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
217 lines
7.4 KiB
Julia
217 lines
7.4 KiB
Julia
using ReachabilityAnalysis
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using Plots
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"""
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Two-Loop Reactor: Temperature Uncertainty Propagation
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Simple, clean approach:
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- Uncertainty ONLY in initial temperatures: T_hot, T_cold1, T_cold2
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- Everything else is FIXED: μ = 0.6, Q1 = 50, Q2 = 50, P_r = 100
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- T_avg is derived from the uncertain temperatures
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This shows how initial temperature measurement uncertainty propagates.
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"""
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println("=== Two-Loop Reactor: Initial Temperature Uncertainty ===\n")
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# ALL parameters are FIXED (no uncertainty)
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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 # FIXED reactor power
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const Q1 = 50.0 # FIXED SG1 heat removal
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const Q2 = 50.0 # FIXED SG2 heat removal
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# System parameters (all fixed)
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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("=== Fixed Parameters ===")
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println("C_0 = $C_0 %-sec/°F")
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println("τ_0 = $τ_0 sec")
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println("μ = $μ (FIXED)")
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println("P_r = $P_r (FIXED)")
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println("Q1 = $Q1 (FIXED)")
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println("Q2 = $Q2 (FIXED)")
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println("\nComputed:")
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println("C_r = $C_r")
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println("C_sg = $C_sg")
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println("W = $W")
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# Initial temperature uncertainty
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# Realistic: ±2°F measurement uncertainty
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const T_hot_nominal = 455.0
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const T_cold_nominal = 450.0
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const δT = 2.0 # ±2°F uncertainty
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println("\n=== Initial Temperature Uncertainty ===")
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println("T_hot ∈ [$(T_hot_nominal - δT), $(T_hot_nominal + δT)] °F")
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println("T_cold1 ∈ [$(T_cold_nominal - δT), $(T_cold_nominal + δT)] °F")
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println("T_cold2 ∈ [$(T_cold_nominal - δT), $(T_cold_nominal + δT)] °F")
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println("\nPhysical meaning: ±$δT°F measurement uncertainty")
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# Define system (no @taylorize, just plain function)
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function two_loop!(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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# Energy balances with FIXED parameters
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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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return dx
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end
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# Try using @taylorize for TMJets
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@taylorize function two_loop_taylor!(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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# Energy balances with FIXED parameters
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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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return dx
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end
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# Initial set: Box around nominal temperatures
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X0 = Hyperrectangle(
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low=[T_hot_nominal - δT, T_cold_nominal - δT, T_cold_nominal - δT],
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high=[T_hot_nominal + δT, T_cold_nominal + δT, T_cold_nominal + δT]
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)
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println("\n=== Attempting TMJets (Taylor Models) ===")
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println("This is FORMAL reachability analysis...")
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# Create IVP with @taylorize version
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prob = @ivp(x' = two_loop_taylor!(x), dim: 3, x(0) ∈ X0)
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try
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# Try TMJets - this should work since all parameters are constants!
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sol = solve(prob, T=30.0, alg=TMJets(abstol=1e-10, orderT=7, orderQ=2))
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println("✓ TMJets SUCCESS! Computed $(length(sol)) reach sets")
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println("\nThis is FORMAL reachability analysis using Taylor models!")
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# Plot results
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println("\n=== Creating Plots ===")
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# Plot 1: T_hot reach tube
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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, alpha=0.5, color=:red,
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lab="Reach tube")
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# Plot 2: T_cold1 reach tube
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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",
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lw=0, alpha=0.5, color=:blue,
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lab="Reach tube")
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# Plot 3: T_cold2 reach tube
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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",
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lw=0, alpha=0.5, color=:green,
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lab="Reach tube")
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# Plot 4: Phase portrait T_hot vs T_cold1
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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, alpha=0.5, color=:purple,
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lab="Reach tube")
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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: Initial Temperature Uncertainty ±$(δT)°F")
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savefig(plot_combined, "temp_uncertainty_reachability.png")
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println("Saved: temp_uncertainty_reachability.png")
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# Compute T_avg for each reach set
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println("\n=== Computing T_avg Reach Tube ===")
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times = Float64[]
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T_avg_min = Float64[]
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T_avg_max = Float64[]
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T_hot_vals = Float64[]
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T_cold1_vals = Float64[]
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T_cold2_vals = Float64[]
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for (i, reach_set) in enumerate(sol)
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if i % 5 == 0 # Sample every 5th set
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t = sup(reach_set.t_start)
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set = reach_set.X
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# Sample points from the set
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n_samples = 100
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T_avg_samples = Float64[]
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for _ in 1:n_samples
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pt = sample(set)
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T_h = pt[1]
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T_c1 = pt[2]
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T_c2 = pt[3]
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# Compute T_avg = μ*T_hot + (1-μ)*(T_cold1 + T_cold2)/2
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T_avg = μ * T_h + (1 - μ) * (T_c1 + T_c2) / 2
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push!(T_avg_samples, T_avg)
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if i == length(sol) # Store final points for phase portrait
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push!(T_hot_vals, T_h)
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push!(T_cold1_vals, T_c1)
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push!(T_cold2_vals, T_c2)
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end
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end
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push!(times, t)
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push!(T_avg_min, minimum(T_avg_samples))
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push!(T_avg_max, maximum(T_avg_samples))
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end
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end
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# Plot T_avg reach tube
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p_tavg = plot(times, T_avg_min, fillrange=T_avg_max,
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xlabel="Time (s)", ylabel="T_avg (°F)",
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title="Average Primary Temperature\n(Derived from uncertain T_hot, T_cold1, T_cold2)",
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fillalpha=0.5, color=:orange, lw=2,
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label="T_avg reach tube", legend=:topright,
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size=(1000, 700))
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savefig(p_tavg, "tavg_reachability.png")
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println("Saved: tavg_reachability.png")
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# Phase portrait: T_hot vs T_avg
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if length(T_hot_vals) > 0
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p_phase = scatter(T_avg_samples, T_hot_vals,
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xlabel="T_avg (°F)", ylabel="T_hot (°F)",
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title="Phase Portrait: T_hot vs T_avg\n(Final reachable set at t=30s)",
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markersize=3, alpha=0.5, color=:purple,
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label="Reachable points", legend=:topright,
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size=(1000, 900))
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savefig(p_phase, "phase_portrait_tavg.png")
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println("Saved: phase_portrait_tavg.png")
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end
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println("\n✓ Complete!")
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println("\n=== Results ===")
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println("This is FORMAL reachability analysis using Taylor models.")
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println("The reach tubes show ALL possible trajectories starting from")
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println("initial temperature uncertainty: T ∈ [T_nominal ± $(δT)°F]")
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println("\nFinal T_avg range: [$(round(minimum(T_avg_min), digits=1)), $(round(maximum(T_avg_max), digits=1))] °F")
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println("Initial uncertainty ±$(δT)°F → Final spread $(round(maximum(T_avg_max) - minimum(T_avg_min), digits=1))°F")
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catch e
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println("❌ TMJets failed: $e")
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println("\n=== Falling back to parameter sweep ===")
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# Fine parameter sweep as backup
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include("two_loop_fine_sweep.jl")
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end
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