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Rainflow Algorithm

Overview

The Rainflow counting algorithm is a widely used method in fatigue analysis for extracting cycle information from time-dependent stress-strain curves. This implementation supports multiple counting methods, including the 4-point method (DIN 45667 / FVA-Richtlinie) and the 3-point method (ASTM E 1049).

Four Main Steps

Rainflow Counting consists of four main steps:

  1. Hysteresis Filtering

    Removes small oscillations below a specified threshold to focus on significant load variations.

  2. Peak-Valley Filtering

    Identifies local maxima (peaks) and minima (valleys) in the filtered signal, representing turning points in the load history.

  3. Discretization

    Maps continuous stress/strain values into discrete classes (bins) for histogram-based counting.

  4. Four Point Counting Method

    The core algorithm that identifies closed cycles using a four-point pattern.

Four-Point Method

The 4-point counting method identifies closed hysteresis loops by examining sequences of four consecutive turning points:

           * D
          / \
   B *<--/
    / \ /
   /   * C
\ /
 * A

A cycle B-C is considered closed if:

min(B,C) >= min(A,D) && max(B,C) <= max(A,D)

When a cycle is closed:

  • The slope B-C is counted as a full cycle
  • Points B and C are removed from the residue
  • The algorithm continues with the remaining points

This process continues until no more closed cycles can be found. The remaining turning points form the residue (unclosed cycles).

Standards and References

This implementation is fully documented in the following standards:

  • ASTM E 1049 - "Standard Practices for Cycle Counting in Fatigue Analysis" [1]_
  • HCM Method (3-point) - Proposed by Clormann/Seeger [2]_
  • FVA Guidelines - German Research Association for Drive Technology [3]_
  • DIN 45667-1:2025-12 - "Fatigue analysis of structures - Part 1: Rainflow counting method" [13]_
  • DIN 45667-2:2025-12 - "Fatigue analysis of structures - Part 2: Cycle counting method" [14]_

The implementation supports multiple counting methods:

  • 4-point method (default) - As described above
  • HCM (Hysteresis Counting Method) - 3-point algorithm by Clormann/Seeger
  • ASTM method - Variant specified in ASTM E 1049 (2011)

Residue Handling

After the main counting process, unclosed cycles (residue) can be processed using various methods:

  • Ignore - Discard residue (conservative approach)
  • DIN 45667 - According to German standard
  • ASTM halfcycle/fullcycle - Half or full cycle counting, according to ASTM E 1049
  • Repeated - Re-feed residue and count closed cycles
  • HCM - Apply Clormann/Seeger method to residue

See features.rst for more details on residue handling options.

Differences between ASTM E 1049 vs. DIN 45667-2

The two standards use different cycle detection algorithms (4-point vs. 3-point), which can produce different cycle counts during normal processing — not only in residue handling. A further critical difference exists in how each standard treats the residue (the unclosed signal stream remaining at the end of the counting process).

ASTM E 1049 (2011) adopts a pragmatic approach, typically classifying these open loops as "half cycles" (count = 0.5). While computationally straightforward, this method can lead to underestimate fatigue damage, particularly in short signals representing repetitive events (e.g., a single test track lap), as the largest stress range often resides within the residue.

DIN 45667-2:2025-12 adheres to a stricter physical definition. It mandates that all significant stress ranges form complete hysteresis loops. Therefore, it requires resolving the residue into full integer cycles (count = 1.0). This is algorithmically achieved by signal reordering (starting the analysis at the absolute global extremum) or block repetition (virtually appending the signal to itself).

Recommendation:

Select ASTM for strict compliance with US standards where half-cycles are explicitly permitted.

Select DIN (or enable "Close Residue") for conservative fatigue life prediction of repeating load blocks, ensuring the global maximum stress range is fully weighted as a complete damage event.

Algorithm Complexity

The algorithm operates in streaming mode, processing data points as they arrive:

  • Time Complexity: O(n) where n is the number of data points
  • Space Complexity: O(r) where r is the residue size
  • Memory: Configurable, supports both static and dynamic allocation

For large datasets, the implementation supports:

  • Sample-by-sample processing
  • Chunk-based streaming
  • Dynamic class range expansion (auto-resize)

See Also