MultiFORM¶

class
MultiFORM
(*args)¶ FORM approximation with multiple design points.
This algorithm searches for several design points by restarting the nearestpoint search. For each design point we add a bulge function that penalizes the limitstate G around it:
The bulge function can be chosed as:
Once these points are found a FORM is computed with each point and the probability of interest is computed as a series system probability: the union of the approximated events:
Beware, as with the regular FORM method the search can fail, or the enumeration of design can be not incomplete.
More details can be found in [kiureghian1998].
 Parameters
 solver
OptimizationAlgorithm
Optimization algorithm used to research the design point.
 event
RandomVector
Failure system event, in disjunctive normal form (either a union of intersections, or a single intersection)
 physicalStartingPointsequence of float
Starting point of the optimization algorithm, declared in the physical space.
 solver
See also
Examples
>>> import openturns as ot >>> dim = 2 >>> f = ot.SymbolicFunction(['x0', 'x1'], ['5.0x10.5*(x00.1)^2']) >>> dist = ot.Normal(dim) >>> X = ot.RandomVector(dist) >>> Y = ot.CompositeRandomVector(f, X) >>> event = ot.ThresholdEvent(Y, ot.Less(), 0.0) >>> solver = ot.Cobyla() >>> starting_pt = dist.getMean() >>> algo = ot.MultiFORM(solver, event, starting_pt) >>> algo.run() >>> result = algo.getResult() >>> n_design_pts = len(result.getFORMResultCollection()) >>> pf = result.getEventProbability()
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.
Accessor to the maximum number of design points.
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.
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.
setMaximumNumberOfDesignPoints
(self, …)Accessor to the maximum number of design points.
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
RandomVector
Event of which the probability is calculated.
 event

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

getMaximumNumberOfDesignPoints
(self)¶ Accessor to the maximum number of design points.
 Returns
 max_dpint
Maximum number of design points

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.
 Returns
 result
MultiFORMResult
Contains the global result as well as the sub FORM results.
 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
RandomVector
Event of which the probability is calculated.
 event

setMaximumNumberOfDesignPoints
(self, numberOfDesignPoints)¶ Accessor to the maximum number of design points.
 Parameters
 max_dpint
Maximum number of design points

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.