Specifying a reliability model

An analysis has three parts: a probability model for inputs, a limit-state function for the event, and an algorithm with its options. Keep physical units and the reference period in the model description: PySTRA does not infer them.

Name inputs explicitly

Variable and constant names must match the limit-state function’s arguments. Most PySTRA marginal constructors take the physical mean and standard deviation, or instead their native parameters as keywords, such as Gumbel("Q", loc=8.9, scale=1.56). ScipyDist wraps an already parameterized SciPy distribution. Check the relevant distribution’s signature. Every distribution also provides tail functions (sf, isf, logcdf and logsf) that keep very small probabilities accurate. A custom distribution should provide them too; see Working at high reliability.

import pystra as ra

def limit_state(R, S, resistance_scale):
    return resistance_scale * R - S

model = ra.StochasticModel()
model.add_variable(ra.Normal("R", 10.0, 1.0))
model.add_variable(ra.Normal("S", 5.0, 1.0))
model.add_variable(ra.Constant("resistance_scale", 1.0))
response = ra.LimitState(limit_state)
result = ra.FORM(model, response).run()
assert result.converged

Here R and S use the same force unit. A negative limit state means failure. Write elementwise NumPy expressions so the function also accepts batches of input values; avoid Python if statements on arrays. The Direct differentiation of the limit state example explains the analytical-gradient return contract. A limit state can also wrap an external solver and evaluate one point at a time; see Reliability with an external finite-element model.

Specify dependence before choosing a transformation

Independent inputs are the simplest starting point. A marginal distribution for each input and a correlation matrix alone do not specify every possible joint distribution. The traditional Gaussian/Nataf route interprets a CorrelationMatrix as physical Pearson correlations; its modified normal-space correlations are computed internally.

For a different dependence model, supply a complete JointDistribution with an explicit copula. Copula parameters and physical Pearson correlations are different inputs. See Copulas and isoprobabilistic transformations for supported transformations and conditioning order, and preserve variable order when supplying matrices, samples and gradients.

Check the physical event

Evaluate a safe and a failed case by hand. Record how load statistics relate to annual, point-in-time or maximum-over-period events. For systems, write the component events and their topology before selecting a solver. For load combinations, retain the assumptions connecting leading and companion actions.

Continue: Comparing FORM, SORM and simulation · Models and analysis options · Distributions and dependence · Structural reliability fundamentals