ResilienceDecisionMaking.jl

This package contains the code and examples for the resilience decision-making method presented in Salomon et al. (2022).

Installation

The package is registered in the Julia General registry and can be installed from Pkg with

julia ] add ResilienceDecisionMaking

Getting started

The main interface of the resilience decision making method is the grid_search method which returns the computed resilience values as a Dict of the endowment configurations, the coefficient of variation and the pareto front. To explain we use the example of the multistage high-speed axial compressor as presented in the paper. First, we define a system representation in this case the adjacency matrix of the system as

julia A = [ 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ]

We further define the maximum values of the endowment configurations we want to explore and the time as a tuple of minimum and maximum as well as the number of time steps

```julia endowments = [20, 20, 20, 20]

t = (0.0, 10.0) tₙ = 200 ```

Next, we define a function failure_rates which returns the current failure rates of all components for all time steps times for the current endowment configuration η

```julia λ = 0.8

function failure_rates(times::Vector{T} where {T<:Real}, η::Vector{T} where {T<:Integer}) rates = [ (λ - 0.03 * η[1]) * ones(2)..., (λ - 0.03 * η[2]), (λ - 0.03 * η[3]), (λ - 0.03 * η[4]) * ones(4)..., ] return hcat([rates for _ in 1:length(times)]...) end ```

Finally, we define the recovery behaviour of the components through the recovery! function. This function must update the components and recovery_times vectors in place (!) and return nothing. Note, that in this example recovery is independent of η. See the other demo example for how to use η to influence the recovery of components.

```julia r_max = 21

function recovery!(components, recoverytimes, η) for (i, (c, r)) in enumerate(zip(components, recoverytimes)) if ~c if r >= rmax - 11 components[i] = true recoverytimes[i] = 1 else recoverytimes[i] = recoverytimes[i] + 1 end end end

return nothing

end ```

Finally, we can run the grid_search where configurations are accepted if the resilience value is above α = 0.85. We also pass a structure function evaluating of the system is currently working (s-t-connectivity) and the number of samples (500) to use per resilience computation.

```julia α = 0.85

res, σ, front = gridsearch( A, endowments, t, tₙ, failurerates, recovery!, ResilienceDecisionMaking.stconnectivity([1, 3], [5, 6, 7, 8]), 500, α, true, # only return the "dominant" entries of the pareto front ) ```

References

Salomon, J., Behrensdorf, J., Winnewisser, N., Broggi, M., & Beer, M. (2022). Multidimensional resilience decision-making for complex and substructured systems. Resilient Cities and Structures, 1(3), 61-78, 10.1016/j.rcns.2022.10.005.