155 lines
5.2 KiB
Python
155 lines
5.2 KiB
Python
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#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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Richards S-Curve Fit for 2010-2025 Data with K=4298
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Fits Richards model to 2010-2025 launch data with carrying capacity
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constrained to K=4298 (close to physical limit of 3650).
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"""
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import pandas as pd
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import numpy as np
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from scipy.optimize import curve_fit
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import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
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import warnings
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warnings.filterwarnings('ignore')
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plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans']
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plt.rcParams['axes.unicode_minus'] = False
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def richards(t, K, r, t0, v):
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"""Richards curve (generalized logistic model)"""
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exp_term = np.exp(-r * (t - t0))
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exp_term = np.clip(exp_term, 1e-10, 1e10)
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return K / np.power(1 + exp_term, 1/v)
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def richards_fixed_K(t, r, t0, v):
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"""Richards curve with fixed K=4298"""
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K = 4298
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exp_term = np.exp(-r * (t - t0))
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exp_term = np.clip(exp_term, 1e-10, 1e10)
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return K / np.power(1 + exp_term, 1/v)
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def load_data(filepath="rocket_launch_counts.csv"):
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"""Load rocket launch data"""
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df = pd.read_csv(filepath)
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df = df.rename(columns={"YDate": "year", "Total": "launches"})
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df["year"] = pd.to_numeric(df["year"], errors="coerce")
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df["launches"] = pd.to_numeric(df["launches"], errors="coerce")
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df = df.dropna(subset=["year", "launches"])
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df = df[(df["year"] >= 1957) & (df["year"] <= 2025)]
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df = df.astype({"year": int, "launches": int})
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df = df.sort_values("year").reset_index(drop=True)
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return df
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def main():
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print("=" * 60)
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print("Richards S-Curve Fit (2010-2025 Data, K=4298)")
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print("=" * 60)
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# Load data
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df = load_data()
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# Filter 2010-2025
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start_year = 2010
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end_year = 2025
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data = df[(df["year"] >= start_year) & (df["year"] <= end_year)].copy()
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years = data["year"].values
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launches = data["launches"].values
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print(f"Data range: {start_year} - {end_year}")
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print(f"Data points: {len(data)}")
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print(f"\nHistorical data:")
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for y, l in zip(years, launches):
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print(f" {y}: {l} launches")
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# Fit with fixed K=4298
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K_fixed = 4298
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t = (years - start_year).astype(float)
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p0 = [0.2, 20.0, 2.0] # r, t0, v
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bounds = ([0.01, 5, 0.5], [1.0, 100, 10.0])
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try:
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popt, pcov = curve_fit(richards_fixed_K, t, launches, p0=p0, bounds=bounds, maxfev=100000)
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r, t0, v = popt
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# Calculate R²
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y_pred = richards_fixed_K(t, *popt)
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ss_res = np.sum((launches - y_pred) ** 2)
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ss_tot = np.sum((launches - np.mean(launches)) ** 2)
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r_squared = 1 - (ss_res / ss_tot)
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print(f"\nFitted Parameters (K fixed at {K_fixed}):")
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print(f" K (carrying capacity) = {K_fixed} launches/year (FIXED)")
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print(f" r (growth rate) = {r:.4f}")
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print(f" t0 (inflection point) = {start_year + t0:.1f}")
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print(f" v (shape parameter) = {v:.3f}")
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print(f" R² = {r_squared:.4f}")
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except Exception as e:
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print(f"Fitting error: {e}")
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return
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# Physical limit
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physical_max = 3650
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print(f"\nPhysical limit: {physical_max} (10 sites × 365 days)")
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print(f"K / Physical limit = {K_fixed/physical_max:.2f}x")
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# ========== Create Visualization ==========
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fig, ax = plt.subplots(figsize=(12, 7))
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# Historical data points
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ax.scatter(years, launches, color='#2C3E50', s=100, alpha=0.9,
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label='Historical Data (2010-2025)', zorder=4, edgecolor='white', linewidth=1)
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# Generate smooth S-curve
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years_smooth = np.linspace(start_year, 2080, 500)
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t_smooth = years_smooth - start_year
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pred_smooth = richards(t_smooth, K_fixed, r, t0, v)
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# S-curve prediction
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ax.plot(years_smooth, pred_smooth, color='#27AE60', lw=3,
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label=f'Richards Model (K={K_fixed}, R²={r_squared:.3f})', zorder=2)
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# K=4298 saturation line
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ax.axhline(K_fixed, color='#27AE60', ls=':', lw=2, alpha=0.7,
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label=f'K = {K_fixed} (Model Saturation)')
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# Mark 2050 line only
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ax.axvline(2050, color='#3498DB', ls=':', lw=2, alpha=0.8)
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ax.text(2051, K_fixed*0.85, '2050\n(Target)', fontsize=10, color='#3498DB')
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# Only show 2050 prediction point
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t_2050 = 2050 - start_year
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pred_2050 = richards(t_2050, K_fixed, r, t0, v)
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ax.scatter([2050], [pred_2050], color='#3498DB', s=80, marker='D', zorder=4)
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ax.annotate(f'{pred_2050:.0f}', xy=(2050, pred_2050),
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xytext=(2051, pred_2050+150),
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fontsize=9, color='#3498DB', fontweight='bold')
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# Formatting
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ax.set_xlabel('Year', fontsize=12)
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ax.set_ylabel('Annual Launches', fontsize=12)
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ax.legend(loc='upper left', fontsize=10)
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ax.grid(True, alpha=0.3)
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ax.set_xlim(2008, 2080)
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ax.set_ylim(0, K_fixed * 1.15)
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plt.tight_layout()
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plt.savefig('richards_curve_2010_K4298.png', dpi=150, bbox_inches='tight')
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plt.close()
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print("\nPlot saved: richards_curve_2010_K4298.png")
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print("=" * 60)
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if __name__ == "__main__":
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main()
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