PostAnalyticalControlledImportanceSampling¶

class PostAnalyticalControlledImportanceSampling(*args)¶

Post analytical controlled importance sampling.

Simulation method where the original distribution is replaced by the distribution in the standard space centered around the provided design point and is controlled by the value of the linearized limit state function.

Parameters:

analyticalResultAnalyticalResult: Result which contains the whole information on the analytical study performed before the simulation study: in particular, the standard distribution of the standard space and the standard space design point.

See also

PostAnalyticalImportanceSampling

Examples

>>> import openturns as ot
>>> f = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['-F*L^3/(3*E*I)'])
>>> distribution = ot.Normal([50.0, 1.0, 10.0, 5.0], [1.0]*4, ot.IdentityMatrix(4))
>>> X = ot.RandomVector(distribution)
>>> Y = ot.CompositeRandomVector(f, X)
>>> event = ot.ThresholdEvent(Y, ot.Less(), -3.0)
>>> solver = ot.AbdoRackwitz()
>>> analytical = ot.FORM(solver, event, [50.0, 1.0, 10.0, 5.0])
>>> analytical.run()
>>> analyticalResult = analytical.getResult()
>>> algo = ot.PostAnalyticalControlledImportanceSampling(analyticalResult)
>>> algo.run()
>>> result = algo.getResult()
>>> pf = result.getProbabilityEstimate()

Methods

`drawProbabilityConvergence`(*args)	Draw the probability convergence at a given level.
`getAnalyticalResult`()	Accessor to the analytical result.
`getBlockSize`()	Accessor to the block size.
`getClassName`()	Accessor to the object's name.
`getControlProbability`()	Accessor to the control probability.
`getConvergenceStrategy`()	Accessor to the convergence strategy.
`getEvent`()	Accessor to the event.
`getId`()	Accessor to the object's id.
`getMaximumCoefficientOfVariation`()	Accessor to the maximum coefficient of variation.
`getMaximumOuterSampling`()	Accessor to the maximum sample size.
`getMaximumStandardDeviation`()	Accessor to the maximum standard deviation.
`getName`()	Accessor to the object's name.
`getResult`()	Accessor to the results.
`getShadowedId`()	Accessor to the object's shadowed id.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`run`()	Launch simulation.
`setBlockSize`(blockSize)	Accessor to the block size.
`setConvergenceStrategy`(convergenceStrategy)	Accessor to the convergence strategy.
`setMaximumCoefficientOfVariation`(...)	Accessor to the maximum coefficient of variation.
`setMaximumOuterSampling`(maximumOuterSampling)	Accessor to the maximum sample size.
`setMaximumStandardDeviation`(...)	Accessor to the maximum standard deviation.
`setName`(name)	Accessor to the object's name.
`setProgressCallback`(*args)	Set up a progress callback.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setStopCallback`(*args)	Set up a stop callback.
`setVisibility`(visible)	Accessor to the object's visibility state.

getVerbose
setVerbose

__init__(*args)¶

drawProbabilityConvergence(*args)¶

Draw the probability convergence at a given level.

Parameters:

levelfloat, optional: The probability convergence is drawn at this given confidence length level. By default level is 0.95.

Returns:

grapha Graph: probability convergence graph

getAnalyticalResult()¶

Accessor to the analytical result.

Returns:

resultAnalyticalResult: Result of the analytical study which has been performed just before the simulation study centered around the importance factor.

getBlockSize()¶

Accessor to the block size.

Returns:

blockSizeint: Number of terms in the probability simulation estimator grouped together. It is set by default to 1.

getClassName()¶

Accessor to the object’s name.

Returns:

class_namestr: The object class name (object.__class__.__name__).

getControlProbability()¶

Accessor to the control probability.

Returns:

pfloat,: The probability of the analytical result.

Notes

The control probability $p$ is deduced from the corresponding analytical result:

$p = E(-\beta_{HL})$

where $\beta_{HL}$ denotes the Hasofer reliability index and $E$ the univariate standard CDF of the elliptical distribution in the standard space.

getConvergenceStrategy()¶

Accessor to the convergence strategy.

Returns:

storage_strategyHistoryStrategy: Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.

getEvent()¶

Accessor to the event.

Returns:

eventRandomVector: Event we want to evaluate the probability.

getId()¶

Accessor to the object’s id.

Returns:

idint: Internal unique identifier.

getMaximumCoefficientOfVariation()¶

Accessor to the maximum coefficient of variation.

Returns:

coefficientfloat: Maximum coefficient of variation of the simulated sample.

getMaximumOuterSampling()¶

Accessor to the maximum sample size.

Returns:

outerSamplingint: Maximum number of groups of terms in the probability simulation estimator.

getMaximumStandardDeviation()¶

Accessor to the maximum standard deviation.

Returns:

sigmafloat, $\sigma > 0$: Maximum standard deviation of the estimator.

getName()¶

Accessor to the object’s name.

Returns:

namestr: The name of the object.

getResult()¶

Accessor to the results.

Returns:

resultsSimulationResult: Structure containing all the results obtained after simulation and created by the method run().

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns:

idint: Internal unique identifier.

getVisibility()¶

Accessor to the object’s visibility state.

Returns:

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns:

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns:

hasVisibleNamebool: True if the name is not empty and not the default one.

run()¶

Launch simulation.

See also

setBlockSize, setMaximumOuterSampling, ResourceMap, SimulationResult

Notes

It launches the simulation and creates a SimulationResult, structure containing all the results obtained after simulation. It computes the probability of occurrence of the given event by computing the empirical mean of a sample of size at most outerSampling * blockSize, this sample being built by blocks of size blockSize. It allows one to use efficiently the distribution of the computation as well as it allows one to deal with a sample size $> 2^{32}$ by a combination of blockSize and outerSampling.

setBlockSize(blockSize)¶

Accessor to the block size.

Parameters:

blockSizeint, $blockSize \geq 1$: Number of terms in the probability simulation estimator grouped together. It is set by default to 1.

Notes

For Monte Carlo, LHS and Importance Sampling methods, this allows one to save space while allowing multithreading, when available we recommend to use the number of available CPUs; for the Directional Sampling, we recommend to set it to 1.

setConvergenceStrategy(convergenceStrategy)¶

Accessor to the convergence strategy.

Parameters:

storage_strategyHistoryStrategy: Storage strategy used to store the values of the probability estimator and its variance during the simulation algorithm.

setMaximumCoefficientOfVariation(maximumCoefficientOfVariation)¶

Accessor to the maximum coefficient of variation.

Parameters:

coefficientfloat: Maximum coefficient of variation of the simulated sample.

setMaximumOuterSampling(maximumOuterSampling)¶

Accessor to the maximum sample size.

Parameters:

outerSamplingint: Maximum number of groups of terms in the probability simulation estimator.

setMaximumStandardDeviation(maximumStandardDeviation)¶

Accessor to the maximum standard deviation.

Parameters:

sigmafloat, $\sigma > 0$: Maximum standard deviation of the estimator.

setName(name)¶

Accessor to the object’s name.

Parameters:

namestr: The name of the object.

setProgressCallback(*args)¶

Set up a progress callback.

Can be used to programmatically report the progress of a simulation.

Parameters:

callbackcallable: Takes a float as argument as percentage of progress.

Examples

>>> import sys
>>> import openturns as ot
>>> experiment = ot.MonteCarloExperiment()
>>> X = ot.RandomVector(ot.Normal())
>>> Y = ot.CompositeRandomVector(ot.SymbolicFunction(['X'], ['1.1*X']), X)
>>> event = ot.ThresholdEvent(Y, ot.Less(), -2.0)
>>> algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
>>> algo.setMaximumOuterSampling(100)
>>> algo.setMaximumCoefficientOfVariation(-1.0)
>>> def report_progress(progress):
...     sys.stderr.write('-- progress=' + str(progress) + '%\n')
>>> algo.setProgressCallback(report_progress)
>>> algo.run()

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters:

idint: Internal unique identifier.

setStopCallback(*args)¶

Set up a stop callback.

Can be used to programmatically stop a simulation.

Parameters:

callbackcallable: Returns an int deciding whether to stop or continue.

Examples

Stop a Monte Carlo simulation algorithm using a time limit

>>> import openturns as ot
>>> experiment = ot.MonteCarloExperiment()
>>> X = ot.RandomVector(ot.Normal())
>>> Y = ot.CompositeRandomVector(ot.SymbolicFunction(['X'], ['1.1*X']), X)
>>> event = ot.ThresholdEvent(Y, ot.Less(), -2.0)
>>> algo = ot.ProbabilitySimulationAlgorithm(event, experiment)
>>> algo.setMaximumOuterSampling(10000000)
>>> algo.setMaximumCoefficientOfVariation(-1.0)
>>> timer = ot.TimerCallback(0.1)
>>> algo.setStopCallback(timer)
>>> algo.run()

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters:

visiblebool: Visibility flag.

Examples using the class¶

Use the post-analytical importance sampling algorithm

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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PostAnalyticalControlledImportanceSampling¶

Examples using the class¶