Four-point Rainflow Counting with residue processing options

Function counts cycles of signal using the "4-point rule" with option for residue treatment: Simple RF or Half-cycles (aka "3-point rule").

Cycle counting function using the "Four-point rule" with option for residual treatment, according to ASTM E1049−85.

By Fabio Aste, www.linkedin.com/in/fabio-aste/

Visit us at: vast.energy

--------------------------------------------------------------------------------------------------

Description:

'rainflow4P' applies "Four-point" rainflow cycle counting to a generic signal.

Option is given for residue treatment: "Simple Rainflow" or "Half-cycle counting".

Equivalence between "Four-point" and "Three-point" rainflow cycle countings has been analysed by Mc Innes (2008).

Validation of the method was achieved against ASTM E1049-85 dataset and against MathWorks 'rainflow' function.

--------------------------------------------------------------------------------------------------

References:

- ASTM E1049−85.

- ISO 12110-2.

- "McInnes, C. H., & Meehan, P. A. (2008). Equivalence of four-point and three-point rainflow cycle counting algorithms. International Journal of Fatigue, 30(3), 547–559. doi:10.1016/j.ijfatigue.2007.03.006"

- "Marsh et al., (2016). Review and application of Rainflow residue processing techniques for accurate fatigue damage estimation. International Journal of Fatigue, 82, 757–765. doi:10.1016/j.ijfatigue.2015.10.007"

--------------------------------------------------------------------------------------------------

Procedure:

Turning points (local extrema) are first identified for the signal vector. Subsequently, the "Four-point rule" is run and full-cycles are found and recorded in the result matrix.

Residues are treated doubling them in a vector as [residue + residue], then The "Four-point rule" is applied again.

Cycles found in this phase are still counted as full-cycles. Remaining uncounted values are counted as half-cycles.

--------------------------------------------------------------------------------------------------

Inputs:

- signal: vector of values

- resType: method for residue processing: 'simple','half'.

- time: vector of same length with time values

- hysteresis (opt): minimum cycle range to consider (default = 0)

- hideDupl (opt): hiding consecutive duplicate signal values - and duplicate residual values (default = true)

- binSize (opt): defining the size of the step for sorting the cycles into histogram (default = 1)

--------------------------------------------------------------------------------------------------

Outputs:

- CC: a Table that contains the following fields:

o [counts]: 0.5 or 1.0 - half-cycle or full-cycle

o [ranges]: range of each cycle (endVal-startVal)

o [meanVals]: mean value of each cycle

o [startVals], [endVals]: values at start and end of the cycle

o [startTimes], [endTimes]: times corresponding to cycle start and end

- RFM: Rainflow Matrix (optional output)

--------------------------------------------------------------------------------------------------

Copyright (c) 2025, Fabio Aste, Vast Renewables Ltd.

Version: 1.0.3

This software is licensed under the MIT License (2023).

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.