Note
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Mix/max search and sensitivity from designΒΆ
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
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.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= [6.19856] with x= [4.23762e+07,20903,253.762,433.463]
max: y= [32.592] with x= [3.09151e+07,65980.5,257.897,374.411]
Get sensitivity at minimum input values.
model.gradient(minX)