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A题/数值分析检验/Response/0.md
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A题/数值分析检验/Response/0.md
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{
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"model_name": "MODEL_SPEC",
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"version": "1.0",
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"status": "frozen",
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"states": [
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{ "name": "z", "unit": "dimensionless", "description": "State of Charge (SOC)", "bounds": [0, 1] },
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{ "name": "v_p", "unit": "V", "description": "Polarization voltage", "bounds": [null, null] },
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{ "name": "T_b", "unit": "K", "description": "Battery temperature", "bounds": [0, null] },
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{ "name": "S", "unit": "dimensionless", "description": "State of Health (SOH)", "bounds": [0, 1] },
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{ "name": "w", "unit": "dimensionless", "description": "Radio tail activation level", "bounds": [0, 1] }
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],
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"inputs": [
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{ "name": "L", "unit": "dimensionless", "description": "Screen brightness level", "bounds": [0, 1] },
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{ "name": "C", "unit": "dimensionless", "description": "Processor load", "bounds": [0, 1] },
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{ "name": "N", "unit": "dimensionless", "description": "Network activity", "bounds": [0, 1] },
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{ "name": "Psi", "unit": "dimensionless", "description": "Signal quality", "bounds": [0, 1] },
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{ "name": "T_a", "unit": "K", "description": "Ambient temperature", "bounds": [null, null] }
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],
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"parameters": [
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{ "name": "P_bg", "unit": "W", "description": "Background power consumption" },
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{ "name": "P_scr0", "unit": "W", "description": "Baseline screen power" },
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{ "name": "k_L", "unit": "W", "description": "Screen power scaling coefficient" },
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{ "name": "gamma", "unit": "dimensionless", "description": "Screen power exponent" },
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{ "name": "P_cpu0", "unit": "W", "description": "Baseline CPU power" },
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{ "name": "k_C", "unit": "W", "description": "CPU power scaling coefficient" },
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{ "name": "eta", "unit": "dimensionless", "description": "CPU power exponent" },
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{ "name": "P_net0", "unit": "W", "description": "Baseline network power" },
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{ "name": "k_N", "unit": "W", "description": "Network power scaling coefficient" },
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{ "name": "epsilon", "unit": "dimensionless", "description": "Signal quality singularity guard" },
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{ "name": "kappa", "unit": "dimensionless", "description": "Signal quality penalty exponent" },
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{ "name": "k_tail", "unit": "W", "description": "Radio tail power coefficient" },
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{ "name": "tau_up", "unit": "s", "description": "Radio activation time constant" },
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{ "name": "tau_down", "unit": "s", "description": "Radio decay time constant" },
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{ "name": "C1", "unit": "F", "description": "Polarization capacitance" },
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{ "name": "R1", "unit": "Ohm", "description": "Polarization resistance" },
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{ "name": "C_th", "unit": "J/K", "description": "Thermal capacitance" },
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{ "name": "hA", "unit": "W/K", "description": "Convective heat transfer coefficient" },
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{ "name": "E0", "unit": "V", "description": "Standard battery potential" },
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{ "name": "K", "unit": "V", "description": "Polarization constant" },
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{ "name": "A", "unit": "V", "description": "Exponential zone amplitude" },
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{ "name": "B", "unit": "dimensionless", "description": "Exponential zone time constant inverse" },
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{ "name": "R_ref", "unit": "Ohm", "description": "Reference internal resistance" },
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{ "name": "E_a", "unit": "J/mol", "description": "Activation energy for resistance" },
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{ "name": "R_g", "unit": "J/(mol*K)", "description": "Universal gas constant" },
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{ "name": "T_ref", "unit": "K", "description": "Reference temperature" },
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{ "name": "eta_R", "unit": "dimensionless", "description": "Aging resistance factor" },
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{ "name": "Q_nom", "unit": "Ah", "description": "Nominal capacity" },
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{ "name": "alpha_Q", "unit": "1/K", "description": "Temperature capacity coefficient" },
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{ "name": "V_cut", "unit": "V", "description": "Cutoff terminal voltage" },
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{ "name": "z_min", "unit": "dimensionless", "description": "SOC singularity guard" },
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{ "name": "Q_eff_floor", "unit": "Ah", "description": "Minimum effective capacity floor" }
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],
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"equations": {
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"power_mapping": [
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"P_scr = P_scr0 + k_L * L^gamma",
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"P_cpu = P_cpu0 + k_C * C^eta",
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"P_net = P_net0 + k_N * (N / (Psi + epsilon)^kappa) + k_tail * w",
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"P_tot = P_bg + P_scr + P_cpu + P_net"
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],
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"constitutive_relations": [
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"z_eff = max(z, z_min)",
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"V_oc = E0 - K * (1/z_eff - 1) + A * exp(-B * (1 - z))",
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"R0 = R_ref * exp((E_a / R_g) * (1/T_b - 1/T_ref)) * (1 + eta_R * (1 - S))",
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"Q_eff = max(Q_nom * S * (1 - alpha_Q * (T_ref - T_b)), Q_eff_floor)"
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],
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"cpl_closure": [
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"Delta = (V_oc - v_p)^2 - 4 * R0 * P_tot",
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"I = (V_oc - v_p - sqrt(Delta)) / (2 * R0)",
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"V_term = V_oc - v_p - I * R0"
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],
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"differential_equations": [
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"dz/dt = -I / (3600 * Q_eff)",
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"dv_p/dt = I/C1 - v_p / (R1 * C1)",
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"dT_b/dt = (I^2 * R0 + I * v_p - hA * (T_b - T_a)) / C_th",
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"dw/dt = (sigma_N - w) / tau_N",
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"sigma_N = min(1, N)",
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"tau_N = (sigma_N >= w) ? tau_up : tau_down"
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]
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},
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"guards": {
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"z_clamping": "z_eff = max(z, z_min)",
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"capacity_protection": "Q_eff = max(Q_calc, Q_eff_floor)",
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"state_projections": "z = clamp(z, 0, 1), S = clamp(S, 0, 1), w = clamp(w, 0, 1)"
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},
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"events": {
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"functions": {
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"gV": "V_term - V_cut",
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"gz": "z",
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"gDelta": "Delta"
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},
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"termination_logic": "Terminate at t* where min(gV(t*), gz(t*), gDelta(t*)) == 0",
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"reasons": [ "V_CUTOFF", "SOC_ZERO", "DELTA_ZERO" ]
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},
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"tte_definition": {
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"formula": "TTE = t* - t0",
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"event_time_interpolation": "t* = t_{n-1} + (t_n - t_{n-1}) * (0 - g(t_{n-1})) / (g(t_n) - g(t_{n-1}))",
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"tie_breaking": "If multiple events trigger in the same step, the one with the smallest t* is recorded as the termination_reason."
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},
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"numerics": {
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"method": "RK4_nested_CPL",
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"dt_symbol": "dt",
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"stage_recompute_current": true,
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"step_halving_verification": "||z_dt - z_dt/2|| < 1e-4"
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},
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"validation": {
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"dimension_check": [
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"Units of P_tot must be Watts",
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"Units of I must be Amperes",
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"Units of dz/dt must be 1/s",
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"Units of dT_b/dt must be K/s"
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],
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"monotonicity_check": "dz/dt <= 0 must hold for all I >= 0",
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"feasibility_check": "Delta must be >= 0 at every evaluation; if Delta < 0, trigger DELTA_ZERO event immediately"
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}
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}
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