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A题/数值分析检验/Response/1.md

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+{
+  "model_name": "MODEL_SPEC",
+  "version": "1.0",
+  "status": "frozen",
+  "states": [
+    { "name": "z", "unit": "dimensionless", "bounds": [0, 1], "description": "State of Charge" },
+    { "name": "v_p", "unit": "V", "bounds": [null, null], "description": "Polarization voltage" },
+    { "name": "T_b", "unit": "K", "bounds": [0, null], "description": "Battery temperature" },
+    { "name": "S", "unit": "dimensionless", "bounds": [0, 1], "description": "State of Health" },
+    { "name": "w", "unit": "dimensionless", "bounds": [0, 1], "description": "Radio tail activation level" }
+  ],
+  "inputs": [
+    { "name": "L", "unit": "dimensionless", "bounds": [0, 1], "description": "Screen brightness" },
+    { "name": "C", "unit": "dimensionless", "bounds": [0, 1], "description": "Processor load" },
+    { "name": "N", "unit": "dimensionless", "bounds": [0, 1], "description": "Network activity" },
+    { "name": "Ψ", "unit": "dimensionless", "bounds": [0, 1], "description": "Signal quality" },
+    { "name": "T_a", "unit": "K", "bounds": [null, null], "description": "Ambient temperature" }
+  ],
+  "parameters": [
+    { "name": "P_bg", "unit": "W", "description": "Background power" },
+    { "name": "P_scr0", "unit": "W", "description": "Screen baseline power" },
+    { "name": "k_L", "unit": "W", "description": "Screen scaling coefficient" },
+    { "name": "gamma", "unit": "dimensionless", "description": "Screen power exponent" },
+    { "name": "P_cpu0", "unit": "W", "description": "CPU baseline power" },
+    { "name": "k_C", "unit": "W", "description": "CPU scaling coefficient" },
+    { "name": "eta", "unit": "dimensionless", "description": "CPU power exponent" },
+    { "name": "P_net0", "unit": "W", "description": "Network baseline power" },
+    { "name": "k_N", "unit": "W", "description": "Network scaling coefficient" },
+    { "name": "epsilon", "unit": "dimensionless", "description": "Signal guard constant" },
+    { "name": "kappa", "unit": "dimensionless", "description": "Signal penalty exponent" },
+    { "name": "k_tail", "unit": "W", "description": "Radio tail power coefficient" },
+    { "name": "tau_up", "unit": "s", "description": "Radio activation time constant" },
+    { "name": "tau_down", "unit": "s", "description": "Radio decay time constant" },
+    { "name": "C1", "unit": "F", "description": "Polarization capacitance" },
+    { "name": "R1", "unit": "Ohm", "description": "Polarization resistance" },
+    { "name": "hA", "unit": "W/K", "description": "Convective heat transfer coefficient" },
+    { "name": "C_th", "unit": "J/K", "description": "Thermal capacitance" },
+    { "name": "E0", "unit": "V", "description": "Standard potential" },
+    { "name": "K", "unit": "V", "description": "Polarization constant" },
+    { "name": "A", "unit": "V", "description": "Exponential zone amplitude" },
+    { "name": "B", "unit": "dimensionless", "description": "Exponential zone time constant" },
+    { "name": "R_ref", "unit": "Ohm", "description": "Reference internal resistance" },
+    { "name": "E_a", "unit": "J/mol", "description": "Activation energy" },
+    { "name": "R_g", "unit": "J/(mol*K)", "description": "Gas constant" },
+    { "name": "T_ref", "unit": "K", "description": "Reference temperature" },
+    { "name": "eta_R", "unit": "dimensionless", "description": "Aging resistance factor" },
+    { "name": "Q_nom", "unit": "Ah", "description": "Nominal capacity" },
+    { "name": "alpha_Q", "unit": "1/K", "description": "Temperature capacity coefficient" },
+    { "name": "V_cut", "unit": "V", "description": "Cutoff voltage" },
+    { "name": "z_min", "unit": "dimensionless", "description": "SOC singularity guard" },
+    { "name": "Q_eff_floor", "unit": "Ah", "description": "Minimum capacity floor" }
+  ],
+  "equations": [
+    "P_scr = P_scr0 + k_L * L^gamma",
+    "P_cpu = P_cpu0 + k_C * C^eta",
+    "P_net = P_net0 + k_N * N / (Ψ + epsilon)^kappa + k_tail * w",
+    "P_tot = P_bg + P_scr + P_cpu + P_net",
+    "z_eff = max(z, z_min)",
+    "V_oc = E0 - K * (1/z_eff - 1) + A * exp(-B * (1 - z))",
+    "R0 = R_ref * exp((E_a / R_g) * (1/T_b - 1/T_ref)) * (1 + eta_R * (1 - S))",
+    "Q_eff = max(Q_nom * S * (1 - alpha_Q * (T_ref - T_b)), Q_eff_floor)",
+    "Delta = (V_oc - v_p)^2 - 4 * R0 * P_tot",
+    "I = (V_oc - v_p - sqrt(Delta)) / (2 * R0)",
+    "V_term = V_oc - v_p - I * R0",
+    "dz/dt = -I / (3600 * Q_eff)",
+    "dv_p/dt = I/C1 - v_p / (R1 * C1)",
+    "dT_b/dt = (I^2 * R0 + I * v_p - hA * (T_b - T_a)) / C_th",
+    "sigma_N = min(1, N)",
+    "tau_N = (sigma_N >= w) ? tau_up : tau_down",
+    "dw/dt = (sigma_N - w) / tau_N"
+  ],
+  "guards": {
+    "z_min": "z_eff = max(z, z_min)",
+    "Q_eff_floor": "Q_eff = max(Q_calc, Q_eff_floor)",
+    "clamp_rules": [
+      "z = clamp(z, 0, 1)",
+      "S = clamp(S, 0, 1)",
+      "w = clamp(w, 0, 1)"
+    ]
+  },
+  "events": {
+    "gV": "V_term(t) - V_cut",
+    "gz": "z(t)",
+    "gDelta": "Delta(t)",
+    "termination_logic": "Terminate at t* = min(t | gV(t) <= 0 OR gz(t) <= 0 OR gDelta(t) <= 0)",
+    "termination_reasons": [
+      "V_CUTOFF",
+      "SOC_ZERO",
+      "DELTA_ZERO"
+    ]
+  },
+  "tte_definition": {
+    "formula": "TTE = t* - t0",
+    "interpolation": "t* = t_{n-1} + (t_n - t_{n-1}) * (0 - g(t_{n-1})) / (g(t_n) - g(t_{n-1}))",
+    "tie_breaking": "Earliest t* across all event functions; if identical, priority: DELTA_ZERO > V_CUTOFF > SOC_ZERO"
+  },
+  "numerics": {
+    "method": "RK4_nested_CPL",
+    "dt_symbol": "dt",
+    "stage_recompute_current": true
+  },
+  "validation": {
+    "dimension_check": [
+      "P_tot [W]",
+      "V_term [V]",
+      "I [A]",
+      "dz/dt [1/s]",
+      "dT_b/dt [K/s]"
+    ],
+    "monotonicity_check": "If I >= 0, then dz/dt must be <= 0",
+    "feasibility_check": "Delta must be >= 0; if Delta < 0 at any evaluation, trigger DELTA_ZERO event"
+  }
+}