MCM/A题/数值分析检验/Response/2.md

TTE_SPEC_v1

FUNCTION compute_tte(t_grid, V_term, z, Delta, V_cut):
    // Constants
    PRIORITY = { "DELTA_ZERO": 1, "V_CUTOFF": 2, "SOC_ZERO": 3 }
    EPSILON = 1e-9

    FOR k FROM 1 TO length(t_grid) - 1:
        // Define event signals
        gV_prev = V_term[k-1] - V_cut
        gV_curr = V_term[k] - V_cut
        gz_prev = z[k-1]
        gz_curr = z[k]
        gD_prev = Delta[k-1]
        gD_curr = Delta[k]

        candidates = []

        // Check for crossings: g[k-1] > 0 and g[k] <= 0
        IF gV_prev > 0 AND gV_curr <= 0:
            denom = gV_curr - gV_prev
            t_star_v = (denom == 0) ? t_grid[k] : t_grid[k-1] + (0 - gV_prev) * (t_grid[k] - t_grid[k-1]) / denom
            candidates.push({ time: t_star_v, reason: "V_CUTOFF", priority: PRIORITY["V_CUTOFF"] })

        IF gz_prev > 0 AND gz_curr <= 0:
            denom = gz_curr - gz_prev
            t_star_z = (denom == 0) ? t_grid[k] : t_grid[k-1] + (0 - gz_prev) * (t_grid[k] - t_grid[k-1]) / denom
            candidates.push({ time: t_star_z, reason: "SOC_ZERO", priority: PRIORITY["SOC_ZERO"] })

        IF gD_prev > 0 AND gD_curr <= 0:
            denom = gD_curr - gD_prev
            t_star_d = (denom == 0) ? t_grid[k] : t_grid[k-1] + (0 - gD_prev) * (t_grid[k] - t_grid[k-1]) / denom
            candidates.push({ time: t_star_d, reason: "DELTA_ZERO", priority: PRIORITY["DELTA_ZERO"] })

        IF length(candidates) > 0:
            // Multi-event tie-breaking
            winner = candidates[0]
            FOR i FROM 1 TO length(candidates) - 1:
                IF candidates[i].time < winner.time - EPSILON:
                    winner = candidates[i]
                ELSE IF abs(candidates[i].time - winner.time) <= EPSILON:
                    IF candidates[i].priority < winner.priority:
                        winner = candidates[i]
            
            t_star = winner.time
            dt_step = t_grid[k] - t_grid[k-1]
            alpha = (t_star - t_grid[k-1]) / dt_step

            // Interpolate termination values
            V_star = V_term[k-1] + alpha * (V_term[k] - V_term[k-1])
            z_star = z[k-1] + alpha * (z[k] - z[k-1])
            D_star = Delta[k-1] + alpha * (Delta[k] - Delta[k-1])

            RETURN {
                TTE_seconds: t_star - t_grid[0],
                termination_reason: winner.reason,
                termination_step_index: k,
                termination_values: { V_term: V_star, z: z_star, Delta: D_star }
            }

    RETURN { TTE_seconds: null, termination_reason: "NO_EVENT_DETECTED" }

TESTS_v1

{
  "tests": [
    {
      "id": 1,
      "description": "Voltage cutoff triggers",
      "params": {
        "V_cut": 3.0
      },
      "data": {
        "t": [0.0, 10.0],
        "V_term": [3.1, 2.8],
        "z": [0.5, 0.4],
        "Delta": [10.0, 9.0]
      },
      "expected": {
        "TTE_seconds": 3.3333333333333335,
        "termination_reason": "V_CUTOFF",
        "termination_step_index": 1,
        "termination_values": {
          "V_term": 3.0,
          "z": 0.4666666666666667,
          "Delta": 9.666666666666666
        }
      }
    },
    {
      "id": 2,
      "description": "SOC hits zero first",
      "params": {
        "V_cut": 3.0
      },
      "data": {
        "t": [0.0, 10.0],
        "V_term": [3.5, 3.4],
        "z": [0.01, -0.02],
        "Delta": [10.0, 9.0]
      },
      "expected": {
        "TTE_seconds": 3.3333333333333335,
        "termination_reason": "SOC_ZERO",
        "termination_step_index": 1,
        "termination_values": {
          "V_term": 3.466666666666667,
          "z": 0.0,
          "Delta": 9.666666666666666
        }
      }
    },
    {
      "id": 3,
      "description": "Delta hits zero first (power infeasible)",
      "params": {
        "V_cut": 3.0
      },
      "data": {
        "t": [0.0, 10.0],
        "V_term": [3.5, 3.4],
        "z": [0.5, 0.4],
        "Delta": [1.0, -2.0]
      },
      "expected": {
        "TTE_seconds": 3.3333333333333335,
        "termination_reason": "DELTA_ZERO",
        "termination_step_index": 1,
        "termination_values": {
          "V_term": 3.466666666666667,
          "z": 0.4666666666666667,
          "Delta": 0.0
        }
      }
    }
  ]
}