Mix/max search and sensitivity from design

In this example, we are going to evaluate the minimum and maximum 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.

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 the inputs.

sampleX = distribution.getSample(100)

Create the model.

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

Evaluate the outputs.

sampleY = model(sampleX)

Get minimum and maximum values of both inputs and output variables.

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= [6.63485]  with x= [3.81821e+07,20263.2,251.912,426.231]
max: y= [24.1319]  with x= [2.8076e+07,46378.5,259.947,400.794]

Get sensitivity at minimum input values.

model.gradient(minX)

[[ -1.73769e-07 ]
[ 0.000327432 ]
[ 0.0790138 ]
[ -0.0155663 ]]