pystra.reliability.line_sampling.LineSampling#

Use it: User guide · Worked example · Theory

class LineSampling(model, limit_state, *, options=None, form=None, rng=None)[source]#

Bases: _FORMReuse, AnalysisObject

Line Sampling (LS) reliability analysis.

Line Sampling exploits the important direction \(\boldsymbol{\alpha}\) obtained from FORM. For each of N random samples drawn uniformly in the (n-1)-dimensional hyperplane perpendicular to \(\boldsymbol{\alpha}\), a one-dimensional root-finding problem locates the limit-state surface along the parallel line.

The failure-probability estimate is

\[\hat{p}_f = \frac{1}{N} \sum_{i=1}^{N} \Phi(-c_i)\]

where \(c_i\) is the signed distance from the foot-point of sample i to the limit-state surface along \(\boldsymbol{\alpha}\), and \(\Phi\) is the standard normal CDF.

Parameters:

  • model (StochasticModel)

  • limit_state (LimitState)

  • options (SimulationOptions | None) – n_samples is the number of lines.

  • form (FORM | None) – A completed FORM analysis. If None, run() first runs FORM, with this analysis’s block size and transformation, to obtain the important direction \(\boldsymbol{\alpha}\) and the initial guess for the root search.

  • rng (int | integer | Sequence[int] | ndarray | SeedSequence | BitGenerator | Generator | None) – Random source; NumPy’s global generator is not used. A seed recreates the same stream on every run, a generator advances its own state, and None draws fresh entropy.

Notes

run() returns a SimulationResult; its diagnostics include the important direction. The line search is restricted to normal coordinates in [-37, 37], including correlated marginal coordinates for Nataf transformations. If that restriction truncates the scan and no crossing is found, an AnalysisError is raised; crossings beyond the representable scan are not assigned a probability.

References

Koutsourelakis, P. S., Pradlwarter, H. J., & Schuëller, G. I. (2004). Reliability of structures in high dimensions, Part I: algorithms and applications. Probabilistic Engineering Mechanics, 19(4), 409–417.

Methods

init_run

Initialize the model's isoprobabilistic transformation.

run

Run line sampling and return a SimulationResult.
property form: FORM | None#

The last FORM analysis; assigning None requests a fresh FORM each run.

run()[source]#

Run line sampling and return a SimulationResult.

Return type:

SimulationResult

init_run()#

Initialize the model’s isoprobabilistic transformation.

Uses the explicit copula or calibrates the legacy Gaussian Nataf correlation. Must be called at the start of every run() method in subclasses.

Return type:

None