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Monte Carlo from the command line

A deterministic analysis uses design values for every input. A Monte Carlo simulation instead draws many random realizations of the uncertain inputs (preload, gap, inclination, loads, S-N curve, Miner's rule), computes the damage of each one and gives the statistical distribution of the results, for example to estimate a probability of failure. This is the approach used to calibrate the safety factors of IEC 61400-6 (refs. [1] and [5], section 6).

This tutorial runs a Monte Carlo simulation with the pyflange command line, without writing code.

1. The case file

Use the example case fatigue-case.json from Getting started. Besides the deterministic data, it contains a Stats section with the random variables:

"Stats": {
    "Preload":            { "Distribution": "Normal", "MeanRatio": 0.77, "CoV": 0.03 },
    "PlasticLoss":        { "Distribution": "Normal", "Mean": 0.03, "CoV": 0.33333 },
    "DFT":                { "Distribution": "Normal", "Mean": 250e-6, "CoV": 0.12 },
    "Gap": {
        "JointDistribution": "IEC 61400-6:2020 AMD1",
        "FlatnessTolerance": 0.0014,
        "Angle":       { "Distribution": "LogNormal", "Mean": 1.745, "CoV": 1.0 },
        "ShapeFactor": { "Distribution": "Normal", "Mean": 1.0, "CoV": 0.15 }
    },
    "Tilt":               { "Distribution": "LogNormal", "Mean": 0.001745, "CoV": 0.5 },
    "LoadRangeFactor":    { "Distribution": "LogNormal", "Mean": 1.0, "CoV": 0.12 },
    "FatigueClassFactor": { "Distribution": "Normal", "Mean": 1.0, "CoV": 0.10, "DS_ref_mean": 62e6 },
    "AllowableDamage":    { "Distribution": "LogNormal", "Mean": 1.0, "CoV": 0.30 },
    "StressMultiplicationFactor": { ... }
}

The values follow the stochastic model of ref. [5], Table 8. Each key is described in the JSON format reference, which also explains how a realization is generated.

2. Generate the sample

C:\Users\yourname\flange-analyses>py -m pyflange sample fatigue-case.json --size 2000 --seed 1
Performing probabilistic analysis for case fatigue-case.json ...
... loading data from 'C:\Users\yourname\flange-analyses\fatigue-case.json'
... generating random sample of 2000 realizations with seed 1
... ... generated 1000 realizations
... ... generated 2000 realizations
... writing results to file '.\fatigue-case-sample.csv'
... DONE!
  • --size is the number of realizations. 2000 takes about 15 seconds. For an estimate of a probability of failure of 10-4 you need well over 105 realizations (the default is 100 000).
  • --seed makes the simulation reproducible: the same seed and case always give the same sample. Without it, every run is different.
  • --xlsx also writes the sample to an Excel file.

The CSV file has one row per realization, numbered from 0, with the random inputs and the results (Damage, AllowableDamage, FatigueLife, Utilization = damage / allowable damage). The columns are listed on the command line page.

3. Statistics

C:\Users\yourname\flange-analyses>py -m pyflange stats fatigue-case-sample.csv

                                         MIN           P05           AVG           P95           MAX           STD       CoV
... ... BoltPreload             2.741725e+06  2.812730e+06  2.861887e+06  2.908429e+06  3.044514e+06  2.906781e+04  0.010157
... ... GapAngle                3.637145e-02  3.154774e-01  1.235215e+00  2.712764e+00  3.131882e+00  7.338239e-01  0.594086
... ... GapHeight               1.509402e-08  3.809575e-05  1.148028e-03  3.626949e-03  9.676416e-03  1.224387e-03  1.066514
... ... Damage                  1.453893e-03  8.273311e-03  1.175896e-01  3.978284e-01  1.148680e+01  3.077050e-01  2.616772
... ... Utilization             8.771545e-04  8.206894e-03  1.296999e-01  4.197863e-01  1.498221e+01  3.874562e-01  2.987328

... ... sample size: 2000

(Some rows are omitted here.) The values are in SI units: angles in radians, gap heights in m, preloads in N.

To compute other statistics, open the CSV file in Excel or in Python. For example, the fraction of realizations with Utilization > 1 estimates the probability of failure; in this sample it is 16 out of 2000 (0.8%).

4. Inspect a realization

The largest utilization of the sample, about 15, belongs to realization 928. To see why, rebuild it and write its complete report, as determ does for the deterministic case:

C:\Users\yourname\flange-analyses>py -m pyflange inspect fatigue-case.json 928
...
... writing data to json file '.\fatigue-case-realization-928.json'
... DONE!

The report shows that this realization has a 92° gap of 4.8 mm, about 1.7 times the AMD1 design gap height for that angle: one of the rare large gaps in the tail of the gap height distribution.

Next steps

  • To use different distributions, or random variables that the JSON format does not support, build the simulation in Python: Monte Carlo in Python.
  • To use the ED2 model and gap statistics, set "type": "PolynomialLFlangeSegmentED2" in FlangeSegment and "JointDistribution": "IEC 61400-6:2020 ED2" in Stats.Gap.