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| Author | SHA1 | Date |
|---|---|---|
Will King
|
9a271d90de | 2 years ago |
|
Will King
|
e6d2f7f93c | 2 years ago |
youainti
|
c9f710b724 | 3 years ago |
|
will king
|
e22fac4ce0 | 3 years ago |
|
will king
|
4719a8504c | 3 years ago |
|
will king
|
48419a530d | 3 years ago |
@ -0,0 +1,87 @@
|
||||
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@ -0,0 +1,70 @@
|
||||
# Thoughts on modelling
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||||
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Initial plan is to handle just two operators.
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## Environment
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### Transition function
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#### Debris
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- Currently using a decay formulation for debris.
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- Probably better to use a mass conversion from satellite -> debris
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- This would have to be a stochastic approach to handle satellite destruction.
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- I envision it would be better because it would represent how much debris
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is created better and would easigly lend itself to a size based debris
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approach.
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- It doesn't represent slow degradation well though. It does handle destructive collisions better.
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- Maybe I can ignore satellite on satellite collisions in an initial model because it is the lowest.
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#### Satellite Stocks
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- Probably just fine as is.
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### Market
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||||
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- Current plan is to use a cournot market approach with inverse demand: \[ P = a-bQ \]
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- Need to look up dynamic cournot market lit.
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||||
## Operator's Problem
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||||
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- Restrict policy to integers (e.g. 1:10)
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- Use a symmetric policy and value function for each operator.
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### Operator State
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- Initally I am going to track one type of debris, the operator's fleet size, and the number of satellites in all other fleets.
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## Social Planner's Problem
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I see two different classes of problems that the Social Planner could face, and both could take various forms.
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Here are the two areas and some variations:
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1. Maximizing long term expected utility/value
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a. Maximize expected value
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b. Preserve value x% of the time
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2. Preserving the resource (manage debris levels)
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a. Keep debris below a threshold.
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b. Keep debris from growing faster than Y rate.
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c. Keep kessler syndrome from occuring in Z% over ZZ periods.
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The first case "should" subsume the second in that minimal debris over a long period should permit more earnings.
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But, if the time-discounting factor is low enough, this might not be the case.
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And this brings up a big issue in that the discount factor of the Social Planner and the Operators might differ
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a lot.
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The question it poses is "Should we use this resource as we best see fit or preserve it for our descendants?"
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## modelling state
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I need to track all constellation sizes and debris size.
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# Thoughts on Interpretation etc,
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One option would be to take derivatives over the value function to get
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Benefit functions. Look at when it is positive etc.
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Another thing to do would be to construct debris tracks.
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Another would be to search for steady states.
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I could compare different versions of the social planner's problem to see
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how they differ, i.e. in debris dynamics etc.
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||||
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@ -0,0 +1,291 @@
|
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using LinearAlgebra
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using Distributions
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using StatsFuns
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using Plots
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abstract type DestructionProbability end
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struct LinearProbability <: DestructionProbability
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spontaneous
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intra_constellation
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inter_constellation
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debris
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end
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function (lp::LinearProbability)(Sᵢ, S, D,)
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min(1,max(0,
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lp.spontaneous + lp.intra_constellation * Sᵢ + lp.inter_constellation * (S-Sᵢ) + lp.debris * D)
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)
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end
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function individual_loss(Sᵢ, S, D,n=1,return_prob=false)
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#=
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This function simulates how many satellites will be lost
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from a given constellation.
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TODO: Requires calibration of some sort
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=#
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β₀ = 3e-4 #probability of spontaneous destruction
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β₁ = 1e-6 #proability of collision with satellite in same constellation
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β₂ = 1e-5 #probability of collision with satellite in different constellation
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β₃ = 1e-4 #probability of collision with debris
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#linear probability (with constraints)
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p = min(1,max(0,β₀ + β₁ * Sᵢ + β₂ * (S-Sᵢ) + β₃ * D))
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#p = logistic(β₀ + β₁ * Sᵢ + β₂ * (S-Sᵢ) + β₃ * D)
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dist = Binomial(Sᵢ, p)
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draw = rand(dist)
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if return_prob
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return draw, p
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else
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return draw
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end
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end
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function debris_transition(D,S⃗, Y⃗, X⃗, δ=0.005, Γ=0.5)
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#δ: 1/δ year decay rate
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#Γ: proportion of the mass of the satellite that is released into orbit during launch
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#new debris released equals the debris lost to deorbit + debris generated by collisions + debris due to launches
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new_debris = (1-δ) * D .+ sum(Y⃗) .+ Γ*sum(X⃗)
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return new_debris
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end
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function stocks_transition(S⃗, Y⃗, X⃗)
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return S⃗ .+ X⃗ .- Y⃗
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end
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function overall_losses(S⃗, D)
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#=
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Simulate the losses for each constellation
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=#
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||||
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individual_outcomes = [ individual_loss(s, sum(S⃗),D,1,true) for s in S⃗ ]
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losses = []
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||||
prob_distruction = []
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||||
for (loss,prob) in individual_outcomes
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append!(losses,loss)
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append!(prob_distruction,prob)
|
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end
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return losses,prob_distruction
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||||
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||||
end
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||||
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||||
# The demand function for the market
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||||
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||||
function inverse_demand_cournot(S⃗,A=100)
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A - sum(S⃗)
|
||||
end
|
||||
|
||||
function profit_function(s,x,C_operation,C_launch,T_launch, T_operation,Price)
|
||||
#=
|
||||
The profit function each participant recieves
|
||||
Includes place for taxes and costs.
|
||||
=#
|
||||
(Price-T_operation-C_operation)*s - (C_launch + T_launch)*x
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
#Get histogram of loss numbers per 10_000
|
||||
histogram(
|
||||
[sum(individual_loss(33,67,500,10_000)) for i in 1:10000]
|
||||
,bins=range(0,200,length=201)
|
||||
,label="Satellites lost per 10,000"
|
||||
)
|
||||
|
||||
|
||||
|
||||
#=
|
||||
Basic simulations
|
||||
1. What happens when both participants always launch a single satellite?
|
||||
2. What happens when a single participant always launches a single satellite?
|
||||
3. What happens when both participants maintain the cournot equilibrium?
|
||||
=#
|
||||
|
||||
#Specify policies
|
||||
|
||||
abstract type Policy end
|
||||
#=
|
||||
Represent any policy as a struct holding parameters that can be called with
|
||||
state variables to get the chosen policy.
|
||||
=#
|
||||
struct ConstantLaunchRatePolicy <: Policy
|
||||
#=
|
||||
Operator launches fixed number of satellites per turn
|
||||
=#
|
||||
rate_numerator
|
||||
end
|
||||
(p::ConstantLaunchRatePolicy)(s,S,D) = p.rate_numerator
|
||||
|
||||
struct SustainmentPolicy <: Policy
|
||||
#=
|
||||
Operator launches enough satellites to maintain a certain size
|
||||
=#
|
||||
level
|
||||
end
|
||||
(p::SustainmentPolicy)(s,S,D) = max(0,p.level - s)
|
||||
|
||||
struct simulation_result
|
||||
state_path
|
||||
profit_path
|
||||
destruction_events
|
||||
launch_choices
|
||||
destruction_probabilities
|
||||
end
|
||||
|
||||
|
||||
function simulate_system(policies,starting_state,n)
|
||||
#=
|
||||
Given a set of policies and a starting state, calculate n steps ahead.
|
||||
=#
|
||||
|
||||
state = fill(starting_state,n)
|
||||
profit_path = []
|
||||
decay_events=[]
|
||||
launch_choices = []
|
||||
destruction_probabilities = []
|
||||
|
||||
for i in 2:n
|
||||
current_state = state[i-1]
|
||||
S⃗ = current_state[2:end]
|
||||
D = current_state[1]
|
||||
|
||||
#Calculate actions from policies
|
||||
X = [policy(s,sum(S⃗),D) for (s,policy) in zip(S⃗,policies)]
|
||||
push!(launch_choices, X)
|
||||
|
||||
#Information generation
|
||||
price = inverse_demand_cournot(S⃗,10000)
|
||||
push!(profit_path,[profit_function(s,x,4,100,0, 0,price) for (s,x) in zip(S⃗,X) ])
|
||||
|
||||
#calculate transition to next state
|
||||
#loss of satellites
|
||||
(Y⃗,prob_distruction) = overall_losses(S⃗, D)
|
||||
push!(decay_events,Y⃗)
|
||||
push!(destruction_probabilities, prob_distruction)
|
||||
|
||||
#debris
|
||||
new_debris = debris_transition(D, S⃗, Y⃗, X,0.05, )
|
||||
|
||||
#stocks
|
||||
new_stocks = stocks_transition(S⃗,Y⃗,X)
|
||||
|
||||
#update vector of states
|
||||
next_state = [new_debris,new_stocks...]
|
||||
|
||||
#update vector
|
||||
state[i] = next_state
|
||||
println(current_state,next_state)
|
||||
end
|
||||
|
||||
k = length(starting_state)
|
||||
|
||||
return simulation_result(
|
||||
[ [v[i] for v in state] for i in 1:k], #states
|
||||
[ [v[i] for v in profit_path] for i in 1:3 ], #profit paths
|
||||
[ [v[i] for v in decay_events ] for i in 1:3], #counts of satellite distructions
|
||||
[ [v[i] for v in launch_choices ] for i in 1:3], #counts of satellite launches
|
||||
[ [v[i] for v in destruction_probabilities] for i in 1:3]
|
||||
)
|
||||
end
|
||||
|
||||
#setup state
|
||||
n=2000
|
||||
starting_state = [10.0,0,0,0]
|
||||
policies = [SustainmentPolicy(x) for x in 25:5:35]
|
||||
|
||||
simulation = simulate_system(policies,starting_state,n)
|
||||
|
||||
|
||||
plot(
|
||||
simulation.state_path[2:4]
|
||||
,labels=["stocks 1" "stocks 2" "Stocks 3"]
|
||||
)
|
||||
|
||||
plot(
|
||||
simulation.state_path[1]
|
||||
,labels="debris"
|
||||
)
|
||||
|
||||
|
||||
plot(
|
||||
simulation.state_path[1][3:end] .- simulation.state_path[1][2:end-1]
|
||||
,labels="debris growth"
|
||||
)
|
||||
|
||||
plot( simulation.state_path
|
||||
,labels=["debris" "stocks 1" "stocks 2" "Stocks 3"]
|
||||
)
|
||||
|
||||
plot(simulation.profit_path)
|
||||
|
||||
bar(
|
||||
simulation.destruction_events
|
||||
,layout = grid(3,1)
|
||||
,legend=:none
|
||||
)
|
||||
|
||||
plot(
|
||||
simulation.launch_choices
|
||||
,layout = grid(3,1)
|
||||
,legend=:none
|
||||
)
|
||||
|
||||
plot(simulation.destruction_probabilities)
|
||||
#= Notes
|
||||
With the (maintain equilibrium) approach, the probability
|
||||
of distruction rises to 100% within a certain amount of time.
|
||||
=#
|
||||
|
||||
bar(
|
||||
[simulation.launch_choices, -1 .* simulation.destruction_events]
|
||||
,layout = grid(3,1)
|
||||
,ylims = (-25,25)
|
||||
#,label = ["Launches 1" "Launches 2" "Launches 3" "Destruction 1" "Destruction 2" "Destruction 3"]
|
||||
, legend = :none
|
||||
, title = ["Operator 1" "Operator 2" "Operator 3"]
|
||||
#,yaxis = (-20:5:20)
|
||||
)
|
||||
|
||||
|
||||
#Many simulations
|
||||
sims = [simulate_system(policies,starting_state,n) for x in 1:1000]
|
||||
|
||||
|
||||
|
||||
state_plots = []
|
||||
for sim in sims
|
||||
push!(state_plots,plot(sim.state_path[2:end]))
|
||||
end
|
||||
|
||||
state_plots[2]
|
||||
|
||||
for p in state_plots
|
||||
display(p)
|
||||
end
|
||||
|
||||
|
||||
plot(sim1.state_path[2:end], color=:skyblue, alpha=0.5)
|
||||
|
||||
|
||||
arr = [sim.state_path[2:end] for sim in sims]
|
||||
plot(arr, color=:blue, alpha=0.01, legend=:none)
|
||||
|
||||
|
||||
debarr = [ sim.state_path[1] for sim in sims]
|
||||
plot(debarr, color=:blue, alpha=0.05, legend=:none)
|
||||
|
||||
profitarr = [sim.profit_path for sim in sims]
|
||||
plot(profitarr, color=:blue, alpha=0.01, legend=:none)
|
||||
|
||||
|
||||
# Plot out probability of distruction
|
||||
@ -0,0 +1,25 @@
|
||||
FROM debian:latest
|
||||
MAINTAINER youainti@youainti.com
|
||||
RUN apt update
|
||||
RUN apt install -y vim
|
||||
RUN apt install -y curl
|
||||
|
||||
#add user
|
||||
RUN useradd julia
|
||||
USER julia
|
||||
WORKDIR /home/julia
|
||||
#setup basic files
|
||||
RUN touch .profile
|
||||
RUN touch .bashrc
|
||||
|
||||
#install julia
|
||||
RUN curl -fsSL https://install.julialang.org > juliaup_installer.sh
|
||||
RUN sh juliaup_installer.sh -y
|
||||
RUN rm juliaup_installer.sh
|
||||
|
||||
|
||||
#install pluto
|
||||
RUN ~/.juliaup/bin/julia -e 'using Pkg; Pkg.add("Pluto")'
|
||||
|
||||
#entrypoint
|
||||
CMD ~/.juliaup/bin/julia -e 'using Pluto; Pluto.run(;host="0.0.0.0")'
|
||||
Loading…
Reference in New Issue