Reliability of a system refers to the assessment of its probability of failure (i.e the system no longer satisfies some performance measures), given the model uncertainty in the structural, environmental and load parameters. Given a vector of random variables X = [X1, X2, …, Xn]T ∈ 𝒟X ⊂ ℝn, where 𝒟 is the domain of interest and fX(x) is its joint probability density function then, the probability that the system will fail is defined as
Pf = ℙ(g(X) ≤ 0) = ∫𝒟ffX(x)dx = ∫{X : g(X) ≤ 0}fX(x)dx
where g(X) is the so-called performance function and 𝒟f = {X : g(X) ≤ 0} is the failure domain. The reliability problem is often formulated in the standard normal space U ∼ 𝒩(0, In), which means that a nonlinear isoprobabilistic transformation from the generally non-normal parameter space X ∼ fX( ⋅ ) to the standard normal space is required (see the :py.transformations module). The performance function in the standard normal space is denoted G(U). :py.UQpy does not require this transformation and can support reliability analysis for problems with arbitrarily distributed parameters.
This module contains functionality for all reliability methods supported in :pyUQpy. The module currently contains the following classes:
.TaylorSeries: Class to perform reliability analysis using First Order Reliability Method (FORM), Inverse First Order Reliability Method (InverseFORM) and Second Order Reliability Method (SORM)..SubsetSimulation: Class to perform reliability analysis using subset simulation.
Subset Simulation <subset> Taylor Series <taylor_series>