FORMResult¶
- class FORMResult(*args)¶
Result of a FORM analysis.
- Available constructors:
FORMResult(designPoint, limitStateVariable, isInFailureSpace)
- Parameters:
- designPointsequence of float
Design point in the standard space resulting from the optimization algorithm.
- limitStateVariable
RandomVector
Event of which the probability is calculated.
- isInFailureSpacebool
Indicates whether the origin of the standard space is in the failure space.
See also
Notes
Structure created by the method run() of the
FORM
class and obtained thanks to its method getResult().Methods
Draw the sensitivities of the FORM failure probability.
Draw the sensitivity of the Hasofer Reliability Index.
drawImportanceFactors
(*args)Draw the importance factors.
Accessor to the object's name.
Accessor to the failure probability .
Accessor to the sensitivities of the FORM failure probability .
Accessor to the Generalised Reliability Index.
Accessor to the Hasofer Reliability Index.
Accessor to the sensitivities of the Hasofer Reliability Index.
getId
()Accessor to the object's id.
getImportanceFactors
(*args)Accessor to the importance factors.
Accessor to know if the standard point origin is in the failure space.
Accessor to the event of which the probability is calculated.
Accessor to the mean point in the standard event domain.
getName
()Accessor to the object's name.
Accessor to the result of the optimization problem.
Accessor to the design point in the physical space.
Accessor to the object's shadowed id.
Accessor to the design point in the standard space.
Accessor to the object's visibility state.
hasName
()Test if the object is named.
Test if the object has a distinguishable name.
Accessor to specify if the standard point origin is in the failure space.
Accessor to the mean point in the standard event domain.
setName
(name)Accessor to the object's name.
setOptimizationResult
(optimizationResult)Accessor to the result of the optimization problem.
setShadowedId
(id)Accessor to the object's shadowed id.
Accessor to the design point in the standard space.
setVisibility
(visible)Accessor to the object's visibility state.
- __init__(*args)¶
- drawEventProbabilitySensitivity(*args)¶
Draw the sensitivities of the FORM failure probability.
- Parameters:
- widthfloat, optional
Value to calculate the shift position of the
BarPlot
. By default it is 1.0.
- Returns:
- graphCollectionlist of two
Graph
containing a barplot The first graph drawing the sensitivities of the FORM failure probability with regards to the parameters of the probabilistic input vector. The second graph drawing the sensitivities of the FORM failure probability with regards to the parameters of the dependence structure of the probabilistic input vector.
- graphCollectionlist of two
- drawHasoferReliabilityIndexSensitivity(*args)¶
Draw the sensitivity of the Hasofer Reliability Index.
- Parameters:
- widthfloat, optional
Value to calculate the shift position of the
BarPlot
. By default it is 1.0.
- Returns:
- graphCollectionsequence of two
Graph
containing a barplot The first graph drawing the sensitivity of the Hasofer Reliability Index to the parameters of the marginals of the probabilistic input vector. The second graph drawing the sensitivity of the Hasofer Reliability Index to the parameters of the dependence structure of the probabilistic input vector.
- graphCollectionsequence of two
- drawImportanceFactors(*args)¶
Draw the importance factors.
- Parameters:
- typeint, optional
- Returns:
- graph
Graph
Pie of the importance factors of the probabilistic variables.
- graph
- getClassName()¶
Accessor to the object’s name.
- Returns:
- class_namestr
The object class name (object.__class__.__name__).
- getEventProbability()¶
Accessor to the failure probability .
- Returns:
- probabilitypositive float
The FORM failure probability .
- getEventProbabilitySensitivity()¶
Accessor to the sensitivities of the FORM failure probability .
- Returns:
- sensitivities
Point
Sensitivities of the FORM failure probability with regards to the parameters of the probabilistic input vector and to parameters of the dependence structure of the probabilistic input vector.
- sensitivities
- getGeneralisedReliabilityIndex()¶
Accessor to the Generalised Reliability Index.
- Returns:
- indexfloat
Generalised reliability index from the FORM failure probability is equal to the Hasofer reliability index according to the fact the standard space center fulfills the event or not.
- getHasoferReliabilityIndex()¶
Accessor to the Hasofer Reliability Index.
- Returns:
- indexfloat
Hasofer Reliability Index which is the distance of the design point from the origin of the standard space .
- getHasoferReliabilityIndexSensitivity()¶
Accessor to the sensitivities of the Hasofer Reliability Index.
- Returns:
- sensitivity
PointWithDescription
Sequence containing the sensitivities of the Hasofer Reliability Index to the parameters of the probabilistic input vector (marginals and dependence structure) with a description for each component.
- sensitivity
- getId()¶
Accessor to the object’s id.
- Returns:
- idint
Internal unique identifier.
- getImportanceFactors(*args)¶
Accessor to the importance factors.
- Parameters:
- typeint, optional
When ot.AnalyticalResult.ELLIPTICAL, the importance factors are evaluated as the square of the co-factors of the design point in the elliptical space of the iso-probabilistic transformation (Y-space).
When ot.AnalyticalResult.CLASSICAL they are evaluated as the square of the co-factors of the design point in the U-space.
When ot.AnalyticalResult.PHYSICAL, the importance factors are evaluated as the square of the physical sensitivities.
By default type = ot.AnalyticalResult.ELLIPTICAL.
- Returns:
- factors
PointWithDescription
Sequence containing the importance factors with a description for each component.
- factors
Notes
If the importance factors are evaluated as the square of the co-factors of the design point in the U-space :
If the importance factors are evaluated as the square of the co-factors of the design point in the Y-space :
where
with is the design point in the physical space and the univariate standard CDF of the elliptical space. In the case where the input distribution of has an elliptical copula , then has the same type as . In the case where the input distribution of has a copula which is not elliptical, then where is the CDF of the standard normal.
If the importance factors are evaluated as the square of the physical sensitivities :
where
- getIsStandardPointOriginInFailureSpace()¶
Accessor to know if the standard point origin is in the failure space.
- Returns:
- isInFailureSpacebool
Indicates whether the origin of the standard space is in the failure space.
- getLimitStateVariable()¶
Accessor to the event of which the probability is calculated.
- Returns:
- limitStateVariable
RandomVector
Event of which the probability is calculated.
- limitStateVariable
- getMeanPointInStandardEventDomain()¶
Accessor to the mean point in the standard event domain.
- Returns:
- meanPoint
Point
Mean point in the standrad event domain.
- meanPoint
Notes
This method is used in the context of the FORM approximation of the probability of an event. Let denote the standard event domain.
In the standard space, the transformed random vector follows a spherical distribution. All the univariate marginals are identical. Let denote the CDF of any univariate marginal and its PDF.
Let denote the design point in the standard space and the associated Hasofer-Lind reliability index.
By symmetry in the standard space, the mean point in the standard event domain is computed as follows:
- getName()¶
Accessor to the object’s name.
- Returns:
- namestr
The name of the object.
- getOptimizationResult()¶
Accessor to the result of the optimization problem.
- Returns:
- result
OptimizationResult
Contains the design point in the standard space and information concerning the convergence of the optimization algorithm.
- result
- getPhysicalSpaceDesignPoint()¶
Accessor to the design point in the physical space.
- Returns:
- designPoint
Point
Design point in the physical space resulting from the optimization algorithm.
- designPoint
- getShadowedId()¶
Accessor to the object’s shadowed id.
- Returns:
- idint
Internal unique identifier.
- getStandardSpaceDesignPoint()¶
Accessor to the design point in the standard space.
- Returns:
- designPoint
Point
Design point in the standard space resulting from the optimization algorithm.
- designPoint
- 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.
- setIsStandardPointOriginInFailureSpace(isStandardPointOriginInFailureSpace)¶
Accessor to specify if the standard point origin is in the failure space.
- Parameters:
- isInFailureSpacebool
Indicates whether the origin of the standard space is in the failure space.
- setMeanPointInStandardEventDomain(meanPointInStandardEventDomain)¶
Accessor to the mean point in the standard event domain.
- Parameters:
- meanPointsequence of float
The mean point of the standard space distribution restricted to the event domain.
- setName(name)¶
Accessor to the object’s name.
- Parameters:
- namestr
The name of the object.
- setOptimizationResult(optimizationResult)¶
Accessor to the result of the optimization problem.
- Parameters:
- result
OptimizationResult
Contains the design point in the standard space and information concerning the convergence of the optimization algorithm.
- result
- setShadowedId(id)¶
Accessor to the object’s shadowed id.
- Parameters:
- idint
Internal unique identifier.
- setStandardSpaceDesignPoint(standardSpaceDesignPoint)¶
Accessor to the design point in the standard space.
- Parameters:
- designPointsequence of float
Design point in the standard space resulting from the optimization algorithm.
- setVisibility(visible)¶
Accessor to the object’s visibility state.
- Parameters:
- visiblebool
Visibility flag.
Examples using the class¶
Use the post-analytical importance sampling algorithm
Estimate a flooding probability
Use the FORM algorithm in case of several design points
Use the FORM - SORM algorithms
Test the design point with the Strong Maximum Test
Axial stressed beam : comparing different methods to estimate a probability
An illustrated example of a FORM probability estimate
Using the FORM - SORM algorithms on a nonlinear function