184 lines
6.1 KiB
Python
184 lines
6.1 KiB
Python
#!/usr/bin/env python3
|
||
# -*- coding: utf-8 -*-
|
||
"""
|
||
Richards S-Curve Fit for 1984-2025 Data
|
||
|
||
Fits and visualizes the Richards growth model to rocket launch data
|
||
starting from 1984.
|
||
"""
|
||
|
||
import pandas as pd
|
||
import numpy as np
|
||
from scipy.optimize import curve_fit
|
||
import matplotlib
|
||
matplotlib.use('Agg')
|
||
import matplotlib.pyplot as plt
|
||
import warnings
|
||
warnings.filterwarnings('ignore')
|
||
|
||
plt.rcParams['font.sans-serif'] = ['Arial Unicode MS', 'SimHei', 'DejaVu Sans']
|
||
plt.rcParams['axes.unicode_minus'] = False
|
||
|
||
|
||
def richards(t, K, r, t0, v):
|
||
"""
|
||
Richards curve (generalized logistic model)
|
||
|
||
N(t) = K / (1 + exp(-r*(t - t0)))^(1/v)
|
||
"""
|
||
exp_term = np.exp(-r * (t - t0))
|
||
exp_term = np.clip(exp_term, 1e-10, 1e10)
|
||
return K / np.power(1 + exp_term, 1/v)
|
||
|
||
|
||
def load_data(filepath="rocket_launch_counts.csv"):
|
||
"""Load rocket launch data"""
|
||
df = pd.read_csv(filepath)
|
||
df = df.rename(columns={"YDate": "year", "Total": "launches"})
|
||
df["year"] = pd.to_numeric(df["year"], errors="coerce")
|
||
df["launches"] = pd.to_numeric(df["launches"], errors="coerce")
|
||
df = df.dropna(subset=["year", "launches"])
|
||
df = df[(df["year"] >= 1957) & (df["year"] <= 2025)]
|
||
df = df.astype({"year": int, "launches": int})
|
||
df = df.sort_values("year").reset_index(drop=True)
|
||
return df
|
||
|
||
|
||
def fit_richards(years, launches, base_year=1984):
|
||
"""Fit Richards model to data"""
|
||
t = (years - base_year).astype(float)
|
||
|
||
# Initial parameters and bounds (unconstrained K)
|
||
p0 = [5000.0, 0.1, 40.0, 2.0]
|
||
bounds = ([500, 0.005, 10, 0.2], [100000, 1.0, 150, 10.0])
|
||
|
||
popt, pcov = curve_fit(richards, t, launches, p0=p0, bounds=bounds, maxfev=100000)
|
||
perr = np.sqrt(np.diag(pcov))
|
||
|
||
# Calculate R²
|
||
y_pred = richards(t, *popt)
|
||
ss_res = np.sum((launches - y_pred) ** 2)
|
||
ss_tot = np.sum((launches - np.mean(launches)) ** 2)
|
||
r_squared = 1 - (ss_res / ss_tot)
|
||
|
||
return popt, perr, r_squared
|
||
|
||
|
||
def main():
|
||
print("=" * 60)
|
||
print("Richards S-Curve Fit (1984-2025)")
|
||
print("=" * 60)
|
||
|
||
# Load data
|
||
df = load_data()
|
||
|
||
# Filter 1984-2025
|
||
start_year = 1984
|
||
data = df[(df["year"] >= start_year) & (df["year"] <= 2025)].copy()
|
||
years = data["year"].values
|
||
launches = data["launches"].values
|
||
|
||
print(f"Data range: {start_year} - 2025")
|
||
print(f"Data points: {len(data)}")
|
||
|
||
# Fit model
|
||
popt, perr, r_squared = fit_richards(years, launches, base_year=start_year)
|
||
K, r, t0, v = popt
|
||
|
||
print(f"\nFitted Parameters:")
|
||
print(f" K (carrying capacity) = {K:.0f} launches/year")
|
||
print(f" r (growth rate) = {r:.4f}")
|
||
print(f" t0 (inflection point) = {start_year + t0:.1f}")
|
||
print(f" v (shape parameter) = {v:.3f}")
|
||
print(f" R² = {r_squared:.4f}")
|
||
|
||
# Physical limit
|
||
physical_max = 3650
|
||
print(f"\nPhysical limit: {physical_max} (10 sites × 365 days)")
|
||
print(f"K / Physical limit = {K/physical_max:.2f}x")
|
||
|
||
# ========== Create Visualization ==========
|
||
fig, ax = plt.subplots(figsize=(12, 7))
|
||
|
||
# Historical data points
|
||
ax.scatter(years, launches, color='#2C3E50', s=80, alpha=0.8,
|
||
label='Historical Data (1984-2025)', zorder=3, edgecolor='white', linewidth=0.5)
|
||
|
||
# Generate smooth S-curve
|
||
years_smooth = np.linspace(start_year, 2100, 500)
|
||
t_smooth = years_smooth - start_year
|
||
pred_smooth = richards(t_smooth, *popt)
|
||
|
||
# S-curve prediction
|
||
ax.plot(years_smooth, pred_smooth, color='#27AE60', lw=3,
|
||
label=f'Richards Model (K={K:.0f}, R²={r_squared:.3f})', zorder=2)
|
||
|
||
# Confidence band (approximate using parameter errors)
|
||
K_low = max(500, K - 2*perr[0])
|
||
K_high = K + 2*perr[0]
|
||
pred_low = richards(t_smooth, K_low, r, t0, v)
|
||
pred_high = richards(t_smooth, K_high, r, t0, v)
|
||
ax.fill_between(years_smooth, pred_low, pred_high, color='#27AE60', alpha=0.15,
|
||
label='95% Confidence Band')
|
||
|
||
# Physical limit line
|
||
ax.axhline(physical_max, color='#E74C3C', ls='--', lw=2.5,
|
||
label=f'Physical Limit: {physical_max} (1/site/day)')
|
||
|
||
# Mark inflection point
|
||
inflection_year = start_year + t0
|
||
inflection_value = K / (v + 1) ** (1/v)
|
||
ax.scatter([inflection_year], [inflection_value], color='#F39C12', s=150,
|
||
marker='*', zorder=5, label=f'Inflection Point ({inflection_year:.0f})')
|
||
|
||
# Mark key years
|
||
ax.axvline(2025, color='gray', ls=':', lw=1.5, alpha=0.7)
|
||
ax.axvline(2050, color='#3498DB', ls=':', lw=2, alpha=0.8)
|
||
ax.text(2026, K*0.95, '2025\n(Now)', fontsize=10, color='gray')
|
||
ax.text(2051, K*0.85, '2050\n(Target)', fontsize=10, color='#3498DB')
|
||
|
||
# Prediction for 2050
|
||
t_2050 = 2050 - start_year
|
||
pred_2050 = richards(t_2050, *popt)
|
||
ax.scatter([2050], [pred_2050], color='#3498DB', s=100, marker='D', zorder=4)
|
||
ax.annotate(f'{pred_2050:.0f}', xy=(2050, pred_2050), xytext=(2055, pred_2050-300),
|
||
fontsize=10, color='#3498DB', fontweight='bold')
|
||
|
||
# Formatting
|
||
ax.set_xlabel('Year', fontsize=12)
|
||
ax.set_ylabel('Annual Launches', fontsize=12)
|
||
ax.set_title('Richards S-Curve Model Fit (1984-2025 Data)\nRocket Launch Capacity Projection',
|
||
fontsize=14, fontweight='bold')
|
||
ax.legend(loc='upper left', fontsize=10)
|
||
ax.grid(True, alpha=0.3)
|
||
ax.set_xlim(1982, 2100)
|
||
ax.set_ylim(0, K * 1.15)
|
||
|
||
# Add text box with model info
|
||
textstr = f'''Model: N(t) = K / (1 + e^(-r(t-t₀)))^(1/v)
|
||
|
||
Data Window: {start_year}-2025 ({len(data)} points)
|
||
K = {K:.0f} launches/year
|
||
r = {r:.4f}
|
||
t₀ = {start_year + t0:.1f}
|
||
v = {v:.3f}
|
||
R² = {r_squared:.4f}
|
||
|
||
Note: Physical limit (3,650) shown as
|
||
dashed red line'''
|
||
|
||
props = dict(boxstyle='round', facecolor='wheat', alpha=0.8)
|
||
ax.text(0.98, 0.35, textstr, transform=ax.transAxes, fontsize=9,
|
||
verticalalignment='top', horizontalalignment='right', bbox=props, family='monospace')
|
||
|
||
plt.tight_layout()
|
||
plt.savefig('richards_curve_1984.png', dpi=150, bbox_inches='tight')
|
||
plt.close()
|
||
|
||
print("\nPlot saved: richards_curve_1984.png")
|
||
print("=" * 60)
|
||
|
||
|
||
if __name__ == "__main__":
|
||
main()
|