FORM

class FORM(*args)

First Order Reliability Method (FORM).

Refer to FORM.

Available constructors:

FORM(nearestPointAlgorithm, event, physicalStartingPoint)

Parameters
nearestPointAlgorithmOptimizationAlgorithm

Optimization algorithm used to research the design point.

eventEvent

Failure event.

physicalStartingPointsequence of float

Starting point of the optimization algorithm, declared in the physical space.

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 G(\vect{U}\,,\,\vect{d}) at the design point, denoted P^*, which is the point on the limit state surface G(\vect{U}\,,\,\vect{d})=0 that is closest to the origin of the standard space.

Then, the probability P_f 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 f_{\vect{U}} :

P_f = \left\{
          \begin{array}{ll}
          \displaystyle E(-\beta_{HL})
          & \text{if the origin of the }\vect{u}\text{-space lies in the domain }\cD_f \\
          \displaystyle E(+\beta_{HL}) & \text{otherwise}
          \end{array}
      \right.

where \beta_{HL} is the Hasofer-Lind reliability index, defined as the distance of the design point \vect{u}^* to the origin of the standard space and E 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 the getResult() 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
resultAnalyticalResult

Result structure which contains the results of the optimisation problem.

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
eventEvent

Event of which the probability is calculated.

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
algorithmOptimizationAlgorithm

Optimization algorithm used to research the design point.

getPhysicalStartingPoint(self)

Accessor to the starting point of the optimization algorithm.

Returns
pointPoint

Starting point of the optimization algorithm, declared in the physical space.

getResult(self)

Accessor to the result of FORM.

Returns
resultFORMResult

Structure containing all the results of the FORM analysis.

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 method getResult().

setEvent(self, event)

Accessor to the event of which the probability is calculated.

Parameters
eventEvent

Event of which the probability is calculated.

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
algorithmOptimizationAlgorithm

Optimization algorithm used to research the design point.

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
resultFORMResult

Structure containing all the results of the FORM analysis.

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.