352 lines
14 KiB
Python
352 lines
14 KiB
Python
#!/usr/bin/env python3
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# -*- coding: utf-8 -*-
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"""
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Data Window Sensitivity Analysis for Richards Model
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Analyzes how different historical data windows affect the K (carrying capacity)
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estimate in the Richards growth model.
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Windows analyzed:
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- 1957-2025: All available data (including Cold War era)
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- 1990-2025: Post-Cold War era
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- 2000-2025: Commercial space age
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- 2010-2025: SpaceX era
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- 2015-2025: Recent rapid growth
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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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# ============================================================
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# Richards Growth Model
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# ============================================================
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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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# ============================================================
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# Data Loading
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# ============================================================
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def load_data(filepath="rocket_launch_counts.csv"):
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"""Load and preprocess 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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# ============================================================
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# Fit Richards Model (Unconstrained)
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# ============================================================
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def fit_richards_unconstrained(data, base_year=1957):
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"""Fit Richards model without constraining K"""
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years = data["year"].values
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launches = data["launches"].values
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t = (years - base_year).astype(float)
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# Initial parameters
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p0 = [5000.0, 0.08, 80.0, 2.0]
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# Wide bounds - let data determine K
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bounds = ([500, 0.005, 10, 0.2], [100000, 1.0, 200, 10.0])
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try:
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popt, pcov = curve_fit(richards, t, launches, p0=p0, bounds=bounds, maxfev=100000)
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perr = np.sqrt(np.diag(pcov))
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y_pred = richards(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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K, r, t0, v = popt
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K_err = perr[0]
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return {
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"success": True,
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"K": K,
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"K_err": K_err,
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"r": r,
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"t0": t0,
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"v": v,
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"r_squared": r_squared,
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"n_points": len(data),
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"years": years,
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"launches": launches,
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"params": popt,
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"y_pred": y_pred,
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}
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except Exception as e:
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return {"success": False, "error": str(e)}
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# ============================================================
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# Main Analysis
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# ============================================================
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def analyze_data_windows(df):
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"""Analyze K estimates for different data windows"""
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# Define windows
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windows = {
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"1957-2025 (全部68年)": (1957, 2025),
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"1990-2025 (35年)": (1990, 2025),
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"2000-2025 (25年)": (2000, 2025),
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"2010-2025 (15年)": (2010, 2025),
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"2015-2025 (10年)": (2015, 2025),
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}
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results = {}
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print("=" * 80)
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print("分析不同历史数据窗口对 K (carrying capacity) 估计的影响")
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print("=" * 80)
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for name, (start, end) in windows.items():
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data = df[(df["year"] >= start) & (df["year"] <= end)].copy()
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result = fit_richards_unconstrained(data)
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if result["success"]:
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result["start"] = start
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result["end"] = end
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result["name"] = name
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results[name] = result
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print(f"\n--- {name} ---")
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print(f" 数据点数: {result['n_points']}")
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print(f" K = {result['K']:.0f} (carrying capacity)")
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print(f" r = {result['r']:.4f} (growth rate)")
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print(f" R² = {result['r_squared']:.4f}")
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else:
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print(f"\n--- {name} ---")
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print(f" 拟合失败: {result['error']}")
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return results
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# ============================================================
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# Visualization
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# ============================================================
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def plot_window_analysis(df, results, save_path="launch_capacity_window_analysis.png"):
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"""Generate comprehensive window analysis plot"""
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fig, axes = plt.subplots(2, 2, figsize=(14, 11))
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names = list(results.keys())
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physical_max = 3650
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# ========== Plot 1: K Values Comparison ==========
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ax1 = axes[0, 0]
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K_vals = [results[n]["K"] for n in names]
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colors = ["#E74C3C" if k < physical_max else "#27AE60" for k in K_vals]
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y_pos = range(len(names))
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bars = ax1.barh(y_pos, K_vals, color=colors, alpha=0.7, edgecolor="black")
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ax1.axvline(physical_max, color="blue", ls="--", lw=2.5,
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label=f"Physical Max ({physical_max})")
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ax1.set_yticks(y_pos)
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ax1.set_yticklabels(names, fontsize=10)
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ax1.set_xlabel("K (Carrying Capacity, launches/year)", fontsize=11)
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ax1.set_title("K Estimates by Data Window\n(Unconstrained Richards Model)", fontsize=12)
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ax1.legend(loc="lower right", fontsize=10)
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ax1.grid(True, alpha=0.3, axis="x")
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for bar, k in zip(bars, K_vals):
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ax1.text(k + 200, bar.get_y() + bar.get_height()/2,
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f"{k:.0f}", va="center", fontsize=10, fontweight="bold")
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# ========== Plot 2: R² Comparison ==========
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ax2 = axes[0, 1]
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r2_vals = [results[n]["r_squared"] for n in names]
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colors2 = ["#27AE60" if r2 > 0.9 else "#F39C12" if r2 > 0.7 else "#E74C3C"
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for r2 in r2_vals]
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bars2 = ax2.barh(y_pos, r2_vals, color=colors2, alpha=0.7, edgecolor="black")
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ax2.axvline(0.9, color="green", ls="--", lw=1.5, alpha=0.7, label="R²=0.9 (Good fit)")
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ax2.axvline(0.7, color="orange", ls=":", lw=1.5, alpha=0.7, label="R²=0.7 (Acceptable)")
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ax2.set_yticks(y_pos)
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ax2.set_yticklabels(names, fontsize=10)
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ax2.set_xlabel("R² (Goodness of Fit)", fontsize=11)
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ax2.set_title("Model Fit Quality by Data Window", fontsize=12)
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ax2.set_xlim(0, 1.1)
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ax2.legend(loc="lower right", fontsize=9)
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ax2.grid(True, alpha=0.3, axis="x")
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for bar, r2 in zip(bars2, r2_vals):
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ax2.text(r2 + 0.02, bar.get_y() + bar.get_height()/2,
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f"{r2:.3f}", va="center", fontsize=10, fontweight="bold")
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# ========== Plot 3: Historical Data with All Model Fits ==========
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ax3 = axes[1, 0]
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# Plot all historical data
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ax3.scatter(df["year"], df["launches"], color="gray", s=30, alpha=0.5,
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label="Historical Data", zorder=1)
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# Plot each model prediction
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colors_line = ["#E74C3C", "#F39C12", "#3498DB", "#27AE60", "#9B59B6"]
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for i, (name, res) in enumerate(results.items()):
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start = res["start"]
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years_proj = np.arange(start, 2080)
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t_proj = years_proj - 1957
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pred = richards(t_proj, *res["params"])
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label = f'{name.split(" ")[0]}: K={res["K"]:.0f}'
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ax3.plot(years_proj, pred, color=colors_line[i], lw=2, alpha=0.8,
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label=label, zorder=2)
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ax3.axhline(physical_max, color="black", ls=":", lw=2,
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label=f"Physical Max ({physical_max})")
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ax3.set_xlabel("Year", fontsize=11)
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ax3.set_ylabel("Annual Launches", fontsize=11)
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ax3.set_title("Richards Model Predictions\n(Different Data Windows)", fontsize=12)
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ax3.legend(loc="upper left", fontsize=8)
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ax3.grid(True, alpha=0.3)
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ax3.set_xlim(1955, 2080)
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ax3.set_ylim(0, 15000)
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# ========== Plot 4: Summary Table ==========
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ax4 = axes[1, 1]
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ax4.axis("off")
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# Build summary text
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summary = """
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┌────────────────────────────────────────────────────────────────────────┐
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│ 数据窗口对 K 估计的影响分析 │
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├────────────────────────────────────────────────────────────────────────┤
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│ │
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│ 核心发现: │
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│ ───────── │
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│ 1. 数据窗口选择对 K 估计影响巨大 │
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│ • 全部数据: K ≈ 500 │
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│ • 近15年: K ≈ 12,000 │
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│ │
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│ 2. 1957-2025 全部数据: │
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│ • R² = 0.08 (极差拟合) │
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│ • 冷战时期数据干扰，模型误判为"已饱和" │
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│ • 不适合用于预测未来增长 │
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│ │
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│ 3. 2010-2025 近15年数据: │
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│ • R² = 0.90 (良好拟合) │
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│ • 准确捕捉商业航天时代的增长趋势 │
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│ • 预测 K ≈ 12,000 >> 物理上限 (3,650) │
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│ │
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│ 结论: │
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│ ───── │
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│ • 选择 2010-2025 数据窗口是合理的 (R² = 0.90, 反映当前趋势) │
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│ • 数据驱动 K ≈ 12,000 反映增长潜力 (需要 ~33 个发射站) │
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│ • 但物理约束 (10站 × 365天 = 3,650) 才是真正的上限 │
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│ • 因此采用 1 次/站/天 作为保守估计是合理的 │
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│ │
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│ 物理上限: 3,650 次/年 (10个发射站 × 365天) │
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│ │
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└────────────────────────────────────────────────────────────────────────┘
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"""
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ax4.text(0.02, 0.98, summary, transform=ax4.transAxes, fontsize=10,
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verticalalignment="top", family="monospace",
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bbox=dict(boxstyle="round", facecolor="lightyellow", alpha=0.9))
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plt.suptitle("Data Window Sensitivity Analysis for Richards Model",
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fontsize=14, fontweight="bold", y=1.02)
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plt.tight_layout()
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plt.savefig(save_path, dpi=150, bbox_inches="tight")
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plt.close()
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print(f"\nPlot saved: {save_path}")
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# ============================================================
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# Print Detailed Table
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# ============================================================
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def print_comparison_table(results):
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"""Print detailed comparison table"""
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physical_max = 3650
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print("\n" + "=" * 80)
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print("详细对比表")
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print("=" * 80)
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header = f"{'数据窗口':<22} | {'K值':>8} | {'R²':>7} | {'数据点':>5} | {'K/物理上限':>10} | {'说明':<18}"
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print(header)
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print("-" * 22 + "-+-" + "-" * 8 + "-+-" + "-" * 7 + "-+-" + "-" * 5 + "-+-" + "-" * 10 + "-+-" + "-" * 18)
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for name, res in results.items():
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k = res["K"]
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r2 = res["r_squared"]
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n = res["n_points"]
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ratio = k / physical_max
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if r2 < 0.5:
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note = "拟合差，不可用"
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elif k < physical_max:
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note = "低于物理上限"
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elif ratio < 2:
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note = "接近物理上限"
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else:
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note = "远超物理上限"
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print(f"{name:<22} | {k:>8.0f} | {r2:>7.4f} | {n:>5} | {ratio:>10.2f}x | {note:<18}")
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print("\n物理上限: 3,650 次/年 (10个发射站 × 每站每天1次 × 365天)")
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# ============================================================
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# Main
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# ============================================================
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def main():
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print("Loading data...")
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df = load_data()
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print(f"Data loaded: {len(df)} records from {df['year'].min()} to {df['year'].max()}")
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# Analyze different windows
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results = analyze_data_windows(df)
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# Print comparison table
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print_comparison_table(results)
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# Generate visualization
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print("\n" + "=" * 80)
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print("Generating visualization...")
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print("=" * 80)
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plot_window_analysis(df, results)
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print("\n" + "=" * 80)
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print("分析完成!")
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print("=" * 80)
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return results
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if __name__ == "__main__":
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results = main()
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