86881171 Rainflow Counting Methods

7/29/2019 86881171 Rainflow Counting Methods

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Simple ra in f lowc o u n t i n g a l g o r i t h m sS . D . Downing and D . F . SocieTwo simple algorithms f o r performing rainflow counting are presented in this paper. The secondalgorithm is suitable f o r microcomputer devices that are placed in vehicles to record field data.Key words: f a t i g u e t e s t s ; r a i n f l o w co u n t i n g ; a l g o r i t h m s ; l o a d m o n i t o r i n g ; g ro u n d ve h i c l e s

I n t h e l a n d - v e h i c l e i n d u s t r y , c u m u l a t i v e d a m a g e f a t i g u ea n a ly s is p r o c e d u r e s a r e u s u a l ly e m p l o y e d t o e s t i m a t e e n d u r -a n c e . 1 - 3 T h e y a l lo w t h e e n g i n e e r t o r e l at e t h e e n d u r a n c eo f a c tu a l c o m p o n e n t s t o s i m p le l a b o r a t o r y s p e c i m e n s .F a t i g u e li ve s o f s p e c im e n s a r e d e t e r m i n e d f r o m c o n s t a n ta m p l i t u d e t e s t s. R e a l s t r u c t u r e s s e l d o m , i f e v e r , e x p e r i e n c ec o n s t a n t a m p l i t u d e l o a d i n g . T h e r e f o r e, s o m e t y p e o f c y c l ec o u n t i n g s c h e m e m u s t b e e m p l o y e d t o r e d u c e a c o m p l e xi r r e g u la r l o a d i n g h i s t o r y i n t o a s e ri e s o f c o n s t a n t a m p l i t u d ee v e n t s . T h e m o s t a c c u r a t e f a t i g u e l i f e e s t i m a t e s a r e o b t a i n e du s i n g a n a n a l y s i s b a s e d o n t h e s t r a i n a t t h e m o s t h i g h l ys t r e s s e d / s t r a i n e d l o c a t i o n . R a i n f l o w c o u n t i n g 4 i s a n e s s e n t i a lp a r t o f t h e s e p r o c e d u r e s . T h i s m e t h o d d e f i n e s c y c l e s a sc losed s t ress / s t ra in hys te res i s loops as i l lus t ra ted in F ig . 1 .F o u r c y c l e s ( b c , e d , f g , a d ) a r e i d e n t i f i e d b y t h e m e t h o d .

S e v e r a l a l g o r i t h m s a r e a v a i l a b l e t o p e r f o r m t h e c o u n t i n g ,h o w e v e r , t h e y a l l r e q u i r e t h a t t h e e n t i r e l o a d h i s t o r y b ek n o w n b e f o r e t h e c o u n t i n g p r o c e ss s t a r ts . 5 - 7 A s a r e s u lt ,t h e y a r e n o t s u i t a b l e f o r ' o n - b o a r d ' d a t a p r o c e s s i n g s i n c et h e e n t i r e l o a d h i s t o r y i s n 't k n o w n u n t il t h e e n d o f t h e t e s t .T h e f i r s t a l g o r i t h m d e s c r i b e d i n t h i s p a p e r h a s t h i s s a m el i m i t a t i o n ; t h a t i s, th e l o a d h i s t o r y m u s t b e r e a r r a n g e d t ob e g i n a n d e n d w i t h t h e m a x i m u m p e a k ( o r m i n i m u mv a l le y ) . I t is p r e s e n t e d b e c a u s e o f i ts s i m p l i c i t y a n d b e c a u s ei t i s u s e f u l a s a c o n t r o l p r o g r a m f o r d e t e r m i n i n g s t r e s s /s t r a i n r e s p o n s e u n d e r v a r i a b l e a m p l i t u d e l o a d i n g . T h e ' o n e -p a s s ' ra i n f l o w c o u n t i n g a l g o r i t h m d e s c r i b ed l a t e r o v e r c o m e st h i s h m i t a t i o n a n d i d e n t i f i e s t h e s a m e c y c l e s a s t h e f i rs ta l g o r i t h m . T h u s , i t c a n o p e r a t e i n ' r e a l - t i m e ' a n d h a s b e e ns u c c e s s f u l l y i m p l e m e n t e d i n a h i s t o g r a m r e c o r d e r . 8

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P R E V I O U S W O R KM o s t p r a c t i c a l r a i n f lo w c o u n t i n g a l g o r i t h m s a r e b a s e d o ne i t h e r t h e ' a v a i l a b i l i ty m a t r i x ' o r t h e ' v e c t o r ' m a t h e m a t i c a lc o n c e p t s . T h e ' a v a i l a b il i t y m a t r i x ' a l g o r i t h m d e v e l o p e d b yW e t z e l 9 re q u i r e s t h a t t h e i n p u t s i g n a l b e d i v i d e d i n t o af i n i te n u m b e r o f b a n d s w h i c h a r e u s e d t o d e f i n e t h en u m e r i c a l v a l u e o f t h e r a n g e a n d m e a n o f e a c h r e v e r s a l .C o r r e s p o n d i n g t o e a c h b a n d i s a n e l e m e n t i n t h e a v a i l a b i l i tym a t r i x . S i m p l y s p e a k in g , t hi s m a t r i x i s u s e d t o d e t e r m i n ew h e n a r a i n f lo w c o u n t e d c y c l e is f o r m e d .' V e c t o r ' b a s e d r a i n fl o w c o u n t i n g a l g o r i t h m s u s e ao n e d i m e n s i o n a l a r r a y t o k e e p t r a c k o f t h o s e p e a k s a n dv a l l e y s w h i c h h a v e n o t f o r m e d a c l o s e d l o o p . I n o t h e rw o r d s , o n c e a c l o s e d l o o p h a s b e e n d e t e r m i n e d , t h e p e a ka n d v a l le y a s s o c ia t e d w i t h i t c a n b e e l i m i n a t e d f r o m t h ev e c t o r . T h is t e c h n i q u e w a s f i rs t d e m o n s t r a t e d b y D o w n i n ge t a l 2 a n d w a s m o d i f i e d b y O k a m u r a et al IO t o a c c o u n tf o r h a l f c y c l e s . B o t h a l g o r i t h m s d e s c r i b e d i n t h i s p a p e r u s et h e ' v e c t o r ' c o n c e p t .

R U L E S FO R B O T H A L G O R I T H M SL e t t h e r a n g e o f e a c h p e a k a n d v a l l e y b e i d e n t i f i e d a sf o l l o w s :

X = r a n g e u n d e r c o n s i d e r a t i o nY ; p r e v i o u s r an g e a d j a c e n t t o X

A s e a c h p e a k o r v a l l e y i s e n c o u n t e r e d , i t is p u t i n a v e c t o rE ( n ) . I n a d d i t i o n , t h e s t a r t i n g p e a k o r v a l l e y is d e s i g n a t e d S .

R A IN F L O W A L G O R I T H M IT h i s a l g o r i t h m r a i n f l o w c o u n t s a h i s t o r y o f p e a k s a n d v a l le y si n s e q u e n c e w h i c h h a s b e e n r e a r r a n g e d t o b e g i n a n d e n dw i t h t h e m a x i m u m p e a k ( o r m i n i m u m v a l l ey ) . R a i n f l o wc o u n t i n g t h e n p r o c e e d s a c c o r d i n g t o t h e f o l l o w i n g s te p s :I - - R e a d t h e n e x t p e a k o r v a l l e y

( i f o u t o f d a t a , S T O P )2 - F o r m r a n g e s X a n d Y

( i f t h e v e c t o r c o n t a i n s l e s s t h a nS p o i n t s , g o t o S t e p i )

3 - C o m p a r e r a n g e s X a n d Ya . I f X < Y , g o t o S t e p lb . I f X > / Y , g o t o S t e p 4

4 - C o u n t r a n g e YD i s c a r d t h e p e a k a n d v a l l e y o f YG o t o S t e p 2

R A I N F L O W A L G O R I T H M I I (O N E-P AS S)T h i s a l g o r i t h m r a i n f l o w c o u n t s a h i s t o r y o f p e a k s a n dv a l l e y s i n s e q u e n c e a s t h e y o c c u r . I t c a l c u l a t e s t h e s a m er a n g es a n d m e a n s a s R a i n f l o w A l g o r i t h m I w h i c h r e q u i r e dt h a t t h e h i s t o r y b e r e a r r a n g e d t o b e g i n a n d e n d w i t h t h em a x i m u m p e a k ( o r m i n i m u m v a l le y ) . R a i n f lo w c o u n t i n gt h e n p r o c e e d s a c c o r d i n g t o t h e f o U o w i n g s t e p s:I - R e a d t h e n e x t p e a k o r v a l l e y

( i f o u t o f d a t a , g o t o S t e p 6 )2 - F o r m r a n g e s X a n d Y( i f t h e v e c t o r c o n t a i n s l e s s t h a n 2 p o i n t sp a s t t h e s t a r t i n g p o i n t , g o t o S t e p I )

S - C o m p a r e r a n g e s X a n d Ya . I f X ' ( Y , g o t o S t e p I

b . I f X = Y a n d Y c o n t a i n s S , g o t o S t e p 1c . I f X > Y a n d Y c o n t a i n s S , g o t o S t e p 4d . I f X ~> Y a n d Y d o e s n o t c o n t a i n S , g o t o S t e p 5

4 - M o v e S t o t h e n e x t p o i n t i n t h e v e c t o rG o t o S t e p 1


6 R e a d t h e n e x t p e a k o r v a l le y f r o m t h e b e g i n n in go f t h e v e c t o r E ( n )( i f t h e s t a r t i n g p o i n t , S , h a s a l r e a d y b e e nr e r e a d , S T O P )

7 - - F o r m r a n g e s X a n d Y( i f t h e v e c t o r c o n t a i n s l e s s t h a n 2 p o i n t s p a s tt h e s t a r t in g p o i n t , g o t o S t e p 6 )

8 - C o m p a r e r a n g e s X a n d Ya . I f X < Y , g o t o S t e p 6b . I f X l > Y , g o t o S t e p 9


E X A M P L E SB o t h a l g o r i t h m s w i l l b e i ll u s t r a t e d b y r a i n f l o w c o u n t i n g t h es t r a i n / t i m e h i s t o r y s h o w n i n F i g . 2 . F i g . S s h o w s t h e s a m eh i s t o r y a f t e r i t h a s b e e n r e a r r a n g e d t o b e g i n a n d e n d w i t ht h e m a x i m u m p e a k , p o i n t C . A l s o gi v en is th e r e s u l t in gs t r e s s / s t r a i n r e s p o n s e w h i c h s h o w s a n u m b e r o f c l o s e dh y s t e r e si s l o o p s . R a i n f l o w c o u n t i n g s h o u l d i d e n t i f y t h er a n g e s o f s t r a i n w h i c h c o r r e s p o n d t o t h e s e c l o s e d h y s t e r e s i sl o o p s .

R a i n f l o w A l g o r i t h m I is i l l u s tr a t e d in c o n j u n c t i o nw i t h F i g s 4 - 1 6 . I n e a c h fi g u re , t h e s t r a i n / ti m e h i s t o r y s h o w nc o r r e s p o n d s t o t h e c o n t e n t s o f t h e v e c t o r E ( n ) . A l s o s h o w ni s t h e s t r e s s / s t r a i n p l o t , t h e v a l u e s o f r a n g e s X a n d Y , a n dt h e d e c i s i o n s w h i c h c o r r e s p o n d t o S t e p 3 o f t h e r u l e s fo rt h i s a l g o r i t h m . T h e h i s t o r y t o b e r a i n f l o w c o u n t e d i sg i v e n i n F i g . S . In F i g 4 , t h e f i r s t p e a k h a s b e e n r e a d i n t ot h e v e c t o r . T h i s e s t a b l i s h e s t h e o r i g i n o f t h e s t r e s s / s t r a i np l o t s in c e e i t h e r t h e m a x i m u m p e a k o r t h e m i n i m u m v a l l e yl i es o n t h e c y c l i c s t r e s s / s t r a i n c u r v e . S i n c e t h e r e a r e l e s st h a n 3 p o i n t s i n t h e v e c t o r , r a n g e s X a n d Y a r e u n d e t e r -m i n e d a n d t h e n e x t p e a k o r v a l l e y m u s t b e r e a d . I n F i g . 5 ,

m

T -: ] : -N - HE -

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L I I I IF i g . 2 V a r i a b l e a m p l i t u d e h i s t o r y

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3 2 I N T . J . F A T I G U E J a n u a r y 1 9 8 2


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smJu]F i g . 3 S t r e s s / s tr a i n r e s p o n s epoint D has been read into the vector and the stress isunloaded from C to D along the outer loop curve. Range Yis still undetermined so the next peak or valley must beread. In Fig. 6, point E has been read and the stress increasesfrom D to E along the outer loop curve. A closed hysteresisloop has been formed and, according to the counting rules,range Y should be counted and its point s discarded sincethey have no bearing on future events. The countingalgorithm identified the same cycle, DC, as was determinedfrom the stress/strain response. In Fig. 7, points D and Chave been eliminated from the contents of the vector.It is left to the reader to follow Figs 7-16 along with thecounting rules to see that the algorithm identifies the samecycles (DC, GF, BA, HE) as were determined from thestress/strain response.Rainflow Algorithm II (One-Pass) will be used tocount the strain/time history given in Fig. 2. It shouldidentify the same cycles as the previous algorithm withoutthe restriction that history be rearranged to begin and endwith the maximum peak. Figs 17 -31 show the contents ofthe vector E ( n ) and the counting decisions for each stepin the counting process. It should be noted that the start-ing point, S, is always the first occurrence of either themaximum peak or the minimum valley at that point in thehistory. When all the peaks and valleys o f the hi story havebeen read, we begin reading points from the beginning ofthe vector as seen in Fig. 17. The counting procedure con-tinues until all the points up to and including the startingpoint have been reread. When we try to read a pointbeyond the starting point, the counting procedure stopsand a l l the cycles have been determined. Fig. 31 shows that

the same cycles (DC, GF, BA, HE) have been identifiedas in the previous algorithm. Again, the reader should care-fully follow Figs 17-31 to fully understand this algorithm.

F O R T R A N P R O G R A M L IS T IN G SA Fortran listing fo r Rainflow Algorithm I is contained inAppendix I. The reader needs to write his own version ofS u b r o u t i n e D a t a (P , K ) compatible with his data files. Thevariable, P, is the value of the data point. The variable, K,should be defined as follows:

K = 0 when the data is valid;K = 1 when the histo ry is finished.The data returned from this subroutine must be peaksand valleys in sequence and must begin and end with themaximum peak (or minimum valley). The maximum sizeof the vector, E ( n ) , is equal to the number of countingranges.

Appendix II gives the F o r t r a n listing for RainflowAlgorithm II (One-Pass). This program checks for datasequence so that the variable, P, in S u b r o u t i n e D a t a ( P , K )may be timed data samples. The meaning of variable, K,remains the same as above. For this algorithm the maximumsize of the vector E ( n ) is equal to twice the number ofcounting ranges.R a i n f l o w A l g o r i t h m I is i l lu s t r a t e d i n c o n j u n c t i o n w i t h F i gs 4 - 1 6

I

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0 0 Q Q 0 0 0B 0 0 0 0 0 1 0

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X = t l eETY = L I C ETREAl) NEXT PEAK OR VALLEYFIB. 4

I NT . J . FAT I GU E January 1982 33


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STI~CYCLES = DC, GFX = /~ C A ~ )Y = ~ ( 1 ~ )X


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R a i n f l o w A l g o r i t h m I I i s i l l u s t r a t e d i n c o n j u n c t i o n w i t h F i g s 1 7 - - 3 1

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READ NI3C[ PEAK OR VALLEY

X = ASS(C.-B)Y = ABS(B--A)b Y AND Y CONTAINSSHOVE UP ST~ RIIHG POINTREAP NEXT PE.q( OR VALLE'Y

F ] [ G . 17 FIG. 18 FIG. 19

A ~ I ] / F ' I T A J C ] ] I G A T A A C T I V E L Y T A Y , .I N G A T A A C T ] ] / E ] . Y A I ( ] ] 4 G A T A

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CYCLES = DCX = Al iCE- -B)Y = B N D E T E 1 ~

READ NE](T PEAK OR V ~L L~

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L I I I I I I I IC Y C L E S = DCX = ABS(F-E)Y = ABS(E-B)X=Y AND Y CONTAINSSREAl) NEXT PEAK OR VALLEY

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C Y C L E S = P CX = ADS(H-G)Y = ABe(G-F)X>Y AND Y DOESNOT CONTAIN SCOUNTY AND DISCARD T'S POINTS

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S U M M A R YT w o s i m p le r a i n f l o w c o u n t i n g a l g o r i t h m s f o r p r o c e s s in gf i e ld d a t a h a v e b e e n p r e s e n t e d . T h e f i r s t is u s e f u l as ac o n t r o l p r o g r a m f o r f o l l o w i n g s tr e s s / r e s p o n s e u n d e r i r r eg u l a rl o a d i n g . T h e s e c o n d a l g o r i t h m g i v es id e n t i c a l r e s u l t s a s t h ef i r s t a n d h a s t h e a d v a n t a g e t h a t t h e c o u n t i n g c a n b e g i nb e f o r e t h e e n t i r e h i s t o r y i s k n o w n .

REFERENCES1 . D a b e l l , B . J . , H i l l , S . J . , E a t o n , D . E . a n d W a t s o n , P . ' Fat iguel i fe p red i c t i ons f o r no t c he d c om po nen t s ' JSoc Env i ronmen ta lEngrs (D ec em ber 1977 )2 . D ow n ing , S . , Ga l l i a r t , D . a n d B e r e y n i , T. 'A Neubers ru lef a t i gue ana ly s is p roc edu re f o r us e w i t h a m ob i l e c om pu t e r 'SAE Paper 760317 p res en t ed a t : SAE Au tomo tove Eng inee r -ing C ongress (D e t ro i t , M ic h igan , 1976 )3 . Fatigue Under Complex Loading: Analysis and Experiment

E d i t ed by : R . M . W e tz e l (S A E I nc , W ar renda l e , P enns y l v an i a ,1 9 7 7 )

4 . i a t s u i s h i , i . a n d E n d o , T. 'Fa t i gue o f me ta l s s ub j ec ted t ov a ry i ng s t ress ' pape r p res en ted t o Japan Soc Mech Engrs( J u k v o k a , J a pa n , 1 9 6 8 )

5 . R i c ha rds , F . , LaP o i n te , N . and W e tz e l , R . 'A c y c le c oun t i nga l go r i t hm f o r f a t i gue damage ana l y s is ' P ape r No 74 (3278p res en ted a t : SAE Automotive Engineering Congress ( D e t r o i t ,M i c h i g a n , 1 9 7 4 )6 . N e l s o n , D . V . a n d F u c h s , H. O . 'P red i c t i ons o f c umu l a t i v edamage us i ng c ondens ed l oad h i s t o r i es ' P ape r 750045 p res en teda t : SA E Automotive Engineering Congress (Detroi t , M i c h igan ,1 9 7 5 )

3 8 I N T . J . F A T I G U E J a n u a r y 1 9 8 2


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7. Soc ie, D . F . 'Fat igue - l i fe predic t ion us ing loca l s tress /s t rainc o n c e p t ' E x p e r i m e n t a l M e c h 1 7 N o 2 (1 9 7 7 ) p p 5 0 - 5 66 . Soc ie , D . F . , Sh i f f l e t , G . a n d B e r n s , H . ' A f i e l d rec o rd ings y s t em w i t h app l i c a t i ons t o f a t i gue ana l y s i s 'I n t d F a t ig u e 1N o 2 ( A p r il 1 9 7 9 ) p p 1 0 3 - 1 1 19 . W e t z e l , R . M . ' A m e t hod o f f a t i gue dam age ana l y s i s 'P h DThesis (D epar t m en t o f C i v i l Eng inee r i ng , U n i v e rs i t y o fW a t e r l oo , O n t a r i o , C anada , 1971 )

10 . Ok am ura , H . , Sak a i , S . and Sus uk i , I . 'C um u la t i v e f a t iguedam age unde r random loads ' 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 t1 ( 19 7 9 ) p p 4 0 9 - 4 1 9

A UTHORSS t e p h e n D o w n i n g is w i th D e e r e a n d C o m p a n y ' s E n g i n e er -in g M ech an ics G r o u p in M o l in e an d D ar re ll S o c i e is w i th t h eD ep ar tm en t o f M ech an ica l an d In d u s t r i a l E n g in ee r in g in t h eU n iv e r s i t y o f I l l i no i s a t U rb an a -C h am p a ig n . In t h e f i r s ti n s t an ce in q u ir i e s sh o u ld b e ad d ressed to : M r S . D . D o w n in g ,E n g in ee r in g M ech an ics, D ee re an d C o m p an y , 3 3 0 0 R iv e rDrive, Moline, I l l ino is 61265 , USA.

A p p e n d i x 1R FI ) N I - L O H l q l _ ( l ( ~ I 1 ~ ITHIS PRtK~ f~INI-'LDW COtlNI.~ Fl HI%IOI,~Y uF I-'ERKSRNI) VALLEYS IN .SEQUENCE WHICH Hf-IS I~FEN RF_HI,~kHNGED10 BEG]N fIND ENI> WllH ]HI-_ MRXIMUM PI~HK (OR MINIM~IMV R L I . F V > . SIRIEMF_NI I_R~I -_I .S CI~, tR I -__~-~ONI> 1u 1H ~ SI E .P 5 INI H F _ R R I N F L . O W C O I ~ N l l N G R U L E S .D I M ~ N . ~ I O N E ( 5 @ )N = ON=-:N+~.C R I. L I ~ R I H ( E ( N ) , K )I F ( K E -Q . : ! ) . t -, lO P2 IF(N l.l..') ((I 1 ( : lX = Rf YS ( E ( N ) - - E ( N - l . ) )V - -- H B S (E ( N - ~ ) - - ~ ( N - 2 ) )3 ] F ( X L I . Y) G I ) I u ' I

4 R H N G E = VX M ~_ FI N= ( E ( N - 1 ) + E (N-z)) /2N = , N - ; ,E ( N ) = F . ( N + 2 )G ~) T{) 2E N D

A p p e n d i x 2l l f - l l ~ L{ ~ l , l f - I L G O f ~ I T I - ~ M ] I ( , C ~ N F - P H ~ '~,

1 H I S P R O G R ft M R f l IN ~ L . ( ~ N [ : O U N I ~ A H ] S I [ ~ t Y R ~ 1 1 O C CL N,C h R N [ ,] D E N ] I F ] E _ ', ] F I E . .~ - ~ M F [ 'Y C ;L .E -~ H ~ ~ I a ] N F I .. U W R L O [ H K , ] ] H M I I ~ H } I - HK ~ -Q U Ik E .- % I H F l l ] H F H I . ~ I I ~ Y N E I , t [ r F I ~ t H N G F I ) . ~ . T H I F M r . N I I F l ~ P I~ - - 9 CL W ~k ES PO N D 1 0 l H f r 5 1 b . P S ] N 1 H E R f l I N P I O W C ( J U N I I N G k t l l II F S| ) 1 M ~ N S ] O N E ( ~ . O B ~N:='. /J =e~C RI_ L. D R I R ( F ( . ~ ) , K )C R I _ L . D ~ I R ( E ( ; : ) , K )I F ( E ( 1 ) . E &I . E ( 2 ' > ) G O 1 0 ~ e ~S L O P E = "1 .] F ( E ( ~ > . G 1 E ( 2 ) ) S I . C ~ k = - I .{ ; A L l_ [ J ~ l l R ( f ~ , K )} F ( K F . (~ 1 ) G U I L I 6N = : N * ~ ..S t O P F . = S I _ O P E * ( - J )E (N ) . ' =P

I N T . J . F A T I G U E J a n u a r y 19 8 2 3 9


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A p p e n d i x ?, ( c t d )~' IF(N. L.1. IS IR RI +~ > [~0 10 :I

X=SI OPI-:~,(I-_(N)-E (N- I ) )] F ( X L E . . i }. ) {iO T O ~ ' _ ~} F ( N 1 .1 . ] S l f - f f , C l 2 ) G O 1 0 :IY : S I . ( I P E W , ( E ( N - 2 ) - E ( . N - ~ ) ):~ ] F ( X . I _ l . Y ) G ( I l( iI F ( X . [ -. (, L Y . F I N i ) l . % . l R W l . ~ -. (~ N - P ) { w U l O .1

IF( X. (;1. Y. FW~[). I.~TF4W1 F~. N- 2) (jo~ l0 4IF (X . GE. Y. FIN[) }SIHW1 Ni- N- ~) fj(1 Ttl

4 } Sl Mr,c1 := ] Sl f-~Rl +d00 10 :t

5 RRNKiE=YXME FIN= ( E (N -i ) ~_ (N- ~-) )/ ;tN=N-2E (N):--~ (N+2~GO I 0 2

6 J : = J + lIF( J. [~I. )SI FIR I) STOPN = ' - N + 3.S L O ~ F = ~ I . C ~ ' . * ( - : I . )F_(N)=:E(J )

7 ] F( N LT. ISIRI ~I+.1) OtJ It) 6X=.~LOPE,~ (I: ( N) -h ~N-~.) )IF( X. LE. e. ) Or; l~J 3e~4] F ( . N I . T ISTFWI~) ( iO l( J e~Y=:SL.( IPE,k ( E ( N.-~. ) - f f ~ N- ~ ) )

B IF(X. L1. Y) OO IO (-IF(X. GE. Y > ( 3 0 l O . ~

.9 f

86881171 Rainflow Counting Methods

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