模型复查

A题/分析/框架2/灵敏度分析.py

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+import numpy as np
+import matplotlib.pyplot as plt
+import pandas as pd
+
+# ==========================================
+# 1. Configuration
+# ==========================================
+def configure_plots():
+    plt.rcParams['font.family'] = 'serif'
+    plt.rcParams['font.serif'] = ['Times New Roman']
+    plt.rcParams['axes.unicode_minus'] = False
+    plt.rcParams['font.size'] = 12
+    plt.rcParams['figure.dpi'] = 150
+
+# ==========================================
+# 2. Simplified Battery Model for Sensitivity
+# ==========================================
+class FastBatteryModel:
+    def __init__(self, capacity_mah=4000, temp_c=25, r_int=0.15, signal_dbm=-90):
+        self.q_design = capacity_mah / 1000.0
+        self.temp_k = temp_c + 273.15
+        self.r_int = r_int
+        self.signal = signal_dbm
+        
+        # Temp correction
+        self.temp_factor = np.clip(np.exp(0.6 * (1 - 298.15 / self.temp_k)), 0.1, 1.2)
+        self.q_eff = self.q_design * self.temp_factor
+
+    def estimate_tte(self, load_power_watts):
+        """
+        Estimate TTE using average current approximation to save time complexity.
+        TTE ~ Q_eff / I_avg
+        Where I_avg is solved from P = V_avg * I - I^2 * R
+        """
+        # Signal power penalty (simplified exponential model)
+        # Baseline -90dBm. If -110dBm, power increases significantly.
+        sig_penalty = 0.0
+        if self.signal < -90:
+            sig_penalty = 0.5 * ((-90 - self.signal) / 20.0)**2
+            
+        total_power = load_power_watts + sig_penalty
+        
+        # Average Voltage approximation (3.7V nominal)
+        # We solve: Total_Power = (V_nom - I * R_int) * I
+        # R * I^2 - V_nom * I + P = 0
+        v_nom = 3.7
+        a = self.r_int
+        b = -v_nom
+        c = total_power
+        
+        delta = b**2 - 4*a*c
+        if delta < 0:
+            return 0.0 # Voltage collapse, immediate shutdown
+            
+        i_avg = (-b - np.sqrt(delta)) / (2*a)
+        
+        # TTE in hours
+        tte = self.q_eff / i_avg
+        return tte
+
+# ==========================================
+# 3. Sensitivity Analysis Logic (OAT)
+# ==========================================
+def run_sensitivity_analysis():
+    configure_plots()
+    
+    # Baseline Parameters
+    base_params = {
+        'Load Power (W)': 1.5,
+        'Temperature (°C)': 25.0,
+        'Internal R (Ω)': 0.15,
+        'Signal (dBm)': -90.0
+    }
+    
+    # Perturbation range (+/- 20%)
+    # Note: For Signal and Temp, we use additive perturbation for physical meaning
+    perturbations = [-0.2, 0.2] 
+    
+    results = []
+    
+    # 1. Calculate Baseline TTE
+    base_model = FastBatteryModel(
+        temp_c=base_params['Temperature (°C)'],
+        r_int=base_params['Internal R (Ω)'],
+        signal_dbm=base_params['Signal (dBm)']
+    )
+    base_tte = base_model.estimate_tte(base_params['Load Power (W)'])
+    
+    print(f"Baseline TTE: {base_tte:.4f} hours")
+    
+    # 2. Iterate parameters
+    for param_name, base_val in base_params.items():
+        row = {'Parameter': param_name}
+        
+        for p in perturbations:
+            # Calculate new parameter value
+            if param_name == 'Temperature (°C)':
+                # For temp, +/- 20% of Celsius is weird, let's do +/- 10 degrees
+                new_val = base_val + (10 if p > 0 else -10)
+                val_label = f"{new_val}°C"
+            elif param_name == 'Signal (dBm)':
+                # For signal, +/- 20% dBm is weird, let's do +/- 20 dBm
+                new_val = base_val + (20 if p > 0 else -20)
+                val_label = f"{new_val}dBm"
+            else:
+                # Standard percentage
+                new_val = base_val * (1 + p)
+                val_label = f"{new_val:.2f}"
+            
+            # Construct model with new param
+            # (Copy base params first)
+            current_params = base_params.copy()
+            current_params[param_name] = new_val
+            
+            model = FastBatteryModel(
+                temp_c=current_params['Temperature (°C)'],
+                r_int=current_params['Internal R (Ω)'],
+                signal_dbm=current_params['Signal (dBm)']
+            )
+            
+            new_tte = model.estimate_tte(current_params['Load Power (W)'])
+            
+            # Calculate % change in TTE
+            pct_change = (new_tte - base_tte) / base_tte * 100
+            
+            if p < 0:
+                row['Low_Change_%'] = pct_change
+                row['Low_Val'] = val_label
+            else:
+                row['High_Change_%'] = pct_change
+                row['High_Val'] = val_label
+                
+        results.append(row)
+        
+    df = pd.DataFrame(results)
+    
+    # ==========================================
+    # 4. Visualization (Tornado Plot)
+    # ==========================================
+    fig, ax = plt.subplots(figsize=(10, 6))
+    
+    # Create bars
+    y_pos = np.arange(len(df))
+    
+    # High perturbation bars
+    rects1 = ax.barh(y_pos, df['High_Change_%'], align='center', height=0.4, color='#d62728', label='High Perturbation')
+    # Low perturbation bars
+    rects2 = ax.barh(y_pos, df['Low_Change_%'], align='center', height=0.4, color='#1f77b4', label='Low Perturbation')
+    
+    # Styling
+    ax.set_yticks(y_pos)
+    ax.set_yticklabels(df['Parameter'])
+    ax.invert_yaxis()  # Labels read top-to-bottom
+    ax.set_xlabel('Change in Time-to-Empty (TTE) [%]')
+    ax.set_title('Sensitivity Analysis: Tornado Diagram (Impact on Battery Life)', fontweight='bold')
+    ax.axvline(0, color='black', linewidth=0.8, linestyle='--')
+    ax.grid(True, axis='x', linestyle='--', alpha=0.5)
+    ax.legend()
+    
+    # Add value labels
+    def autolabel(rects, is_left=False):
+        for rect in rects:
+            width = rect.get_width()
+            label_x = width + (1 if width > 0 else -1) * 0.5
+            ha = 'left' if width > 0 else 'right'
+            ax.text(label_x, rect.get_y() + rect.get_height()/2, 
+                    f'{width:.1f}%', ha=ha, va='center', fontsize=9)
+
+    autolabel(rects1)
+    autolabel(rects2)
+    
+    plt.tight_layout()
+    plt.savefig('sensitivity_tornado.png')
+    plt.show()
+    
+    print("\nSensitivity Analysis Complete.")
+    print(df[['Parameter', 'Low_Change_%', 'High_Change_%']])
+
+if __name__ == "__main__":
+    run_sensitivity_analysis()