Note
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Estimate a flooding probability¶
In this example, we estimate the probability that the output of a function exceeds a given threshold with the FORM method. We consider the flooding model.
Define the model¶
from openturns.usecases import flood_model
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)
We load the flooding model from the usecases module :
fm = flood_model.FloodModel()
distribution = fm.distribution
model = fm.model.getMarginal(1)
See the input distribution
distribution
See the model
model.getOutputDescription()
Draw the distribution of a sample of the output.
sampleSize = 1000
inputSample = distribution.getSample(sampleSize)
outputSample = model(inputSample)
graph = ot.HistogramFactory().build(outputSample).drawPDF()
_ = viewer.View(graph)
Define the event¶
Then we create the event whose probability we want to estimate.
vect = ot.RandomVector(distribution)
G = ot.CompositeRandomVector(model, vect)
event = ot.ThresholdEvent(G, ot.Greater(), 0.0)
event.setName("overflow")
Estimate the probability with FORM¶
Define a solver.
optimAlgo = ot.Cobyla()
optimAlgo.setMaximumCallsNumber(1000)
optimAlgo.setMaximumAbsoluteError(1.0e-8)
optimAlgo.setMaximumRelativeError(1.0e-10)
optimAlgo.setMaximumResidualError(1.0e-10)
optimAlgo.setMaximumConstraintError(1.0e-10)
Run FORM.
startingPoint = distribution.getMean()
algo = ot.FORM(optimAlgo, event, startingPoint)
algo.run()
result = algo.getResult()
standardSpaceDesignPoint = result.getStandardSpaceDesignPoint()
Retrieve results.
result = algo.getResult()
probability = result.getEventProbability()
print("Pf=", probability)
Pf= 0.000650134456773035
Importance factors.
graph = result.drawImportanceFactors()
view = viewer.View(graph)
plt.show()