This page contains the bibliography and citations for the standards, publications, and resources referenced in the rainflow counting package.
| [1] | ASTM E 1049 - Standard Practices for Cycle Counting in Fatigue Analysis ASTM Standard E 1049, 1985 (2011). West Conshohocken, PA: ASTM International, 2011. This standard provides comprehensive guidance on cycle counting methods for fatigue analysis, including the 3-point rainflow algorithm variant implemented as an alternative counting method in this package. |
| [2] | Rainflow - HCM / Ein Hysteresisschleifen-Zählalgorithmus auf werkstoffmechanischer Grundlage U.H. Clormann, T. Seeger 1985, TU Darmstadt, Fachgebiet Werkstoffmechanik Introduces the Hysteresis Counting Method (HCM), a 3-point algorithm based on material mechanics principles. This method is implemented as an alternative counting approach in the package. |
| [3] | Zählverfahren zur Bildung von Kollektiven und Matrizen aus Zeitfunktionen FVA-Richtlinie, 2010. Available: https://fva-net.de/fileadmin/content/Richtlinien/FVA-Richtlinie_Zaehlverfahren_2010.pdf German Research Association for Drive Technology (FVA) guideline describing counting methods for creating collectives and matrices from time series data. |
| [4] | Rainflow Counting Siemens Product Lifecycle Management Software Inc., 2018. Available: https://community.plm.automation.siemens.com/t5/Testing-Knowledge-Base/Rainflow-Counting/ta-p/383093 Technical documentation on rainflow counting implementation and practical applications in fatigue testing. |
| [5] | Review and application of Rainflow residue processing techniques for accurate fatigue damage estimation
International Journal of Fatigue 82 (2016) 757-765 DOI: https://doi.org/10.1016/j.ijfatigue.2015.10.007 Comprehensive review of different methods for handling the residue (unclosed cycles) in rainflow counting, comparing accuracy and computational efficiency. |
| [6] | Betriebsfestigkeit - Verfahren und Daten zur Bauteilberechnung Haibach, Erwin Springer Verlag Comprehensive German-language reference on operational strength (fatigue under service loading), covering calculation methods and material data for component design. |
| [7] | Schaedigungsbasierte Hysteresefilter Hack, M. D386 (Diss. Univ. Kaiserslautern), Shaker Verlag Aachen, 1998 ISBN 3-8265-3936-2 Dissertation on damage-based hysteresis filters for fatigue analysis. |
| [8] | Hysteresis and Phase Transition Brokate, M.; Sprekels, J. Applied Mathematical Sciences 121, Springer, New York, 1996 Mathematical treatment of hysteresis phenomena with applications to material behavior and phase transitions. |
| [9] | Rainflow counting and energy dissipation in elastoplasticity Brokate, M.; Dressler, K.; Krejci, P. Eur. J. Mech. A/Solids 15, pp. 705-737, 1996 Theoretical foundation connecting rainflow counting to energy dissipation in elastoplastic materials. |
| [10] | Multivariate Density Estimation: Theory, Practice and Visualization Scott, D. New York, Chichester, Wiley & Sons, 1992 Statistical methods relevant to histogram-based analysis and density estimation in cycle counting. |
| [11] | Werkstoffmechanik - Bauteile sicher beurteilen und Werkstoffe richtig einsetzen Ralf Bürgel, Hans Albert Richard, André Riemer Springer Fachmedien Wiesbaden 2005, 2014 German textbook on materials mechanics, covering safe assessment of components and proper material selection. |
| [12] | Zählverfahren und Lastannahme in der Betriebsfestigkeit Michael Köhler, Sven Jenne / Kurt Pötter, Harald Zenner Springer-Verlag Berlin Heidelberg 2012 Comprehensive German reference on counting methods and load assumptions in operational fatigue strength analysis. |
| [13] | DIN 45667-1:2025-12 Mechanische Schwingungen - Zählverfahren für die Betriebsfestigkeit - Teil 1: Vorverarbeitung Beuth Verlag GmbH, Berlin Current standard defining signal preprocessing, specifically the extraction of turning points and discretization (binning) for fatigue analysis. |
| [14] | DIN 45667-2:2025-12 Mechanische Schwingungen - Zählverfahren für die Betriebsfestigkeit - Teil 2: Zählverfahren Beuth Verlag GmbH, Berlin Current standard defining cycle counting algorithms (Rainflow) and residue handling (closed vs. open cycles) for fatigue analysis. |
A source code preprocessing tool used to conditionally compile different feature sets. Can be used to create minimal versions of the rainflow library with only required features enabled.
https://github.com/a-ma72/rainflow
Official repository containing the source code, issue tracker, and release downloads.
Forschungskuratorium Maschinenbau (FKM) - Analytical strength assessment of components in mechanical engineering.
German standard for analytical strength assessment, including methods for mean stress correction (Haigh diagram) implemented in the amplitude transformation features.
If you use this software in your research, please cite:
@software{rainflow,
author = {Andreas Martin},
title = {Rainflow Counting Algorithm},
year = {2026},
url = {https://github.com/a-ma72/rainflow},
version = {0.5.2}
}Contributions to improve documentation, add examples, or fix issues are welcome. Please see the GitHub repository for contribution guidelines.
- algorithm.rst - How these methods are implemented
- features.rst - Which standards/methods are supported