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2026-02-16 21:52:26 +08:00
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--- a/A题/数值分析检验/Response/2.md
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+TTE_SPEC_v1
+
+```pseudocode
+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
+
+```json
+{
+  "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
+        }
+      }
+    }
+  ]
+}
+```