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