UncertaintyQuantification.jl

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Power Spectral Density Functions ​

Construction and evaluation of different Power Spectral Density (PSD) functions. Correpsonding theory and literature can be found here Semi-empirical-PSD-functions.

Index ​

Types of PSD functions ​

UncertaintyQuantification.CloughPenzien Method
julia
CloughPenzien(ω::AbstractVector{<:Real}, S_0::Real, ω_f::Real, ζ_f::Real, ω_g::Real, ζ_g::Real)

Constructs a CloughPenzien instance representing a power spectral density function with the given parameters.

Arguments / Parameters

  • ω::AbstractVector{<:Real}: A vector of angular frequencies.

  • S_0::Real: A scaling factor.

  • ω_f::Real: Frequency parameter for the first oscillator.

  • ζ_f::Real: Damping ratio for the first oscillator.

  • ω_g::Real: Frequency parameter for the second oscillator.

  • ζ_g::Real: Damping ratio for the second oscillator.

Returns

A discretized CloughPenzien power spectral density function specified by given arguments (parameters).

Example

julia
w = 0:0.1:10
S_0 = 1.0
ω_f = 2.0
ζ_f = 0.05
ω_g = 3.0
ζ_g = 0.1
cp_psd = CloughPenzien(w, S_0, ω_f, ζ_f, ω_g, ζ_g)

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UncertaintyQuantification.KanaiTajimi Method
julia
KanaiTajimi(ω::AbstractVector{<:Real}, S_0::Real, ω_0::Real, ζ::Real) -> KanaiTajimi

Constructs a KanaiTajimi instance representing a power spectral density function with the given parameters.

Arguments

  • ω::AbstractVector{<:Real}: A vector of angular frequencies.

  • S_0::Real: A scaling factor.

  • ω_0::Real: Natural frequency of the oscillator.

  • ζ::Real: Damping ratio of the oscillator.

Returns

A discretized KanaiTajimi power spectral density function specified by given arguments (parameters).

Example

julia
w = 0:0.1:10
S_0 = 1.0
ω_0 = 2.0
ζ = 0.05
kt = KanaiTajimi(w, S_0, ω_0, ζ)

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UncertaintyQuantification.ShinozukaDeodatis Method
julia
ShinozukaDeodatis(ω::AbstractVector{<:Real}, σ::Real, b::Real)

Constructs a ShinozukaDeodatis instance representing a power spectral density function with the given parameters.

Arguments

  • ω::AbstractVector{<:Real}: A vector of angular frequencies.

  • σ::Real: A hyperparamter related to the variance of the stochastic process.

  • b::Real: A parameter related to the correlation length of the stochastic process.

Returns

A discretized ShinozukaDeodatis instance with the power spectral density function specified by given arguments (parameters).

Example

julia
w = 0:0.1:10
σ = 1.0
b = 0.5
sd = ShinozukaDeodatis(w, σ, b)

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UncertaintyQuantification.EmpiricalPSD Type
julia
EmpiricalPSD(ω::AbstractVector{<:Real}, p::AbstractVector{<:Real}) -> EmpiricalPSD

Constructs an EmpiricalPSD instance with the given angular frequencies and manually provided power spectral density values.

Arguments

  • ω::AbstractVector{<:Real}: A vector of angular frequencies.

  • p::AbstractVector{<:Real}: A vector of power spectral density values corresponding to the frequencies in ω.

Returns

A discretized EmpiricalPSD instance with manually pre-specified provided power spectral density values.

Example

julia
w = 0:0.1:10
p_values = rand(length(w))  # Example empirical PSD values
emp_psd = EmpiricalPSD(w, p_values)

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