A New Definition

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A new definition of the rainflow cycle countingmethod

Article in International Journal of Fatigue · April 1987

Impact Factor: 2.28 · DOI: 10.1016/0142-1123(87)90054-5

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Igor Rychlik

Chalmers University of Technology

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I n t J F a t i g u e 9 N o 2 1 9 8 7 ) p p 1 1 9 - 1 2 1

n e w d e f i n i t i o n o f t h e r a i n f l o w

c y c l e c o u n t i n g m e t h o d

I . R y c h l i k

A n ew equiva lent def in i t ion of the ra inflow cyc le cou nt ing m ethod is presented, wh ich

expresses the ra inf low cyc le ampl i tudes in expl ic it ana ly t ica l formulae . The m ethod

at taches to each m aximum of the s t ra in funct ion the amp l itude of a corresponding

cycle or tw o ha l f cyc les , wh ich are eva luated indepen dent ly f rom each other . Th is

def in i t ion is more convenient for the s ta t is t ica l ana lys is of ra in f low cyc le ampl i tudes

for a random loading process.

Ke y wo rd s: fa t igue; ra inf low count ing; top lev e l -up count ing; cyc le amp l itude; random

loading

T h e r a i n f l o w c y c l e ( R F C ) c o u n t i n g m e t h o d , f i r s t p r o p o s e d

b y M a t s u is h i a n d E n d o , 1 i s n o w g e n e r a l ly r e g a r d e d a s t h e

m e t h o d l e a d i n g t o t h e b e s t e s t im a t o r s o f f a t i g u e l if e , s ee

D o w l i n g . 2 D u e t o t h e g r e a t i m p o r t a n c e o f t h e R F C c o u n t i n g

m e t h o d , m a n y d i f f e r e n t a l g o r i t h m s h a v e b e e n p r o p o s e d i n

t h e l i t e r a t u r e ) - s H o w e v e r , a l l th e s e p r o c e d u r e s h a v e a c o m p l i -

c a t e d s e q u e n t i a l s t r u c tu r e , w h i c h m a k e s t h e m d i f fi c u lt t o

a pp l y whe n t he i r s t a t i s t i c a l p r ope r t i e s a r e t o be s t ud i e d .

I t i s w e l l k n o w n t h a t t h e r a i n f l o w c o u n t i n g m e t h o d

c o r r e s pon ds t o t he s t a b l e c yc l i c s t r e s s /s t r a i n be h a v i o u r o f

a me t a l i n t ha t a ll s t r a i n r a nge s c o un t e d a s c yc l e s w i l l f o r m

c l os e d s t r e s s / s t r a i n hys t e r e s i s l oops , a nd t hos e c oun t e d a s

ha l f c yc le s w i l l no t . T he r a nge o f a c lo s e d hys t e r e s i s l oop

i s de f i ne d by i t s h i ghe s t a nd l owe s t po i n t , ie b y t h e p a i r

o f a l o c al m a x i m u m a n d m i n i m u m i n t h e s t ra i n f u n c t i o n

( s e e a l s o t he s e c t i on e n t i t l e d Re ma r ks be l ow) .

T h e m e t h o d p r e s e n t e d h e r e u s e s t h i s c o r r e s p o n d e n c e

e x p l ic i tl y b y a t t a c h in g t o e a c h m a x i m u m o f t h e s t r a in f u n c t i o n

( o r s t re s s f u n c t io n ) t h e a m p l i t u d e o f a c o r r e s p o n d i n g c y c l e

( c l o s e d hys te r e s i s loop ) . Th i s wa y o f de f i n i ng t he r a i n f l ow

c y c l e c o u n t i n g m e t h o d m a k e s i t p o s s ib l e t o e v a l u a te t h e

l o n g - r u n d i s t r ib u t i o n o f t h e R F C a m p l i t u d e f o r a r a n d o m

l oa d i ng p r oc e s s ; s e e Re f e r e nc e s 6 a nd 7 .

D e f i n i t i o n 1 : t o p l e v e l - u p c y c l e ( T U C )

c o u n t i n g m e t h o d

Le t y ( s ) be t he s t r e ss f unc t i on o bs e r v e d f o r - T ~< s ~< T .

F o r e a c h l o c a l y - m a x i m u m o n e c y c l e o r t w o h a l f c y c le s w i l l

b e c o u n t e d , a c c o r d i n g t o t h e f o l l o w i n g p r o c e d u r e .

L e t t h e m a x i m u m o c c u r a t t i m e t , a n d l e t t + b e t h e

t i me f o r t he f i rs t up - c r o s s i ng a f t e r t o f t he l e ve l y t ) ( o r

t + = T i f no s uc h up - c r o s s i n g e x i s ts f o r t < s < T ) ,

a n d l e t t - b e t h e la s t d o w n - c r o s s i n g b e f o r e t o f t h e s a m e

l e ve l ( o r t - = - T i f n o s u c h d o w n - c r o s s i n g e x is ts f o r

- T < s < t ). Tw o r a nge s o r i g i n a t i ng a t t , y t ) ) a r e n o w

def ined, see Fig . 1 ;

n - t ) = y t ) - mi n { y( s ) ; t - < s < t } ( 1 )

H + t ) = y t ) - m in{ y(s ) ; t < s < t +}

0142-1 123/87 /02119 -03 3.00 © 1987

Int J Fat igue Apri l 1987

_ _ S ÷ < t2 . /

t - t -1 t t l t

F i g . 1 I l lu s t r a t io n s o f t h e t o p l e v e l - u p c y c l e w i t h a m p l i t u d e

H t

= m i n H - t ) , H + t ) ) , d e fi n e d b y D e f i n it i o n 1

ules

(a) I f H + t ) >>. H - t ) a n d t - > - T , o r H + t ) < H - t )

a nd t + < T , t he n a toplevel-up cycle i s de f i ne d wi t h

a n a mp l i t ude o f f

H t )

= m i n

H - t ) , H + t ))

( 2 )

( b ) I f t h e m a x i m u m a t t i s t h e fi rs t o r th e l as t y - e x t r e m u m

i n t h e i n t e rv a l [ - T , T ] , o n e h a l f c y c l e i s def ined

w i t h a n a m p l i t u d e o f e i t h er H + t ) o r H - t ) , respect i -

ve ly .

(c) In a l l o th er cases two

h a l f c yc le s

w i t h a m p l i t u d e s o f

H + ( t) a nd H - ( t ) a r e de f i ne d .

Fo r e xa mpl e , i n F i g . 2 t op l e ve l - up c yc l e s a r e a t t a c he d

t o t he m a x i m a a t t l , t2 a nd t 3 due t o r u l e ( a ). Fu r t he r m or e ,

o n e h a l f c y c l e i s a t t a c h e d t o t h e m a x i m u m a t to , a n d t w o

ha l f c yc l e s t o t he m a x i m um a t t 4 .

W e s h al l n o w p r o v e t h a t t h e t o p l e v e l - u p c y c le c o u n t i n g

m e t h o d i s e q u i v a l e n t t o t h e r a i n f lo w c y c l e c o u n t i n g m e t h o d ,

a n d b e g i n b y d e fi n in g t h e R F C c o u n t i n g m e t h o d f o l lo w i n g

C o l l i n s )

D e f i n i t i o n 2 : r a i n f l o w c y c l e ( R F C )

c o u n t i n g m e t h o d

I : T h e r a i n f lo w c y c l e c o u n t i n g m e t h o d i s i l lu s t ra t e d i n F i g .

3 . The s t r a i n / t i me h i s t o r y i s p l o t t e d s o t ha t t he t i me a x i s

But terwor th Co (Publ ishers) L td

1 1 9


3/4

H - t 4 ) H + t 4 )

- T + T

I I I I I I

t o t l t2 t 3 t 4

T i m e

F i g . 2 E x a m p l e o f t h e t o p l e v e l - u p c y c l e c o u n t i n g m e t h o d

S t r a i n

I.-

i i

4 IL I I AI

1

II

= H + t o )

H - t 4 )

= i = H ( t a )

( t 2 )

H ( t 3 )

H + t 4 )

F i g . 3 E x a m p l e o f t h e r a i n f l o w c y c l e c o u n t i n g m e t h o d a p p l i e d t o

t h e s t r a i n h i s to r y o f F i g . 2

i s v e r t i c a l l y d o w n w a r d , a n d t h e l i n e s c o n n e c t i n g t h e s t r a i n

p e a k s a r e i m a g i n e d t o b e a s e ri e s o f p a g o d a r o o f s . S e v e r a l

r u l e s a r e i m p o s e d o n r a i n d r i p p i n g d o w n t h e s e r o o f s s o

t h a t h a l f c y c l e s a r e d e f i n e d . R a i n f l o w b e g i n s s u c c e s s i v e l y

a t t h e i n s id e o f e a c h s t ra i n p e a k . T h e r a i n f l o w i n i t i a t i n g

a t e a c h p e a k i s a l l o w e d t o d r i p d o w n a n d c o n t i n u e e x c e p t

t h a t , i f i t in i t ia t e s a t a m i n i m u m , i t m u s t s t o p w h e n i t c o m e s

o p p o s i te a m i n i m u m m o r e n e g a t i v e t h a n t h e m i n i m u m f ro m

w h i c h i t i n i ti a t e d . S i m i l a rl y , i f t h e r a i n f l o w i n i t ia t e s a t a

m a x i m u m , i t m u s t s t o p w h e n i t c o m e s o p p o s i t e a m a x i m u m

m o r e p o s i t i v e t h a n t h e m a x i m u m f r o m w h i c h i t in i ti a te d .

A r a i n f l o w m u s t a l s o s t o p i f i t m e e t s r a i n f r o m a r o o f a b o v e .

I I : W h e n t h i s p r o c e d u r e i s a p p l i e d t o a s t r a i n h i s t o r y ,

a h a l f c y c l e i s c o u n t e d b e t w e e n t h e m o s t p o s i t i v e m a x i m u m

a n d t h e m o s t n e g a t i v e m i n i m u m . I n F i g . 4 , f o r e x a m p l e ,

a h a l f c y c le is c o u n t e d b e t w e e n t h e p e a k s 7 a n d 8 . A s s u m e

t h a t o f t h e se t w o t h e m o s t p o s i t i v e m a x i m u m o c c u r s f ir st .

H a l f c y c le s a r e a ls o c o u n t e d b e t w e e n t h e m o s t p o s i t i v e

m a x i m u m a n d t h e m o s t n e g a t i v e m i n i m u m t h a t o c c u rs b e f o re

i t i n th e h i s t o r y , b e t w e e n t h is m i n i m u m a n d t h e m o s t p o s i t i v e

m a x i m u m o c c u r r i n g p r i o r t o it , a n d s o o n t o t h e b e g i n n i n g

7

3 ~

1

6

i 9

8

T i m e

F i g . 4 I l l u s t r a t i o n s o f t h e h a l f c y c l e c o u n t i n g p r o c e d u r e b y d e f i n i t i o n

2 : 1 1

H - ( t 0 )

H - t I )

- T t 3 t 2 t ~ t

I I I I I I I

t3 1 = t 2 _ 1 ~ = t 1 _ 1 t I = t ° _ l

H + , t o }

T

I I _

t o T i m e

F i g . 5 I l l u s t r a t i o n o f t h e s t r a in h i s t o r y u s e d t o p r o v e t h e e q u i v a l e n c e

o f t h e T U C a n d R F C c o u n t i n g m e t h o d s

o f t h e h i s t o r y . T h i s i n F i g . 4 h a l f c y c l e s a r e a l so c o u n t e d

b e t w e e n p e a k s 6 a n d 5 , 5 a n d 4 , a n d s o o n . A f t e r t h e m o s t

n e g a t i v e m i n i m u m i n t h e h i s t o ry , h a l f c y c le s ar e c o u n t e d

w h i c h t e r m i n a t e a t th e m o s t p o s i t i v e m a x i m u m o c c u r r i n g

s u b s e q u e n t l y i n t h e h i s t o r y , t h e m o s t n e g a t i v e m i n i m u m

o c c u r r i n g a f t e r t h is m a x i m u m , a n d s o o n t o t h e e n d o f

t h e h i s t o r y . A g a i n r e f e r r i n g t o F i g . 4 , h a l f c y c l e s a r e c o u n t e d

b e t w e e n p e a k s 8 a n d 9 , 9 a n d 1 0 , a n d s o o n . T h e s t r a i n

r a n g e s c o u n t e d a s h a l f c y c l e s t h e r e f o r e i n c r e a s e i n m a g n i t u d e

t o t h e m a x i m u m a n d t h e n d e c r e a s e .

P r o o f o f t h e e q u i v a le n c e o f T U C a n d R F C

c o u n t i n g m e t h o d s

A s s u m e t h a t t h e m o s t p o s i t i v e m a x i m u m o f t h e j - s t r e s s

f u n c t i o n i n t h e i n t e r v a l [ - T , 7 ] o c c u r s a t t° . Le t {t i}, _ T

~ < . . . < t 2 < t 1 < t o b e t h e t i m e s o f m a x i m a w h i c h

s a t is f y t h e c o n d i t i o n b ) o r c ) , a n d l e t t~ a n d t _ il b e t h e

t i m e p o i n t s d e f i n e d o n F i g . 1 . T h e n , f o r e a c h i > 0 , H + t i)

/ > H - t i) a n d t i ) - = - T , i e t i i s t h e m o s t p o s i t i v e m a x i -

m u m i n t h e i n t e r v a l [ - T , t~ ] a n d t i l i s t h e m o s t n e g a t i v e

m i n i m u m i n t h e i n t e r v a l [ - T , t i] , s e e F i g . 5 . B y D e f i n i t i o n

2: I I , the h al f cy cle s t ° ~ t°l = t ll ~ t 1 ~ t_11 = t~ - -*

t 2 - -* t_21 = t~ -* . . . . w i th r an ge s

H - t ° ) , H + I 1 ) , H - I 1 ) ,

H + t 2 ), H - t 2 ) . . . , r e s p e c t i v e l y , a r e c o u n t e d . C o n s e q u e n t l y ,

t o t h e m a x i m u m a t t i o n e c a n a t t a c h t w o h a l f c y c l e s , H + t i)

a n d H - t i ) . T h e s e t o f h a l f c y c l es w h i c h o c c u r a f te r t o c a n

b e t r e a t e d i n a s i m i l a r w a y , a n d h e n c e t h e s a m e h a l f c y c l e s

a r e c o u n t e d b y b o t h p r o c e d u r e s .

S i n c e f o r a n y m a x i m u m a t t i m e t , s a y , w h i c h s a t i s f i e s

c o n d i t i o n a ) a fu l l c y c le m u s t b e c o u n t e d , w e n e e d o n l y

p r o v e t h a t t h e a m p l i t u d e o f th e c y c le i s H t ) = m i n H - t ) ,

H + t ) ) .

1 2 0 I n t J F a t i g u e A p r i l 1 9 8 7


4/4

y (s) , st rain h istory

)_

s , T i m e

F i g . 6 I l lu s t ra ti o n o f a s tra in f u n c t i o n i n w h i ch a mi n i mu m i s t h e

l o w est p o i n t o f t w o cyc l es

W e b e g i n w i t h a m a x i m u m s u c h t h a t H+ t) >1 H - ( t ) ,

a n d t - > - T . S i n c e t - > - T , t h e r e e x is ts a m a x i m u m

a t t i me t* , s a y - T ~< t * < t - , s uc h t ha t t he ra i n pa t h

s t a r t e d a t t * d r o p s d o w n f r o m t h e m i n i m u m a t t i m e t - 1 .

S i nc e y ( t * ) > ) , ( t ) a nd j ( t _ l ) I > . Y( 6 ), t he r a i n p a t h s t a r t e d

a t t h e m a x i m u m a t t i s s t o p p e d b y t h e r a i n p a t h s t a r t e d

a t t* , a n d a h a l f c y c l e w i t h r a n g e H - ( t ) i s c o u n t e d . O b s e r v e

t ha t a l l r a i n pa t h s s t a r t e d a t ma x i ma i n t he i n t e r va l ( t - ,

t ) a r e s t oppe d be f o r e o r a t t i me t , a nd t he r a i n pa t h s t a r t e d

a t t* c a n no t be s t op pe d be f o r e t he t i m e t + .

Ne x t , t he r a i n pa t h s t a r t e d a t a mi n i mum a t t - 1 i s

s t o p p e d i n t h e i n t e r v a l 6 tO, g i v i n g a h a l f c y c l e w i t h r a n g e

H - t ) ,

a n d t h e R F C p r o c e d u r e c o u n t s a c y c l e w i t h a m p l i t u d e

H t ) = m i n ( H - ( t ) , H+ t)) .

W e t u r n n o w t o a m a x i m u m s u c h t h a t H - t ) > H + t )

a nd t ÷ < T . Th e r a i n p a t h s t a r t e d a t t is s t opp e d a t t + ,

g i v i n g a ha l f c yc l e w i t h r a nge H + ( t) . Fu r t h e r m or e , t he r a i n

p a t h s t a r t e d a t a m i n i m u m a t t i m e t l w i l l b e s t o p p e d b y

t h e r a in f lo w d r o p p i n g d o w n f r o m t h e m a x i m u m a t t, g i v in g

a h a l f cy c l e w i t h t h e r a n g e H+ t) , a nd a f u l l c yc l e w i t h

a m p l i t u d e H t) = m i n ( H - ( t ) , H+ t) ) i s c oun t e d .

Remarks

W e f i n is h w i t h s o m e r e m a r k s a b o u t t h e r e l a ti o n s h i p b e t w e e n

t h e R F C a n d T U C m e t h o d s .

T h e R F C p r o c e d u r e h as a c o m p l i c a t e d s e q u e n t i a l s t r u c -

t u r e , a nd t h e a mp l i t ude o f t he c yc l e s a nd h a l f c yc l e s c a n

d e p e n d o n t h e o r d e r i n w h i c h o n e i n i t i a t e s t h e r a i n f l o w s .

U s u a l ly , r a i n f l o w s b e g i n s u c c e s si v e ly f r o m t h e f i r s t e x t r e m u m

o f t h e s t r a in f u n c t i o n . H o w e v e r , t h e y c a n a l s o b e i n it i at e d

f r o m t h e l a s t e x t r e m u m , c h a n g i n g t h e t i m e d i r e c t i o n , a n d

t he s a me c yc l e s a nd ha l f c yc l e s w i l l be ob t a i ne d . Th us t he

R F C m e t h o d i s t i m e i n v a r i a n t .

T h e s e q u e n ti a l s t r u c t u r e o f th e R F C m e t h o d i s c a u s e d

b y t h e f a c t t h a t i t m u s t k e e p t r a c k o f t h o s e e x t r e m e s w h i c h

h a v e n o t y e t f o r m e d a c y c l e ( c l o s e d h y s t e r e s i s l o o p ) . O n c e

a c y c l e h a s b e e n d e t e r m i n e d , t h e m a x i m u m a n d m i ni m um

a s s oc i a t e d w i t h i t c a n be e l i mi na t e d f r om f u r t he r a na l y s i s .

Cons e que n t l y , a c yc l e de f i ne s un i que l y a pa i r o f m x i m u m

a n d m i n i m u m v a l u e s w h i c h a r e it s h i g h e s t a n d l o w e s t p o i n t s ,

k w h a t w e h a v e e x t e n s i v el y u s e d i n t h e d e f i n it i o n o f t h e

T U C m e t h o d.

S i n c e t h e T U C p r o c e d u r e , w h i c h i s e q u i v a l e n t t o R F C

m e t h o d , c a n b e s t a r t e d a t a n y m a x i m u m , l e t t h e R F C

a l go r i t hm s t a r t a t a l oc a l ma x i mum a t t i me , s a y t . By

De f i n i t i on 2 : 1 , t he r a i n f l ow i n i t i a t e d a t t h a s a r a nge H+ t) .

N e x t , w e c h a n g e t h e t i m e d i r e c t i o n a n d s t a r t a ( n ew ) r a i n f i o w

f r o m t h e s a m e m a x i m u m . T h e r a n g e o f th i s p a th i s

H - t ) .

N o w , i f t h e m a x i m u m i s a h i g h e s t p o i n t o f a c y c le (c l o se d

hys t e r e s i s l oop ) , t he a m p l i t ude o f t h is c yc l e i s m i n ( H - ( t ) ,

H + ( t ) ) b y t h e T U C m e t h o d . S o t h e T U C p r o c e d u r e c a n

be s e e n a s a s t a t i ona r y ( i nde p e nde n t o f t he s t a r t i ng po i n t )

a n d t i m e - i n v a r i a n t R F C p r o c e d u r e .

F i n a l l y , n o t e t h a t t h e T U C p r o c e d u r e , w h i c h c h o o s e s

m a x ( H - ( t ) , H+ t) ) a s th e a m p l i t u d e o f a cy c l e, c a n n o t b e

e q u i v a l e n t t o t h e R F C p r o c e d u r e s i nc e it is p o ss i b le t o h a v e

a s t r a i n f u n c t i o n w i t h a m i n i m u m w h i c h i s t h e l o w e s t p o i n t

o f t w o c yc l e s se e F i g . 6 .

c k now l e dg emen t s

T h e a u t h o r i s i n d e b t e d t o P r o f e s s o r G e o r g L i n d g r e n f o r

d i s c u s si o n a n d v a l u a b l e c o m m e n t s .

Refe rences

1 . M a t s u i s h i , M . e n d E n d o , T . 'F a t ig u e o f m e t al s s u b je c t e d

t o va ry i n g s t ress '

P a p e r p r e s e n te d o J a p a n S o c M e c h E n g r s

( J u k v o k a , J a p a n , 1 9 6 8 )

2 . D o w l i n g , N . E . ' F a t ig u e p r ed ic t io n s f o r c o m p l ic a t e d s tr e s s-

strain h istor ies

J M a t e r

( 1 9 7 2 ) p p 7 1 - 8 7

3 . D o w n i n g , S . D . a n d S o c i e , D . F . ' S im p l e r a in f lo w c o u n ti n g

algori thms I n t J F a t i g u e 4 N o 1 ( J a n u a r y 1 9 8 2 ) p p 3 1- - 4 0

4 . O k a m u r a , H . , S a k a i , S . a n d S u s u k i , I . ' C u m u l a t iv e f a ti g u e

d a m a g e u n d e r ra n d o m l oa d s

F a t i g u e E n g n g M a t e r a n d S t r u c t

1 ( 1 9 7 9 ) p p 4 0 9 - 4 1 9

5 . S o c i a , D . F . F a t i g u e - l i f e p red i c t i o n u s i n g l o ca l s t ress /s t ra in

c o n c e p t s '

E x p t l M e c h

1 7 N o 2 ( 1 9 7 7 ) p p 5 0 - 5 6

6 . L i n d g r e n , G . a n d R y c h l i k , I . ' R a i n f l o w c y c l e d i s t ri b u t io n s

f o r f a t i g u e l i fe p re d i c t i o n u n d e r G au ss i an l o ad p ro cesses '

S t a r

R e s R e p

( U n i v e r s i ty o f L u n d , S w e d e n , 1 9 8 6 ) p p 1 - 1 7 t o

a p p e a r i n

F a t i g u e E n g n g M a t e r a n d S t r u c t

7 . Ry ch l i k , I . ' Ra i n f l o w cyc l e d i s t r i b u t i o n f o r a s t a ti o n ary

G au ss i an l o ad p ro cess

S t a t R e s R e p 9 8 6 : 4

U n i v e r s i t y o f

L u n d , S w e d e n , 1 9 8 6 ) p p 1 - 3 6

8 . C o l l i n s , J . A .

F a i l u r e o f M a t e r i a ls i n M e c h a n i c a l D e s i g n

( W i l e y I n te r s ci e nc e , N e w Y o r k, N Y , U S A , 1 9 8 1 ) p p 2 8 2 - 2 8 5

u t h o r

D r R y c h l i k is w i t h t h e D e p a r t m e n t o f M a t h e m a t i c a l S t a t is t ic s ,

U n i v e r s i t y o f L u n d , B o x 1 18 , S -2 21 0 0 L u n d , S w e d e n .

I n t J F a t i g u e A p r i l 1 9 8 7 1 2 1
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jected_to_Varying_Stress?el=1_x_8&enrichId=rgreq-9e9239de-1866-4dfa-85f9-a52c5f42a5a8&enrichSource=Y292ZXJQYWdlOzI0MDQzMjM3MTtBUzoxNjU1MjI2MTIxNzA3NTJAMTQxNjQ3NTA3NDMyMg==https://www.researchgate.net/publication/246172371_Fatigue_of_Metals_Subjected_to_Varying_Stress?el=1_x_8&enrichId=rgreq-9e9239de-1866-4dfa-85f9-a52c5f42a5a8&enrichSource=Y292ZXJQYWdlOzI0MDQzMjM3MTtBUzoxNjU1MjI2MTIxNzA3NTJAMTQxNjQ3NTA3NDMyMg==https://www.researchgate.net/publication/223128697_Simple_rainflow_counting_algorithm?el=1_x_8&enrichId=rgreq-9e9239de-1866-4dfa-85f9-a52c5f42a5a8&enrichSource=Y292ZXJQYWdlOzI0MDQzMjM3MTtBUzoxNjU1MjI2MTIxNzA3NTJAMTQxNjQ3NTA3NDMyMg==https://www.researchgate.net/publication/223128697_Simple_rainflow_counting_algorithm?el=1_x_8&enrichId=rgreq-9e9239de-1866-4dfa-85f9-a52c5f42a5a8&enrichSource=Y292ZXJQYWdlOzI0MDQzMjM3MTtBUzoxNjU1MjI2MTIxNzA3NTJAMTQxNjQ3NTA3NDMyMg==

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