Jump to content

Rainflow-counting algorithm: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous edit
Content deleted Content added
VisualWikitext
ADDED content on Fatigue, Classification of Fatigue, Steps Involved ,Advantages and Limitations.
Tags: Reverted Visual edit
Undid revision 1282514477 by NiTCvasu (talk) remove largely off topic low quality ai slop. So sad that people would include this.
 
Line 15: Line 15:


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.

== Fatigue<ref>{{Cite web |title=Practical Introduction to Fatigue Analysis Using Rainflow Counting |url=https://in.mathworks.com/help/signal/ug/practical-introduction-to-fatigue-analysis-using-rainflow-counting.html |url-status=live}}</ref> ==
[[Fatigue (material)|Fatigue]] refers to the gradual degradation of a material's structural properties due to repeated or fluctuating stresses. Unlike a single, overpowering load that causes immediate failure, fatigue damage results from successive loading and unloading that, are too weak to break the material on thier own. According to the American Society for Testing and Materials (ASTM), fatigue is defined as

''a progressive, localized, and permanent structural change within a material subjected to fluctuating stresses and strains. Over time, this damage may lead to the formation of cracks and, ultimately, complete fracture.''

Fatigue failure often is difficult to detect, even though the underlying damage may have begun from the moment the structure was first loaded<ref>{{Cite web |title=Practical Introduction to Fatigue Analysis Using Rainflow Counting |url=https://in.mathworks.com/help/signal/ug/practical-introduction-to-fatigue-analysis-using-rainflow-counting.html |url-status=live}}</ref>. Rather than affecting the entire component uniformly, fatigue is concentrated in localized regions where stress and strain levels are higher. These stress concentrations may arise from factors such as external loading, abrupt design changes, temperature differences, residual stresses, or material defects.

Fatigue analysis is a crucial aspect of engineering design, as it enables the prediction of material and structural performance under repeated loading conditions. The capacity to foresee and prevent fatigue failures is essential for ensuring a product's safety and longevity, distinguishing it from a potentially catastrophic failure.<ref name=":0">{{Cite web |title=Rainflow Counting Approach |url=https://sdcverifier.com/structural-engineering-101/rainflow-counting-approach/}}</ref>

Among the most effective methods for fatigue analysis, particularly under variable amplitude loading, is the Rainflow Counting technique.

== Classifications of Fatigue ==
Fatigue is further classified into two main types:

High-Cycle Fatigue: This form of fatigue occurs whenever low-stress levels that remain largely within the elastic range of the material. Failures generally occur after more than 10,000 cycles.

Low-Cycle Fatigue: This type results from high-stress levels that exceed the material's yield strength, causing plastic deformation. It typically leads to failure within a lower number of cycles.

Understanding fatigue behavior is essential in designing durable structures and preventing catastrophic failure

== Steps Involved ==
Prior to the advent of modern computing capabilities, Rainflow Counting was employed to segment the loading time history into manageable categories, known as bins. Each bin comprised a set of loads with varying amplitudes, and fatigue damage was calculated based on the maximum amplitude within each bin. The total damage across all bins was then aggregated using Miner's rule. Although this method significantly reduced computational time, it was overly conservative. With the advancement of computing power, fatigue damage is now calculated on the basis of each actual load reversal, eliminating the need to group loads into bins. However, bins are still utilized for presenting the cycles that constitute the time history in a more organized manner.<ref>{{Cite web |title=Rainflow Counting - Metal fatigue Life Prediction |url=https://fatigue-life.com/rainflow-counting/ |url-status=live}}</ref>

The rainflow counting method consists of four steps:<ref>{{Cite web |date=August 29, 2019 |title=Rainflow counting |url=https://community.sw.siemens.com/s/article/rainflow-counting |url-status=live}}</ref>

# Histerisis Filtering: Considering the given load-time history data, very small cycles are removed from the data. These loads only amount to a negligble amount of damage. A gate of a specific amplitude is defined for the purpose of filtering. Any cycle that has an amplitude smaller than the gate is removed from the load-time history. This is done by projecting the gate from left to right from each turning point in the time series. If a turning point is smaller than the gate, it is eliminated from the time history
# Peak Value Filtering: Out of all the available data points, only the ones which are the reversal is direction/slope is kept. The points except the maximum and minimum value of a cycle are not necessary for the calculation of fatigue.
# Discretization: The ordinate axis of the load-time history data is divided into several discrete 'bins' having a fixed amplitude range for the data to be mapped into.
# Four Point Counting Method: ''Refer below.''


== Algorithms ==
== Algorithms ==
Line 121: Line 91:
|1
|1
|}
|}

== Advantages and Limitations<ref name=":0" /> ==
The key benefits include:

* '''Handling Complex Load Histories:''' Rainflow Counting is particularly beneficial in analyzing complex load histories, commonly encountered in automotive, aerospace, and civil engineering structures. It effectively identifies cycles and assesses stress levels that contribute to fatigue, providing valuable insights into the structural integrity under varied loading conditions.
* '''Industry Standard:''' '''I'''ts reliability and accuracy regularly attract the likeness of industrial application of the counting method. It is often incorporated into design codes like ASTM E1049 for consistent fatigue analysis practices.
* '''Compatibility with Fatigue Life Prediction Models:''' Rainflow Counting is a popular choice for engineers due to its compatibility with fatigue life prediction models like the [[S-N curve]] and [[Miner's rule|Miner’s Rule]].
* '''Implementation in Software Programming''': Computational software like MATLAB, with some fatigue analysis tools do integrate Rainflow Counting directly, such as the Rainflow Counting Tool. Large datasets are managed through databases such as SQL Server making it more organized.

However, the method also has its limitations such as :

* '''Effect of Noise:''' The method’s sensitivity to noise present in the loading data set can lead to spurious cycles and overestimation of fatigue damage, especially when data isn’t properly filtered or smoothed.
* '''Computational Complexity:''' For extensive datasets, especially those with long load histories or high-frequency data, the computational effort required to apply Rainflow Counting can become significant.
* '''Simplification Assumptions:''' While Rainflow Counting is a robust technique, its accuracy in predicting fatigue life may be limited due to simplifying assumptions, such as linear material behavior under cyclic loading


==References==
==References==

Latest revision as of 22:44, 26 March 2025

Rainflow counting identifies the closed cycles in a stress-strain curve

The rainflow-counting algorithm is used in calculating the fatigue life of a component in order to convert a loading sequence of varying 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.[1] This simplification allows the number of cycles until failure of a component to be determined for each rainflow cycle using either Miner's rule to calculate the fatigue damage, or in a crack growth equation to calculate the crack increments.[2] 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 and M. Matsuishi in 1968.[3]

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.[1]

Figure 1: Uniform alternating loading
Figure 2: Spectrum loading

History

[edit]

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.[1]

Downing and Socie created one of the more widely referenced and utilized rainflow cycle-counting algorithms in 1982,[4] which was included as one of many cycle-counting algorithms in ASTM E1049-85.[5]

Igor Rychlik gave a mathematical definition for the rainflow counting method,[6] thus enabling closed-form computations from the statistical properties of the load signal.

Algorithms

[edit]

There are a number of different algorithms for identifying the rainflow cycles within a sequence. They all find the closed cycles and may be left with half closed residual cycles at the end. All methods start with the process of eliminating non turning points from the sequence. A completely closed set of rainflow cycles can be obtained for a repeated load sequence such as used in fatigue testing by starting at the largest peak and continue to the end and wrapping around to the beginning.

Four point method

[edit]
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:[7]

  1. Any pair of points B-C that lies within or equal to A-D is a rainflow cycle.
  2. Remove the pair B-C and re-evaluate the sequence from the beginning.
  3. Continue until no further pairs can be identified.

Pagoda roof method

[edit]

This method considers the flow of water down of a series of pagoda roofs. Regions where the water will not flow identify the rainflow cycles which are seen as an interruption to the main cycle.

  1. Reduce the time history to a sequence of (tensile) peaks and (compressive) valleys.
  2. Imagine that the time history is a template for a rigid sheet (pagoda roof).
  3. Turn the sheet clockwise 90° (earliest time to the top).
  4. Each "tensile peak" is imagined as a source of water that "drips" down the pagoda.
  5. Count the number of half-cycles by looking for terminations in the flow occurring when either:
    • case (a) It reaches the end of the time history;
    • case (b) It merges with a flow that started at an earlier tensile peak; or
    • case (c) An opposite tensile peak has greater or equal magnitude.
  6. Repeat step 5 for compressive valleys.
  7. Assign a magnitude to each half-cycle equal to the stress difference between its start and termination.
  8. Pair up half-cycles of identical magnitude (but opposite sense) to count the number of complete cycles. Typically, there are some residual half-cycles.

Example

[edit]
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. 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 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).

Similar half-cycles are calculated for compressive stresses (Figure 4) and the half-cycles are then matched.

Figure 4: Rainflow analysis for compressive valleys
Stress (MPa) Whole cycles Half cycles
10 2 0
13 0 1
16 1 1
17 0 1
19 0 1
20 1 0
22 1 0
29 0 1

References

[edit]
  1. ^ a b c Endo, Tatsuo; Mitsunaga, Koichi; Takahashi, Kiyohum; Kobayashi, Kakuichi; Matsuishi, Masanori (1974). "Damage evaluation of metals for random or varying loading—three aspects of rain flow method". Mechanical Behavior of Materials. 1: 371–380.
  2. ^ Sunder, R.; Seetharam, S. A.; Bhaskaran, T. A. (1984). "Cycle counting for fatigue crack growth analysis". International Journal of Fatigue. 6 (3): 147–156. doi:10.1016/0142-1123(84)90032-X.
  3. ^ Matsuishi, M.; Endo, T. (1968). "Fatigue of metals subjected to varying stress". Japan Society of Mechanical Engineering.
  4. ^ Downing, S.D.; Socie, D.F. (1982). "Simple rainflow counting algorithms". International Journal of Fatigue. 4 (1): 31–40. doi:10.1016/0142-1123(82)90018-4.
  5. ^ Standard practices for cycle counting in fatigue analysis. ASTM E 1049-85. ASTM International. 2005.
  6. ^ Rychlik, I. (1987). "A New Definition of the Rainflow Cycle Counting Method". International Journal of Fatigue. 9 (2): 119–121. doi:10.1016/0142-1123(87)90054-5.
  7. ^ Lee, Yung-Li; Tjhung, Tana (2012). "Rainflow Cycle Counting Techniques". Metal Fatigue Analysis Handbook. pp. 89–114. doi:10.1016/B978-0-12-385204-5.00003-3. ISBN 9780123852045.
[edit]
Retrieved from "https://en.wikipedia.org/w/index.php?title=Rainflow-counting_algorithm&oldid=1282519853"