pystra.system_form.SystemFORM#

class SystemFORM(system, stochastic_model, analysis_options=None, *, maxpts=1000000, abseps=1e-10, releps=1e-05)[source]#

Bases: AnalysisObject

Approximate a series or parallel system using component tangent planes.

All components use the same complete stochastic model and Nataf transform. Homogeneous nested series/parallel systems are flattened; mixed topologies are rejected. Use original-system Monte Carlo for general topologies.

Parameters:

system (SeriesSystem or ParallelSystem) – System failure event.
stochastic_model (StochasticModel) – Shared variables, constants and dependence model.
analysis_options (AnalysisOptions, optional) – Component FORM settings. DDM gradients must use full model ordering.
maxpts (int, optional) – Maximum integration points per multivariate normal CDF call.
abseps (float, optional) – Requested absolute and relative integration tolerances. These are numerical targets, not certified error bounds or FORM model errors.
releps (float, optional) – Requested absolute and relative integration tolerances. These are numerical targets, not certified error bounds or FORM model errors.

component_results#

Component names mapped to completed Form objects (beta, alpha, design points and convergence residuals).

Type:: dict

correlation#

Correlation of linearized normal scores, alpha @ alpha.T. This is neither the physical-variable nor binary-failure correlation matrix.

Type:: ndarray

bounds#

Ditlevsen bounds for a series system; marginal/Frechet bounds for a parallel system. These bound the linearized event only.

Type:: tuple

intersections#

Pairwise failure probabilities of the component tangent planes.

Type:: ndarray

Notes

Exact up to integration error for affine limit states in standard normal space. Nonlinear components remain first-order approximations, and FORM can find a local rather than global design point. Normal integration may vary between runs; tight tolerances do not certify rare-tail accuracy.

Methods

`getBeta`	Return -Phi^-1(Pf), the equivalent system reliability index.
`getFailure`	Return the system FORM probability after a successful run.
`init_run`	Initialise the Nataf transformation before the analysis loop.
`run`	Run each unique component once, then integrate the system event.
`showResults`	Print the approximation and bounds for its linearized event.

run()[source]#: Run each unique component once, then integrate the system event.

getFailure()[source]#: Return the system FORM probability after a successful run.

getBeta()[source]#: Return -Phi^-1(Pf), the equivalent system reliability index.

showResults()[source]#: Print the approximation and bounds for its linearized event.

init_run()#

Initialise the Nataf transformation before the analysis loop.

Computes the modified (Nataf) correlation matrix and its factorisation. Must be called at the start of every run() method in subclasses.