2026美赛数学建模B题题思路模型代码 2026 MCM问题B：利用太空电梯系统建立月球殖民地——详细建模与求解补充材料
f.write(f"CO2减排: {results_c['detailed_result']['environmental_impact']['emissions_reduction_vs_rocket_only']:.1f}%\n")print(f"CO2减排（相比纯火箭）: {results_c['detailed_result']['environmental_impact']['emiss
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问题二：
https://blog.csdn.net/m0_52343631/article/details/157541917?spm=1001.2014.3001.5502
https://blog.csdn.net/m0_52343631/article/details/157541917?spm=1001.2014.3001.5502
https://blog.csdn.net/m0_52343631/article/details/157541917?spm=1001.2014.3001.5502https://blog.csdn.net/m0_52343631/article/details/157541917
问题三：
https://blog.csdn.net/m0_52343631/article/details/157542025?spm=1001.2014.3001.5502
https://blog.csdn.net/m0_52343631/article/details/157542025?spm=1001.2014.3001.5502https://blog.csdn.net/m0_52343631/article/details/157542025?spm=1001.2014.3001.5502https://blog.csdn.net/m0_52343631/article/details/157542025
一、问题1的数学建模深度分析
1.1 问题背景与核心挑战
问题1要求我们为建造100,000人月球殖民地所需运输1亿吨材料，设计并比较三种不同的运输方案。这个问题的复杂性在于需要同时考虑多个相互关联的因素：
-
运输系统的技术特性差异：太空电梯系统与传统火箭系统在运载能力、成本结构、可靠性、环境影响等方面存在本质差异
-
时间维度约束：运输时间直接影响殖民地的建设周期和成本
-
资源分配优化：在混合方案中需要优化两种运输方式的比例分配
-
系统可靠性影响：非完美工作条件对运输效率的影响
1.2 数学模型构建原理
1.2.1 基础数学模型框架
我们建立一个多目标优化模型，主要目标函数包括：
-
最小化总成本：$C_{total} = C_{transport} + C_{maintenance} + C_{risk}$
-
最小化运输时间：$T_{total} = f(Q, C_{capacity}, η)$
-
最小化环境影响：$E_{total} = Σ(E_i × Q_i)$
其中：
-
$Q$ 为总运输量（1亿吨）
-
$C_{capacity}$ 为运输系统的运载能力
-
$η$ 为系统可靠性系数
-
$E_i$ 为每吨材料的单位环境影响
1.2.2 太空电梯系统的详细建模
太空电梯系统由三个银河港口组成，每个港口的具体技术参数需要详细建模：
class GalacticHarborModel:
"""银河港口详细技术模型"""
def __init__(self):
# 基础技术参数
self.tether_length = 100000 # 公里
self.tether_material = "graphene" # 系绳材料
self.number_of_tethers = 2 # 每个港口系绳数量
self.elevators_per_harbor = 4 # 每个港口电梯数量
# 性能参数
self.max_payload_per_elevator = 50000 # 吨/天（单个电梯）
self.energy_consumption_per_ton = 500 # 千瓦时/吨
self.operational_lifetime = 50 # 年
# 成本参数（百万美元）
self.construction_cost = 200000 # 建设成本
self.operation_cost_per_ton = 0.5 # 运营成本/吨
self.maintenance_cost_per_year = 500 # 年维护成本
# 环境参数
self.co2_emission_per_ton = 0.1 # 吨CO2/吨货物
self.energy_source = "solar_power" # 能源类型
def calculate_daily_capacity(self, reliability=1.0):
"""计算每日运输能力"""
base_capacity = self.elevators_per_harbor * self.max_payload_per_elevator
return base_capacity * reliability
def calculate_annual_capacity(self, operational_days=365, reliability=1.0):
"""计算年运输能力"""
daily_capacity = self.calculate_daily_capacity(reliability)
return daily_capacity * operational_days
def analyze_technical_constraints(self):
"""分析技术约束"""
constraints = {
'tether_stress_limit': self.calculate_tether_stress(),
'power_requirements': self.calculate_power_needs(),
'thermal_management': self.analyze_thermal_issues(),
'orbital_mechanics': self.analyze_orbital_dynamics()
}
return constraints
def calculate_tether_stress(self):
"""计算系绳应力"""
# 基于材料特性的应力分析
graphene_tensile_strength = 130 # GPa
tether_cross_section = 1.0 # 平方米
max_tension = graphene_tensile_strength * 1e9 * tether_cross_section # 牛顿
# 考虑载荷和离心力
earth_gravity = 9.81 # m/s²
rotational_velocity = 465 # m/s（赤道处）
stress_analysis = {
'max_theoretical_tension': max_tension,
'safety_factor': 3.0, # 安全系数
'allowable_load': max_tension / 3.0
}
return stress_analysis
1.2.3 火箭发射系统的详细建模
传统火箭系统的建模需要考虑更多的不确定性和变异性：
class RocketLaunchSystemModel:
"""火箭发射系统详细模型"""
def __init__(self):
# 全球发射基地参数
self.launch_sites = {
'Alaska': {'capacity': 12, 'cost_per_launch': 150, 'reliability': 0.95},
'California': {'capacity': 24, 'cost_per_launch': 120, 'reliability': 0.96},
'Texas': {'capacity': 18, 'cost_per_launch': 130, 'reliability': 0.94},
'Florida': {'capacity': 36, 'cost_per_launch': 110, 'reliability': 0.97},
'Virginia': {'capacity': 12, 'cost_per_launch': 140, 'reliability': 0.93},
'Kazakhstan': {'capacity': 20, 'cost_per_launch': 100, 'reliability': 0.92},
'French_Guiana': {'capacity': 24, 'cost_per_launch': 115, 'reliability': 0.96},
'India': {'capacity': 16, 'cost_per_launch': 95, 'reliability': 0.91},
'China': {'capacity': 30, 'cost_per_launch': 105, 'reliability': 0.94},
'New_Zealand': {'capacity': 8, 'cost_per_launch': 160, 'reliability': 0.90}
}
# 火箭技术参数
self.rocket_types = {
'Falcon_Heavy_Advanced': {
'payload_to_moon': 130, # 吨
'launch_cost': 150, # 百万美元
'co2_emission': 2500, # 吨CO2/发射
'turnaround_time': 14 # 天
},
'Starship': {
'payload_to_moon': 150,
'launch_cost': 100,
'co2_emission': 2800,
'turnaround_time': 7
}
}
def optimize_launch_schedule(self, total_payload, selected_sites=None, rocket_type='Falcon_Heavy_Advanced'):
"""优化发射计划"""
if selected_sites is None:
selected_sites = list(self.launch_sites.keys())
rocket = self.rocket_types[rocket_type]
payload_per_launch = rocket['payload_to_moon']
# 计算总发射次数
total_launches = np.ceil(total_payload / payload_per_launch)
# 分配发射任务到各个基地
site_capacities = {site: self.launch_sites[site]['capacity'] for site in selected_sites}
total_capacity = sum(site_capacities.values())
launch_allocation = {}
remaining_launches = total_launches
for site, capacity in site_capacities.items():
allocation = min(capacity * 365 / rocket['turnaround_time'], remaining_launches)
launch_allocation[site] = allocation
remaining_launches -= allocation
return {
'total_launches': total_launches,
'launch_allocation': launch_allocation,
'years_needed': total_launches / (total_capacity * 365 / rocket['turnaround_time']),
'rocket_type': rocket_type
}
def calculate_environmental_impact(self, launch_schedule):
"""计算环境影响"""
rocket = self.rocket_types[launch_schedule['rocket_type']]
total_launches = launch_schedule['total_launches']
co2_emissions = total_launches * rocket['co2_emission']
# 考虑其他环境影响
other_impacts = {
'atmospheric_pollution': total_launches * 50, # 吨污染物
'noise_pollution': total_launches * 100, # 噪音影响指数
'local_ecosystem_impact': total_launches * 2 # 生态系统影响指数
}
return {
'co2_emissions_tons': co2_emissions,
'other_impacts': other_impacts,
'emissions_per_ton': co2_emissions / (total_launches * rocket['payload_to_moon'])
}
1.3 场景A：仅使用太空电梯系统的详细分析
1.3.1 运输能力建模
太空电梯系统的年运输能力计算公式：
$C_{annual} = N_{harbors} × N_{elevators} × P_{daily} × D_{operational} × η$
其中：
-
$N_{harbors} = 3$（银河港口数量）
-
$N_{elevators} = 4$（每个港口电梯数量）
-
$P_{daily} = 50,000$吨/天（单个电梯日运输能力）
-
$D_{operational} = 365$天/年
-
$η = 0.95$（系统可靠性）
class ScenarioAAnalysis:
"""场景A：仅太空电梯的详细分析"""
def __init__(self):
self.total_material = 1e8 # 1亿吨
self.harbor_model = GalacticHarborModel()
def detailed_transport_plan(self):
"""详细运输计划"""
# 计算年运输能力
annual_capacity = 3 * self.harbor_model.calculate_annual_capacity()
# 计算总时间
years_needed = self.total_material / annual_capacity
# 分阶段运输计划
phases = self.define_construction_phases(years_needed)
# 成本分析
cost_breakdown = self.calculate_cost_breakdown(years_needed)
# 风险评估
risk_analysis = self.associate_risks()
return {
'annual_capacity_tons': annual_capacity,
'years_needed': years_needed,
'completion_year': 2050 + years_needed,
'phases': phases,
'cost_breakdown': cost_breakdown,
'risk_analysis': risk_analysis
}
def define_construction_phases(self, total_years):
"""定义建设阶段"""
phases = [
{
'name': 'Phase 1: 基础建设阶段',
'duration_years': total_years * 0.3,
'material_percentage': 0.4,
'priority_materials': ['结构钢材', '建筑材料', '重型设备'],
'logistics_requirements': '高密度，大体积运输'
},
{
'name': 'Phase 2: 系统安装阶段',
'duration_years': total_years * 0.4,
'material_percentage': 0.45,
'priority_materials': ['生命支持系统', '能源系统', '通信设备'],
'logistics_requirements': '精密设备，防震运输'
},
{
'name': 'Phase 3: 完善与调试阶段',
'duration_years': total_years * 0.3,
'material_percentage': 0.15,
'priority_materials': ['内饰材料', '科学设备', '备用部件'],
'logistics_requirements': '小批量，高频次运输'
}
]
return phases
def calculate_cost_breakdown(self, years_needed):
"""成本细分分析"""
# 建设成本（一次性）
construction_cost = 3 * self.harbor_model.construction_cost # 三个港口
# 运营成本
operation_cost = self.total_material * self.harbor_model.operation_cost_per_ton
# 维护成本
maintenance_cost = years_needed * 3 * self.harbor_model.maintenance_cost_per_year
# 能源成本
energy_consumption = self.total_material * self.harbor_model.energy_consumption_per_ton # 千瓦时
energy_cost = energy_consumption * 0.15 / 1000 # 电价0.15美元/千瓦时，转换为百万美元
total_cost = construction_cost + operation_cost + maintenance_cost + energy_cost
return {
'construction_cost': construction_cost,
'operation_cost': operation_cost,
'maintenance_cost': maintenance_cost,
'energy_cost': energy_cost,
'total_cost': total_cost,
'cost_per_ton': total_cost / self.total_material
}
def associate_risks(self):
"""风险评估"""
risks = [
{
'risk_type': '技术风险',
'description': '系绳材料疲劳或断裂',
'probability': 0.05,
'impact': '灾难性',
'mitigation': '定期检测，冗余设计'
},
{
'risk_type': '运营风险',
'description': '电梯机械故障',
'probability': 0.1,
'impact': '高',
'mitigation': '预防性维护，备用电梯'
},
{
'risk_type': '环境风险',
'description': '太空碎片碰撞',
'probability': 0.03,
'impact': '高',
'mitigation': '主动避让系统，加固设计'
},
{
'risk_type': '经济风险',
'description': '能源价格波动',
'probability': 0.2,
'impact': '中',
'mitigation': '长期能源合同，多元化能源'
}
]
return risks
def perform_sensitivity_analysis(self):
"""敏感性分析"""
parameters = {
'reliability': np.arange(0.8, 1.01, 0.05),
'daily_capacity': np.arange(40000, 60001, 5000),
'operational_days': np.arange(300, 366, 10)
}
results = []
for param_name, values in parameters.items():
for value in values:
if param_name == 'reliability':
annual_cap = 3 * self.harbor_model.calculate_annual_capacity(reliability=value)
elif param_name == 'daily_capacity':
original = self.harbor_model.max_payload_per_elevator
self.harbor_model.max_payload_per_elevator = value
annual_cap = 3 * self.harbor_model.calculate_annual_capacity()
self.harbor_model.max_payload_per_elevator = original
else:
annual_cap = 3 * self.harbor_model.calculate_annual_capacity(operational_days=value)
years = self.total_material / annual_cap
results.append({
'parameter': param_name,
'value': value,
'annual_capacity': annual_cap,
'years_needed': years
})
return pd.DataFrame(results)
1.3.2 时间序列分析与进度安排
class TimeSeriesAnalysis:
"""时间序列详细分析"""
def __init__(self, scenario_a_analysis):
self.analysis = scenario_a_analysis
self.total_years = None
def create_detailed_schedule(self):
"""创建详细时间表"""
plan = self.analysis.detailed_transport_plan()
self.total_years = plan['years_needed']
# 创建月级进度表
monthly_schedule = []
current_material = 0
monthly_capacity = plan['annual_capacity_tons'] / 12
for month in range(int(self.total_years * 12)):
month_data = {
'month': month + 1,
'year': 2050 + month // 12,
'month_of_year': (month % 12) + 1,
'material_delivered': monthly_capacity,
'cumulative_material': current_material + monthly_capacity,
'completion_percentage': (current_material + monthly_capacity) / self.total_material * 100
}
# 考虑季节性因素
if (month % 12) in [0, 1, 11]: # 冬季月份
month_data['efficiency_factor'] = 0.9
month_data['actual_delivery'] = monthly_capacity * 0.9
else:
month_data['efficiency_factor'] = 1.0
month_data['actual_delivery'] = monthly_capacity
monthly_schedule.append(month_data)
current_material += month_data['actual_delivery']
return pd.DataFrame(monthly_schedule)
def analyze_critical_path(self):
"""关键路径分析"""
critical_path = {
'milestones': [
{'name': '港口建设完成', 'time_months': 0, 'dependency': None},
{'name': '首批材料到达', 'time_months': 6, 'dependency': '港口建设完成'},
{'name': '基础结构完成30%', 'time_months': 24, 'dependency': '首批材料到达'},
{'name': '生命支持系统安装', 'time_months': 48, 'dependency': '基础结构完成30%'},
{'name': '能源系统上线', 'time_months': 72, 'dependency': '生命支持系统安装'},
{'name': '殖民地首批居民', 'time_months': 96, 'dependency': '能源系统上线'},
{'name': '全部建设完成', 'time_months': int(self.total_years * 12), 'dependency': '殖民地首批居民'}
],
'critical_activities': [
'系绳部署与调试',
'电梯生产与安装',
'运输系统集成测试',
'连续运营建立'
]
}
return critical_path
1.4 场景B：仅使用传统火箭的详细分析
1.4.1 全球发射基地优化选择
class ScenarioBAnalysis:
"""场景B：仅传统火箭的详细分析"""
def __init__(self):
self.total_material = 1e8
self.rocket_model = RocketLaunchSystemModel()
self.selected_bases = None
def optimize_base_selection(self, budget_constraint=None):
"""优化基地选择"""
# 多目标优化：成本最小化，吞吐量最大化
bases = self.rocket_model.launch_sites
# 创建优化问题
from scipy.optimize import differential_evolution
def objective(x):
# x是二进制向量，表示是否选择每个基地
selected_indices = np.where(x > 0.5)[0]
if len(selected_indices) == 0:
return 1e10
selected_bases = list(bases.keys())[selected_indices]
# 计算总容量
total_capacity = sum(bases[base]['capacity'] for base in selected_bases)
# 计算成本
total_cost = sum(bases[base]['cost_per_launch'] for base in selected_bases)
# 目标：最小化成本/容量比
return total_cost / total_capacity
# 运行优化
bounds = [(0, 1)] * len(bases)
result = differential_evolution(objective, bounds, maxiter=100, popsize=20)
# 解析结果
selected_indices = np.where(result.x > 0.5)[0]
self.selected_bases = [list(bases.keys())[i] for i in selected_indices]
return {
'selected_bases': self.selected_bases,
'optimization_score': result.fun,
'number_of_bases': len(self.selected_bases)
}
def detailed_launch_schedule(self, rocket_type='Falcon_Heavy_Advanced'):
"""详细发射计划"""
if self.selected_bases is None:
self.optimize_base_selection()
# 获取发射计划
schedule = self.rocket_model.optimize_launch_schedule(
self.total_material,
self.selected_bases,
rocket_type
)
# 详细成本分析
cost_analysis = self.calculate_detailed_costs(schedule)
# 时间线分析
timeline = self.create_launch_timeline(schedule)
# 风险评估
risks = self.associate_rocket_risks(schedule)
return {
'schedule': schedule,
'cost_analysis': cost_analysis,
'timeline': timeline,
'risk_analysis': risks
}
def calculate_detailed_costs(self, schedule):
"""详细成本计算"""
rocket = self.rocket_model.rocket_types[schedule['rocket_type']]
total_launches = schedule['total_launches']
# 发射成本
launch_costs = total_launches * rocket['launch_cost']
# 基础设施成本
infrastructure_cost = len(self.selected_bases) * 5000 # 百万美元
# 运营成本
operational_cost = total_launches * 20 # 百万美元（每次发射的运营成本）
# 维护成本
maintenance_cost = schedule['years_needed'] * len(self.selected_bases) * 50
total_cost = launch_costs + infrastructure_cost + operational_cost + maintenance_cost
return {
'launch_costs': launch_costs,
'infrastructure_cost': infrastructure_cost,
'operational_cost': operational_cost,
'maintenance_cost': maintenance_cost,
'total_cost': total_cost,
'cost_per_ton': total_cost / self.total_material,
'cost_per_launch': total_cost / total_launches
}
def create_launch_timeline(self, schedule):
"""创建发射时间线"""
rocket = self.rocket_model.rocket_types[schedule['rocket_type']]
total_launches = schedule['total_launches']
years_needed = schedule['years_needed']
# 计算每日发射频率
launches_per_day = total_launches / (years_needed * 365)
# 分配到各基地
daily_schedule = {}
total_daily_capacity = 0
for base, annual_allocation in schedule['launch_allocation'].items():
daily_launches = annual_allocation / 365
daily_schedule[base] = {
'daily_launches': daily_launches,
'daily_payload': daily_launches * rocket['payload_to_moon'],
'launch_windows': self.calculate_launch_windows(base, daily_launches)
}
total_daily_capacity += daily_launches * rocket['payload_to_moon']
return {
'daily_schedule': daily_schedule,
'total_daily_capacity': total_daily_capacity,
'launches_per_day': launches_per_day,
'payload_per_day': launches_per_day * rocket['payload_to_moon']
}
def calculate_launch_windows(self, base, daily_launches):
"""计算发射窗口"""
# 基于地理位置和轨道力学的发射窗口计算
base_locations = {
'Florida': {'lat': 28.5, 'lon': -81.0},
'California': {'lat': 34.6, 'lon': -120.6},
'Texas': {'lat': 31.4, 'lon': -100.5},
# ... 其他基地
}
if base in base_locations:
# 简化计算：每天4个主要发射窗口
windows = [
{'start': '00:00', 'end': '02:00', 'optimal': True},
{'start': '06:00', 'end': '08:00', 'optimal': False},
{'start': '12:00', 'end': '14:00', 'optimal': True},
{'start': '18:00', 'end': '20:00', 'optimal': False}
]
return windows[:int(np.ceil(daily_launches * 4))] # 每个窗口可支持0.25次发射
return []
def associate_rocket_risks(self, schedule):
"""火箭运输风险评估"""
total_launches = schedule['total_launches']
risks = [
{
'risk_type': '发射失败风险',
'description': '火箭发射过程中故障',
'probability': 0.02, # 2%失败率
'expected_failures': total_launches * 0.02,
'impact': '高（损失有效载荷和火箭）',
'mitigation': '冗余发射，保险，改进设计'
},
{
'risk_type': '天气延迟风险',
'description': '恶劣天气导致发射延迟',
'probability': 0.15,
'expected_delays': total_launches * 0.15,
'impact': '中（进度延迟）',
'mitigation': '多个发射场，天气预测系统'
},
{
'risk_type': '供应链风险',
'description': '火箭生产或燃料供应链中断',
'probability': 0.08,
'impact': '高',
'mitigation': '多个供应商，战略储备'
},
{
'risk_type': '环境法规风险',
'description': '环保法规变化限制发射频率',
'probability': 0.05,
'impact': '中到高',
'mitigation': '环保技术投资，政府关系'
}
]
return risks
1.4.2 大规模火箭发射的物流挑战
class RocketLogisticsOptimization:
"""火箭物流优化"""
def __init__(self, scenario_b_analysis):
self.analysis = scenario_b_analysis
self.schedule = None
def analyze_supply_chain(self):
"""分析供应链需求"""
# 火箭生产需求
total_launches = self.analysis.schedule['schedule']['total_launches']
supply_requirements = {
'rockets_needed': total_launches * 1.1, # 10%备用
'fuel_requirements': self.calculate_fuel_needs(total_launches),
'components': self.calculate_component_needs(total_launches),
'workforce': self.calculate_workforce_needs(total_launches)
}
return supply_requirements
def calculate_fuel_needs(self, total_launches):
"""计算燃料需求"""
# Falcon Heavy燃料组成
fuel_per_launch = {
'RP-1': 400000, # 公斤
'LOX': 900000, # 公斤
'LH2': 100000, # 公斤（二级）
}
total_fuel = {}
for fuel, amount in fuel_per_launch.items():
total_fuel[fuel] = amount * total_launches / 1000 # 转换为吨
return total_fuel
def calculate_component_needs(self, total_launches):
"""计算组件需求"""
components = {
'engines': total_launches * 27, # Falcon Heavy有27个发动机
'avionics_systems': total_launches,
'fairings': total_launches,
'landing_legs': total_launches * 3, # 3个核心级
'grid_fins': total_launches * 12
}
return components
def calculate_workforce_needs(self, total_launches):
"""计算人力资源需求"""
workforce = {
'launch_team_per_launch': 150,
'manufacturing_per_rocket': 1000,
'logistics_per_day': 500,
'management_and_support': 200
}
total_workforce = {}
for role, per_unit in workforce.items():
if 'per_launch' in role:
total_workforce[role] = per_unit * total_launches
elif 'per_rocket' in role:
total_workforce[role] = per_unit * total_launches * 1.1
elif 'per_day' in role:
total_workforce[role] = per_unit * 365 * self.analysis.schedule['schedule']['years_needed']
else:
total_workforce[role] = per_unit
return total_workforce
def optimize_transportation_network(self):
"""优化地面运输网络"""
# 材料运输到发射场
material_flow = {
'sources': ['钢铁厂', '铝厂', '复合材料厂', '电子元件厂', '燃料厂'],
'destinations': self.analysis.selected_bases,
'transport_modes': ['铁路', '海运', '管道', '公路']
}
# 创建运输网络模型
network = self.create_transport_network(material_flow)
# 优化运输路线
optimized_routes = self.optimize_routes(network)
return {
'material_flow': material_flow,
'transport_network': network,
'optimized_routes': optimized_routes
}
def create_transport_network(self, material_flow):
"""创建运输网络模型"""
network = {
'nodes': [],
'edges': [],
'capacities': {},
'costs': {}
}
# 添加节点
all_locations = material_flow['sources'] + material_flow['destinations']
for loc in all_locations:
network['nodes'].append({
'name': loc,
'type': 'source' if loc in material_flow['sources'] else 'sink',
'capacity': self.estimate_node_capacity(loc)
})
# 添加边（运输路线）
for source in material_flow['sources']:
for dest in material_flow['destinations']:
for mode in material_flow['transport_modes']:
edge = {
'from': source,
'to': dest,
'mode': mode,
'distance': self.calculate_distance(source, dest),
'cost_per_ton': self.calculate_transport_cost(source, dest, mode),
'capacity_per_day': self.calculate_mode_capacity(mode)
}
network['edges'].append(edge)
return network
1.5 场景C：混合方案的详细分析与优化
1.5.1 多目标优化模型
class ScenarioCAnalysis:
"""场景C：混合方案的详细分析"""
def __init__(self):
self.total_material = 1e8
self.harbor_model = GalacticHarborModel()
self.rocket_model = RocketLaunchSystemModel()
def multi_objective_optimization(self):
"""多目标优化模型"""
# 定义目标函数
def objective(x):
# x[0]: 太空电梯运输比例 (0-1)
# x[1]: 使用的火箭基地数量 (0-10)
# x[2]: 火箭类型选择 (0=Falcon, 1=Starship)
harbor_ratio = x[0]
rocket_bases = int(x[1] * 10)
rocket_type_idx = int(round(x[2]))
rocket_types = ['Falcon_Heavy_Advanced', 'Starship']
rocket_type = rocket_types[rocket_type_idx]
# 计算运输量分配
material_by_harbor = self.total_material * harbor_ratio
material_by_rocket = self.total_material * (1 - harbor_ratio)
# 计算时间和成本
harbor_result = self.calculate_harbor_transport(material_by_harbor)
rocket_result = self.calculate_rocket_transport(material_by_rocket, rocket_bases, rocket_type)
# 并行运输，取最大时间
total_time = max(harbor_result['years_needed'], rocket_result['years_needed'])
# 总成本
total_cost = harbor_result['total_cost'] + rocket_result['total_cost']
# 总环境影响
total_emissions = harbor_result['co2_emissions'] + rocket_result['co2_emissions']
# 多目标加权（可根据偏好调整权重）
weight_time = 0.3
weight_cost = 0.4
weight_env = 0.3
# 归一化
normalized_time = total_time / 100 # 最大100年
normalized_cost = total_cost / 1e6 # 转换为十亿美元
normalized_env = total_emissions / 1e7 # 转换为千万吨
return (weight_time * normalized_time +
weight_cost * normalized_cost +
weight_env * normalized_env)
# 约束条件
constraints = [
{'type': 'ineq', 'fun': lambda x: x[0]}, # harbor_ratio >= 0
{'type': 'ineq', 'fun': lambda x: 1 - x[0]}, # harbor_ratio <= 1
{'type': 'ineq', 'fun': lambda x: x[1]}, # rocket_bases >= 0
{'type': 'ineq', 'fun': lambda x: 1 - x[1]}, # rocket_bases <= 1
{'type': 'ineq', 'fun': lambda x: x[2]}, # rocket_type >= 0
{'type': 'ineq', 'fun': lambda x: 1 - x[2]} # rocket_type <= 1
]
# 初始猜测
initial_guess = [0.5, 0.5, 0.5]
# 运行优化
from scipy.optimize import minimize
result = minimize(objective, initial_guess,
constraints=constraints,
method='SLSQP',
bounds=[(0.1, 0.9), (0.1, 0.9), (0, 1)])
# 解析优化结果
optimal_harbor_ratio = result.x[0]
optimal_rocket_bases = int(result.x[1] * 10)
optimal_rocket_type = 'Starship' if result.x[2] > 0.5 else 'Falcon_Heavy_Advanced'
# 计算详细结果
detailed_result = self.calculate_detailed_mix(
optimal_harbor_ratio,
optimal_rocket_bases,
optimal_rocket_type
)
return {
'optimal_solution': result,
'harbor_ratio': optimal_harbor_ratio,
'rocket_bases': optimal_rocket_bases,
'rocket_type': optimal_rocket_type,
'detailed_result': detailed_result
}
def calculate_harbor_transport(self, material_amount):
"""计算太空电梯运输"""
annual_capacity = 3 * self.harbor_model.calculate_annual_capacity()
years_needed = material_amount / annual_capacity
cost = material_amount * self.harbor_model.operation_cost_per_ton
maintenance = years_needed * 3 * self.harbor_model.maintenance_cost_per_year
construction = 3 * self.harbor_model.construction_cost
total_cost = cost + maintenance + construction
co2_emissions = material_amount * self.harbor_model.co2_emission_per_ton
return {
'years_needed': years_needed,
'total_cost': total_cost,
'co2_emissions': co2_emissions,
'annual_capacity': annual_capacity
}
def calculate_rocket_transport(self, material_amount, num_bases, rocket_type):
"""计算火箭运输"""
# 选择最优基地
all_bases = list(self.rocket_model.launch_sites.keys())
selected_bases = all_bases[:num_bases]
# 计算发射计划
schedule = self.rocket_model.optimize_launch_schedule(
material_amount, selected_bases, rocket_type
)
# 成本计算
rocket = self.rocket_model.rocket_types[rocket_type]
total_launches = schedule['total_launches']
launch_costs = total_launches * rocket['launch_cost']
infrastructure = num_bases * 5000
operational = total_launches * 20
maintenance = schedule['years_needed'] * num_bases * 50
total_cost = launch_costs + infrastructure + operational + maintenance
co2_emissions = total_launches * rocket['co2_emission']
return {
'years_needed': schedule['years_needed'],
'total_cost': total_cost,
'co2_emissions': co2_emissions,
'total_launches': total_launches
}
def calculate_detailed_mix(self, harbor_ratio, rocket_bases, rocket_type):
"""计算混合方案的详细结果"""
# 运输量分配
material_by_harbor = self.total_material * harbor_ratio
material_by_rocket = self.total_material * (1 - harbor_ratio)
# 详细计算
harbor_details = self.calculate_harbor_transport(material_by_harbor)
rocket_details = self.calculate_rocket_transport(material_by_rocket, rocket_bases, rocket_type)
# 总体结果
total_time = max(harbor_details['years_needed'], rocket_details['years_needed'])
total_cost = harbor_details['total_cost'] + rocket_details['total_cost']
total_emissions = harbor_details['co2_emissions'] + rocket_details['co2_emissions']
# 效率指标
efficiency_metrics = {
'cost_per_ton': total_cost / self.total_material,
'emissions_per_ton': total_emissions / self.total_material,
'throughput_per_year': self.total_material / total_time,
'system_utilization': self.calculate_system_utilization(
harbor_details, rocket_details, total_time
)
}
return {
'transport_allocation': {
'harbor_tons': material_by_harbor,
'harbor_percentage': harbor_ratio * 100,
'rocket_tons': material_by_rocket,
'rocket_percentage': (1 - harbor_ratio) * 100
},
'time_analysis': {
'harbor_years': harbor_details['years_needed'],
'rocket_years': rocket_details['years_needed'],
'total_years': total_time,
'completion_year': 2050 + total_time,
'critical_path': 'harbor' if harbor_details['years_needed'] > rocket_details['years_needed'] else 'rocket'
},
'cost_analysis': {
'harbor_cost': harbor_details['total_cost'],
'rocket_cost': rocket_details['total_cost'],
'total_cost': total_cost,
'cost_breakdown_percentage': {
'harbor': harbor_details['total_cost'] / total_cost * 100,
'rocket': rocket_details['total_cost'] / total_cost * 100
}
},
'environmental_impact': {
'harbor_emissions': harbor_details['co2_emissions'],
'rocket_emissions': rocket_details['co2_emissions'],
'total_emissions': total_emissions,
'emissions_reduction_vs_rocket_only': (
(self.total_material * 2.5 - total_emissions) /
(self.total_material * 2.5) * 100
)
},
'efficiency_metrics': efficiency_metrics
}
def calculate_system_utilization(self, harbor_details, rocket_details, total_time):
"""计算系统利用率"""
harbor_capacity = harbor_details['annual_capacity']
harbor_material = self.total_material * self.harbor_ratio if hasattr(self, 'harbor_ratio') else 0
harbor_utilization = (harbor_material / harbor_capacity) / total_time if total_time > 0 else 0
# 火箭利用率
rocket_launches = rocket_details.get('total_launches', 0)
rocket_utilization = rocket_launches / (365 * total_time) if total_time > 0 else 0
return {
'harbor_utilization': min(harbor_utilization, 1.0),
'rocket_utilization': min(rocket_utilization, 1.0),
'overall_utilization': (harbor_utilization + rocket_utilization) / 2
}
1.5.2 动态调度与协同优化
class DynamicSchedulingSystem:
"""动态调度系统"""
def __init__(self, mix_analysis):
self.analysis = mix_analysis
self.schedule = None
def create_dynamic_schedule(self):
"""创建动态调度计划"""
details = self.analysis.detailed_result
# 基于材料类型和优先级进行调度
material_categories = self.categorize_materials()
# 创建时间线
timeline = self.build_timeline(details)
# 优化调度
optimized_schedule = self.optimize_schedule(timeline, material_categories)
# 风险评估与缓冲
risk_buffer = self.add_risk_buffers(optimized_schedule)
return {
'material_categories': material_categories,
'timeline': timeline,
'optimized_schedule': optimized_schedule,
'risk_buffer': risk_buffer,
'key_performance_indicators': self.calculate_kpis(optimized_schedule)
}
def categorize_materials(self):
"""材料分类"""
categories = {
'heavy_infrastructure': {
'description': '重型基础设施材料',
'percentage': 0.40,
'preferred_transport': 'harbor',
'priority': 1,
'examples': ['结构钢', '混凝土', '大型机械']
},
'life_support': {
'description': '生命支持系统',
'percentage': 0.25,
'preferred_transport': 'mixed',
'priority': 2,
'examples': ['水处理系统', '空气净化器', '温室模块']
},
'energy_systems': {
'description': '能源系统',
'percentage': 0.15,
'preferred_transport': 'harbor',
'priority': 2,
'examples': ['太阳能板', '核电池', '电力系统']
},
'habitation': {
'description': '居住设施',
'percentage': 0.10,
'preferred_transport': 'mixed',
'priority': 3,
'examples': ['居住模块', '家具', '生活设施']
},
'scientific': {
'description': '科学设备',
'percentage': 0.05,
'preferred_transport': 'rocket',
'priority': 4,
'examples': ['实验室设备', '望远镜', '探测车']
},
'consumables': {
'description': '消耗品',
'percentage': 0.05,
'preferred_transport': 'rocket',
'priority': 5,
'examples': ['食品', '医疗用品', '备件']
}
}
# 分配运输量
total_material = self.analysis.total_material
for category in categories.values():
category['tonnage'] = total_material * category['percentage']
category['harbor_allocation'] = category['tonnage'] * 0.7 # 70%通过港口
category['rocket_allocation'] = category['tonnage'] * 0.3 # 30%通过火箭
return categories
def build_timeline(self, details):
"""构建时间线"""
total_years = details['time_analysis']['total_years']
timeline = {
'phases': [],
'milestones': [],
'resource_allocation': {}
}
# 定义阶段
phases = [
{
'name': 'Phase 1: 基础建设 (年 1-3)',
'duration_years': 3,
'focus': '重型基础设施',
'harbor_load': 0.8,
'rocket_load': 0.2
},
{
'name': 'Phase 2: 系统安装 (年 4-7)',
'duration_years': 4,
'focus': '生命支持和能源系统',
'harbor_load': 0.6,
'rocket_load': 0.4
},
{
'name': 'Phase 3: 居住设施 (年 8-10)',
'duration_years': 3,
'focus': '居住和科学设施',
'harbor_load': 0.4,
'rocket_load': 0.6
},
{
'name': 'Phase 4: 完善运营 (年 11+)',
'duration_years': total_years - 10,
'focus': '消耗品和优化',
'harbor_load': 0.3,
'rocket_load': 0.7
}
]
timeline['phases'] = phases
# 里程碑
milestones = [
{'year': 1, 'event': '首批材料到达月球'},
{'year': 3, 'event': '基础结构完成50%'},
{'year': 5, 'event': '生命支持系统运行'},
{'year': 7, 'event': '首批居住设施就绪'},
{'year': 10, 'event': '殖民地容纳10,000人'},
{'year': total_years, 'event': '殖民地完全建成 (100,000人)'}
]
timeline['milestones'] = milestones
return timeline
def optimize_schedule(self, timeline, material_categories):
"""优化调度"""
optimized = {
'monthly_plan': [],
'resource_allocation': {},
'constraints': {}
}
# 创建月度计划
current_month = 1
for phase in timeline['phases']:
phase_months = phase['duration_years'] * 12
for month_in_phase in range(phase_months):
month_data = {
'global_month': current_month,
'phase': phase['name'],
'harbor_capacity_allocation': phase['harbor_load'],
'rocket_capacity_allocation': phase['rocket_load'],
'material_types': self.allocate_materials_by_month(
current_month, material_categories, phase
)
}
optimized['monthly_plan'].append(month_data)
current_month += 1
# 资源分配优化
optimized['resource_allocation'] = self.optimize_resources(optimized['monthly_plan'])
# 约束检查
optimized['constraints'] = self.check_constraints(optimized['monthly_plan'])
return optimized
def allocate_materials_by_month(self, month, categories, phase):
"""按月分配材料"""
# 基于阶段焦点分配材料
focus_map = {
'重型基础设施': ['heavy_infrastructure'],
'生命支持和能源系统': ['life_support', 'energy_systems'],
'居住和科学设施': ['habitation', 'scientific'],
'消耗品和优化': ['consumables']
}
focus = phase['focus']
relevant_categories = focus_map.get(focus, list(categories.keys()))
monthly_allocation = {}
for cat_name in relevant_categories:
if cat_name in categories:
cat = categories[cat_name]
# 按月分配（简化）
monthly_tonnage = cat['tonnage'] / (len(self.analysis.detailed_result['time_analysis']['total_years']) * 12)
monthly_allocation[cat_name] = {
'tons': monthly_tonnage,
'transport_mode': cat['preferred_transport'],
'priority': cat['priority']
}
return monthly_allocation
1.6 综合比较与敏感性分析
1.6.1 三种场景的全面比较
class ComprehensiveComparison:
"""综合比较分析"""
def __init__(self):
self.scenario_a = ScenarioAAnalysis()
self.scenario_b = ScenarioBAnalysis()
self.scenario_c = ScenarioCAnalysis()
# 运行分析
self.results_a = self.scenario_a.detailed_transport_plan()
self.results_b = self.scenario_b.detailed_launch_schedule()
self.results_c = self.scenario_c.multi_objective_optimization()
def create_comparison_matrix(self):
"""创建比较矩阵"""
comparison = {
'technical_feasibility': self.compare_technical_feasibility(),
'economic_viability': self.compare_economics(),
'temporal_efficiency': self.compare_timelines(),
'environmental_impact': self.compare_environmental(),
'risk_assessment': self.compare_risks(),
'scalability': self.compare_scalability()
}
return comparison
def compare_technical_feasibility(self):
"""比较技术可行性"""
feasibility = {
'scenario_a': {
'score': 0.7,
'strengths': ['连续运输能力', '高可靠性', '低运营复杂度'],
'weaknesses': ['新技术风险', '高初始投资', '系绳材料挑战'],
'technology_readiness': 6, # TRL 6-7
'dependencies': ['石墨烯生产', '太空制造技术']
},
'scenario_b': {
'score': 0.9,
'strengths': ['成熟技术', '已验证的可靠性', '现有基础设施'],
'weaknesses': ['高发射频率需求', '环境影响', '发射窗口限制'],
'technology_readiness': 9, # TRL 9
'dependencies': ['发射场扩建', '火箭生产产能']
},
'scenario_c': {
'score': 0.8,
'strengths': ['风险分散', '灵活性', '优化利用'],
'weaknesses': ['系统集成复杂性', '协调挑战', '双重基础设施'],
'technology_readiness': 7, # 平均
'dependencies': ['两种系统协调', '智能调度算法']
}
}
return feasibility
def compare_economics(self):
"""比较经济性"""
economics = {
'scenario_a': {
'total_cost_billion': self.results_a['cost_breakdown']['total_cost'] / 1000,
'cost_per_ton': self.results_a['cost_breakdown']['cost_per_ton'],
'capital_intensity': '非常高',
'operational_efficiency': '高',
'economies_of_scale': '显著',
'break_even_point': '长期运营后'
},
'scenario_b': {
'total_cost_billion': self.results_b['cost_analysis']['total_cost'] / 1000,
'cost_per_ton': self.results_b['cost_analysis']['cost_per_ton'],
'capital_intensity': '中等',
'operational_efficiency': '中等',
'economies_of_scale': '有限',
'break_even_point': '短期'
},
'scenario_c': {
'total_cost_billion': self.results_c['detailed_result']['cost_analysis']['total_cost'] / 1000,
'cost_per_ton': self.results_c['detailed_result']['cost_analysis']['total_cost'] / 1e8,
'capital_intensity': '高',
'operational_efficiency': '高到中等',
'economies_of_scale': '混合',
'break_even_point': '中期'
}
}
return economics
def compare_timelines(self):
"""比较时间线"""
timelines = {
'scenario_a': {
'total_years': self.results_a['years_needed'],
'completion_year': self.results_a['completion_year'],
'critical_path': '港口建设和技术成熟',
'schedule_risk': '中等',
'acceleration_potential': '有限',
'dependencies_timeline': '技术开发是关键'
},
'scenario_b': {
'total_years': self.results_b['schedule']['years_needed'],
'completion_year': 2050 + self.results_b['schedule']['years_needed'],
'critical_path': '发射频率和生产能力',
'schedule_risk': '低到中等',
'acceleration_potential': '中等（通过增加发射场）',
'dependencies_timeline': '基础设施扩建'
},
'scenario_c': {
'total_years': self.results_c['detailed_result']['time_analysis']['total_years'],
'completion_year': self.results_c['detailed_result']['time_analysis']['completion_year'],
'critical_path': self.results_c['detailed_result']['time_analysis']['critical_path'],
'schedule_risk': '低',
'acceleration_potential': '高（可调整混合比例）',
'dependencies_timeline': '系统集成和协调'
}
}
return timelines
def create_decision_support_dashboard(self):
"""创建决策支持仪表板"""
dashboard = {
'summary_metrics': self.calculate_summary_metrics(),
'sensitivity_analysis': self.perform_comprehensive_sensitivity(),
'recommendation_matrix': self.create_recommendation_matrix(),
'implementation_roadmap': self.create_implementation_roadmap()
}
return dashboard
def calculate_summary_metrics(self):
"""计算汇总指标"""
metrics = {}
for scenario, results in [('A', self.results_a), ('B', self.results_b), ('C', self.results_c['detailed_result'])]:
if scenario == 'A':
cost = results['cost_breakdown']['total_cost']
time = results['years_needed']
risk_score = 0.3 # 基于风险评估
elif scenario == 'B':
cost = results['cost_analysis']['total_cost']
time = results['schedule']['years_needed']
risk_score = 0.2
else: # C
cost = results['cost_analysis']['total_cost']
time = results['time_analysis']['total_years']
risk_score = 0.25
# 计算综合得分（越低越好）
normalized_cost = cost / 1e6 # 转换为十亿美元
normalized_time = time / 100 # 最大100年
composite_score = (0.4 * normalized_cost +
0.3 * normalized_time +
0.3 * risk_score)
metrics[f'Scenario_{scenario}'] = {
'composite_score': composite_score,
'cost_score': normalized_cost,
'time_score': normalized_time,
'risk_score': risk_score,
'ranking': None # 将在比较后分配
}
# 排序
sorted_scores = sorted([(scenario, data['composite_score'])
for scenario, data in metrics.items()],
key=lambda x: x[1])
for rank, (scenario, _) in enumerate(sorted_scores, 1):
metrics[scenario]['ranking'] = rank
return metrics
1.6.2 高级敏感性分析
class AdvancedSensitivityAnalysis:
"""高级敏感性分析"""
def __init__(self, comparison):
self.comparison = comparison
def monte_carlo_simulation(self, n_simulations=1000):
"""蒙特卡洛模拟"""
np.random.seed(42)
simulation_results = {
'scenario_a': {'costs': [], 'times': []},
'scenario_b': {'costs': [], 'times': []},
'scenario_c': {'costs': [], 'times': []}
}
for i in range(n_simulations):
# 随机参数变化
harbor_reliability = np.random.normal(0.95, 0.03)
rocket_reliability = np.random.normal(0.98, 0.02)
cost_variance = np.random.uniform(0.8, 1.2)
# 场景A模拟
scenario_a_cost = self.comparison.results_a['cost_breakdown']['total_cost'] * cost_variance
scenario_a_time = self.comparison.results_a['years_needed'] / harbor_reliability
simulation_results['scenario_a']['costs'].append(scenario_a_cost)
simulation_results['scenario_a']['times'].append(scenario_a_time)
# 场景B模拟
scenario_b_cost = self.comparison.results_b['cost_analysis']['total_cost'] * cost_variance
scenario_b_time = self.comparison.results_b['schedule']['years_needed'] / rocket_reliability
simulation_results['scenario_b']['costs'].append(scenario_b_cost)
simulation_results['scenario_b']['times'].append(scenario_b_time)
# 场景C模拟（混合）
# 使用优化后的混合比例
optimal_ratio = self.comparison.results_c['harbor_ratio']
harbor_part = optimal_ratio / harbor_reliability
rocket_part = (1 - optimal_ratio) / rocket_reliability
scenario_c_time = max(
self.comparison.results_c['detailed_result']['time_analysis']['harbor_years'] / harbor_reliability,
self.comparison.results_c['detailed_result']['time_analysis']['rocket_years'] / rocket_reliability
)
scenario_c_cost = (self.comparison.results_c['detailed_result']['cost_analysis']['harbor_cost'] *
optimal_ratio * cost_variance +
self.comparison.results_c['detailed_result']['cost_analysis']['rocket_cost'] *
(1 - optimal_ratio) * cost_variance)
simulation_results['scenario_c']['costs'].append(scenario_c_cost)
simulation_results['scenario_c']['times'].append(scenario_c_time)
# 统计分析
stats = {}
for scenario in simulation_results:
costs = np.array(simulation_results[scenario]['costs'])
times = np.array(simulation_results[scenario]['times'])
stats[scenario] = {
'cost_mean': np.mean(costs),
'cost_std': np.std(costs),
'cost_95ci': (np.percentile(costs, 2.5), np.percentile(costs, 97.5)),
'time_mean': np.mean(times),
'time_std': np.std(times),
'time_95ci': (np.percentile(times, 2.5), np.percentile(times, 97.5)),
'probability_best_cost': self.calculate_probability_best(scenario, simulation_results, 'costs'),
'probability_best_time': self.calculate_probability_best(scenario, simulation_results, 'times')
}
return stats
def calculate_probability_best(self, target_scenario, results, metric):
"""计算成为最佳方案的概率"""
n_simulations = len(results[list(results.keys())[0]][metric])
best_counts = {scenario: 0 for scenario in results.keys()}
for i in range(n_simulations):
values = {scenario: results[scenario][metric][i] for scenario in results.keys()}
best_scenario = min(values, key=values.get) # 越小越好
best_counts[best_scenario] += 1
probability = best_counts[target_scenario] / n_simulations
return probability
def tornado_analysis(self):
"""龙卷风分析（敏感性分析）"""
base_params = {
'harbor_daily_capacity': 50000,
'harbor_reliability': 0.95,
'harbor_cost_per_ton': 0.5,
'rocket_payload': 130,
'rocket_reliability': 0.98,
'rocket_cost_per_launch': 150,
'material_requirement': 1e8
}
variations = {
'harbor_daily_capacity': (40000, 60000),
'harbor_reliability': (0.85, 0.99),
'harbor_cost_per_ton': (0.3, 0.7),
'rocket_payload': (100, 150),
'rocket_reliability': (0.95, 0.995),
'rocket_cost_per_launch': (100, 200),
'material_requirement': (0.8e8, 1.2e8)
}
sensitivity_results = {}
for param, (low, high) in variations.items():
# 测试低值
test_params_low = base_params.copy()
test_params_low[param] = low
# 测试高值
test_params_high = base_params.copy()
test_params_high[param] = high
# 计算三种场景的结果
results_low = self.evaluate_scenarios(test_params_low)
results_high = self.evaluate_scenarios(test_params_high)
sensitivity_results[param] = {
'low_value': low,
'high_value': high,
'impact_on_scenario_a': {
'cost_change': (results_high['A']['cost'] - results_low['A']['cost']) / results_low['A']['cost'] * 100,
'time_change': (results_high['A']['time'] - results_low['A']['time']) / results_low['A']['time'] * 100
},
'impact_on_scenario_b': {
'cost_change': (results_high['B']['cost'] - results_low['B']['cost']) / results_low['B']['cost'] * 100,
'time_change': (results_high['B']['time'] - results_low['B']['time']) / results_low['B']['time'] * 100
},
'impact_on_scenario_c': {
'cost_change': (results_high['C']['cost'] - results_low['C']['cost']) / results_low['C']['cost'] * 100,
'time_change': (results_high['C']['time'] - results_low['C']['time']) / results_low['C']['time'] * 100
}
}
return sensitivity_results
def evaluate_scenarios(self, params):
"""评估场景"""
# 场景A：仅太空电梯
harbor_annual = 3 * 4 * params['harbor_daily_capacity'] * 365 * params['harbor_reliability']
time_a = params['material_requirement'] / harbor_annual
cost_a = (params['material_requirement'] * params['harbor_cost_per_ton'] +
time_a * 3 * 500) # 维护成本
# 场景B：仅火箭
launches_needed = params['material_requirement'] / params['rocket_payload']
time_b = launches_needed / (10 * 365 / 14) # 10个基地，14天周转
cost_b = launches_needed * params['rocket_cost_per_launch']
# 场景C：混合（优化比例）
# 简化计算：使用70/30比例
harbor_part = params['material_requirement'] * 0.7
rocket_part = params['material_requirement'] * 0.3
time_harbor = harbor_part / harbor_annual
time_rocket = rocket_part / (params['rocket_payload'] * 10 * 365 / 14)
time_c = max(time_harbor, time_rocket)
cost_c = (harbor_part * params['harbor_cost_per_ton'] +
rocket_part / params['rocket_payload'] * params['rocket_cost_per_launch'])
return {
'A': {'cost': cost_a, 'time': time_a},
'B': {'cost': cost_b, 'time': time_b},
'C': {'cost': cost_c, 'time': time_c}
}
1.7 代码执行与结果分析
def main_analysis():
"""主分析函数"""
print("=" * 80)
print("月球殖民地运输方案详细分析 - 问题1")
print("=" * 80)
# 1. 初始化各场景分析
print("\n1. 初始化分析模型...")
scenario_a = ScenarioAAnalysis()
scenario_b = ScenarioBAnalysis()
scenario_c = ScenarioCAnalysis()
# 2. 运行详细分析
print("\n2. 运行场景A分析（仅太空电梯）...")
results_a = scenario_a.detailed_transport_plan()
print("\n3. 运行场景B分析（仅传统火箭）...")
base_selection = scenario_b.optimize_base_selection()
results_b = scenario_b.detailed_launch_schedule()
print("\n4. 运行场景C分析（混合方案）...")
results_c = scenario_c.multi_objective_optimization()
# 3. 综合比较
print("\n5. 进行综合比较分析...")
comparison = ComprehensiveComparison()
comparison_matrix = comparison.create_comparison_matrix()
# 4. 敏感性分析
print("\n6. 运行高级敏感性分析...")
sensitivity = AdvancedSensitivityAnalysis(comparison)
mc_results = sensitivity.monte_carlo_simulation(n_simulations=500)
tornado_results = sensitivity.tornado_analysis()
# 5. 输出结果
print("\n" + "=" * 80)
print("分析结果摘要")
print("=" * 80)
print(f"\n场景A（仅太空电梯）:")
print(f" 所需时间: {results_a['years_needed']:.1f} 年")
print(f" 总成本: ${results_a['cost_breakdown']['total_cost']/1000:.1f} 十亿美元")
print(f" 完成年份: {results_a['completion_year']:.0f}")
print(f"\n场景B（仅传统火箭）:")
print(f" 所需时间: {results_b['schedule']['years_needed']:.1f} 年")
print(f" 总成本: ${results_b['cost_analysis']['total_cost']/1000:.1f} 十亿美元")
print(f" 使用基地: {', '.join(scenario_b.selected_bases)}")
print(f"\n场景C（优化混合方案）:")
print(f" 太空电梯比例: {results_c['harbor_ratio']*100:.1f}%")
print(f" 所需时间: {results_c['detailed_result']['time_analysis']['total_years']:.1f} 年")
print(f" 总成本: ${results_c['detailed_result']['cost_analysis']['total_cost']/1000:.1f} 十亿美元")
print(f" CO2减排（相比纯火箭）: {results_c['detailed_result']['environmental_impact']['emissions_reduction_vs_rocket_only']:.1f}%")
# 6. 推荐方案
print("\n" + "=" * 80)
print("推荐方案")
print("=" * 80)
# 基于多准则决策分析
scores = comparison.calculate_summary_metrics()
best_scenario = min(scores.items(), key=lambda x: x[1]['composite_score'])[0]
print(f"\n基于综合分析，推荐方案: {best_scenario}")
print(f"综合得分: {scores[best_scenario]['composite_score']:.3f}")
if best_scenario == 'Scenario_C':
print("\n推荐采用混合方案，具体配置:")
print(f" • 太空电梯承担: {results_c['harbor_ratio']*100:.1f}% 的运输")
print(f" • 传统火箭承担: {(1-results_c['harbor_ratio'])*100:.1f}% 的运输")
print(f" • 使用火箭类型: {results_c['rocket_type']}")
print(f" • 使用火箭基地数量: {results_c['rocket_bases']}")
# 实施建议
print("\n实施建议:")
print(" 1. 第一阶段（2050-2060）: 主要建设太空电梯系统")
print(" 2. 第二阶段（2060-2080）: 混合运输，优先重型材料通过电梯")
print(" 3. 第三阶段（2080-2100）: 优化调度，增加人员运输")
print(" 4. 运营阶段（2100后）: 定期补给和维护")
# 7. 生成详细报告
print("\n" + "=" * 80)
print("生成详细分析报告...")
generate_detailed_report(results_a, results_b, results_c, comparison_matrix,
mc_results, tornado_results, scores)
print("分析完成！详细结果已保存到文件。")
def generate_detailed_report(results_a, results_b, results_c, comparison,
mc_results, tornado_results, scores):
"""生成详细报告"""
timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
filename = f"moon_colony_transport_analysis_{timestamp}.txt"
with open(filename, 'w', encoding='utf-8') as f:
f.write("月球殖民地运输方案详细分析报告\n")
f.write("=" * 80 + "\n\n")
f.write("1. 执行摘要\n")
f.write("-" * 40 + "\n")
f.write(f"分析时间: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}\n")
f.write(f"总材料需求: {1e8:,.0f} 吨\n")
f.write(f"目标人口: 100,000人\n")
f.write(f"起始年份: 2050\n\n")
f.write("2. 各场景详细分析\n")
f.write("-" * 40 + "\n")
# 场景A
f.write("\n2.1 场景A: 仅太空电梯\n")
f.write(f" 年运输能力: {results_a['annual_capacity_tons']:,.0f} 吨/年\n")
f.write(f" 所需时间: {results_a['years_needed']:.1f} 年\n")
f.write(f" 总成本: ${results_a['cost_breakdown']['total_cost']/1000:.2f} 十亿美元\n")
f.write(f" 成本细分:\n")
for cost_type, amount in results_a['cost_breakdown'].items():
if cost_type != 'total_cost':
f.write(f" - {cost_type}: ${amount/1000:.2f} 十亿美元\n")
# 场景B
f.write("\n2.2 场景B: 仅传统火箭\n")
f.write(f" 使用基地: {', '.join(list(results_b['schedule']['launch_allocation'].keys()))}\n")
f.write(f" 总发射次数: {results_b['schedule']['total_launches']:,.0f}\n")
f.write(f" 所需时间: {results_b['schedule']['years_needed']:.1f} 年\n")
f.write(f" 总成本: ${results_b['cost_analysis']['total_cost']/1000:.2f} 十亿美元\n")
# 场景C
f.write("\n2.3 场景C: 混合方案\n")
f.write(f" 优化后的太空电梯比例: {results_c['harbor_ratio']*100:.1f}%\n")
f.write(f" 所需时间: {results_c['detailed_result']['time_analysis']['total_years']:.1f} 年\n")
f.write(f" 总成本: ${results_c['detailed_result']['cost_analysis']['total_cost']/1000:.2f} 十亿美元\n")
f.write(f" CO2减排: {results_c['detailed_result']['environmental_impact']['emissions_reduction_vs_rocket_only']:.1f}%\n")
f.write("\n3. 综合比较\n")
f.write("-" * 40 + "\n")
for metric, data in comparison.items():
f.write(f"\n3.{list(comparison.keys()).index(metric)+1} {metric.replace('_', ' ').title()}\n")
for scenario, details in data.items():
f.write(f" {scenario}:\n")
if isinstance(details, dict):
for key, value in details.items():
if isinstance(value, (int, float)):
f.write(f" {key}: {value}\n")
elif isinstance(value, list):
f.write(f" {key}: {', '.join(str(v) for v in value[:3])}...\n")
else:
f.write(f" {details}\n")
f.write("\n4. 敏感性分析结果\n")
f.write("-" * 40 + "\n")
f.write("\n4.1 蒙特卡洛模拟结果\n")
for scenario, stats in mc_results.items():
f.write(f"\n {scenario}:\n")
f.write(f" 成本均值: ${stats['cost_mean']/1000:.2f} 十亿美元\n")
f.write(f" 成本95%置信区间: [${stats['cost_95ci'][0]/1000:.2f}, ${stats['cost_95ci'][1]/1000:.2f}] 十亿美元\n")
f.write(f" 时间均值: {stats['time_mean']:.1f} 年\n")
f.write(f" 成为最佳成本方案概率: {stats['probability_best_cost']*100:.1f}%\n")
f.write("\n4.2 关键参数敏感性（龙卷风分析）\n")
for param, impacts in tornado_results.items():
f.write(f"\n {param}:\n")
for scenario in ['A', 'B', 'C']:
cost_impact = impacts[f'impact_on_scenario_{scenario.lower()}']['cost_change']
time_impact = impacts[f'impact_on_scenario_{scenario.lower()}']['time_change']
f.write(f" 场景{scenario}: 成本影响{ cost_impact:+.1f}%, 时间影响{ time_impact:+.1f}%\n")
f.write("\n5. 最终推荐\n")
f.write("-" * 40 + "\n")
best_scenario = min(scores.items(), key=lambda x: x[1]['composite_score'])[0]
f.write(f"\n基于多准则决策分析，推荐方案: {best_scenario}\n")
f.write(f"综合得分: {scores[best_scenario]['composite_score']:.3f}\n\n")
f.write("推荐理由:\n")
f.write("1. 技术可行性: 混合方案分散了技术风险\n")
f.write("2. 经济性: 在长期运营中成本效益最优\n")
f.write("3. 时间效率: 通过并行运输缩短总时间\n")
f.write("4. 环境影响: 显著减少CO2排放\n")
f.write("5. 灵活性: 可根据实际情况调整混合比例\n")
f.write("\n" + "=" * 80 + "\n")
f.write("报告结束\n")
print(f"详细报告已保存到: {filename}")
# 执行主分析
if __name__ == "__main__":
main_analysis()
二、问题1分析的关键见解
2.1 技术可行性分析
2.1.1 太空电梯系统的技术挑战
-
材料科学挑战：需要100,000公里长的石墨烯系绳，目前最大生产长度有限
-
动力学稳定性：系绳摆动、轨道共振、太空碎片碰撞风险
-
能源需求：巨大的电能需求，需要太空太阳能或地面无线输电
-
维护复杂性：在轨维修的难度和成本
2.1.2 火箭系统的可扩展性限制
-
发射频率上限：物理限制（发射场数量、天气窗口、安全间隔）
-
生产成本：大规模生产火箭的经济性和供应链挑战
-
环境影响：高频次发射对大气和局部生态的影响
-
人力资源：需要大量训练有素的技术人员
2.2 经济性深度分析
2.2.1 成本结构比较
# 成本结构分析代码
def analyze_cost_structures():
"""深度成本结构分析"""
# 太空电梯的固定成本高，可变成本低
harbor_cost_structure = {
'fixed_costs': {
'研发': 50000, # 百万美元
'建设': 600000, # 3个港口
'初始部署': 200000
},
'variable_costs_per_ton': {
'能源': 0.1,
'维护': 0.05,
'运营': 0.15,
'人工': 0.1
}
}
# 火箭的可变成本高
rocket_cost_structure = {
'fixed_costs': {
'发射场升级': 5000, # 每个基地
'生产设施': 10000
},
'variable_costs_per_launch': {
'火箭制造成本': 80, # 百万美元
'燃料': 5,
'运营': 10,
'保险': 5
}
}
# 计算盈亏平衡点
def calculate_break_even(total_material):
harbor_total_fixed = sum(harbor_cost_structure['fixed_costs'].values())
harbor_variable_per_ton = sum(harbor_cost_structure['variable_costs_per_ton'].values())
rocket_total_fixed = sum(rocket_cost_structure['fixed_costs'].values()) * 5 # 5个基地
rocket_variable_per_ton = 100 # 每吨火箭运输成本（估计）
# 计算不同运输量下的成本
quantities = np.linspace(1e7, 2e8, 20)
harbor_costs = harbor_total_fixed + quantities * harbor_variable_per_ton
rocket_costs = rocket_total_fixed + quantities * rocket_variable_per_ton
# 找到盈亏平衡点
diff = harbor_costs - rocket_costs
break_even_idx = np.where(np.diff(np.sign(diff)))[0]
return {
'quantities': quantities,
'harbor_costs': harbor_costs,
'rocket_costs': rocket_costs,
'break_even_points': quantities[break_even_idx] if len(break_even_idx) > 0 else []
}
return calculate_break_even(1e8)
2.3 时间效率优化策略
2.3.1 并行运输优化
class ParallelTransportOptimizer:
"""并行运输优化"""
def optimize_parallel_schedule(self, material_categories, transport_capacities):
"""优化并行运输计划"""
# 使用线性规划优化
from scipy.optimize import linprog
# 决策变量：每种材料通过每种运输方式的数量
n_materials = len(material_categories)
n_transport = 2 # 港口和火箭
# 目标：最小化总时间（近似为最大化吞吐量）
c = [-1] * n_materials * n_transport # 最大化运输量
# 约束：总材料需求
A_eq = []
b_eq = []
for i in range(n_materials):
row = [0] * (n_materials * n_transport)
row[i * n_transport] = 1 # 港口
row[i * n_transport + 1] = 1 # 火箭
A_eq.append(row)
b_eq.append(material_categories[i]['tonnage'])
# 运输能力约束
A_ub = []
b_ub = []
# 港口容量约束
harbor_row = [0] * (n_materials * n_transport)
for i in range(n_materials):
harbor_row[i * n_transport] = 1 # 只计数港口运输
A_ub.append(harbor_row)
b_ub.append(transport_capacities['harbor_annual'])
# 火箭容量约束
rocket_row = [0] * (n_materials * n_transport)
for i in range(n_materials):
rocket_row[i * n_transport + 1] = 1 # 只计数火箭运输
A_ub.append(rocket_row)
b_ub.append(transport_capacities['rocket_annual'])
# 边界
bounds = [(0, None)] * (n_materials * n_transport)
# 求解
result = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds)
return result
2.4 风险管理框架
2.4.1 风险量化模型
class RiskQuantificationModel:
"""风险量化模型"""
def quantify_transport_risks(self, scenario_results):
"""量化运输风险"""
risk_factors = {
'technical': {
'harbor': {
'tether_failure': {'probability': 0.001, 'impact': 1.0},
'power_outage': {'probability': 0.01, 'impact': 0.3},
'mechanical_failure': {'probability': 0.05, 'impact': 0.5}
},
'rocket': {
'launch_failure': {'probability': 0.02, 'impact': 0.8},
'weather_delay': {'probability': 0.1, 'impact': 0.2},
'supply_chain_disruption': {'probability': 0.05, 'impact': 0.4}
}
},
'operational': {
'harbor': {
'maintenance_downtime': {'probability': 0.1, 'impact': 0.2},
'staffing_issues': {'probability': 0.05, 'impact': 0.1}
},
'rocket': {
'range_safety_violation': {'probability': 0.01, 'impact': 0.5},
'regulatory_delay': {'probability': 0.03, 'impact': 0.3}
}
},
'external': {
'both': {
'solar_storm': {'probability': 0.005, 'impact': 0.7},
'space_debris': {'probability': 0.002, 'impact': 0.9},
'political_instability': {'probability': 0.02, 'impact': 0.4}
}
}
}
# 计算各场景的风险指数
risk_indices = {}
for scenario_name, results in scenario_results.items():
total_risk = 0
if 'harbor' in scenario_name.lower() or '混合' in scenario_name:
# 计算太空电梯风险
harbor_risk = 0
for category, risks in risk_factors['technical']['harbor'].items():
harbor_risk += risks['probability'] * risks['impact']
for category, risks in risk_factors['operational']['harbor'].items():
harbor_risk += risks['probability'] * risks['impact']
if 'rocket' in scenario_name.lower() or '混合' in scenario_name:
# 计算火箭风险
rocket_risk = 0
for category, risks in risk_factors['technical']['rocket'].items():
rocket_risk += risks['probability'] * risks['impact']
for category, risks in risk_factors['operational']['rocket'].items():
rocket_risk += risks['probability'] * risks['impact']
# 外部风险（共同）
external_risk = 0
for category, risks in risk_factors['external']['both'].items():
external_risk += risks['probability'] * risks['impact']
# 加权总风险
if '仅太空电梯' in scenario_name:
total_risk = harbor_risk + external_risk
elif '仅传统火箭' in scenario_name:
total_risk = rocket_risk + external_risk
else: # 混合方案
# 使用混合比例加权
harbor_ratio = results.get('harbor_ratio', 0.5)
total_risk = (harbor_ratio * harbor_risk +
(1 - harbor_ratio) * rocket_risk +
external_risk)
risk_indices[scenario_name] = {
'total_risk_index': total_risk,
'components': {
'harbor_risk': harbor_risk if 'harbor' in scenario_name.lower() or '混合' in scenario_name else 0,
'rocket_risk': rocket_risk if 'rocket' in scenario_name.lower() or '混合' in scenario_name else 0,
'external_risk': external_risk
}
}
return risk_indices
三、结论与建议
3.1 主要发现
-
技术可行性：三种方案在技术上都是可行的，但挑战不同
-
经济性：混合方案在长期视角下最具成本效益
-
时间效率：并行运输可以显著缩短总建设时间
-
环境影响：太空电梯的环境优势明显，混合方案可平衡需求
-
风险分散：混合方案提供了天然的风险分散机制
3.2 推荐实施方案
基于全面分析，我们推荐采用动态混合方案：
第一阶段（2050-2065）：
-
主要依赖传统火箭运输
-
同步建设太空电梯系统
-
运输优先级：基础设施和建设设备
第二阶段（2065-2085）：
-
太空电梯承担60-70%运输
-
火箭承担剩余部分
-
重点：生命支持系统和居住模块
第三阶段（2085-2100）：
-
优化运输比例至70/30（电梯/火箭）
-
增加人员运输频率
-
建立定期补给体系
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