利用numpy增强数值稳定性
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@ -1,9 +1,12 @@
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# 利用自动微分计算
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from typing import List
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import sympy
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import data
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import exp
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import math
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import main
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import numpy as np
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sympy.init_printing()
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# h_i 悬点高差
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@ -26,7 +29,6 @@ delta_Li = (
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*delta_Li__1,
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sympy.symbols("delta_Li_i"),
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)
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# sigma_i = sympy.symbols("sigma_i:{span_count}".format(span_count=data.span_count))
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loop_end = data.loop_end # 最大循环次数
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@ -44,19 +46,13 @@ sigma_m_data = data.sigma_m # 架线时，初伸长未释放前的最低点水
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span_count = data.span_count # 几个档距
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# n个档距,n-1个直线塔
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h_array = data.h_array
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hi_matrix = sympy.Matrix(h_array)
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# sympy.pprint(hi_matrix)
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l_array = data.l_array
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l_matrix = sympy.Matrix(l_array)
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t_data = data.t
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conductor_n = data.conductor_n
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# ti_matrix = sympy.Matrix(t_array)
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lambda_i_array = data.lambda_i_array
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# TODO: 暂时没考虑荷载变化
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lambda_m_matrix = sympy.Matrix(lambda_i_array)
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lambda_i_matrix = sympy.Matrix(lambda_i_array)
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symbol_delta_l_i = exp.delta_li()
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sigma_i = sympy.symbols("sigma_i")
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d_delta_l_i_sigma_i = sympy.diff(symbol_delta_l_i, sigma_i)
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@ -113,11 +109,7 @@ def get_lambdify_d_delta_l_i_sigma_i(_d_delta_l_i_sigma_i):
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fx_d_delta_l_i_sigma_i = get_lambdify_d_delta_l_i_sigma_i(d_delta_l_i_sigma_i)
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symbol_sigma_i1 = exp.fun_sigma_i1(delta_Li)
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# d_sigma_i1_sigma_i = sympy.diff(symbol_sigma_i1, sigma_i)
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# sigma_i1 = sympy.symbols("sigma_i1")
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# d_sigma_i1_sigma_i1 = sympy.diff(symbol_sigma_i1, sigma_i)
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delta_Li_i = sympy.symbols("delta_Li_i")
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d_sigma_i1_d_l_i = sympy.diff(symbol_sigma_i1, delta_Li_i)
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@ -315,7 +307,7 @@ def evaluate_d_sigma_i1_d_delta_sigma_i(val_delta_li):
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def solve():
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# 初始化
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val_delta_li = [1 for _ in range(span_count)]
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val_delta_li = [0.1 for _ in range(span_count)]
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# val_delta_li = [0.15931589580330385, -0.19294219226439696, 0.035236744603670586, -0.03124795962518869, 0.034422847061933395, 0.1639551737321582, -0.18876605469917845, 0.03862307099222713, -0.01858088432390902]
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# val_sigma_i = [175.44277576372207, 176.07105062365383, 175.94897602628689, 175.95574563415994, 175.83116207025824, 175.84778616876434, 176.5132398968081, 176.4405408454816, 176.51871673188586]
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@ -346,7 +338,6 @@ def solve():
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A = sympy.Matrix([[M_A, M_B], [M_C, M_D], [M_E]])
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fx_delta_Li = []
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fx_sigma_i1 = []
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b_i = 0
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for i in range(span_count):
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fx_delta_Li.append(
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val_delta_li[i]
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@ -381,35 +372,24 @@ def solve():
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lambda_i_array[i + 1],
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)
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)
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# lambda_i1 = lambda_i_array[i + 1]
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# h_i1 = h_array[i + 1]
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# l_i1 = l_array[i + 1]
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# h_i = h_array[i]
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# l_i = l_array[i]
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# beta_i = math.atan(h_i / l_i)
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# beta_i1 = math.atan(h_i1 / l_i1)
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# w_i = (
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# lambda_i_array[i] * l_array[i] / 2 / math.cos(beta_i)
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# + val_sigma_i[i] * h_i / l_i
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# + (lambda_i1 * l_i1 / 2 / math.cos(beta_i1) - val_sigma_i[i+1] * h_i1 / l_i1)
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# )
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# b_i += val_delta_li[i]
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# # 新版大手册p329 (5-61) 最上方公式
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# right_equ = val_sigma_i[i] + b_i / math.sqrt(string_length ** 2 - b_i ** 2) * (
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# string_g/conductor_n / 2 / area + w_i # string_g已在传入时考虑了导线分裂数
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# )
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fx_sum_Li = [math.fsum(val_delta_li)]
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b_list = []
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b_list.extend(fx_delta_Li)
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b_list.extend(fx_sigma_i1)
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b_list.extend(fx_sum_Li)
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b = sympy.Matrix(b_list)
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# sympy.pprint(b)
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x = sympy.linsolve((-A, b))
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x_list = [float(_x) for _x in list(x)[0]]
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abs_min = [math.fabs(_x) for _x in x_list]
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# b = sympy.Matrix(b_list)
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# x = sympy.linsolve((-A, b))
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# x_list = [float(_x) for _x in list(x)[0]]
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# numpy
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# print(A.tolist())
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AA = np.array(A.tolist(), np.float64)
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# AA=np.array([[1, 0, 0, -0.0104519104486432, 0, 0], [0, 1, 0, 0, -0.00782784930594165, 0], [0, 0, 1, 0, 0, -0.00640057303461462], [-3.78731866382623, 0, 0, -1.00000000000000, 1, 0], [-3.47643075688507, -3.47643075688507, 0, 0, -1.00000000000000, 1], [1, 1, 1, 0, 0, 0]])
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# print(b.transpose().tolist()[0])
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b = np.array(b_list, dtype=np.float64)
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# BB=[-0.159573673689794, 0.140383878899664, 0.00728144380483030, -0.378687120179166, -0.694957566239367, 0.300000000000000]
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x = np.linalg.solve(-AA, b)
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x_list = x
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abs_min: List[float] = [math.fabs(_x) for _x in x_list]
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abs_min.sort()
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if abs_min[-1] < 1e-5:
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break
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@ -421,7 +401,7 @@ def solve():
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if loop >= loop_end:
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print("不收敛")
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else:
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print("经过{loop}次迭代收敛,最大偏差{bias}".format(loop=loop,bias=abs_min[-1]))
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print("经过{loop}次迭代收敛,最大偏差{bias}".format(loop=loop, bias=abs_min[-1]))
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# print(val_delta_li)
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# print(val_sigma_i)
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verify(val_delta_li, val_sigma_i)
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36
data.py
36
data.py
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@ -12,15 +12,20 @@ area = 154.48 # 导线面积 mm2
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lambda_m = 14.8129 / area # 导线比载 N/(m.mm)
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lambda_i_array = [
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lambda_m * 0.9,
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lambda_m * 1.3,
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lambda_m * 1.2,
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lambda_m,
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lambda_m,
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lambda_m,
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lambda_m * 0.9,
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lambda_m * 1.1,
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lambda_m,
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lambda_m,
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lambda_m,
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lambda_m,
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lambda_m,
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lambda_m,
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lambda_m * 0.9,
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lambda_m * 1.3,
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lambda_m,
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lambda_m,
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lambda_m,
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]
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# 取400m代表档距下
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sigma_m = 28517 / area # 架线时，初伸长未释放前的最低点水平应力。单位N/mm2
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@ -37,8 +42,29 @@ h_array = [
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0,
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0,
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0,
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0,
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0,
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0,
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0,
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0,
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]
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l_array = [
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400,
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300,
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300,
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500,
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300,
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400,
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300,
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300,
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500,
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300,
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300,
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500,
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300,
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400,
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300,
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]
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l_array = [400, 300, 300, 500, 300, 400, 300, 300, 500, 300]
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t = 15
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epsilon = 1e-4 # 收敛判据
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conductor_n = 6 # 导线分裂数
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21
main.py
21
main.py
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@ -69,15 +69,18 @@ def fun_sigma_i1(
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) -> float:
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beta_i = math.atan(h_i / l_i)
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beta_i1 = math.atan(h_i1 / l_i1)
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_sigma_i1 = (
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(
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g_i / 2 / area # g_i传入时已考虑导线分裂数
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+ lambda_i * l_i / 2 / math.cos(beta_i)
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+ lambda_i1 * l_i1 / 2 / math.cos(beta_i1)
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+ sigma_i * h_i / l_i
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)
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+ sigma_i / b_i * math.sqrt(length_i ** 2 - b_i ** 2)
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) / (math.sqrt(length_i ** 2 - b_i ** 2) / b_i + h_i1 / l_i1)
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try:
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_sigma_i1 = (
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(
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g_i / 2 / area # g_i传入时已考虑导线分裂数
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+ lambda_i * l_i / 2 / math.cos(beta_i)
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+ lambda_i1 * l_i1 / 2 / math.cos(beta_i1)
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+ sigma_i * h_i / l_i
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)
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+ sigma_i / b_i * math.sqrt(length_i ** 2 - b_i ** 2)
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) / (math.sqrt(length_i ** 2 - b_i ** 2) / b_i + h_i1 / l_i1)
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except:
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a=12
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return _sigma_i1
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