Dane Sabo
ed59b30dd0
D Presentations/ERLM/bouncing_ball_hybrid.png A Presentations/ERLM/images/4_research_approach/phase_portrait_sg1.png A Presentations/ERLM/images/4_research_approach/two_loop.png A Presentations/ERLM/images/7_broader_impacts/billion.jpg M Presentations/ERLM/main.aux M Presentations/ERLM/main.fdb_latexmk M Presentations/ERLM/main.fls M Presentations/ERLM/main.log
151 lines
5.0 KiB
Julia
151 lines
5.0 KiB
Julia
using ReachabilityAnalysis
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using Plots
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"""
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Two-Loop Reactor: Formal Reachability Analysis with SG1 Efficiency Uncertainty
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Attempt #2: Using LGG09 algorithm which doesn't require @taylorize
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This uses zonotope overapproximation instead of Taylor models.
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"""
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println("=== Two-Loop Reactor: Formal Reachability (LGG09) ===\n")
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# Constants from Python script
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const C_0 = 33.33 # Base Heat Capacity [%-sec/°F]
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const τ_0 = 0.75 * C_0 # Base Time Constant [sec]
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const μ = 0.6 # Fixed reactor water mass fraction
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const P_r = 100.0 # Reactor power
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const Q2 = 50.0 # SG2 heat removal (KNOWN)
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# System parameters
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C_r = μ * C_0
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C_sg = (1 - μ) * C_0 / 2
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W = C_0 / (2 * τ_0)
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println("=== Parameters ===")
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println("C_0 = $C_0, τ_0 = $τ_0, μ = $μ")
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println("C_r = $C_r, C_sg = $C_sg, W = $W")
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println("P_r = $P_r, Q2 = $Q2")
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# Initial conditions (non-equilibrium)
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const T_hot_0 = 455.0
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const T_cold1_0 = 450.0
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const T_cold2_0 = 450.0
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# Q1 uncertainty range
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const Q1_min = 45.0
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const Q1_max = 55.0
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println("\n=== Q1 Uncertainty ===")
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println("Q1 ∈ [$Q1_min, $Q1_max]")
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# Define system WITHOUT @taylorize (for LGG09 algorithm)
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# Treat Q1 as 4th state with Q̇1 = 0
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function two_loop_with_Q1!(dx, x, p, t)
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T_hot = x[1]
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T_cold1 = x[2]
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T_cold2 = x[3]
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Q1 = x[4]
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# Energy balances
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dx[1] = (P_r - W * (T_hot - T_cold1) - W * (T_hot - T_cold2)) / C_r
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dx[2] = (W * (T_hot - T_cold1) - Q1) / C_sg
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dx[3] = (W * (T_hot - T_cold2) - Q2) / C_sg
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dx[4] = 0.0 # Q1 is constant uncertain parameter
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return dx
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end
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# Initial set
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X0 = Hyperrectangle(
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low=[T_hot_0 - 0.1, T_cold1_0 - 0.1, T_cold2_0 - 0.1, Q1_min],
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high=[T_hot_0 + 0.1, T_cold1_0 + 0.1, T_cold2_0 + 0.1, Q1_max]
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)
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println("\n=== Initial Set ===")
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println("X0 = Hyperrectangle(4D)")
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# Create IVP
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prob = @ivp(x' = two_loop_with_Q1!(x), dim: 4, x(0) ∈ X0)
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println("\n=== Solving with LGG09 (Zonotope) ===")
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println("This uses zonotope overapproximation...")
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# Try LGG09 algorithm (doesn't require @taylorize)
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try
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sol = solve(prob, T=30.0, alg=LGG09(δ=0.1))
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println("✓ Success! Computed $(length(sol)) reach sets")
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# Plot results
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p1 = plot(sol, vars=(0, 1),
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xlabel="Time (s)", ylabel="T_hot (°F)",
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title="Hot Leg Temperature",
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lw=0.5, alpha=0.6, color=:red, lab="Reach sets")
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p2 = plot(sol, vars=(0, 2),
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xlabel="Time (s)", ylabel="T_cold1 (°F)",
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title="Cold Leg 1 (SG1 - Uncertain)",
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lw=0.5, alpha=0.6, color=:blue, lab="Reach sets")
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p3 = plot(sol, vars=(0, 3),
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xlabel="Time (s)", ylabel="T_cold2 (°F)",
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title="Cold Leg 2 (SG2 - Known)",
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lw=0.5, alpha=0.6, color=:green, lab="Reach sets")
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p4 = plot(sol, vars=(2, 1),
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xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
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title="Phase Portrait",
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lw=0.5, alpha=0.6, color=:purple, lab="Reach sets")
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plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
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plot_title="Formal Reachability (LGG09): Q1 ∈ [$Q1_min, $Q1_max]")
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savefig(plot_combined, "two_loop_reachability_lgg09.png")
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println("\nSaved: two_loop_reachability_lgg09.png")
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catch e
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println("❌ LGG09 failed: $e")
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println("\nTrying GLGM06 instead...")
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try
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sol = solve(prob, T=30.0, alg=GLGM06(δ=0.1))
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println("✓ Success with GLGM06! Computed $(length(sol)) reach sets")
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# Plot results
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p1 = plot(sol, vars=(0, 1),
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xlabel="Time (s)", ylabel="T_hot (°F)",
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title="Hot Leg Temperature",
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lw=0.5, alpha=0.6, color=:red, lab="Reach sets")
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p2 = plot(sol, vars=(0, 2),
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xlabel="Time (s)", ylabel="T_cold1 (°F)",
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title="Cold Leg 1 (SG1 - Uncertain)",
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lw=0.5, alpha=0.6, color=:blue, lab="Reach sets")
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p3 = plot(sol, vars=(0, 3),
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xlabel="Time (s)", ylabel="T_cold2 (°F)",
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title="Cold Leg 2 (SG2 - Known)",
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lw=0.5, alpha=0.6, color=:green, lab="Reach sets")
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p4 = plot(sol, vars=(2, 1),
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xlabel="T_cold1 (°F)", ylabel="T_hot (°F)",
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title="Phase Portrait",
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lw=0.5, alpha=0.6, color=:purple, lab="Reach sets")
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plot_combined = plot(p1, p2, p3, p4, layout=(2, 2), size=(1400, 1000),
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plot_title="Formal Reachability (GLGM06): Q1 ∈ [$Q1_min, $Q1_max]")
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savefig(plot_combined, "two_loop_reachability_glgm06.png")
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println("\nSaved: two_loop_reachability_glgm06.png")
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catch e2
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println("❌ GLGM06 also failed: $e2")
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println("\n=== Both algorithms failed ===")
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println("The system may be too nonlinear for these approximation methods.")
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println("\nParameter sweep (our previous approach) may be the most practical")
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println("method for this system, even if it's not formally reachability analysis.")
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end
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end
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println("\n✓ Complete!")
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