# FORMResult¶

class FORMResult(*args)

Result of a FORM analysis.

Available constructors:
FORMResult(designPoint, limitStateVariable, isInFailureSpace)
Parameters: designPoint : sequence of float Design point in the standard space resulting from the optimization algorithm. limitStateVariable : Event Event of which the probability is calculated. isInFailureSpace : bool Indicates whether the origin of the standard space is in the failure space.

Notes

Structure created by the method run() of the FORM class and obtained thanks to its method getResult().

Methods

 drawEventProbabilitySensitivity(*args) Draw the sensitivities of the FORM failure probability. drawHasoferReliabilityIndexSensitivity(*args) Draw the sensitivity of the Hasofer Reliability Index. drawImportanceFactors(*args) Draw the importance factors. getClassName() Accessor to the object’s name. getEventProbability() Accessor to the failure probability . getEventProbabilitySensitivity() Accessor to the sentivities of the FORM failure probability . getGeneralisedReliabilityIndex() Accessor to the Generalised Reliability Index. getHasoferReliabilityIndex() Accessor to the Hasofer Reliability Index. getHasoferReliabilityIndexSensitivity() Accessor to the sensitivities of the Hasofer Reliability Index. getId() Accessor to the object’s id. getImportanceFactors(*args) Accessor to the importance factors. getIsStandardPointOriginInFailureSpace() Accessor to know if the standard point origin is in the failure space. getLimitStateVariable() Accessor to the event of which the probability is calculated. getMeanPointInStandardEventDomain() Accessor to the mean point in the standard event domain. getName() Accessor to the object’s name. getOptimizationResult() Accessor to the result of the optimization problem. getPhysicalSpaceDesignPoint() Accessor to the design point in the physical space. getShadowedId() Accessor to the object’s shadowed id. getStandardSpaceDesignPoint() Accessor to the design point in the standard space. getVisibility() Accessor to the object’s visibility state. hasName() Test if the object is named. hasVisibleName() Test if the object has a distinguishable name. setIsStandardPointOriginInFailureSpace(…) Accessor to specify if the standard point origin is in the failure space. setMeanPointInStandardEventDomain(…) 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. setStandardSpaceDesignPoint(…) 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: width : float, optional Value to calculate the shift position of the BarPlot. By default it is 1.0. graphCollection : list 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.
drawHasoferReliabilityIndexSensitivity(*args)

Draw the sensitivity of the Hasofer Reliability Index.

Parameters: width : float, optional Value to calculate the shift position of the BarPlot. By default it is 1.0. graphCollection : sequence 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.
drawImportanceFactors(*args)

Draw the importance factors.

Parameters: type : int, optional graph : Graph Pie of the importance factors of the probabilistic variables.
getClassName()

Accessor to the object’s name.

Returns: class_name : str The object class name (object.__class__.__name__).
getEventProbability()

Accessor to the failure probability .

Returns: probability : positive 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.
getGeneralisedReliabilityIndex()

Accessor to the Generalised Reliability Index.

Returns: index : float 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: index : float 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.
getId()

Accessor to the object’s id.

Returns: id : int Internal unique identifier.
getImportanceFactors(*args)

Accessor to the importance factors.

Parameters: type : int, 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. factors : PointWithDescription Sequence containing the importance factors with a description for each component.

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: isInFailureSpace : bool 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 : Event Event of which the probability is calculated.
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.
getName()

Accessor to the object’s name.

Returns: name : str 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.
getPhysicalSpaceDesignPoint()

Accessor to the design point in the physical space.

Returns: designPoint : Point Design point in the physical space resulting from the optimization algorithm.
getShadowedId()

Accessor to the object’s shadowed id.

Returns: id : int 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.
getVisibility()

Accessor to the object’s visibility state.

Returns: visible : bool Visibility flag.
hasName()

Test if the object is named.

Returns: hasName : bool True if the name is not empty.
hasVisibleName()

Test if the object has a distinguishable name.

Returns: hasVisibleName : bool 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: isInFailureSpace : bool 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: meanPoint : sequence 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: name : str 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.
setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters: id : int Internal unique identifier.
setStandardSpaceDesignPoint(standardSpaceDesignPoint)

Accessor to the design point in the standard space.

Parameters: designPoint : sequence of float Design point in the standard space resulting from the optimization algorithm.
setVisibility(visible)

Accessor to the object’s visibility state.

Parameters: visible : bool Visibility flag.