pystra.form.Form#

class Form(stochastic_model=None, limit_state=None, analysis_options=None)[source]#

Bases: AnalysisObject

First Order Reliability Method (FORM)

Let \({\\bf Z}\) be a set of uncorrelated and standardized normally distributed random variables \(( Z_1 ,\dots, Z_n )\) in the normalized z-space, corresponding to any set of random variables \({\\bf X} = ( X_1 , \dots , X_n )\) in the physical x-space, then the limit state surface in x-space is also mapped on the corresponding limit state surface in z-space.

The reliability index \(\\beta\) is the minimum distance from the z-origin to the failure surface. This distance \(\\beta\) can directly be mapped to a probability of failure

\[\begin{split}p_f \\approx p_{f1} = \Phi(-\\beta)\end{split}\]

this corresponds to a linearization of the failure surface. The linearization point is the design point \({\\bf z}^*\). This procedure is called First Order Reliability Method (FORM) and \(\beta\) is the First Order Reliability Index. [Madsen2006]

Attributes:

stochastic_model (StochasticModel): Information about the model
limit_state (LimitState): Information about the limit state
analysis_option (AnalysisOption): Option for the structural analysis

Methods

`computeAlpha`	Compute alpha vector
`computeBeta`	Compute beta value
`computeFailureProbability`	Compute probability of failure
`computeGamma`	Compute gamma vector
`computeJacobian`	Compute the Jacobian
`computeLimitState`	Evaluate limit-state function and its gradient
`computeSearchDirection`	Determine search direction
`computeStartingPoint`	Compute starting point for the algorithm
`computeStepSize`	Calculate the step size for the calculation
`computeTransformation`	Compute transformation from u to x space
`getAlpha`	Returns the alpha vector
`getBeta`	Returns the beta value
`getDesignPoint`	Returns the design point, defaults to u-space
`getFailure`	Returns the probability of failure
`getNoFunctionCalls`	Returns the number of function evaluations used
`getStepSize`	Determine step size
`init_run`	Derived classes call this at top of their run()
`run`	Executes the FORM analysis
`showDetailedOutput`	Get detailed output to console
`showResults`	Show results

run()[source]#: Executes the FORM analysis

computeStartingPoint()[source]#: Compute starting point for the algorithm

computeTransformation()[source]#: Compute transformation from u to x space

computeJacobian()[source]#: Compute the Jacobian

computeLimitState()[source]#: Evaluate limit-state function and its gradient

computeAlpha()[source]#: Compute alpha vector

computeGamma()[source]#: Compute gamma vector

computeSearchDirection()[source]#: Determine search direction

getStepSize()[source]#: Determine step size

computeStepSize(G, gradient, u, d)[source]#

Calculate the step size for the calculation

Returns:

step_size (float): Returns the value of the step size.

computeBeta()[source]#: Compute beta value

computeFailureProbability()[source]#: Compute probability of failure

showResults()[source]#: Show results

showDetailedOutput()[source]#: Get detailed output to console

getBeta()[source]#

Returns the beta value

Returns:

beta (float): Returns the beta value

getFailure()[source]#

Returns the probability of failure

Returns:

Pf (float): Returns the probability of failure

getDesignPoint(uspace=True)[source]#

Returns the design point, defaults to u-space

Returns:

u (float): Returns the design point in u- or x-space

getAlpha(as_dict=False)[source]#

Returns the alpha vector

Returns:

alpha (np.array): Returns the alpha vector

getNoFunctionCalls()[source]#

Returns the number of function evaluations used

Returns:

n (int): Returns the number of function evaluations

init_run()#: Derived classes call this at top of their run()