The description below is written with Rainflow in mind, but the algorithm equally applies to any other post-processing case where automatic bin sizing is requested.
Essentially what Bladed does is:
(1) Find the maximum and minimum in the time series (or group of time series for multiple runs);
(2) Find the range by subtracting the minimum value from the maximum in the time-series (or group of time series). A small tolerance (0.5%) is added to the minimum and maximum values(see note 1);
(3) Calculate the width of the bin by dividing the range by the chosen number of bin. The bin width is rounded by the following rules(see note 2) ;
(4) The same bin size is now used for the cycle range discretization. The first bin is centred at BinSize/2 and rest of the N bins are spaced by BinSize.
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Note 1: Please see the attached spreadsheet for an example about the algorithm.
Note 2: The round rules will be applied to the calculated bin width. It may cause some unused bins as it is a "rough" bin width.
If the adjusted width is expressed in normalised scientific notation m × 10n where m is the significand and is greater or equal to 1 and less than 10, then:
(1) If the significand is greater than 4.5 then the width is rounded up and given to 1 significant figure.
For example, 0.004526 would be rounded to 0.005000 and 6132 would be rounded to 7000.
(2) If the significand is less than 4.5 but more than 2.0 then the width is rounded up given to two significant figures such that the second digit is 0 or 5.
For example 0.237 would be rounded to 0.25 and 367372 would be rounded to 400000.
(3) Otherwise the width is rounded up to 2 significant figures.
For example 0.01826 would be rounded to 0.019 and 12345 would be rounded to 13000.