Using the Waarts four-branch serial system

References

• Waarts, P.-H. (2000). Structural reliability using finite element methods: an appraisal of DARS: Directional Adaptive Response Surface Sampling. Ph. D. thesis, Technical University of Delft, The Netherlands. Pages 58, 69, 160.

• Thèse Vincent Dubourg 2011, Méta-modèles adaptatifs pour l’analyse de fiabilité et l’optimisation sous contrainte fiabiliste, section “A two-dimensional four-branch serial system”, page 182

import openturns as ot
import openturns.viewer as otv
import otbenchmark as otb

problem = otb.FourBranchSerialSystemReliability()

event = problem.getEvent()
g = event.getFunction()

inputVector = event.getAntecedent()
distribution = inputVector.getDistribution()

Draw isolines

lowerBound = ot.Point([-5.0, -5.0])
upperBound = ot.Point([5.0, 5.0])
nbPoints = [100, 100]
_ = otv.View(g.draw(lowerBound, upperBound, nbPoints))

sampleSize = 500

drawEvent = otb.DrawEvent(event)

cloud = drawEvent.drawSampleCrossCut(sampleSize)
_ = otv.View(cloud)

Draw the limit state surface

bounds = ot.Interval(lowerBound, upperBound)

graph = drawEvent.drawLimitStateCrossCut(bounds)
graph.add(cloud)
_ = otv.View(graph)

Fill the event domain with a color

_ = otv.View(drawEvent.fillEventCrossCut(bounds))

otv.View.ShowAll()