Rainflow Counting Algorithm (4-point-methods), C99 compliant

"Rainflow Counting" consists of four main steps:

1. Hysteresis Filtering

2. Peak-Valley Filtering

3. Discretization

4. Four Point Counting Method:

               * D  
              / \       Closed, if min(B,C) >= min(A,D) && max(B,C) <= max(A,D)  
       B *<--/          Slope B-C is counted and removed from residue  
        / \ /  
       /   * C  
    \ /  
     * A  
   

These steps are fully documented in standards such as
ASTM E 1049 "Standard Practices for Cycle Counting in Fatigue Analysis" [1]
This implementation uses the 4-point algorithm mentioned in [3,4] and the 3-point HCM method proposed in [2] as well as the ASTM E 1049 (2011) standard in [1]. To take the residue into account, you may implement a custom method or use some predefined functions.

Features of this package

1. Modular architecture in two layers:
   a) Module rainflow.c (with rainflow.h) holds all necessary functions for rainflow counting and histogram extraction. You may select multiple optional features at compile time:
   RFC_MINIMAL: To use core functions for rainflow counting only (for porting to µControllers for example).
   RFC_TP_SUPPORT: Turning point storage.
   RFC_HCM_SUPPORT: HCM algorithm (Clormann/Seeger).
   RFC_ASTM_SUPPORT: ASTM E 1049 (2011) algorithm.
   RFC_AT_SUPPORT: User defined amplitude transformation (Haigh diagram).
   RFC_DH_SUPPORT: Damage history storage.
   RFC_USE_DELEGATES: Delegates for various core functions to implement user defined behavior.
   RFC_GLOBAL_EXTREMA: Store global data extrema.
   RFC_DAMAGE_FAST: Using lookup tables for damage and amplitude transformation.
   RFC_EXPORT_MEX: Export a mexFunction() to use the rainflow counting in MATLAB (R).
   Using COAN [[http://coan2.sourceforge.net/]] for example, you can tidy up the code from unwanted features. (The minimal version of this package is created using COAN with option RFC_MINMALset.)
   b) C++ wrapper rainflow.hpp encapsulates functions from rainflow.h in a namespace and offers a template class Rainflow for object oriented access and inheritance. This class also offers container class based turning point storage.
2. Streamable: You're able to count your data at once, as data packages or sample-wise.
3. Class width fit to your needs. Dynamically increase class width, when needed. (Needs turning point storage.)
4. Four point counting method, optionally HCM counting method (Clormann/Seeger).
5. Woehler curve with up to two slopes, fatigue limit and omission.
6. Miners rule for damage accumulation (elementary, original, modified and consequent).
7. In-time damage indicator (Miners' consequent rule).
8. In-time histograms: rainflow matrix, level crossing and range pair counting.
9. Turning points with hysteresis filtering. Turning points involved in a closed hysteresis are marked as pairs, with its partial assigned damage. (Compact history)
10. Look-up tables for damage calculation and amplitude transformation.
11. Amplitude transformation (Haigh diagram) according to FKM (symmetrical, non-symmetrical or user defined).
12. Damage history (uncompressed)
13. Various methods on residual data:
    • According to DIN 45667
    • ASTM method (halfcycle, fullcycle)
    • Second run
    • HCM
14. Various function pointers to implement user defined behavior.
15. Conversions supporting RFM->LC, RFM->RP, RFM->Damage and RP->Damage (original, elementar, modifiziert, konsequent).

---

References:

[1] "Standard Practices for Cycle Counting in Fatigue Analysis."
ASTM Standard E 1049, 1985 (2011). West Conshohocken, PA: ASTM International, 2011.
[2] "Rainflow - HCM / Ein Hysteresisschleifen-Zaehlalgorithmus auf werkstoffmechanischer Grundlage"
U.H. Clormann, T. Seeger
1985 TU Darmstadt, Fachgebiet Werkstoffmechanik
[3] "Zaehlverfahren zur Bildung von Kollektiven und Matrizen aus Zeitfunktionen"
FVA-Richtlinie, 2010.
[https://fva-net.de/fileadmin/content/Richtlinien/FVA-Richtlinie_Zaehlverfahren_2010.pdf]
[4] Siemens Product Lifecycle Management Software Inc., 2018.
[https://community.plm.automation.siemens.com/t5/Testing-Knowledge-Base/Rainflow-Counting/ta-p/383093]
[5] "Review and application of Rainflow residue processing techniques for accurate fatigue damage estimation"
G.Marsh;
International Journal of Fatigue 82 (2016) 757-765, [https://doi.org/10.1016/j.ijfatigue.2015.10.007]
[6] "Betriebsfestigkeit - Verfahren und Daten zur Bauteilberechnung"
Haibach, Erwin; Springer Verlag
[] "Schaedigungsbasierte Hysteresefilter"; Hack, M, D386 (Diss Univ. Kaiserslautern), Shaker Verlag Aachen, 1998, ISBN 3-8265-3936-2
[] "Hysteresis and Phase Transition"
Brokate, M.; Sprekels, J.; Applied Mathematical Sciences 121; Springer, New York, 1996
[] "Rainflow counting and energy dissipation in elastoplasticity"; Eur. J. Mech. A/Solids 15, pp. 705-737, 1996
Brokate, M.; Dressler, K.; Krejci, P.
[] "Multivariate Density Estimation: Theory, Practice and Visualization". New York, Chichester, Wiley & Sons, 1992
Scott, D.
[] "Werkstoffmechanik - Bauteile sicher beurteilen undWerkstoffe richtig einsetzen";
Ralf Buergel, Hans Albert Richard, Andre Riemer; Springer FachmedienWiesbaden 2005, 2014
[] "Zaehlverfahren und Lastannahme in der Betriebsfestigkeit";
Michael Koehler, Sven Jenne / Kurt Poetter, Harald Zenner; Springer-Verlag Berlin Heidelberg 2012