SimulationSensitivityAnalysis

class SimulationSensitivityAnalysis(*args)

Class to perform a sensitivity analysis based on a reliability event.

Available constructor:

SimulationSensitivityAnalysis(event, inputSample, outputSample)

SimulationSensitivityAnalysis(event)

SimulationSensitivityAnalysis(simulationRes)

Parameters:
eventRandomVector

An event which it composite (test is with the method isComposite).

inputSample, outputSample2-d sequence of float

Input sample and output sample of a model evaluated apart.

simulationResProbabilitySimulationResult

A simulation result.

Notes

The simulation sensitivity analysis is based on:

  • in the first usage, the inputSample and outputSample given:

  • in the second usage, the samples which have been stored by the function defining the event. Care if the sample is not a statistical sample: post treatment proposed by the object might not be right.

  • in the third usage, the samples generated by the EventSimulation that produced simulationRes.

Methods

computeEventProbabilitySensitivity()

Compute the sensitivity to the probability.

computeImportanceFactors(*args)

Compute the importance factors.

computeMeanPointInEventDomain(*args)

Accessor to the mean point.

drawImportanceFactors()

Draw the importance factors.

drawImportanceFactorsRange(*args)

Draw the importance factors evolution.

getClassName()

Accessor to the object's name.

getComparisonOperator()

Accessor to the comparison operator.

getInputSample()

Accessor to the input sample.

getName()

Accessor to the object's name.

getOutputSample()

Accessor to the output sample.

getThreshold()

Accessor to the threshold.

getTransformation()

Accessor to the isoprobabilistic transformation function.

hasName()

Test if the object is named.

setName(name)

Accessor to the object's name.
__init__(*args)
computeEventProbabilitySensitivity()

Compute the sensitivity to the probability.

The sensitivity of the probability Pf wrt the distribution parameters \theta is written:

\vect{sens_{Pf}}_j = \frac{1}{n} \sum_{i=1}^n \mathbf{1}_{event} \vect{\frac{\delta log(f_{\uX})(\vect{X}_i)}{\delta \theta_j}}

Returns:
sensitivity_pfPointWithDescription

The probability sensitivity.

computeImportanceFactors(*args)

Compute the importance factors.

Returns:
impFactorsPointWithDescription

The importance factors.

Notes

The importance factors, given in (2), are evaluated from the coordinates of the mean point (1) of the event domain, mapped into the standard space as follows:

(1)\vect{X}^*_{event} = \frac{1}{n} \sum_{i=1}^n \vect{X}_i 1_{event} (\vect{X}_i)

(2)\alpha_i = \frac{ (U_i^*)^2 }{ \left\| \vect{U}^* \right\| }

where

\vect{U}^* = T(\vect{X}^*_{event})

Be careful: this notion is only valid for MonteCarloExperiment or LHSExperiment sampling as the mean is evaluated from the equation (2) (only uniform weights over the realizations \vect{X}_i.

computeMeanPointInEventDomain(*args)

Accessor to the mean point.

Returns:
meanPoint

The mean point in the failure domain.

Notes

This method computes the mean point in the physical space of all the simulations generated by the simulation that failed into the event domain.

Be careful: this notion is only valid for Monte Carlo or LHS sampling as the mean is evaluated from the equation (1) (only uniform weights over the realizations \vect{X}_i.

drawImportanceFactors()

Draw the importance factors.

Returns:
graphGraph

Graph containing the pie corresponding to the importance factors of the probabilistic variables.

drawImportanceFactorsRange(*args)

Draw the importance factors evolution.

Parameters:
probabilityScaleboolean

Set True if the limits are the probability levels; set False if the limits are the thresholds defining the event.

lower, upperfloats

Define the boundaries of the probability levels p_{min} and p_{max} or those of the thresholds s_{min} and s_{max}.

Returns:
graphGraph

A graph that draws the evolution of the importance factors of each direction with respect to p \in [p_{min}, p_{max}] or s \in [s_{min}, s_{max}]. The importance factors are evaluated from the definition (2) for each threshold s or probability p.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getComparisonOperator()

Accessor to the comparison operator.

Returns:
operatorComparisonOperator

The comparison operator.

getInputSample()

Accessor to the input sample.

Returns:
inputSampleSample

The input sample.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOutputSample()

Accessor to the output sample.

Returns:
outputSampleSample

The output sample.

getThreshold()

Accessor to the threshold.

Returns:
sfloat

The threshold.

getTransformation()

Accessor to the isoprobabilistic transformation function.

Returns:
transformationFunction

The isoprobabilistic transformation function.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.