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 sentivities 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)¶ Initialize self. See help(type(self)) for accurate signature.

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 sentivities of the FORM failure probability .
 Returns
 sentivities
Point
Sentivities 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.
 sentivities

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.
Refer to Sensitivity Factors from FORM method.
 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.
Refer Importance factors from FORM method.
 Parameters
 typeint, optional
When ot.AnalyticalResult.ELLIPTICAL, the importance factors are evaluated as the square of the cofactors of the design point in the elliptical space of the isoprobabilistic transformation (Yspace).
When ot.AnalyticalResult.CLASSICAL they are evaluated as the square of the cofactors of the design point in the Uspace.
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 cofactors of the design point in the Uspace :
If the importance factors are evaluated as the square of the cofactors of the design point in the Yspace :
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 of the standard space distribution restricted to the event domain: where is the spheric univariate distribution of the standard space and the reliability index.
 meanPoint

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
Mean point of the standard space distribution restricted to the event domain: where is the spheric univariate distribution of the standard space and the reliability index.

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.