A number of methods have been derived for performing rainflow cycle counting for a response PSD. Note that they tend to be conservative.
The Dirlik method is an example of a semi-empirical method for cycle identification.
A Matlab script for performing this method is given at: Dirlik_rainflow.zip
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The following script calculates the Dirlik fatigue cycles for a single-degree-of-freedom (SDOF) system subjected to a base input PSD: sdof_ran.zip
The natural frequency and damping value for the system are required inputs.
The immediate output of the Dirlik method is a “Cumulative Histogram of Range (peak-valley).”
This can readily be converted into individual cycles with their respective amplitudes, where: amplitude=(peak-valley)/2
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The following script has a function which calculates the Dirlik fatigue damage spectrum for an array of degree-of-freedom (SDOF) systems subjected to a base input PSD.
Matlab script: Vibrationdata Signal Analysis Package
The natural frequency is an independent variable. The damping value is required. The fatigue exponent from the S-N curve slope is also required.
The calculation can be performed faster using a C++ program. Here is the source code for a C++ vibration response program which has a fatigue damage spectrum option: vrs.cpp
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T. Irvine, Experimental Verification of the Dirlik Fatigue Cycle Method. Download
Halfpenny & Kim, Rainflow Cycle Counting and Acoustic Fatigue Analysis Techniques for Random Loading. Download
Halfpenny, A frequency domain approach for fatigue life estimation from Finite Element Analysis, nCode International Ltd., Sheffield UK. Download
Mrsnik, Janko Slavic, Boltezar, Frequency-domain methods for a vibration-fatigue-life estimation – Application to real data: mrsnik_article_vib_fatigue.pdf* * *
– Tom Irvine