UncertaintyQuantification.jl

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Reliability ​

Index ​

Types ​

UncertaintyQuantification.FORM Type
julia
FORM(n::Integer=10,tol::Real=1e-3,fdm::FiniteDifferencesMethod=CentralFiniteDifferences(3))

used to perform the first order reliability method using the HLRF algorithm with n iterations and tolerance tol. Gradients are estimated through fdm.

References

[13]

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UncertaintyQuantification.DoubleLoop Type
julia
DoubleLoop(lb::AbstractSimulation, ub::AbstractSimulation)

Used to estimate imprecise reliability with the double loop Monte Carlo method.

Wraps two simulation objects — one for lower-bound (lb) and one for upper-bound (ub).

The two simulations can differ in simulation type, complexity, or accuracy settings, since estimating the lower bound often requires more simulation effort.

This approach runs an optimisation loop over interval parameters (outer loop) and computes reliability bounds in an inner loop using the lb and ub simulation methods.

Use DoubleLoop(sim::AbstractSimulation) for creating a DoubleLoop with same simulation method for both bounds.

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UncertaintyQuantification.RandomSlicing Type
julia
RandomSlicing(lb::AbstractSimulation, ub::AbstractSimulation)

Used to estimate imprecise reliability with random slicing Monte Carlo method, sometimes known as interval Monte Carlo.

Wraps two simulation objects — one for lower-bound (lb) and one for upper-bound (ub).

The two simulations can differ in simulation type, complexity, or accuracy settings, since estimating the lower bound often requires more simulation effort.

In this approach, the lb and ub simulation methods generate random intervals from the imprecise variables. These intervals are then propagated through the model via optimisation-based interval propagation, yielding lower and upper bounds on the reliability estimate.

Use RandomSlicing(sim::AbstractSimulation) for creating a RandomSlicing with same simulation method for both bounds.

References

[21]

source

Methods ​

UncertaintyQuantification.probability_of_failure Method
julia
probability_of_failure(models::Union{Vector{<:UQModel},UQModel},performance::Function),inputs::Union{Vector{<:UQInput},UQInput},sim::FORM)

Perform a reliability analysis using the first order reliability method (FORM), see FORM. Returns the estimated probability of failure pf, the reliability index β and the design point dp.

Examples

pf, β, dp = probability_of_failure(model, performance, inputs, sim)
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UncertaintyQuantification.probability_of_failure Method
julia
probability_of_failure(models::Union{Vector{<:UQModel},UQModel},performance::Function),inputs::Union{Vector{<:UQInput},UQInput},sim::AbstractMonteCarlo)

Perform a reliability analysis with a standard Monte Carlo simulation. Returns the estimated probability of failure pf, the standard deviation σ and the DataFrame containing the evaluated samples. The simulation sim can be any instance of AbstractMonteCarlo.

Examples

pf, σ, samples = probability_of_failure(model, performance, inputs, sim)
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UncertaintyQuantification.probability_of_failure Method
julia
probability_of_failure(
    models::Union{Vector{<:UQModel}, UQModel},
    performance::Function,
    inputs::Union{Vector{<:UQInput}, UQInput},
    dl::DoubleLoop
)

Perform an imprecise reliability analysis using the double loop Monte Carlo method.

The inputs must include at least one imprecise variable.

Returns

  • pf_bounds: An Interval giving the lower and upper bounds on the probability of failure.

  • result_lb: The outputs of the reliability simulation that achieved the lower bound.

  • result_ub: The outputs of the reliability simulation that achieved the upper bound.

If the lower and upper bounds are equal, returns only the scalar probability of failure.

See DoubleLoop for details of the random slicing configuration.

source
UncertaintyQuantification.probability_of_failure Method
julia
probability_of_failure(
    models::Union{Vector{<:UQModel}, UQModel},
    performance::Function,
    inputs::Union{Vector{<:UQInput}, UQInput},
    rs::RandomSlicing
)

Perform an imprecise reliability analysis using the random slicing Monte Carlo method

The inputs must include at least one imprecise variable.

Returns

  • pf_bounds: An Interval giving the lower and upper bounds on the probability of failure.

  • result_lb: The outputs of the reliability simulation that achieved the lower bound.

  • result_ub: The outputs of the reliability simulation that achieved the upper bound.

See RandomSlicing for details of the random slicing configuration.

source