PCE

PCE

This submodule provides all the functionality for building a PCE surrogate from an FEM sample obtained through the Sampling submodule.

PolyChaosExpansion{T<: Real}

Struct for holding the PCE surrogate

PolyChaosExpansion(sample::UnivariateFEMSample{T};polynomials::AbstractCanonicalOrthoPoly = GaussOrthoPoly(8),vector_distribution::UnivariateDistribution=Normal(0,1)) where T<:Real

Represent the sampled random variable $Y$(sample) as a Polynomial Chaos Expansion (PCE) surrogate $Y = ∑_{i∈ℕ} cᵢΨᵢ(𝐗)$ with:

• $Ψᵢ$ being a polynomial basis function from polynomials, default gaussion/probabilists' Hermite of degree 8
• $𝐗$ a random vector of distribution vector_distribution, default $𝐗∼𝒩(0,1)$,
• $cᵢ$ the PCE coefficients to be calculated.

compute_statistics(sample::UnivariateFEMSample{T}) where {T}

Compute empirical mean and standard deviation for the given sample

compute_statistics(pce::PolyChaosExpansion)

Compute mean and standard deviation of the given PCE

cov(sensor_set::EqualSensorSet{T})::T where T

Returns the cov matrix of the sensor_set. For equal sensors this is a diagonal matrix containing the common sensor variance.

cov(pce::PolyChaosExpansion{T})::AbstractMatrix{T} where T <: Real

Compute cov matrix of the given PCE

mean(pce::PolyChaosExpansion{T})::AbstractVector{T} where T<:Real

Compute mean values of the given PCE