FORM¶

class
FORM
(*args)¶ First Order Reliability Method (FORM).
Refer to FORM.
 Available constructors:
FORM(nearestPointAlgorithm, event, physicalStartingPoint)
 Parameters
 nearestPointAlgorithm
OptimizationAlgorithm
Optimization algorithm used to research the design point.
 event
Event
Failure event.
 physicalStartingPointsequence of float
Starting point of the optimization algorithm, declared in the physical space.
 nearestPointAlgorithm
See also
Notes
See
Analytical
for the description of the first steps of the FORM analysis.The First Order Reliability Method (FORM) consists in linearizing the limit state function at the design point, denoted , which is the point on the limit state surface that is closest to the origin of the standard space.
Then, the probability where the limit state surface has been approximated by a linear surface (hyperplane) can be obtained exactly, thanks to the rotation invariance of the standard distribution :
where is the HasoferLind reliability index, defined as the distance of the design point to the origin of the standard space and the marginal cumulative density function of the spherical distributions in the standard space.
The evaluation of the failure probability is stored in the data structure
FORMResult
recoverable with thegetResult()
method.Examples
>>> import openturns as ot >>> myFunction = ot.SymbolicFunction(['E', 'F', 'L', 'I'], ['F*L^3/(3*E*I)']) >>> myDistribution = ot.Normal([50.0, 1.0, 10.0, 5.0], [1.0]*4, ot.IdentityMatrix(4)) >>> vect = ot.RandomVector(myDistribution) >>> output = ot.CompositeRandomVector(myFunction, vect) >>> event = ot.Event(output, ot.Less(), 3.0) >>> # We create an OptimizationAlgorithm algorithm >>> solver = ot.AbdoRackwitz() >>> algo = ot.FORM(solver, event, [50.0, 1.0, 10.0, 5.0]) >>> algo.run() >>> result = algo.getResult()
Methods
getAnalyticalResult
(self)Accessor to the result.
getClassName
(self)Accessor to the object’s name.
getEvent
(self)Accessor to the event of which the probability is calculated.
getId
(self)Accessor to the object’s id.
getName
(self)Accessor to the object’s name.
getNearestPointAlgorithm
(self)Accessor to the optimization algorithm used to find the design point.
getPhysicalStartingPoint
(self)Accessor to the starting point of the optimization algorithm.
getResult
(self)Accessor to the result of FORM.
getShadowedId
(self)Accessor to the object’s shadowed id.
getVisibility
(self)Accessor to the object’s visibility state.
hasName
(self)Test if the object is named.
hasVisibleName
(self)Test if the object has a distinguishable name.
run
(self)Evaluate the failure probability.
setEvent
(self, event)Accessor to the event of which the probability is calculated.
setName
(self, name)Accessor to the object’s name.
setNearestPointAlgorithm
(self, solver)Accessor to the optimization algorithm used to find the design point.
setPhysicalStartingPoint
(self, …)Accessor to the starting point of the optimization algorithm.
setResult
(self, formResult)Accessor to the result of FORM.
setShadowedId
(self, id)Accessor to the object’s shadowed id.
setVisibility
(self, visible)Accessor to the object’s visibility state.

__init__
(self, *args)¶ Initialize self. See help(type(self)) for accurate signature.

getAnalyticalResult
(self)¶ Accessor to the result.
 Returns
 result
AnalyticalResult
Result structure which contains the results of the optimisation problem.
 result

getClassName
(self)¶ Accessor to the object’s name.
 Returns
 class_namestr
The object class name (object.__class__.__name__).

getEvent
(self)¶ Accessor to the event of which the probability is calculated.
 Returns
 event
Event
Event of which the probability is calculated.
 event

getId
(self)¶ Accessor to the object’s id.
 Returns
 idint
Internal unique identifier.

getName
(self)¶ Accessor to the object’s name.
 Returns
 namestr
The name of the object.

getNearestPointAlgorithm
(self)¶ Accessor to the optimization algorithm used to find the design point.
 Returns
 algorithm
OptimizationAlgorithm
Optimization algorithm used to research the design point.
 algorithm

getPhysicalStartingPoint
(self)¶ Accessor to the starting point of the optimization algorithm.
 Returns
 point
Point
Starting point of the optimization algorithm, declared in the physical space.
 point

getResult
(self)¶ Accessor to the result of FORM.
 Returns
 result
FORMResult
Structure containing all the results of the FORM analysis.
 result

getShadowedId
(self)¶ Accessor to the object’s shadowed id.
 Returns
 idint
Internal unique identifier.

getVisibility
(self)¶ Accessor to the object’s visibility state.
 Returns
 visiblebool
Visibility flag.

hasName
(self)¶ Test if the object is named.
 Returns
 hasNamebool
True if the name is not empty.

hasVisibleName
(self)¶ Test if the object has a distinguishable name.
 Returns
 hasVisibleNamebool
True if the name is not empty and not the default one.

run
(self)¶ Evaluate the failure probability.
Notes
Evaluate the failure probability and create a
FORMResult
, the structure result which is accessible with the methodgetResult()
.

setEvent
(self, event)¶ Accessor to the event of which the probability is calculated.
 Parameters
 event
Event
Event of which the probability is calculated.
 event

setName
(self, name)¶ Accessor to the object’s name.
 Parameters
 namestr
The name of the object.

setNearestPointAlgorithm
(self, solver)¶ Accessor to the optimization algorithm used to find the design point.
 Parameters
 algorithm
OptimizationAlgorithm
Optimization algorithm used to research the design point.
 algorithm

setPhysicalStartingPoint
(self, physicalStartingPoint)¶ Accessor to the starting point of the optimization algorithm.
 Parameters
 pointsequence of float
Starting point of the optimization algorithm, declared in the physical space.

setResult
(self, formResult)¶ Accessor to the result of FORM.
 Parameters
 result
FORMResult
Structure containing all the results of the FORM analysis.
 result

setShadowedId
(self, id)¶ Accessor to the object’s shadowed id.
 Parameters
 idint
Internal unique identifier.

setVisibility
(self, visible)¶ Accessor to the object’s visibility state.
 Parameters
 visiblebool
Visibility flag.