name="lee12"> {{cite book \|title=Metal Fatigue Analysis Handbook\|chapter=Rainflow Cycle Counting Techniques \|first1=Yung-Li \|last1=Lee \|first2=Tana \|last2=Tjhung \|year=2012 \|pages=89–114 \|doi=10.1016/B978-0-12-385204-5.00003-3\|isbn=9780123852045 }} </ref>

	# Any pair of points B-C that lies within or equal to A-D is a rainflow cycle.		# Any pair of points B-C that lies within or equal to A-D is a rainflow cycle.

AresLiam: + info on multiaixal analysis

2022-10-25T20:52:42Z

+ info on multiaixal analysis

← Previous revision		Revision as of 20:52, 25 October 2022
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	[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]		[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]

	The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a uniaxial loading sequence of varying [[stress (physics)\|stress]] into an equivalent set of constant amplitude stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>		The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a uniaxial loading sequence of varying [[stress (physics)\|stress]] into an equivalent set of constant amplitude stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. In cases of multiaxial loading, [[critical plane analysis]] can be used together with rainflow counting to identify the uniaxial history associated with the plane that maximizes damage. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>

	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.<ref name="endo74"/>		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.<ref name="endo74"/>

AresLiam at 13:54, 25 October 2022

2022-10-25T13:54:34Z

← Previous revision		Revision as of 13:54, 25 October 2022
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	[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]		[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]

	The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a loading sequence of varying [[stress (physics)\|stress]] into an equivalent set of constant amplitude stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>		The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a uniaxial loading sequence of varying [[stress (physics)\|stress]] into an equivalent set of constant amplitude stress reversals. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>

	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.<ref name="endo74"/>		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.<ref name="endo74"/>

68.147.237.158: /* Example */

2022-10-25T12:34:19Z

Example

← Previous revision		Revision as of 12:34, 25 October 2022
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	*The half-cycle starting at peak 9 terminates where it is interrupted by a flow from earlier peak 8 (case '''b'''); its magnitude is 16 MPa (8 - (-8) = 16).		*The half-cycle starting at peak 9 terminates where it is interrupted by a flow from earlier peak 8 (case '''b'''); its magnitude is 16 MPa (8 - (-8) = 16).
	*The half-cycle starting at peak 11 terminates at the end of the time history (case '''a'''); its magnitude is 19 MPa (15 - (-4) = 19).		*The half-cycle starting at peak 11 terminates at the end of the time history (case '''a'''); its magnitude is 19 MPa (15 - (-4) = 19).
	*Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched.		Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched.

	[[File:Rainflow analysis for compressive valleys.svg\|thumb\|right\|Figure 4: Rainflow analysis for compressive valleys]]		[[File:Rainflow analysis for compressive valleys.svg\|thumb\|right\|Figure 4: Rainflow analysis for compressive valleys]]

68.147.237.158: /* Example */

2022-10-25T12:33:59Z

Example

← Previous revision		Revision as of 12:33, 25 October 2022
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	[[File:Rainflow analysis for tensile peaks.svg\|thumb\|right\|Figure 3: Rainflow analysis for tensile peaks]]		[[File:Rainflow analysis for tensile peaks.svg\|thumb\|right\|Figure 3: Rainflow analysis for tensile peaks]]

	*The stress history in Figure 2 is reduced to tensile peaks in Figure 3 and compressive valleys in Figure 4.		The stress history in Figure 2 is reduced to tensile peaks in Figure 3 and compressive valleys in Figure 4. From the tensile peaks in Figure 3:
	*The first half-cycle starts at tensile peak 1 and terminates opposite a greater tensile stress, peak 3 (case '''c'''); its magnitude is 16 MPa (2 - (-14) = 16).		*The first half-cycle starts at tensile peak 1 and terminates opposite a greater tensile stress, peak 3 (case '''c'''); its magnitude is 16 MPa (2 - (-14) = 16).
	*The half-cycle starting at peak 9 terminates where it is interrupted by a flow from earlier peak 8 (case '''b'''); its magnitude is 16 MPa (8 - (-8) = 16).		*The half-cycle starting at peak 9 terminates where it is interrupted by a flow from earlier peak 8 (case '''b'''); its magnitude is 16 MPa (8 - (-8) = 16).

← Previous revision		Revision as of 03:13, 3 January 2025
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	[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]		[[File:Rainflow counting vs stress-strain curve.svg\|thumb\|Rainflow counting identifies the closed cycles in a stress-strain curve]]

	The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a loading sequence of varying [[stress (physics)\|stress]] into a set of constant amplitude stress reversals with equivalent fatigue damage. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref> {{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. In cases of multiaxial loading, [[critical plane analysis]] can be used together with rainflow counting to identify the uniaxial history associated with the plane that maximizes damage. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>		The '''rainflow-counting algorithm''' is used in calculating the [[fatigue (material)\|fatigue]] life of a component in order to convert a loading sequence of varying [[stress (physics)\|stress]] into a set of constant amplitude stress reversals with equivalent fatigue damage. The method successively extracts the smaller interruption cycles from a sequence, which models the material memory effect seen with stress-strain [[hysteresis]] cycles.<ref name="endo74">{{cite journal \|first1=Tatsuo \|last1=Endo \|first2=Koichi \|last2=Mitsunaga \|first3=Kiyohum \|last3=Takahashi \|first4=Kakuichi \|last4=Kobayashi \|first5=Masanori \|last5=Matsuishi \|title=Damage evaluation of metals for random or varying loading—three aspects of rain flow method \|journal=Mechanical Behavior of Materials \|year=1974 \|volume=1 \|pages=371–380}}</ref> This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either [[Fatigue (material)#Miner's rule\|Miner's rule]] to calculate the ''fatigue damage'', or in a [[crack growth equation]] to calculate the crack increments.<ref>{{cite journal \|last1=Sunder \|first1=R. \|last2=Seetharam \|first2=S. A. \|last3=Bhaskaran \|first3=T. A. \|year=1984 \|title=Cycle counting for fatigue crack growth analysis \|journal=International Journal of Fatigue \|volume=6 \|number=3 \|pages=147–156\|doi=10.1016/0142-1123(84)90032-X }}</ref> Both methods give an estimate of the ''fatigue life'' of a component. In cases of multiaxial loading, [[critical plane analysis]] can be used together with rainflow counting to identify the uniaxial history associated with the plane that maximizes damage. The [[algorithm]] was developed by [[Tatsuo Endo (engineer)\|Tatsuo Endo]] and M. Matsuishi in 1968.<ref name="matsuishi68">{{cite journal \|last1=Matsuishi \|first1=M. \|last2=Endo \|first2=T. \|year=1968 \|title=Fatigue of metals subjected to varying stress \|journal=Japan Society of Mechanical Engineering}}</ref>

	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.<ref name="endo74"/>		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.<ref name="endo74"/>

	[[File:Rainflow_fig1.PNG\|thumb\|right\|Figure 1: Uniform alternating loading]]		[[File:Rainflow_fig1.PNG\|thumb\|right\|Figure 1: Uniform alternating loading]]
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	== History ==		== History ==
	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.<ref name="endo74"/>		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.<ref name="endo74"/>

	Downing and Socie created one of the more widely referenced and utilized rainflow cycle-counting algorithms in 1982,<ref>{{cite journal \|last1=Downing \|first1=S.D. \|last2=Socie \|first2=D.F. \|year=1982 \|title=Simple rainflow counting algorithms \|journal=International Journal of Fatigue \|volume=4 \|number=1 \|pages=31–40\|doi=10.1016/0142-1123(82)90018-4 }}</ref> which was included as one of many cycle-counting algorithms in ASTM E1049-85.<ref>{{cite book \|series=ASTM E 1049-85. \|year=2005 \|title=Standard practices for cycle counting in fatigue analysis \|publisher=ASTM International}}</ref>		Downing and Socie created one of the more widely referenced and utilized rainflow cycle-counting algorithms in 1982,<ref>{{cite journal \|last1=Downing \|first1=S.D. \|last2=Socie \|first2=D.F. \|year=1982 \|title=Simple rainflow counting algorithms \|journal=International Journal of Fatigue \|volume=4 \|number=1 \|pages=31–40\|doi=10.1016/0142-1123(82)90018-4 }}</ref> which was included as one of many cycle-counting algorithms in ASTM E1049-85.<ref>{{cite book \|series=ASTM E 1049-85. \|year=2005 \|title=Standard practices for cycle counting in fatigue analysis \|publisher=ASTM International}}</ref>

	Igor Rychlik gave a mathematical definition for the rainflow counting method,<ref>{{cite journal \|last=Rychlik \|first=I. \|year=1987 \|title=A New Definition of the Rainflow Cycle Counting Method \|journal=International Journal of Fatigue \|volume=9 \|number=2 \|pages=119–121\|doi=10.1016/0142-1123(87)90054-5 }}</ref> thus enabling closed-form computations from the statistical properties of the load signal.		Igor Rychlik gave a mathematical definition for the rainflow counting method,<ref>{{cite journal \|last=Rychlik \|first=I. \|year=1987 \|title=A New Definition of the Rainflow Cycle Counting Method \|journal=International Journal of Fatigue \|volume=9 \|number=2 \|pages=119–121\|doi=10.1016/0142-1123(87)90054-5 }}</ref> thus enabling closed-form computations from the statistical properties of the load signal.
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	=== Four point method ===		=== Four point method ===
	[[File:Rainflow-4point-method.png\|thumb\|Rainflow counting using the four point method. Any pair of turning points B,C that lie between adjacent points A and D is a rainflow cycle. Count and eliminate the pair B,C and continue processing the sequence until no more cycles can be extracted.]]		[[File:Rainflow-4point-method.png\|thumb\|Rainflow counting using the four point method. Any pair of turning points B,C that lie between adjacent points A and D is a rainflow cycle. Count and eliminate the pair B,C and continue processing the sequence until no more cycles can be extracted.]]
	This method evaluates each set of 4 adjacent turning points A-B-C-D in turn:<ref name="lee12"> {{cite book \|title=Metal Fatigue Analysis Handbook\|chapter=Rainflow Cycle Counting Techniques \|first1=Yung-Li \|last1=Lee \|first2=Tana \|last2=Tjhung \|year=2012 \|pages=89–114 \|doi=10.1016/B978-0-12-385204-5.00003-3\|isbn=9780123852045 }} </ref>		This method evaluates each set of 4 adjacent turning points A-B-C-D in turn:<ref name="lee12">{{cite book \|title=Metal Fatigue Analysis Handbook\|chapter=Rainflow Cycle Counting Techniques \|first1=Yung-Li \|last1=Lee \|first2=Tana \|last2=Tjhung \|year=2012 \|pages=89–114 \|doi=10.1016/B978-0-12-385204-5.00003-3\|isbn=9780123852045 }}</ref>

	# Any pair of points B-C that lies within or equal to A-D is a rainflow cycle.		# Any pair of points B-C that lies within or equal to A-D is a rainflow cycle.