Mix/max search and sensitivity from design

In this example we are going to evaluate the min and max values of the output variable of interest from a sample and to evaluate the gradient of the limit state function defining the output variable of interest at a particular point.

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)

Create the marginal distributions of the parameters

dist_E = ot.Beta(0.93, 2.27, 2.8e7, 4.8e7)
dist_F = ot.LogNormalMuSigma(30000, 9000, 15000).getDistribution()
dist_L = ot.Uniform(250, 260)
dist_I = ot.Beta(2.5, 1.5, 3.1e2, 4.5e2)
marginals = [dist_E, dist_F, dist_L, dist_I]
distribution = ot.ComposedDistribution(marginals)

Sample inputs

sampleX = distribution.getSample(100)

Create the model

model = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['F*L^3/(3*E*I)'])

Evaluate outputs

sampleY = model(sampleX)

Get min and max

minY = sampleY.getMin()
minX = sampleX[sampleY.find(minY)]
print('min: y=', minY, ' with x=', minX)
maxY = sampleY.getMax()
maxX = sampleX[sampleY.find(maxY)]
print('max: y=', maxY, ' with x=', maxX)

Out:

min: y= [6.35444]  with x= [4.36732e+07,19232.1,257.238,393.206]
max: y= [29.9854]  with x= [3.45218e+07,63587.7,258.04,351.814]

Get sensitivity at min

model.gradient(minX)

[[ -1.455e-07 ]
[ 0.000330408 ]
[ 0.0741076 ]
[ -0.0161606 ]]