Metallic materials — Fatigue testing — Variable amplitude fatigue testing — Part 2: Cycle counting and related data reduction methods

ISO 12110-2:2013 presents cycle counting techniques and data reduction methods which are used in variable amplitude fatigue testing. For each test or test series, cycle counting is mandatory whereas data reduction methods are optional. ISO 12110-2:2013 supports ISO 12110-1 which contains the general principles and describes the common requirements about variable amplitude fatigue testing. ISO 12110-2:2013, the term "loading" refers either to force, stress, or strain since the methods presented here are valid for all. The following issues are not within the scope of this document and therefore are not addressed: constant amplitude tests with isolated overloads or underloads; large components or structures; environmental effects like corrosion, creep, etc. linked to temperature/time interactions leading to frequency and waveform effects; multiaxial loading.

Matériaux métalliques — Essais de fatigue — Essais sous amplitude variable — Partie 2: Méthodes de comptage des cycles et méthodes associées de réduction des données

General Information

Status
Published
Publication Date
24-Jun-2013
Current Stage
9093 - International Standard confirmed
Start Date
24-Sep-2018
Completion Date
24-Sep-2018
Ref Project

Buy Standard

Standard
ISO 12110-2:2013 - Metallic materials -- Fatigue testing -- Variable amplitude fatigue testing
English language
33 pages
sale 15% off
Preview
sale 15% off
Preview

Standards Content (sample)

INTERNATIONAL ISO
STANDARD 12110-2
First edition
2013-07-01
Metallic materials — Fatigue testing —
Variable amplitude fatigue testing —
Part 2:
Cycle counting and related data
reduction methods
Matériaux métalliques — Essais de fatigue — Essais sous
amplitude variable —
Partie 2: Méthodes de comptage des cycles et méthodes associées de
réduction des données
Reference number
ISO 12110-2:2013(E)
ISO 2013
---------------------- Page: 1 ----------------------
ISO 12110-2:2013(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2013

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form

or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior

written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of

the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2013 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 12110-2:2013(E)
Contents Page

Foreword ........................................................................................................................................................................................................................................iv

1 Scope ................................................................................................................................................................................................................................. 1

2 Normative references ...................................................................................................................................................................................... 1

3 Terms and definitions ..................................................................................................................................................................................... 1

4 Cycle counting techniques .......................................................................................................................................................................... 2

4.1 General ........................................................................................................................................................................................................... 2

4.2 Cycle counting methods .................................................................................................................................................................. 3

5 Counting technique selection .................................................................................................................................................................. 7

Annex A (informative) Rainflow counting ....................................................................................................................................................... 8

Annex B (informative) Examples of quantification, cycle extraction, and open cycle sequence

composition of cycles ....................................................................................................................................................................................21

Annex C (informative) Example of result presentation for the Rainflow counting method ....................26

Bibliography .............................................................................................................................................................................................................................32

© ISO 2013 – All rights reserved iii
---------------------- Page: 3 ----------------------
ISO 12110-2:2013(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards

bodies (ISO member bodies). The work of preparing International Standards is normally carried out

through ISO technical committees. Each member body interested in a subject for which a technical

committee has been established has the right to be represented on that committee. International

organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.

ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of

electrotechnical standardization.

The procedures used to develop this document and those intended for its further maintenance are

described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the

different types of ISO documents should be noted. This document was drafted in accordance with the

editorial rules of the ISO/IEC Directives, Part 2. www.iso.org/directives

Attention is drawn to the possibility that some of the elements of this document may be the subject of

patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of

any patent rights identified during the development of the document will be in the Introduction and/or

on the ISO list of patent declarations received. www.iso.org/patents

Any trade name used in this document is information given for the convenience of users and does not

constitute an endorsement.

The committee responsible for this document is ISO/TC 164, Mechanical testing of metals, Subcommittee

SC 5, Fatigue testing.

ISO 12110 consists of the following parts, under the general title Metallic materials — Fatigue testing —

Variable amplitude fatigue testing:
— Part 1: General principles, test method and reporting requirements
— Part 2: Cycle counting and related data reduction methods
iv © ISO 2013 – All rights reserved
---------------------- Page: 4 ----------------------
INTERNATIONAL STANDARD ISO 12110-2:2013(E)
Metallic materials — Fatigue testing — Variable amplitude
fatigue testing —
Part 2:
Cycle counting and related data reduction methods
1 Scope

This part of ISO 12110 presents cycle counting techniques and data reduction methods which are used

in variable amplitude fatigue testing.

For each test or test series, cycle counting is mandatory whereas data reduction methods are optional.

This part of ISO 12110 supports ISO 12110-1 which contains the general principles and describes the

common requirements about variable amplitude fatigue testing.

In this part of ISO 12110, the term “loading” refers either to force, stress, or strain since the methods

presented here are valid for all.

The following issues are not within the scope of this part of ISO 12110 and therefore will not be addressed:

— constant amplitude tests with isolated overloads or underloads;
— large components or structures;

— environmental effects like corrosion, creep, etc. linked to temperature/time interactions leading to

frequency and waveform effects;
— multiaxial loading.

NOTE 1 Phasing is of prime importance when dealing with multiaxial tests under either constant or variable

amplitude controlled loading.

NOTE 2 Although frequency variations during cycling are not outside of the scope of this part of ISO 12110, the

following clauses deal only with constant frequency cycling.
2 Normative references

The following documents, in whole or in part, are normatively referenced in this document and are

indispensable for its application. For dated references, only the edition cited applies. For undated

references, the latest edition of the referenced document (including any amendments) applies.

ISO 12110-1, Metallic materials — Fatigue testing — Variable amplitude fatigue testing — Part 1: General

principles, test method and reporting requirements
3 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 12110-1 and the following apply.

© ISO 2013 – All rights reserved 1
---------------------- Page: 5 ----------------------
ISO 12110-2:2013(E)
3.1
mean crossing

number of times that the load-time history crosses the mean-load level with a positive slope or a negative

slope, or both, if specified during a given length of the history

Note 1 to entry: For purposes related to cycle counting, a mean crossing may be defined as a crossing of the

reference load level.
3.2
range
algebraic difference between two successive reversals

Note 1 to entry: In variable amplitude loading, range may have a different definition depending on the counting

method used. For example, “overall range” is defined by the algebraic difference between the highest peak and the

lowest valley (absolute maximum and minimum, respectively) of a given load-time history.

Note 2 to entry: In cycle counting by various methods, it is common to employ ranges between valley and peak

loads which are not successive events. In these practices, the definition of “range” is broadened so that events of

this type are also included.
3.3
reference load

loading level which is fixed for counting upon which load variations are superimposed

Note 1 to entry: The reference load may be identical to the mean load of the loading time histories, but this is

not required.
3.4
reversal

point at which the first derivative of the load-time history changes sign (from + to – or – to +)

Note 1 to entry: Reversals occur at peaks or valleys.
3.5
irregularity factor

characterization of the irregularity of the signal, i.e. number of cycles not crossing the mean value, I = N /N

0 p
Note 1 to entry: N is the number of mean crossings.
Note 2 to entry: N is the number of peaks.
3.6
mean-load level
mean value of the peak and valley values
4 Cycle counting techniques
4.1 General

Cycle counting is used to summarize irregular load-time histories by providing the number of cycles of

various sizes which simulates the real loading of the specimen or component under study.

NOTE The definition of a cycle varies with the cycle counting method used.

Cycle counts can be made for load-time histories of force, stress, strain, deflection, or other loading parameters.

The following subclauses present the following cycle counting methods:
— level-crossing counting;
— peak counting;
2 © ISO 2013 – All rights reserved
---------------------- Page: 6 ----------------------
ISO 12110-2:2013(E)
— simple range counting;
— range-pair counting;
— Rainflow counting.
4.2 Cycle counting methods
4.2.1 Loading signal sampling

Loading signal recording generally consists of measuring the continuous evolution of the signal versus

time (either analog or digital values against time). If the initial loading time history is analog, it needs to

be converted into a digital file so that further computer processing of the loading time histories can be

accomplished. The operation of digitization consists of sampling the signal that means measuring and

recording values at regular time intervals.

The digital signal is representative of the real analog one if the following precautions are taken:

— Filter the output signal to eliminate noise and other disturbances which are not linked to the fatigue

process believed to be part of the real loading time histories of the structure.

— The sampling frequency shall be such that every analog loading cycle is represented by at least

20 digital points at least 20 times that of the observed maximum frequency of the real or expected

analog signal.
Care shall be taken when filtering the original analog signal. See ISO 12110-1.
4.2.2 Level-crossing counting

4.2.2.1 Results of a level-crossing count are shown in Figure 1. One count is recorded each time the positive

sloped portion of the load exceeds a preset level above the reference load, and each time the negative

sloped portion of the load exceeds a preset level below the reference load. Reference load crossings are

typically counted on the positive sloped portion of the loading time histories. It makes no difference

whether positive or negative slope crossings are counted. The distinction is made only to reduce the total

number of events by a factor of 2.

4.2.2.2 In practice, restrictions on the level-crossing counts are often specified to eliminate small amplitude

variations which can give rise to a large number of counts. This may be accomplished by filtering small

load excursions prior to cycle counting. A second method is to make no counts at the reference load and to

specify that only one count be made between successive crossings of a secondary lower level associated

with each level above the reference load, or a secondary higher level associated with each level below the

reference load. Figure 1 b) illustrates this second method. A variation of the second method is to use the

same secondary level for all counting levels above the reference load, and another for all levels below the

reference load. In this case, the levels are generally not evenly spaced.

4.2.2.3 The most common cycle count for fatigue analysis is derived from the level-crossing count by

first constructing the largest possible cycle, followed by the second largest, etc., until all level crossings

are used. Reversal points are assumed to occur halfway between levels.

This process is illustrated by Figure 1 c). Note that once this cycle count is obtained, the cycles could

be applied in any desired order, and this order could have a secondary effect on the amount of damage.

Other methods of deriving a cycle count from the level-crossing count could be used.

4.2.3 Peak counting

4.2.3.1 Peak counting identifies the occurrence of a relative maximum or minimum load value. Peaks

above the reference load level are counted, and valleys below the reference load level are counted, as

© ISO 2013 – All rights reserved 3
---------------------- Page: 7 ----------------------
ISO 12110-2:2013(E)

shown in Figure 2 a). Results for peaks and valleys are usually reported separately. A variation of this

method is to count all peaks and valleys without regard to the reference load.

4.2.3.2 To eliminate small amplitude loadings, mean-crossing peak counting is often used. Instead of

counting all peaks and valleys, only the largest peak or valley between two successive mean crossings is

counted, as shown in Figure 2 b).

4.2.3.3 The most common cycle count for fatigue analysis is derived from the peak count by first

constructing the largest possible cycle, using the highest peak and lowest valley, followed by the second

largest cycle, etc., until all peak counts are used. This process is illustrated by Figure 2 c). Note that once

this most damaging cycle count is obtained, the cycles could be applied in any desired order, and this

order could have a secondary effect on the amount of damage. Alternate methods of deriving a cycle

count, such as randomly selecting pairs of peaks and valleys, are sometimes used.

4.2.4 Simple-range counting

4.2.4.1 The method is illustrated in Figure 3. Positive ranges, negative ranges, or both, may be counted

with this method. If only positive or only negative ranges are counted, then each is counted as one cycle.

If both positive and negative ranges are counted, then each is counted as one-half cycle. Ranges smaller

than preset levels are usually eliminated before counting.

4.2.4.2 It is widely recognized that mean load also affects the measured fatigue results, which is why the

mean value of each range is also important and should be counted. This method is called simple range-

mean counting.

For the example in Figure 3, the result of a simple range-mean count is given in the table in Figure 3 in

the form of a range and mean matrix.
4 © ISO 2013 – All rights reserved
---------------------- Page: 8 ----------------------
ISO 12110-2:2013(E)
Level Counts
+3 2
+2 3
+1 5
0 2
-1 2
-2 1
-3 1
a) Level-crossing counting
Level Counts
+3 2
+2 3
+1 2
0 0
-1 1
-2 1
-3 1
b) Restricted level-crossing counting
Range (levels) Cycle Counts
7 1
6 0
5 1
4 0
3 0
2 1
1 2
c) Cycles derived from level-crossing count f (a)
Key
X time
Y load levels
Figure 1 — Level-crossing counting example
© ISO 2013 – All rights reserved 5
---------------------- Page: 9 ----------------------
ISO 12110-2:2013(E)
Level Counts
+3,5 2
+2,5 1
+1,5 2
-1,5 1
-2,5 1
-2,7 1
-3,5 1
a) Peak counting
Level Counts
+3,5 2
-3,5 1
b) Mean crossing peak counting
Level Counts
7 1
6,2 1
5 1
3 1,5
c) Cycles derived from level-crossing count f (a)
Key
X time
Y load levels
Figure 2 — Peak counting example
6 © ISO 2013 – All rights reserved
---------------------- Page: 10 ----------------------
ISO 12110-2:2013(E)
Range (level) Cycle Events
counts
6 0,5 EF
5 0
4 1,5 BC-FG-HI
3 1 DE-GH
2 1,5 AB-CD-IJ
1 0
Mean (levels)
-2 -1,5 -1 -0,5 0 0,5 1 1,5 2
Range 1
(lev-
2 1 0.5
els)
3 0,5 0,5
4 1 0,5
6 0,5
Key
X time
Y load levels

Figure 3 — Simple range counting example — Both positive and negative ranges counted

4.2.5 Rainflow counting
See Annex A.
5 Counting technique selection

There are other cycle counting techniques which are not reported in this part of ISO 12110.

A major problem that has to be solved in each fatigue case (change of loading, of specimen, etc.) is to

select which counting method is best adapted for the fatigue situation encountered.

A selection criterion may be narrow or large bandwidth energy spectrum and/or the irregularity factor.

Many choose the Rainflow method. Others use counting methods which are typical of their industrial sector.

In all cases, the selection of the counting method should follow a set of criteria or requirements.

© ISO 2013 – All rights reserved 7
---------------------- Page: 11 ----------------------
ISO 12110-2:2013(E)
Annex A
(informative)
Rainflow counting
A.1 General

The fatigue behaviour of structures depends on the complex interaction between the nature of the in-

service loading, the features of the material, and the geometry of the components.

The Rainflow method is a cycle counting method that permits decomposing the measurements recorded

in service using a format adapted to the fatigue analysis of the structures: fatigue life determination and

performance of modelling tests.

The Rainflow analysis permits the determination of the level exceedances, their relative ranges, and

cycle ranges.

The purpose of the present subclause is to give recommendations and requirements for

— performing the Rainflow cycle counting method, and
— presenting the results of the Rainflow counting.

An example of a loading sequence and the Rainflow analysis of it are presented as a test case to check

how to use the Rainflow counting method and as a help for computer programming.
A.2 Preliminary treatment of the loading
A.2.1 General

Before applying the Rainflow method, the loading signal requires a preliminary treatment which

consists of extracting peaks and valleys and putting them in classes or levels which had been previously

established (see 4.2).
A.2.2 Peak and valley extraction

The Rainflow counting only requires the successive peaks and valleys of the loading which need to be

extracted for processing from the sampled signal. The time between the successive peaks and valleys

is not part of the process because this part of ISO 12110 is only valid for conducting fatigue tests on

materials that yield results which are time or frequency independent. Therefore, environmental and

temperature or time interactions are not included in this part of ISO 12110. The fatigue life is expressed

in number of cycles or in number of repetitions of the loading sequence.

Figures A.1 and A.2 show the principles of signal sampling and peak and valley extraction from the

sampled signal.
8 © ISO 2013 – All rights reserved
---------------------- Page: 12 ----------------------
ISO 12110-2:2013(E)
Key
1 real loading
2 sampled loading
X time
Y stress range
Figure A.1 — Loading signal before extracting peaks and valleys
© ISO 2013 – All rights reserved 9
---------------------- Page: 13 ----------------------
ISO 12110-2:2013(E)
Key
1 real loading
2 peaks and valleys
X time
Y stress range
Figure A.2 — Loading signal after extracting peaks and valleys
A.2.3 Loading classes

The storage of the Rainflow counting results, on the one hand, and the speed of use of these results for

further exploiting the fatigue signal, on the other hand, requires the quantification of the loading signal.

Practically, the predicted or real loading range is partitioned into classes or levels of constant width

intervals, and all values (peaks or valleys) located within a given class are conventionally equal to a

representative value of this class. The representative value is mostly the arithmetic mean of the class.

If a peak falls on a class limit, it is conventionally equal to the representative value of the neighbouring

higher class; if a valley falls on a class limit, it is conventionally equal to the representative value of the

neighbouring lower class.

Two sets of values are obtained through this process: the representative values and the values which

correspond to class limits.
32 classes are recommended as a minimum (see ISO 12110-1).
NOTE General industrial practices adopt 64 load levels (see ISO 12110-1).

Loading signal treatment using class partitioning is shown in Figures A.3 and A.4.

10 © ISO 2013 – All rights reserved
---------------------- Page: 14 ----------------------
ISO 12110-2:2013(E)
Key
1 class width or class step
2 class 2
X time
Y stress range
Figure A.3 — Loading before treatment based on class partitioning
© ISO 2013 – All rights reserved 11
---------------------- Page: 15 ----------------------
ISO 12110-2:2013(E)
Key
1 class width or class step
2 class 2
X time
Y stress range
Figure A.4 — Loading after treatment

This treatment may lead to eliminate some successive values within the same class. If this happens too

often, the present class partitioning is too loose and the number of classes has to be increased and the

class width will be reduced (see ISO 12110-1).
A.3 Cycle counting procedure using the Rainflow method
A.3.1 Principle

The general principle of extraction of a loading cycle by the Rainflow method uses four successive points

noted 1, 2, 3, and 4, respectively.

This can be illustrated in the following way: when S represents a stress level (as an example), the cycle

is represented by, or considered as, a closed loop in the stress versus strain (S, e) plot.

Two cases of cycle occurrence have to be distinguished (Figure A.5).

The following three stress ranges are calculated: ΔS = | S – S |, ΔS = | S - S , |, ΔS = | S - S |.

1 2 1 2 3 2 3 4 3

If ΔS ≤ ΔS and ΔS ≤ ΔS (the range ΔS is lower or equal to the two other ranges), then

2 1 2 3 2

— the cycle represented by the extreme values S and S is extracted from the signal for further processing,

2 3
— the two S points and S are eliminated from the signal,
2 3

— the two parts of the signal situated on both sides of the extracted cycle extract are connected together.

12 © ISO 2013 – All rights reserved
---------------------- Page: 16 ----------------------
ISO 12110-2:2013(E)

Otherwise, the rank of appearance of the four points is shifted by one unit and the same procedure is

applied again.
The procedure is repeated until the end of the signal.
Key
X time
Y stress range
Figure A.5 — The two possible cases of cycle occurrence

When this operation is completed, some peaks and valleys have not been extracted because they do not

belong to closed loops. So, the remaining points belong to the open cycle sequence which is defined as such.

The number of points of the open cycle sequence cannot exceed 2k-1, where k is the number of levels or

classes.

The counts are reported in a matrix “starting class – destination class” or “minimal value S – S ”

min max

or “S – ΔS” (see A.3.4.1), where S , S , and ΔS are minimum value, maximum value, and range,

m min max
respectively.

If the global sequence is artificially closed by moving the part of the signal from the beginning to the

absolute maximum at the end of the sequence (see Figure A.6), no open cycle sequence remains after the

counting procedure.
© ISO 2013 – All rights reserved 13
---------------------- Page: 17 ----------------------
ISO 12110-2:2013(E)
Figure A.6 — Procedure to artificially close a loading time history
A.3.2 Algorithm

The initial data are the successive values S (1 ≤ i ≤ N) of the peaks and valleys of the loading which are

the results of the preliminary treatment (see A.2).
The algorithm is presented in the flow chart of Figure A.6.
14 © ISO 2013 – All rights reserved
---------------------- Page: 18 ----------------------
ISO 12110-2:2013(E)
Figure A.7 — Algorithm of the Rainflow method
A.3.3 Use and treatment of the open cycle sequence
A.3.3.1 General

At the end of the counting, the open cycle sequence contains the non-closed cycles as defined in A.3.1 in the

same order as the original signal. It can be either a signal where the successive ranges are increasing or

decreasing (see Figure A.8). The greatest range consists of the highest maximum and the lowest minimum.

The open cycle sequence is then processed according to one of the two following methods:

— duplication of the open cycle sequence;
© ISO 2013 – All rights reserved 15
---------------------- Page: 19 ----------------------
ISO 12110-2:2013(E)
— closure of the open cycle sequence.
Figure A.8 — Open cycle sequence of the signal
A.3.3.2 Duplication of the open cycle sequence

The determination of the fatigue life requires that the loading signal can be regarded as a sequence of

cycles. So, the open cycle sequence has to be treated to become a sequence of cycles.

The same open cycle sequence is added to that obtained from the counting process, but some precautions

have to be taken regarding the link between the two identical sequences taking into account the values

of the peaks or valleys to be linked as well as the first and last slopes of the open cycle sequence (see

Figure A.9).

Figure A.9 — Signal used for the treatment of the open cycle sequence (duplication of the open

cycle sequence)

When the Rainflow counting method is applied to the sequence formed by the two successive identical

open cycle sequences, the initial open cycle sequence is obtained again (see Figure A.8). The extracted

cycles correspond, therefore, to the cycles of the open cycle sequence.

The interest of applying this procedure is that it uses the Rainflow counting method already used.

The whole signal fatigue loading signal is processed entirely to get a sequence of successive identical cycles.

When linking successive sequences of cycles, the following precautions shall be taken.

The last point of the open cycle sequence is followed by the first point of the entire loading sequence.

These points may no more be considered as peaks or valleys. In this case, these points shall be eliminated.

16 © ISO 2013 – All rights reserved
---------------------- Page: 20 ----------------------
ISO 12110-2:2013(E)

Eight different cases may occur (see Figure A.10). To describe them explicitly, let’s call R and R the two

1 2
first points of the open cycle sequence and R and R the last two points.
n−1 n

a) Linking without any trouble: transition (R , R ) b) Linking: transition (R , R), R and R

n 1 n - 1 2 1 n
eliminated

c) Linking: transition (R , R), R is eliminated d) Linking: transition (R – R), R is elimi-

n 2 1 n-1 1 n
nated
Key
1 case encountered (R -R ). (R –R ) > 0 and (R -R ). (R –R ) < 0
n n-1 2 1 n n-1 1 n
2 case encountered (R -R ). (R –R ) > 0 and (R -R ). (R –R ) ≥ 0
n n-1 2 1 n n-1 1 n
3 case encountered (R -R ). (R –R ) < 0 and (R -R ). (R –R ) ≥ 0
n n-1 2 1 n n-1 1 n
4 case encountered (R -R ). (R –R ) < 0 and (R -R ). (R –R ) < 0
n n-1 2 1 n n-1 1 n
5 linking
Figure A.10 — Sequence linking cases
A.3.3.3 Closure of the open cycle sequence

The determination of the fatigue life requires that the loading signal can be regarded as a sequence of

cycles. So, the open cycle sequence has to be treated to become a sequence of cycles.

© ISO 2013 – All rights reserved 17
---------------------- Page: 21 ----------------------
ISO 12110-2:2013(E)

The open cycle sequence is closed, moving the part of the signal from the beginning to the absolute

maximum at the end of the sequence.
Figure A.11 — Closure of the open cycle sequence
Then, the Rainflow counting method is applied to the closed sequence.
A.3.4 Presentation of the results
A.3.4.1 Presentation in matrix form

The results of the counting are reported in matrixes “starting class-destination class” or “minimum

value S – maximum value S ”, or “amplitude S – mean value S ”.
min max a m

Depending on their subsequent use, the results can be presented following different matrix types. Five

matrix types are described below:

1) Matrix [a ] “starting class-destination class» of the cycles as they are extracted and another one

for the open cycle sequence. The recommended designation is: Rainflow matrix “starting class-

destination class” of the cycles and open cycle sequence.

2) Matrix [b ] «starting class-destination class «of the cycles of the whole processed sequence,

integrating the open cycle sequence. The recommended designation is: Rainflow matrix “starting

class-destination class «of the cycles of the whole sequence.

3) Matrix [c ] “starting class-destination class” that shows all the transitions of the extracted cycles

as well as those of the open cycle sequence. The recommended designation is: Rainflow matrix

“starting class-destination class” of the transitions of the whole sequence.

This matrix resulting from a Rainflow counting is evidently different from the matrix of the transformation

(Markov) of the original sequence.
The matrix [c ] can be derived from the matrix [a ] by the transformation
ij ij
ca=+a + transitions of the open cycle sequence (1)
...

Questions, Comments and Discussion

Ask us and Technical Secretary will try to provide an answer. You can facilitate discussion about the standard in here.