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

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.JointDistribution(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)

min: y= [6.02873]  with x= [3.8573e+07,18145.3,255.091,431.737]
max: y= [33.2052]  with x= [3.22315e+07,83949.1,250.519,411.084]

Get sensitivity at minimum input values.

model.gradient(minX)

[[ -1.56294e-07 ]
[ 0.000332246 ]
[ 0.0709009 ]
[ -0.0139639 ]]