diff --git a/combined_decision.png b/combined_decision.png new file mode 100644 index 0000000..67197a1 Binary files /dev/null and b/combined_decision.png differ diff --git a/decision_recommendation.png b/decision_recommendation.png new file mode 100644 index 0000000..0dd6828 Binary files /dev/null and b/decision_recommendation.png differ diff --git a/p1/README.md b/p1/README.md index dc7c631..52ccccf 100644 --- a/p1/README.md +++ b/p1/README.md @@ -23,6 +23,8 @@ 纯火箭方案（10 发射场 * 每日 1 发）排布与能量-工期曲线；并做发射频率敏感性分析。 - **`combined_scenario.py`** 混合方案（电梯优先 + 火箭补齐），输出组合方案能量-工期曲线，并生成 **100–300 年**区间三方案同图对比。 +- **`../pareto_optimization.py`**（新增） + **Pareto 前沿 + “膝点（knee point）”**分析：在**组合方案可行区间（约 101–186 年）**内，寻找“时间–能量”双目标权衡的拐点，并输出推荐决策点与图表/CSV。 - **`launch_capacity_analysis.py`** （可选）对历史火箭年发射量做 Logistic / Gompertz / Richards 拟合与预测，生成 `launch_capacity_*.png` 与 `launch_capacity_results.csv`。 @@ -38,6 +40,8 @@ | `combined_scenario_analysis.png` | 混合方案：总能量/电梯能量/火箭能量随工期变化 + 电梯占比 + 需要启用的火箭站点数 | | `scenario_comparison.png` | elevator-only / rocket-only / combined 的完工时间与能量柱状对比 | | **`three_scenarios_comparison.png`** | **100–300 年区间**：纯火箭、纯电梯、混合方案的“年份-能量”折线同图对比 | +| **`../pareto_combined_range.png`** | **组合方案（101–186 年）Pareto 前沿 + 膝点检测**（多方法对比、边际收益、构成变化） | +| **`../combined_decision.png`** | 组合方案（101–186 年）推荐拐点的“决策图”（更适合直接放报告） | | `launch_capacity_analysis.png` `launch_capacity_physical.png` `launch_capacity_predictions.png` | （可选）火箭发射能力上限/趋势拟合与预测 | #### 数据文件（如存在） @@ -126,7 +130,22 @@
-5) 其它历史遗留图 +5) Pareto 前沿与“膝点”（组合方案 101–186 年） + +> 说明：`pareto_optimization.py` 当前将图片/CSV 输出到上一级目录（`../`），因此这里用相对路径引用。 + +#### `../pareto_combined_range.png` + +![pareto_combined_range](../pareto_combined_range.png) + +#### `../combined_decision.png` + +![combined_decision](../combined_decision.png) + +
+ +
+6) 其它历史遗留图 本目录还包含 `earth_moon_transfer_analysis.png`（早期“地月转移：载荷–燃料/能量关系”图）。当前目录下未发现对应的 `earth_moon_transfer.py` 源码文件；如果你需要我把该脚本补回并与现有口径统一，我可以再加一个文件。 @@ -271,6 +290,33 @@ Rocket Only (219 years): Total energy: 50609 PJ - 当工期 ≥ 186 年时，电梯即可独立完成，混合方案会自动退化为纯电梯曲线（能耗趋于同一水平）。 - 纯火箭能耗显著更高（本模型下约为纯电梯的 **3×** 量级）。 +#### 4）Pareto 前沿与“膝点”（只在组合方案 101–186 年区间内找拐点） + +> 这个分析回答“在可行区间内，选择多少年最划算”的决策问题：既不想太慢、也不想能耗太高。 +> 我们把目标写成双目标：**最小化完工时间 \(T\)** 与 **最小化总能量 \(E\)**，并在 \(T\in[101, 186]\) 年上寻找“边际收益开始明显递减”的拐点（knee point）。 + +从本目录运行： + +```bash +python ../pareto_optimization.py +``` + +会生成（输出在上一级目录 `../`）： + +- `../pareto_combined_range.png` +- `../combined_decision.png` +- `../pareto_combined_range.csv`（组合区间的 Pareto 数据） + +**组合区间（101–186 年）推荐膝点（示例输出）**： + +| 推荐方法 | 年份 | 总能量 (PJ) | 电梯占比 | 火箭占比 | +|---|---:|---:|---:|---:| +| 最大距离法（最稳健） | **139** | **24361** | **74.6%** | **25.4%** | + +解读要点： +- **101→139 年**：多给一些时间，能量下降很快（大量火箭任务转移到电梯/低纬火箭站）。 +- **139→186 年**：继续拉长工期仍能省能量，但**边际节省明显变小**；186 年达到纯电梯可独立完成的极限点。 + --- ### 发射场（10 个）与纬度效应（月球任务场景） @@ -354,4 +400,5 @@ Rocket Only (219 years): Total energy: 50609 PJ - **纯火箭**在“10 站 * 每日 1 发 * 125 吨/发”的约束下，最短约 **219 年**，且能耗约 **5×10⁴ PJ** 量级。 - **纯电梯**能耗最低（约 **1.57×10⁴ PJ**），但最短约 **186 年**。 - **混合方案**能把工期压到约 **101 年**，能耗介于两者之间，并随着工期增加逐步趋近纯电梯能耗。 +- **在混合方案可行区间（101–186 年）内**，用 Pareto/膝点法可给出一个“最划算”的折中点：本模型下约 **139 年**（约 **2.44×10⁴ PJ**，电梯约 **75%**、火箭约 **25%**）。 diff --git a/pareto_combined_range.csv b/pareto_combined_range.csv new file mode 100644 index 0000000..798e4a9 --- /dev/null +++ b/pareto_combined_range.csv @@ -0,0 +1,301 @@ +years,energy_PJ,elevator_fraction,sites_used,rocket_launches +101.0,31679.76095710881,0.54237,10,366104 +101.28501585047614,31620.609850415538,0.5439005351170569,10,364880 +101.57003170095227,31561.45874372226,0.5454310702341137,10,363656 +101.85504755142841,31502.241823054243,0.5469616053511706,10,362431 +102.14006340190454,31443.090716360963,0.5484921404682274,10,361207 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Elevator + Rocket combination: +- Objective 1: Minimize completion time T +- Objective 2: Minimize total energy E + +Finds the Pareto front and identifies the "knee point" as the optimal trade-off. +""" + +import numpy as np +import matplotlib +matplotlib.use('Agg') +import matplotlib.pyplot as plt +from matplotlib import rcParams +from dataclasses import dataclass +from typing import List, Tuple, Dict, Optional +import pandas as pd + +# 设置字体 +rcParams['font.sans-serif'] = ['Arial Unicode MS', 'DejaVu Sans', 'SimHei'] +rcParams['axes.unicode_minus'] = False + +# ============== 物理常数与参数 ============== +G0 = 9.81 # m/s² +OMEGA_EARTH = 7.27e-5 # rad/s +R_EARTH = 6.371e6 # m + +# 任务参数 +TOTAL_PAYLOAD = 100e6 # 100 million metric tons + +# 太空电梯参数 +NUM_ELEVATORS = 3 +ELEVATOR_CAPACITY_PER_YEAR = 179000 # metric tons per elevator per year +TOTAL_ELEVATOR_CAPACITY = NUM_ELEVATORS * ELEVATOR_CAPACITY_PER_YEAR # 537,000 tons/year +ELEVATOR_SPECIFIC_ENERGY = 157.2e9 # J per metric ton (157.2 MJ/kg * 1000) + +# 火箭参数 +PAYLOAD_PER_LAUNCH = 125 # metric tons per launch +ISP = 450 +SPECIFIC_FUEL_ENERGY = 15.5e6 # J/kg +ALPHA = 0.10 +NUM_STAGES = 3 +DELTA_V_BASE = 13300 # m/s + + +# ============== 发射场定义 ============== +@dataclass +class LaunchSite: + name: str + short_name: str + latitude: float + max_launches_per_day: int = 1 + + @property + def abs_latitude(self) -> float: + return abs(self.latitude) + + @property + def delta_v_loss(self) -> float: + v_equator = OMEGA_EARTH * R_EARTH + v_site = OMEGA_EARTH * R_EARTH * np.cos(np.radians(self.abs_latitude)) + return v_equator - v_site + + @property + def total_delta_v(self) -> float: + return DELTA_V_BASE + self.delta_v_loss + + +LAUNCH_SITES = sorted([ + LaunchSite("Kourou (French Guiana)", "Kourou", 5.2), + LaunchSite("Satish Dhawan (India)", "SDSC", 13.7), + LaunchSite("Boca Chica (Texas)", "Texas", 26.0), + LaunchSite("Cape Canaveral (Florida)", "Florida", 28.5), + LaunchSite("Vandenberg (California)", "California", 34.7), + LaunchSite("Wallops (Virginia)", "Virginia", 37.8), + LaunchSite("Taiyuan (China)", "Taiyuan", 38.8), + LaunchSite("Mahia (New Zealand)", "Mahia", 39.3), + LaunchSite("Baikonur (Kazakhstan)", "Baikonur", 45.6), + LaunchSite("Kodiak (Alaska)", "Alaska", 57.4), +], key=lambda x: x.abs_latitude) + + +# ============== 核心计算函数 ============== + +def fuel_ratio_multistage(delta_v: float) -> float: + """多级火箭燃料/载荷比""" + ve = ISP * G0 + delta_v_per_stage = delta_v / NUM_STAGES + R_stage = np.exp(delta_v_per_stage / ve) + + denominator = 1 - ALPHA * (R_stage - 1) + if denominator <= 0: + return np.inf + + k_stage = (R_stage - 1) / denominator + + total_fuel_ratio = 0 + remaining_ratio = 1.0 + + for _ in range(NUM_STAGES): + fuel_this_stage = remaining_ratio * k_stage + total_fuel_ratio += fuel_this_stage + remaining_ratio *= (1 + k_stage * (1 + ALPHA)) + + return total_fuel_ratio + + +def rocket_energy_per_ton(site: LaunchSite) -> float: + """火箭发射每吨载荷的能量消耗 (J/ton)""" + k = fuel_ratio_multistage(site.total_delta_v) + fuel_per_ton = k * 1000 # kg fuel per metric ton payload + return fuel_per_ton * SPECIFIC_FUEL_ENERGY + + +def calculate_scenario(completion_years: float) -> Optional[Dict]: + """ + 计算给定完成年限下的最优方案（电梯优先+低纬火箭） + + 返回: 方案详情字典，如果无法完成则返回None + """ + # 太空电梯运输量 + elevator_payload = min(TOTAL_ELEVATOR_CAPACITY * completion_years, TOTAL_PAYLOAD) + elevator_energy = elevator_payload * ELEVATOR_SPECIFIC_ENERGY + + # 剩余需要火箭运输的载荷 + remaining_payload = TOTAL_PAYLOAD - elevator_payload + + if remaining_payload <= 0: + # 完全由电梯完成 + return { + 'years': completion_years, + 'elevator_payload': elevator_payload, + 'rocket_payload': 0, + 'elevator_energy_PJ': elevator_energy / 1e15, + 'rocket_energy_PJ': 0, + 'total_energy_PJ': elevator_energy / 1e15, + 'rocket_launches': 0, + 'sites_used': 0, + 'elevator_fraction': 1.0, + } + + # 需要火箭发射 + rocket_launches_needed = int(np.ceil(remaining_payload / PAYLOAD_PER_LAUNCH)) + + # 按纬度优先分配火箭发射 + days_available = completion_years * 365 + max_launches_per_site = int(days_available) + + # 检查是否能在规定时间内完成 + total_rocket_capacity = len(LAUNCH_SITES) * max_launches_per_site * PAYLOAD_PER_LAUNCH + if remaining_payload > total_rocket_capacity: + return None # 无法完成 + + rocket_energy = 0 + sites_used = 0 + remaining_launches = rocket_launches_needed + + for site in LAUNCH_SITES: + if remaining_launches <= 0: + break + allocated = min(remaining_launches, max_launches_per_site) + rocket_energy += rocket_energy_per_ton(site) * PAYLOAD_PER_LAUNCH * allocated + remaining_launches -= allocated + if allocated > 0: + sites_used += 1 + + rocket_payload = rocket_launches_needed * PAYLOAD_PER_LAUNCH + total_energy = elevator_energy + rocket_energy + + return { + 'years': completion_years, + 'elevator_payload': elevator_payload, + 'rocket_payload': rocket_payload, + 'elevator_energy_PJ': elevator_energy / 1e15, + 'rocket_energy_PJ': rocket_energy / 1e15, + 'total_energy_PJ': total_energy / 1e15, + 'rocket_launches': rocket_launches_needed, + 'sites_used': sites_used, + 'elevator_fraction': elevator_payload / TOTAL_PAYLOAD, + } + + +# ============== Pareto 前沿计算 ============== + +def generate_pareto_front( + year_min: float = 100, + year_max: float = 300, + num_points: int = 500 +) -> pd.DataFrame: + """ + 生成 Pareto 前沿数据 + + 对于此问题，由于"时间越长→能量越低"是单调关系， + 所有可行解都在Pareto前沿上（这是一个双目标单调权衡问题）。 + """ + years_range = np.linspace(year_min, year_max, num_points) + + results = [] + for years in years_range: + scenario = calculate_scenario(years) + if scenario is not None: + results.append({ + 'years': years, + 'energy_PJ': scenario['total_energy_PJ'], + 'elevator_fraction': scenario['elevator_fraction'], + 'sites_used': scenario['sites_used'], + 'rocket_launches': scenario['rocket_launches'], + }) + + return pd.DataFrame(results) + + +# ============== 膝点检测算法 ============== + +def find_knee_point_max_curvature(df: pd.DataFrame) -> int: + """ + 方法1: 最大曲率法 + + 在归一化后的 (T, E) 曲线上找曲率最大的点。 + 曲率 κ = |y''| / (1 + y'^2)^(3/2) + """ + # 归一化 + T = df['years'].values + E = df['energy_PJ'].values + + T_norm = (T - T.min()) / (T.max() - T.min()) + E_norm = (E - E.min()) / (E.max() - E.min()) + + # 计算一阶和二阶导数（使用有限差分） + dE = np.gradient(E_norm, T_norm) + d2E = np.gradient(dE, T_norm) + + # 计算曲率 + curvature = np.abs(d2E) / np.power(1 + dE**2, 1.5) + + # 排除边界点 + curvature[:5] = 0 + curvature[-5:] = 0 + + knee_idx = np.argmax(curvature) + return knee_idx + + +def find_knee_point_max_distance(df: pd.DataFrame) -> int: + """ + 方法2: 最大距离法（L-method / Kneedle思想） + + 找到距离"起点-终点连线"最远的点。 + 这通常对应于"边际收益递减"最明显的拐点。 + """ + T = df['years'].values + E = df['energy_PJ'].values + + # 归一化到 [0, 1] + T_norm = (T - T.min()) / (T.max() - T.min()) + E_norm = (E - E.min()) / (E.max() - E.min()) + + # 起点和终点 + p1 = np.array([T_norm[0], E_norm[0]]) + p2 = np.array([T_norm[-1], E_norm[-1]]) + + # 计算每个点到直线 p1-p2 的距离 + line_vec = p2 - p1 + line_len = np.linalg.norm(line_vec) + line_unit = line_vec / line_len + + distances = [] + for i in range(len(T)): + point = np.array([T_norm[i], E_norm[i]]) + point_vec = point - p1 + # 投影长度 + proj_len = np.dot(point_vec, line_unit) + # 垂直距离 + proj_point = p1 + proj_len * line_unit + dist = np.linalg.norm(point - proj_point) + distances.append(dist) + + distances = np.array(distances) + knee_idx = np.argmax(distances) + return knee_idx + + +def find_knee_point_marginal(df: pd.DataFrame, threshold: float = 0.1) -> int: + """ + 方法3: 边际收益法 + + 找到"多投入1年时间，能量下降比例"开始低于阈值的点。 + 即：|dE/dT| / |E| < threshold 的第一个点 + """ + T = df['years'].values + E = df['energy_PJ'].values + + # 计算边际能量变化率 + dE_dT = np.gradient(E, T) + + # 相对变化率 + marginal_ratio = np.abs(dE_dT) / E + + # 找到第一个低于阈值的点（跳过前面几个点） + for i in range(10, len(marginal_ratio)): + if marginal_ratio[i] < threshold: + return i + + return len(df) // 2 # 默认返回中点 + + +def find_knee_point_elbow(df: pd.DataFrame) -> int: + """ + 方法4: 肘部法则（Elbow Method） + + 类似K-means的肘部法则，找到曲线"弯曲"最明显的点。 + 使用二阶导数的符号变化或绝对值。 + """ + T = df['years'].values + E = df['energy_PJ'].values + + # 归一化 + T_norm = (T - T.min()) / (T.max() - T.min() + 1e-10) + E_norm = (E - E.min()) / (E.max() - E.min() + 1e-10) + + # 计算二阶差分 + d2E = np.diff(np.diff(E_norm)) + + # 找到绝对值最大的点 + knee_idx = np.argmax(np.abs(d2E)) + 1 + return min(knee_idx, len(df) - 1) + + +# ============== 综合膝点分析 ============== + +def analyze_knee_points(df: pd.DataFrame) -> Dict: + """ + 使用多种方法找膝点，并综合给出推荐 + """ + methods = { + 'max_curvature': find_knee_point_max_curvature(df), + 'max_distance': find_knee_point_max_distance(df), + 'elbow': find_knee_point_elbow(df), + } + + # 每种方法对应的年份和能量 + results = {} + for method, idx in methods.items(): + results[method] = { + 'index': idx, + 'years': df.iloc[idx]['years'], + 'energy_PJ': df.iloc[idx]['energy_PJ'], + 'elevator_fraction': df.iloc[idx]['elevator_fraction'], + 'sites_used': df.iloc[idx]['sites_used'], + } + + # 推荐：使用最大距离法（最稳健） + recommended = results['max_distance'] + + return { + 'methods': results, + 'recommended': recommended, + } + + +# ============== 可视化 ============== + +def plot_pareto_analysis( + df: pd.DataFrame, + knee_analysis: Dict, + save_path: str = '/Volumes/Files/code/mm/20260130_b/pareto_knee_analysis.png' +): + """ + 绘制 Pareto 前沿与膝点分析图 + """ + fig, axes = plt.subplots(2, 2, figsize=(16, 14)) + + # ========== 图1: Pareto 前沿（时间 vs 能量） ========== + ax1 = axes[0, 0] + + ax1.plot(df['years'], df['energy_PJ'], 'b-', linewidth=2, label='Pareto Front') + ax1.fill_between(df['years'], df['energy_PJ'], alpha=0.2) + + # 标记各方法找到的膝点 + colors = {'max_curvature': 'red', 'max_distance': 'green', 'elbow': 'orange'} + markers = {'max_curvature': 'o', 'max_distance': 's', 'elbow': '^'} + + for method, data in knee_analysis['methods'].items(): + ax1.scatter(data['years'], data['energy_PJ'], + c=colors[method], marker=markers[method], s=150, zorder=5, + label=f'{method}: {data["years"]:.0f}y, {data["energy_PJ"]:.0f}PJ') + + # 标记推荐点 + rec = knee_analysis['recommended'] + ax1.axvline(x=rec['years'], color='green', linestyle='--', alpha=0.7) + ax1.axhline(y=rec['energy_PJ'], color='green', linestyle='--', alpha=0.7) + + ax1.set_xlabel('Completion Time (years)', fontsize=12) + ax1.set_ylabel('Total Energy (PJ)', fontsize=12) + ax1.set_title('Pareto Front: Time vs Energy Trade-off\n(Knee Points by Different Methods)', fontsize=13) + ax1.legend(loc='upper right', fontsize=9) + ax1.grid(True, alpha=0.3) + + # ========== 图2: 归一化 Pareto 前沿 + 距离可视化 ========== + ax2 = axes[0, 1] + + T = df['years'].values + E = df['energy_PJ'].values + T_norm = (T - T.min()) / (T.max() - T.min()) + E_norm = (E - E.min()) / (E.max() - E.min()) + + ax2.plot(T_norm, E_norm, 'b-', linewidth=2, label='Normalized Pareto Front') + + # 画起点-终点连线 + ax2.plot([T_norm[0], T_norm[-1]], [E_norm[0], E_norm[-1]], + 'r--', linewidth=1.5, label='Baseline (Start-End)') + + # 标记最大距离点 + knee_idx = knee_analysis['methods']['max_distance']['index'] + ax2.scatter(T_norm[knee_idx], E_norm[knee_idx], + c='green', marker='s', s=200, zorder=5, label='Knee Point (Max Distance)') + + # 画垂直距离线 + p1 = np.array([T_norm[0], E_norm[0]]) + p2 = np.array([T_norm[-1], E_norm[-1]]) + line_vec = p2 - p1 + line_unit = line_vec / np.linalg.norm(line_vec) + point = np.array([T_norm[knee_idx], E_norm[knee_idx]]) + proj_len = np.dot(point - p1, line_unit) + proj_point = p1 + proj_len * line_unit + ax2.plot([T_norm[knee_idx], proj_point[0]], [E_norm[knee_idx], proj_point[1]], + 'g-', linewidth=2, label='Max Distance') + + ax2.set_xlabel('Normalized Time', fontsize=12) + ax2.set_ylabel('Normalized Energy', fontsize=12) + ax2.set_title('Knee Point Detection\n(Maximum Distance to Baseline)', fontsize=13) + ax2.legend(fontsize=9) + ax2.grid(True, alpha=0.3) + ax2.set_xlim(-0.05, 1.05) + ax2.set_ylim(-0.05, 1.05) + + # ========== 图3: 边际收益分析 ========== + ax3 = axes[1, 0] + + # 计算边际能量变化 + dE_dT = np.gradient(E, T) + marginal_savings = -dE_dT # 每多1年节省的能量 + + ax3.plot(T, marginal_savings, 'purple', linewidth=2) + ax3.fill_between(T, marginal_savings, alpha=0.2, color='purple') + + # 标记推荐点 + ax3.axvline(x=rec['years'], color='green', linestyle='--', linewidth=2, + label=f'Recommended: {rec["years"]:.0f} years') + + ax3.set_xlabel('Completion Time (years)', fontsize=12) + ax3.set_ylabel('Marginal Energy Saving (PJ/year)', fontsize=12) + ax3.set_title('Marginal Benefit Analysis\n(Energy Saved per Additional Year)', fontsize=13) + ax3.legend() + ax3.grid(True, alpha=0.3) + + # ========== 图4: 方案构成随时间变化 ========== + ax4 = axes[1, 1] + + ax4.fill_between(df['years'], 0, df['elevator_fraction'] * 100, + alpha=0.7, color='green', label='Space Elevator') + ax4.fill_between(df['years'], df['elevator_fraction'] * 100, 100, + alpha=0.7, color='red', label='Rockets') + + # 标记推荐点 + ax4.axvline(x=rec['years'], color='black', linestyle='--', linewidth=2, + label=f'Recommended: {rec["years"]:.0f}y ({rec["elevator_fraction"]*100:.0f}% elevator)') + + ax4.set_xlabel('Completion Time (years)', fontsize=12) + ax4.set_ylabel('Payload Share (%)', fontsize=12) + ax4.set_title('Payload Distribution at Different Timelines', fontsize=13) + ax4.legend(loc='center right') + ax4.set_ylim(0, 100) + ax4.grid(True, alpha=0.3) + + plt.suptitle('Pareto Optimization: Space Elevator + Rocket Combination\n' + f'Recommended Knee Point: {rec["years"]:.0f} years, {rec["energy_PJ"]:.0f} PJ', + fontsize=15, y=1.02) + + plt.tight_layout() + plt.savefig(save_path, dpi=150, bbox_inches='tight') + print(f"Pareto分析图已保存至: {save_path}") + + return fig + + +def plot_decision_recommendation( + df: pd.DataFrame, + knee_analysis: Dict, + save_path: str = '/Volumes/Files/code/mm/20260130_b/decision_recommendation.png' +): + """ + 绘制决策建议图（更适合放在报告中） + """ + rec = knee_analysis['recommended'] + + fig, ax = plt.subplots(figsize=(12, 8)) + + # 主曲线 + ax.plot(df['years'], df['energy_PJ'], 'b-', linewidth=3, label='Energy-Time Trade-off') + + # 填充区域 + ax.fill_between(df['years'], df['energy_PJ'], alpha=0.15, color='blue') + + # 标记推荐点 + ax.scatter(rec['years'], rec['energy_PJ'], c='red', s=300, zorder=5, + marker='*', edgecolors='black', linewidth=2) + + # 标注推荐点 + ax.annotate(f"RECOMMENDED\n{rec['years']:.0f} years\n{rec['energy_PJ']:.0f} PJ\n" + f"({rec['elevator_fraction']*100:.0f}% Elevator)", + xy=(rec['years'], rec['energy_PJ']), + xytext=(rec['years'] + 30, rec['energy_PJ'] + 3000), + fontsize=12, fontweight='bold', + bbox=dict(boxstyle='round,pad=0.5', facecolor='yellow', alpha=0.8), + arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0.2', + color='black', lw=2)) + + # 标记几个关键时间点 + key_points = [ + (100, 'Minimum\nfeasible'), + (186, 'Elevator-only\nfeasible'), + (219, 'Rocket-only\nfeasible'), + ] + + for year, label in key_points: + if year >= df['years'].min() and year <= df['years'].max(): + idx = np.argmin(np.abs(df['years'] - year)) + energy = df.iloc[idx]['energy_PJ'] + ax.axvline(x=year, color='gray', linestyle=':', alpha=0.7) + ax.text(year, ax.get_ylim()[1] * 0.95, label, ha='center', fontsize=9, + bbox=dict(facecolor='white', alpha=0.7)) + + ax.set_xlabel('Completion Time (years)', fontsize=14) + ax.set_ylabel('Total Energy Consumption (PJ)', fontsize=14) + ax.set_title('Optimal Decision Point for Moon Colony Construction\n' + '(100 Million Metric Tons Payload)', fontsize=16) + ax.grid(True, alpha=0.3) + + # 添加文字说明 + textstr = (f"Knee Point Analysis Result:\n" + f"• Optimal Timeline: {rec['years']:.0f} years\n" + f"• Total Energy: {rec['energy_PJ']:.0f} PJ\n" + f"• Elevator Share: {rec['elevator_fraction']*100:.1f}%\n" + f"• Rocket Sites Used: {rec['sites_used']}") + + props = dict(boxstyle='round', facecolor='lightgreen', alpha=0.8) + ax.text(0.98, 0.55, textstr, transform=ax.transAxes, fontsize=11, + verticalalignment='top', horizontalalignment='right', bbox=props) + + plt.tight_layout() + plt.savefig(save_path, dpi=150, bbox_inches='tight') + print(f"决策建议图已保存至: {save_path}") + + return fig + + +def print_analysis_report(df: pd.DataFrame, knee_analysis: Dict): + """ + 打印详细分析报告 + """ + print("\n" + "=" * 80) + print("PARETO FRONT & KNEE POINT ANALYSIS REPORT") + print("Moon Colony Logistics Optimization") + print("=" * 80) + + print(f"\n1. PROBLEM DEFINITION") + print(f" - Total payload: {TOTAL_PAYLOAD/1e6:.0f} million metric tons") + print(f" - Elevator capacity: {TOTAL_ELEVATOR_CAPACITY:,} tons/year") + print(f" - Rocket capacity: {len(LAUNCH_SITES) * 365 * PAYLOAD_PER_LAUNCH:,} tons/year") + + print(f"\n2. PARETO FRONT RANGE") + print(f" - Minimum feasible time: {df['years'].min():.1f} years") + print(f" - Analysis range: {df['years'].min():.0f} - {df['years'].max():.0f} years") + print(f" - Energy range: {df['energy_PJ'].min():.0f} - {df['energy_PJ'].max():.0f} PJ") + + print(f"\n3. KNEE POINT DETECTION (Multiple Methods)") + print("-" * 60) + print(f" {'Method':<20} {'Years':>10} {'Energy (PJ)':>15} {'Elev. %':>10}") + print("-" * 60) + + for method, data in knee_analysis['methods'].items(): + print(f" {method:<20} {data['years']:>10.0f} {data['energy_PJ']:>15.0f} " + f"{data['elevator_fraction']*100:>9.1f}%") + + print("-" * 60) + + rec = knee_analysis['recommended'] + print(f"\n4. RECOMMENDED OPTIMAL POINT (Max Distance Method)") + print(f" ┌─────────────────────────────────────────────┐") + print(f" │ Completion Time: {rec['years']:>10.0f} years │") + print(f" │ Total Energy: {rec['energy_PJ']:>10.0f} PJ │") + print(f" │ Elevator Share: {rec['elevator_fraction']*100:>10.1f} % │") + print(f" │ Rocket Sites Used: {rec['sites_used']:>10.0f} │") + print(f" └─────────────────────────────────────────────┘") + + print(f"\n5. INTERPRETATION") + print(f" At the recommended {rec['years']:.0f}-year timeline:") + + # 计算方案详情 + scenario = calculate_scenario(rec['years']) + print(f" - Space Elevator delivers: {scenario['elevator_payload']/1e6:.1f}M tons") + print(f" - Rockets deliver: {scenario['rocket_payload']/1e6:.1f}M tons") + print(f" - Total rocket launches: {scenario['rocket_launches']:,}") + + # 与极端方案对比 + min_time_scenario = calculate_scenario(df['years'].min() + 1) + max_time_idx = len(df) - 1 + + print(f"\n Compared to minimum-time ({df['years'].min():.0f}y):") + if min_time_scenario: + time_diff = rec['years'] - df['years'].min() + energy_diff = min_time_scenario['total_energy_PJ'] - rec['energy_PJ'] + print(f" - Extra time: +{time_diff:.0f} years") + print(f" - Energy saved: {energy_diff:.0f} PJ ({energy_diff/min_time_scenario['total_energy_PJ']*100:.1f}%)") + + print(f"\n Compared to elevator-only (~186y):") + elevator_only_energy = TOTAL_PAYLOAD * ELEVATOR_SPECIFIC_ENERGY / 1e15 + energy_overhead = rec['energy_PJ'] - elevator_only_energy + time_saved = 186 - rec['years'] + print(f" - Time saved: {time_saved:.0f} years") + print(f" - Extra energy: {energy_overhead:.0f} PJ ({energy_overhead/elevator_only_energy*100:.1f}%)") + + print("\n" + "=" * 80) + print("CONCLUSION: The knee point represents the optimal trade-off where") + print("extending the timeline further yields diminishing energy savings.") + print("=" * 80) + + +# ============== 组合方案范围内的膝点分析 ============== + +def analyze_combined_range(): + """ + 在组合方案有效范围内（101-186年）进行膝点分析 + 186年后电梯可独立完成，曲线平坦，无意义 + """ + # 计算电梯独立完成的时间 + elevator_only_years = TOTAL_PAYLOAD / TOTAL_ELEVATOR_CAPACITY + print(f"电梯独立完成需要: {elevator_only_years:.1f} 年") + + # 在组合方案范围内生成Pareto前沿 + year_min = 101 + year_max = elevator_only_years # ~186年 + + df = generate_pareto_front(year_min=year_min, year_max=year_max, num_points=300) + + return df, year_min, year_max + + +def plot_combined_range_analysis( + df: pd.DataFrame, + knee_analysis: Dict, + year_range: Tuple[float, float], + save_path: str = '/Volumes/Files/code/mm/20260130_b/pareto_combined_range.png' +): + """ + 绘制组合方案范围内的Pareto分析图 + """ + fig, axes = plt.subplots(2, 2, figsize=(16, 14)) + + year_min, year_max = year_range + + # ========== 图1: Pareto 前沿（时间 vs 能量） ========== + ax1 = axes[0, 0] + + ax1.plot(df['years'], df['energy_PJ'], 'b-', linewidth=2.5, label='Pareto Front') + ax1.fill_between(df['years'], df['energy_PJ'], alpha=0.2) + + # 标记各方法找到的膝点 + colors = {'max_curvature': 'red', 'max_distance': 'green', 'elbow': 'orange'} + markers = {'max_curvature': 'o', 'max_distance': 's', 'elbow': '^'} + labels = {'max_curvature': 'Max Curvature', 'max_distance': 'Max Distance', 'elbow': 'Elbow'} + + for method, data in knee_analysis['methods'].items(): + ax1.scatter(data['years'], data['energy_PJ'], + c=colors[method], marker=markers[method], s=200, zorder=5, + edgecolors='black', linewidth=1.5, + label=f'{labels[method]}: {data["years"]:.0f}y, {data["energy_PJ"]:.0f}PJ') + + # 标记推荐点 + rec = knee_analysis['recommended'] + ax1.axvline(x=rec['years'], color='green', linestyle='--', alpha=0.7, linewidth=2) + ax1.axhline(y=rec['energy_PJ'], color='green', linestyle='--', alpha=0.7, linewidth=2) + + ax1.set_xlabel('Completion Time (years)', fontsize=12) + ax1.set_ylabel('Total Energy (PJ)', fontsize=12) + ax1.set_title(f'Pareto Front: Combined Scenario ({year_min:.0f}-{year_max:.0f} years)\n' + f'Knee Points by Different Methods', fontsize=13) + ax1.legend(loc='upper right', fontsize=10) + ax1.grid(True, alpha=0.3) + + # ========== 图2: 归一化 + 距离可视化 ========== + ax2 = axes[0, 1] + + T = df['years'].values + E = df['energy_PJ'].values + T_norm = (T - T.min()) / (T.max() - T.min()) + E_norm = (E - E.min()) / (E.max() - E.min()) + + ax2.plot(T_norm, E_norm, 'b-', linewidth=2.5, label='Normalized Pareto Front') + + # 画起点-终点连线 + ax2.plot([T_norm[0], T_norm[-1]], [E_norm[0], E_norm[-1]], + 'r--', linewidth=2, label='Baseline (Start→End)') + + # 标记最大距离点 + knee_idx = knee_analysis['methods']['max_distance']['index'] + ax2.scatter(T_norm[knee_idx], E_norm[knee_idx], + c='green', marker='s', s=250, zorder=5, edgecolors='black', linewidth=2, + label='Knee Point') + + # 画垂直距离线 + p1 = np.array([T_norm[0], E_norm[0]]) + p2 = np.array([T_norm[-1], E_norm[-1]]) + line_vec = p2 - p1 + line_unit = line_vec / np.linalg.norm(line_vec) + point = np.array([T_norm[knee_idx], E_norm[knee_idx]]) + proj_len = np.dot(point - p1, line_unit) + proj_point = p1 + proj_len * line_unit + ax2.plot([T_norm[knee_idx], proj_point[0]], [E_norm[knee_idx], proj_point[1]], + 'g-', linewidth=3, label=f'Max Distance') + + ax2.set_xlabel('Normalized Time (0=min, 1=max)', fontsize=12) + ax2.set_ylabel('Normalized Energy (0=min, 1=max)', fontsize=12) + ax2.set_title('Knee Point Detection\n(Maximum Distance to Baseline)', fontsize=13) + ax2.legend(fontsize=10) + ax2.grid(True, alpha=0.3) + ax2.set_xlim(-0.05, 1.05) + ax2.set_ylim(-0.05, 1.05) + + # ========== 图3: 曲率分析 ========== + ax3 = axes[1, 0] + + # 计算曲率 + dE = np.gradient(E_norm, T_norm) + d2E = np.gradient(dE, T_norm) + curvature = np.abs(d2E) / np.power(1 + dE**2, 1.5) + + ax3.plot(T, curvature, 'purple', linewidth=2) + ax3.fill_between(T, curvature, alpha=0.2, color='purple') + + # 标记最大曲率点 + curv_idx = knee_analysis['methods']['max_curvature']['index'] + ax3.scatter(T[curv_idx], curvature[curv_idx], c='red', s=200, zorder=5, + marker='o', edgecolors='black', linewidth=2, + label=f'Max Curvature: {T[curv_idx]:.0f} years') + + ax3.set_xlabel('Completion Time (years)', fontsize=12) + ax3.set_ylabel('Curvature κ', fontsize=12) + ax3.set_title('Curvature Analysis\n(Higher curvature = sharper bend)', fontsize=13) + ax3.legend(fontsize=10) + ax3.grid(True, alpha=0.3) + + # ========== 图4: 边际收益 + 方案构成 ========== + ax4 = axes[1, 1] + + # 边际节省 + dE_dT = np.gradient(E, T) + marginal_savings = -dE_dT # 每多1年节省的能量 + + ax4_twin = ax4.twinx() + + # 边际收益曲线 + line1, = ax4.plot(T, marginal_savings, 'b-', linewidth=2, label='Marginal Saving (PJ/year)') + ax4.fill_between(T, marginal_savings, alpha=0.15, color='blue') + + # 电梯占比 + line2, = ax4_twin.plot(df['years'], df['elevator_fraction'] * 100, 'g--', linewidth=2, + label='Elevator Share (%)') + + # 标记推荐点 + ax4.axvline(x=rec['years'], color='red', linestyle=':', linewidth=2, + label=f'Recommended: {rec["years"]:.0f}y') + + ax4.set_xlabel('Completion Time (years)', fontsize=12) + ax4.set_ylabel('Marginal Energy Saving (PJ/year)', fontsize=12, color='blue') + ax4_twin.set_ylabel('Elevator Share (%)', fontsize=12, color='green') + ax4.set_title('Marginal Benefit & Payload Distribution', fontsize=13) + + # 合并图例 + lines = [line1, line2] + labels = [l.get_label() for l in lines] + ax4.legend(lines, labels, loc='upper right', fontsize=10) + ax4.grid(True, alpha=0.3) + + plt.suptitle(f'Pareto Optimization: Combined Scenario (Elevator + Rockets)\n' + f'Analysis Range: {year_min:.0f} - {year_max:.0f} years | ' + f'Recommended: {rec["years"]:.0f} years, {rec["energy_PJ"]:.0f} PJ', + fontsize=15, y=1.02) + + plt.tight_layout() + plt.savefig(save_path, dpi=150, bbox_inches='tight') + print(f"组合方案Pareto分析图已保存至: {save_path}") + + return fig + + +def plot_combined_decision( + df: pd.DataFrame, + knee_analysis: Dict, + year_range: Tuple[float, float], + save_path: str = '/Volumes/Files/code/mm/20260130_b/combined_decision.png' +): + """ + 绘制组合方案决策图 + """ + rec = knee_analysis['recommended'] + year_min, year_max = year_range + + fig, ax = plt.subplots(figsize=(14, 9)) + + T = df['years'].values + E = df['energy_PJ'].values + + # 主曲线 + ax.plot(T, E, 'b-', linewidth=3, label='Energy-Time Trade-off') + ax.fill_between(T, E, alpha=0.15, color='blue') + + # 标记三种方法的膝点 + methods_info = knee_analysis['methods'] + + # 最大距离法（推荐） + ax.scatter(methods_info['max_distance']['years'], methods_info['max_distance']['energy_PJ'], + c='green', s=400, zorder=5, marker='*', edgecolors='black', linewidth=2) + + # 最大曲率法 + ax.scatter(methods_info['max_curvature']['years'], methods_info['max_curvature']['energy_PJ'], + c='red', s=200, zorder=5, marker='o', edgecolors='black', linewidth=1.5) + + # 肘部法 + ax.scatter(methods_info['elbow']['years'], methods_info['elbow']['energy_PJ'], + c='orange', s=200, zorder=5, marker='^', edgecolors='black', linewidth=1.5) + + # 标注推荐点 + ax.annotate(f"★ RECOMMENDED (Max Distance)\n" + f"{rec['years']:.0f} years | {rec['energy_PJ']:.0f} PJ\n" + f"Elevator: {rec['elevator_fraction']*100:.0f}%", + xy=(rec['years'], rec['energy_PJ']), + xytext=(rec['years'] + 15, rec['energy_PJ'] + 2500), + fontsize=12, fontweight='bold', + bbox=dict(boxstyle='round,pad=0.5', facecolor='lightgreen', alpha=0.9), + arrowprops=dict(arrowstyle='->', connectionstyle='arc3,rad=0.2', + color='green', lw=2)) + + # 标注最大曲率点（如果不同） + if abs(methods_info['max_curvature']['years'] - rec['years']) > 5: + mc = methods_info['max_curvature'] + ax.annotate(f"● Max Curvature\n{mc['years']:.0f}y | {mc['energy_PJ']:.0f}PJ", + xy=(mc['years'], mc['energy_PJ']), + xytext=(mc['years'] - 20, mc['energy_PJ'] - 2000), + fontsize=10, + bbox=dict(boxstyle='round,pad=0.3', facecolor='lightyellow', alpha=0.8), + arrowprops=dict(arrowstyle='->', color='red', lw=1.5)) + + # 标记端点 + ax.scatter(T[0], E[0], c='red', s=150, marker='D', edgecolors='black', zorder=5) + ax.annotate(f'Fastest\n{T[0]:.0f}y, {E[0]:.0f}PJ', + xy=(T[0], E[0]), xytext=(T[0]+5, E[0]-1500), + fontsize=10, ha='left') + + ax.scatter(T[-1], E[-1], c='green', s=150, marker='D', edgecolors='black', zorder=5) + ax.annotate(f'Lowest Energy\n{T[-1]:.0f}y, {E[-1]:.0f}PJ', + xy=(T[-1], E[-1]), xytext=(T[-1]-25, E[-1]+1500), + fontsize=10, ha='right') + + ax.set_xlabel('Completion Time (years)', fontsize=14) + ax.set_ylabel('Total Energy Consumption (PJ)', fontsize=14) + ax.set_title(f'Optimal Decision Point for Combined Scenario\n' + f'(Elevator + Rockets, {year_min:.0f}-{year_max:.0f} years)', fontsize=16) + ax.grid(True, alpha=0.3) + + # 图例 + from matplotlib.lines import Line2D + legend_elements = [ + Line2D([0], [0], marker='*', color='w', markerfacecolor='green', markersize=20, + markeredgecolor='black', label='Max Distance (Recommended)'), + Line2D([0], [0], marker='o', color='w', markerfacecolor='red', markersize=12, + markeredgecolor='black', label='Max Curvature'), + Line2D([0], [0], marker='^', color='w', markerfacecolor='orange', markersize=12, + markeredgecolor='black', label='Elbow Method'), + ] + ax.legend(handles=legend_elements, loc='upper right', fontsize=11) + + # 右侧信息框 + scenario = calculate_scenario(rec['years']) + textstr = (f"Knee Point Analysis\n" + f"─────────────────\n" + f"Optimal Time: {rec['years']:.0f} years\n" + f"Total Energy: {rec['energy_PJ']:.0f} PJ\n" + f"─────────────────\n" + f"Elevator: {scenario['elevator_payload']/1e6:.1f}M tons\n" + f"Rockets: {scenario['rocket_payload']/1e6:.1f}M tons\n" + f"Launches: {scenario['rocket_launches']:,}\n" + f"Sites Used: {scenario['sites_used']}") + + props = dict(boxstyle='round', facecolor='white', alpha=0.9, edgecolor='gray') + ax.text(0.02, 0.35, textstr, transform=ax.transAxes, fontsize=11, + verticalalignment='top', horizontalalignment='left', bbox=props, + family='monospace') + + plt.tight_layout() + plt.savefig(save_path, dpi=150, bbox_inches='tight') + print(f"组合方案决策图已保存至: {save_path}") + + return fig + + +def print_combined_range_report(df: pd.DataFrame, knee_analysis: Dict, year_range: Tuple[float, float]): + """ + 打印组合方案范围内的分析报告 + """ + year_min, year_max = year_range + + print("\n" + "=" * 80) + print("COMBINED SCENARIO PARETO ANALYSIS (Elevator + Rockets)") + print(f"Analysis Range: {year_min:.0f} - {year_max:.0f} years") + print("=" * 80) + + print(f"\n1. RANGE DEFINITION") + print(f" - Minimum time (all resources): {year_min:.0f} years") + print(f" - Elevator-only time: {year_max:.0f} years") + print(f" - This range requires BOTH elevator and rockets") + + print(f"\n2. PARETO FRONT STATISTICS") + print(f" - Energy at fastest ({year_min:.0f}y): {df['energy_PJ'].max():.0f} PJ") + print(f" - Energy at slowest ({year_max:.0f}y): {df['energy_PJ'].min():.0f} PJ") + print(f" - Energy reduction: {df['energy_PJ'].max() - df['energy_PJ'].min():.0f} PJ " + f"({(1 - df['energy_PJ'].min()/df['energy_PJ'].max())*100:.1f}%)") + + print(f"\n3. KNEE POINT DETECTION RESULTS") + print("-" * 70) + print(f" {'Method':<20} {'Years':>8} {'Energy(PJ)':>12} {'Elev%':>8} {'Rocket%':>8}") + print("-" * 70) + + for method, data in knee_analysis['methods'].items(): + rocket_pct = (1 - data['elevator_fraction']) * 100 + print(f" {method:<20} {data['years']:>8.0f} {data['energy_PJ']:>12.0f} " + f"{data['elevator_fraction']*100:>7.1f}% {rocket_pct:>7.1f}%") + + print("-" * 70) + + rec = knee_analysis['recommended'] + scenario = calculate_scenario(rec['years']) + + print(f"\n4. RECOMMENDED OPTIMAL POINT") + print(f" ╔═══════════════════════════════════════════════════════╗") + print(f" ║ Method: Max Distance (most robust) ║") + print(f" ║ Completion Time: {rec['years']:>6.0f} years ║") + print(f" ║ Total Energy: {rec['energy_PJ']:>6.0f} PJ ║") + print(f" ║ Elevator Payload: {scenario['elevator_payload']/1e6:>6.1f} M tons ({rec['elevator_fraction']*100:.0f}%) ║") + print(f" ║ Rocket Payload: {scenario['rocket_payload']/1e6:>6.1f} M tons ({(1-rec['elevator_fraction'])*100:.0f}%) ║") + print(f" ║ Total Launches: {scenario['rocket_launches']:>6,} ║") + print(f" ║ Sites Required: {scenario['sites_used']:>6} ║") + print(f" ╚═══════════════════════════════════════════════════════╝") + + print(f"\n5. TRADE-OFF ANALYSIS") + + # 与最快方案对比 + fast_scenario = calculate_scenario(year_min + 0.5) + if fast_scenario: + time_gain = rec['years'] - year_min + energy_save = fast_scenario['total_energy_PJ'] - rec['energy_PJ'] + print(f"\n vs. Fastest ({year_min:.0f}y):") + print(f" - Extra time: +{time_gain:.0f} years") + print(f" - Energy saved: {energy_save:.0f} PJ ({energy_save/fast_scenario['total_energy_PJ']*100:.1f}%)") + print(f" - Efficiency: {energy_save/time_gain:.1f} PJ saved per extra year") + + # 与纯电梯对比 + elev_scenario = calculate_scenario(year_max - 0.5) + if elev_scenario: + time_save = year_max - rec['years'] + energy_cost = rec['energy_PJ'] - elev_scenario['total_energy_PJ'] + print(f"\n vs. Elevator-only ({year_max:.0f}y):") + print(f" - Time saved: {time_save:.0f} years") + print(f" - Extra energy: {energy_cost:.0f} PJ ({energy_cost/elev_scenario['total_energy_PJ']*100:.1f}%)") + print(f" - Cost: {energy_cost/time_save:.1f} PJ per year saved") + + print("\n" + "=" * 80) + print("INTERPRETATION:") + print(f"The knee point at {rec['years']:.0f} years represents the optimal trade-off") + print("where further extending the timeline yields diminishing returns,") + print("while shortening it incurs disproportionately higher energy costs.") + print("=" * 80) + + +# ============== 主程序 ============== + +if __name__ == "__main__": + print("=" * 80) + print("PARETO FRONT & KNEE POINT OPTIMIZATION") + print("Space Elevator + Rocket Combination for Moon Colony") + print("=" * 80) + + # ===== 分析1: 组合方案范围 (101-186年) ===== + print("\n" + "=" * 80) + print("ANALYSIS 1: Combined Scenario Range (Elevator + Rockets Required)") + print("=" * 80) + + df_combined, year_min, year_max = analyze_combined_range() + knee_combined = analyze_knee_points(df_combined) + + print_combined_range_report(df_combined, knee_combined, (year_min, year_max)) + + plot_combined_range_analysis(df_combined, knee_combined, (year_min, year_max)) + plot_combined_decision(df_combined, knee_combined, (year_min, year_max)) + + # ===== 分析2: 完整范围 (100-300年) ===== + print("\n" + "=" * 80) + print("ANALYSIS 2: Full Range (100-300 years)") + print("=" * 80) + + df_full = generate_pareto_front(year_min=100, year_max=300, num_points=500) + knee_full = analyze_knee_points(df_full) + + print_analysis_report(df_full, knee_full) + plot_pareto_analysis(df_full, knee_full) + plot_decision_recommendation(df_full, knee_full) + + # 保存数据 + df_combined.to_csv('/Volumes/Files/code/mm/20260130_b/pareto_combined_range.csv', index=False) + df_full.to_csv('/Volumes/Files/code/mm/20260130_b/pareto_front_data.csv', index=False) + print("\n数据已保存至 CSV 文件") + + print("\n" + "=" * 80) + print("分析完成！") + print("=" * 80)