=== 最优测线优化 ===
Traceback (most recent call last):
File "c:\Users\Yeah\Desktop\数模\第七题\B题\33333.py", line 240, in <module>
survey_lines, optimal_solution = design_optimal_survey_lines(beta=90)
~~~~~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^
File "c:\Users\Yeah\Desktop\数模\第七题\B题\33333.py", line 220, in design_optimal_survey_lines
elif i <= len(overlaps) and not math.isnan(overlaps[i-1]):
~~~~~~~~~~^^^^^^^^^^^^^^^
TypeError: must be real number, not str
import math
import numpy as np
# 参数设置
theta = 120 # 仪器开角
alpha = 1.5 # 入射角
D_center = 110 # 中心点水深
length_n_mile = 2 # 测线南北长度（海里）
width_n_mile = 4 # 测线东西宽度（海里）
overlap_min = 0.1 # 最小重叠率
overlap_max = 0.2 # 最大重叠率
# 单位转换
theta_rad = math.radians(theta)
alpha_rad = math.radians(alpha)
length_m = length_n_mile * 1852 # 南北长(米)
width_m = width_n_mile * 1852 # 东西宽(米)
def get_mu(beta):
"""计算μ角"""
beta = beta % 360
if beta == 0 or beta == 180:
return 0
elif beta == 90 or beta == 270:
return 90
elif 0 < beta < 90:
return 90 - beta
elif 90 < beta < 180:
return beta - 90
elif 180 < beta < 270:
return 270 - beta
else:
return beta - 270
def get_lambda(alpha_rad, beta):
"""计算λ角"""
if beta in [0, 180]:
return alpha_rad
elif beta in [90, 270]:
return 0.0
else:
mu_rad = math.radians(get_mu(beta))
return math.atan(math.tan(alpha_rad) * math.cos(mu_rad))
def get_angles(theta_rad, lambda_rad):
"""计算∠1与∠2"""
angle1 = (math.pi - theta_rad) / 2 - lambda_rad
angle2 = (math.pi - theta_rad) / 2 + lambda_rad
return angle1, angle2
def get_depth(x, beta):
"""计算给定位置x的水深"""
mu = get_mu(beta)
mu_rad = math.radians(mu)
lambda_rad = get_lambda(alpha_rad, beta)
return D_center - (x - width_m / 2) * math.sin(alpha_rad) * math.sin(mu_rad)
def coverage_width(x, beta):
"""计算给定位置x的覆盖宽度"""
depth = get_depth(x, beta)
lambda_rad = get_lambda(alpha_rad, beta)
angle1, angle2 = get_angles(theta_rad, lambda_rad)
sin_half_theta = math.sin(theta_rad / 2)
W_1 = depth * sin_half_theta / math.sin(angle1)
W_2 = depth * sin_half_theta / math.sin(angle2)
return W_1 + W_2
def calculate_overlap_rate(prev_W_2, curr_W_1, d, alpha_rad, curr_W_1_plus_W_2):
"""计算重叠率"""
if curr_W_1_plus_W_2 <= 0:
return float('nan')
overlap_width = prev_W_2 + curr_W_1 - d / math.cos(alpha_rad)
return (overlap_width / curr_W_1_plus_W_2) * 100
def optimize_survey_lines(beta=90, min_overlap=0.1, max_overlap=0.2, precision=0.1):
"""优化测线方案"""
# 计算中心点的覆盖宽度
center_coverage = coverage_width(length_m / 2, beta)
# 有效测线间距范围
min_d = center_coverage * (1 - max_overlap)
max_d = center_coverage * (1 - min_overlap)
valid_solutions = []
best_solution = None
# 遍历可能的测线间距
for d in np.arange(min_d, max_d, precision):
num_lines = math.ceil(width_m / d)
actual_d = width_m / num_lines
# 验证所有测线的重叠率
valid = True
overlaps = []
for i in range(1, num_lines):
prev_x = (i-1) * actual_d
curr_x = i * actual_d
prev_depth = get_depth(prev_x, beta)
prev_W_1 = prev_depth * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[0])
prev_W_2 = prev_depth * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[1])
curr_depth = get_depth(curr_x, beta)
curr_W_1 = curr_depth * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[0])
curr_W_2 = curr_depth * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[1])
overlap_percent = calculate_overlap_rate(
prev_W_2, curr_W_1, curr_x - prev_x, alpha_rad, curr_W_1 + curr_W_2)
# 检查重叠率是否在要求范围内
if overlap_percent < min_overlap*100 or overlap_percent > max_overlap*100:
valid = False
break
overlaps.append(overlap_percent)
if valid:
avg_overlap_deviation = sum(abs((overlap/100 - 0.15)/0.05) for overlap in overlaps) / len(overlaps)
solution = {
"测线间距": actual_d,
"所需测线数量": num_lines,
"总测线长度": num_lines * length_m / 1852,
"平均重叠率偏离度": avg_overlap_deviation,
"所有重叠率": overlaps.copy()
}
valid_solutions.append(solution)
# 如果是当前最佳方案或首次找到有效解
if best_solution is None or (solution["总测线长度"] < best_solution["总测线长度"]):
best_solution = solution
# 如果没有找到有效解，返回最接近的候选解
if best_solution is None:
candidate_solutions = []
for d in np.arange(min_d * 0.8, max_d * 1.2, precision * 5): # 扩大搜索范围
num_lines = math.ceil(width_m / d)
actual_d = width_m / num_lines
overlaps = []
valid = True
for i in range(1, num_lines):
prev_x = (i-1) * actual_d
curr_x = i * actual_d
prev_W_2 = get_depth(prev_x, beta) * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[1])
curr_W_1 = get_depth(curr_x, beta) * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[0])
curr_W_1_plus_W_2 = get_depth(curr_x, beta) * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[0]) + \
get_depth(curr_x, beta) * math.sin(theta_rad/2) / math.sin(
get_angles(theta_rad, get_lambda(alpha_rad, beta))[1])
overlap_percent = calculate_overlap_rate(
prev_W_2, curr_W_1, curr_x - prev_x, alpha_rad, curr_W_1_plus_W_2)
# 记录所有重叠率
overlaps.append(overlap_percent)
# 检查重叠率是否接近要求范围
if overlap_percent < min_overlap*100 - 5 or overlap_percent > max_overlap*100 + 5: # 放宽条件
valid = False
break
if not valid:
continue
if overlaps:
avg_overlap_deviation = sum(abs((overlap/100 - 0.15)/0.05) for overlap in overlaps if not math.isnan(overlap)) / len(overlaps)
candidate_solutions.append({
"测线间距": actual_d,
"所需测线数量": num_lines,
"总测线长度": num_lines * length_m / 1852,
"平均重叠率偏离度": avg_overlap_deviation if not math.isnan(avg_overlap_deviation) else float('inf'),
"所有重叠率": overlaps.copy()
})
# 按偏离度排序候选解
candidate_solutions.sort(key=lambda x: (x["平均重叠率偏离度"], x["总测线长度"]))
if candidate_solutions:
best_solution = candidate_solutions[0]
else:
# 如果所有方案都失败，返回默认方案
best_solution = {
"测线间距": max_d / 1.5, # 选择中间值
"所需测线数量": math.ceil(width_m / (max_d / 1.5)),
"总测线长度": math.ceil(width_m / (max_d / 1.5)) * length_m / 1852,
"平均重叠率偏离度": float('inf'),
"所有重叠率": ["无有效解"]
}
return best_solution
def design_optimal_survey_lines(beta=90, min_overlap=0.1, max_overlap=0.2):
"""设计最优测线方案"""
optimal_solution = optimize_survey_lines(beta, min_overlap, max_overlap)
spacing = optimal_solution["测线间距"]
num_lines = optimal_solution["所需测线数量"]
overlaps = optimal_solution.get("所有重叠率", [])
survey_lines = []
for i in range(num_lines):
x = i * spacing
depth = get_depth(x, beta)
coverage = coverage_width(x, beta)
# 处理重叠率信息
if i == 0:
overlap_info = "首条测线，无重叠"
elif i <= len(overlaps) and not math.isnan(overlaps[i-1]):
overlap_info = f"{overlaps[i-1]:.2f}%"
else:
overlap_info = "计算异常"
survey_lines.append({
"序号": i+1,
"x坐标": x,
"相对位置(海里)": x / 1852,
"水深": depth,
"覆盖宽度": coverage,
"相邻重叠率(%)": overlap_info
})
return survey_lines, optimal_solution
if __name__ == "__main__":
print("=== 最优测线优化 ===")
# 获取最优测线方案
survey_lines, optimal_solution = design_optimal_survey_lines(beta=90)
# 打印测线方案
print(f"\n最优测线方案 (β={90}°):")
print(f"共需布设 {len(survey_lines)} 条测线")
print(f"平均测线间距: {optimal_solution['测线间距']/1852:.2f} 海里")
print(f"总测线长度: {optimal_solution['总测线长度']:.2f} 海里")
print(f"平均重叠率偏离度: {optimal_solution['平均重叠率偏离度']:.2f}")
print("\n详细测线信息:")
for line in survey_lines:
print(f"测线 {line['序号']}: "
f"x坐标 = {line['x坐标']:.2f} 米, "
f"相对位置 = {line['相对位置(海里)']:.2f} 海里, "
f"水深 = {line['水深']:.2f} 米, "
f"覆盖宽度 = {line['覆盖宽度']:.2f} 米, "
f"相邻重叠率 = {line['相邻重叠率(%)']}")
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