353 lines
11 KiB
Python
353 lines
11 KiB
Python
# 利用自动微分计算
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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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sympy.init_printing()
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# h_i 悬点高差
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# l_i 悬点档距
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# _alpha 导线膨胀系数 1/°C
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# _elastic 弹性系数 N/mm2
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# _t_e 架线时考虑初伸长的降温，取正值。单位°C
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# lambda_i 计算不平衡张力时导线比载 N/(m.mm)
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# sigma_i 计算不平衡张力时最低点水平应力 单位N/mm2
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# t_i 计算不平衡张力时导线温度 单位°C
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# _lambda_m 导线架线时时导线比载 N/(m.mm)
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# _sigma_m 导线架线时时最低点水平应力 单位N/mm2
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# _t_m 导线架线时时导线温度 单位°C
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delta_Li__1 = sympy.symbols(
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"delta_Li:{span_count}".format(span_count=data.span_count - 1)
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)
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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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# 架线时的状态
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# 取外过无风
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string_length = data.string_length # 串长 单位m
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string_g = data.string_g # 串重 单位N
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t_m_data = data.t_m # 导线架设时的气温。单位°C
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t_e_data = data.t_e # 架线时考虑初伸长的降温，取正值。单位°C
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alpha_data = data.alpha # 导线膨胀系数 1/°C
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elastic = data.elastic # 弹性系数 N/mm2
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area = data.area # 导线面积 mm2
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lambda_m_data = data.lambda_m # 导线比载 N/(m.mm)
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sigma_m_data = data.sigma_m # 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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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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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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# 一共2n个变量，n个delta_Li，n个sigma_i
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# 分 [
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# A B
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# C D
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# E1 E2
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# ]
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# 6块
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# B为dΔli/dσi
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def evaluate_d_delta_l_i_sigma_i(val_delta_l_li, val_sigma_i):
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(
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delta_l_i,
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l_i,
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lambda_i,
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alpha,
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E,
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t_e,
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t_i,
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lambda_m,
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t_m,
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sigma_m,
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_sigma_i,
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beta_i,
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) = sympy.symbols(
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"""
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delta_l_i,
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l_i,
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lambda_i,
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alpha,
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E,
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t_e,
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t_i,
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lambda_m,
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t_m,
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sigma_m,
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sigma_i,
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beta_i
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"""
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)
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val_list = []
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for i in range(span_count):
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val = d_delta_l_i_sigma_i.subs(
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[
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(delta_l_i, val_delta_l_li[i]),
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(l_i, l_array[i]),
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(lambda_i, lambda_i_array[i]),
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(alpha, alpha_data),
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(E, elastic),
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(t_e, t_e_data),
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(t_i, t_data),
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(lambda_m, lambda_m_data),
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(t_m, t_m_data),
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(sigma_m, sigma_m_data),
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(_sigma_i, val_sigma_i[i]),
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(beta_i, math.atan(h_array[i] / l_array[i])),
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]
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)
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val_list.append(val)
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return val_list
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# C为dσi1dΔli
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# C只有n-1行
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def evaluate_d_sigma_i1_d_delta_l_i(val_delta_l_li, val_sigma_i):
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(
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G_i,
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A,
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lambda_i,
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lambda_i1,
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_sigma_i,
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h_i,
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h_i1,
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l_i,
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l_i1,
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stringlen_i,
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_sigma_i1,
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beta_i,
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beta_i1,
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) = sympy.symbols(
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"""
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G_i,
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A,
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lambda_i,
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lambda_i1,
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sigma_i,
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h_i,
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h_i1,
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l_i,
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l_i1,
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stringlen_i,
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sigma_i1,
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beta_i,
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beta_i1,
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"""
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)
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row = []
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for i in range(span_count - 1):
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col = []
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for j in range(span_count):
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if i < j:
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col.append(0)
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else:
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_val = d_sigma_i1_d_l_i.subs(
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[
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(G_i, string_g / conductor_n),
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(A, area),
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(lambda_i, lambda_i_array[i]),
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(lambda_i1, lambda_i_array[i + 1]),
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(_sigma_i, val_sigma_i[i]),
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(h_i, h_array[i]),
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(h_i1, h_array[i + 1]),
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(l_i, l_array[i]),
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(l_i1, l_array[i + 1]),
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(stringlen_i, string_length),
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(_sigma_i1, val_sigma_i[i + 1]),
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(beta_i, math.atan(h_array[i] / l_array[i])),
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(beta_i1, math.atan(h_array[i + 1] / l_array[i + 1])),
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]
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)
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_val_delta_l_li = list(val_delta_l_li)
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_val_delta_l_li[-1] = _val_delta_l_li[j] # 把需要求导的Δlj放最后一个位置
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_val_delta_l_li[j] = 0
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# σi1的第i+1行至倒数第2行全部清0
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for k in range(i + 1, len(_val_delta_l_li) - 1):
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_val_delta_l_li[k] = 0
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# if index == i:
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# _val = _val.subs(li, val_delta_l_li[index])
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# if index > i:
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# _val = _val.subs(li, 0)
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for index, li in enumerate(delta_Li):
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_val = _val.subs(li, _val_delta_l_li[index])
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pass
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col.append(_val)
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row.append(col)
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return sympy.Matrix(row)
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# D为dΔσi1dσi
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# D只有n-1行
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def evaluate_d_sigma_i1_d_delta_sigma_i(val_delta_li):
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row = []
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for i in range(span_count - 1):
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col = []
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for j in range(span_count):
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if i == j:
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sum_delta_li = math.fsum(val_delta_li)
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_val = -(
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(
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h_array[i] / l_array[i]
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+ ((string_g / conductor_n) ** 2 - sum_delta_li ** 2) ** 0.5
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)
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/ (
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((string_g / conductor_n) ** 2 - sum_delta_li ** 2) ** 0.5
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+ h_array[i + 1] / l_array[i + 1]
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)
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)
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col.append(_val)
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continue
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if i == j - 1:
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col.append(1)
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continue
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col.append(0)
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row.append(col)
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return sympy.Matrix(row)
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def solve():
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# 初始化
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val_delta_li = [0.1 for i in range(span_count)]
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# val_delta_li = [0.15864687475316822, -0.1935189734784845, 0.03478489898855073]
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val_sigma_i = [sigma_m_data for _ in range(span_count)]
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# val_sigma_i = [175.38451579479482, 176.01015153076614, 175.88355419459572]
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loop = 0
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while True:
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loop += 1
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print("第{loop}次迭代".format(loop=loop))
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if loop >= 20:
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break
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# A为dΔli/dli
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M_A = sympy.eye(span_count)
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# B为dΔli/dσi
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M_B = sympy.diag(
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evaluate_d_delta_l_i_sigma_i(val_delta_li, val_sigma_i), unpack=True
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)
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# C为dΔσi1dli
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M_C = evaluate_d_sigma_i1_d_delta_l_i(val_delta_li, val_sigma_i)
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# D为dΔσi1dσi
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M_D = evaluate_d_sigma_i1_d_delta_sigma_i(val_delta_li)
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E1 = [1 for _ in range(span_count)]
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E2 = [0 for _ in range(span_count)]
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E = list(E1)
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E.extend(E2)
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M_E = sympy.Matrix([E])
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# 解方程
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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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- main.delta_li(
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h_array[i],
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l_array[i],
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lambda_i_array[i],
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alpha_data,
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elastic,
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t_e_data,
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t_data,
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val_sigma_i[i],
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lambda_m_data,
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t_m_data,
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sigma_m_data,
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)
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)
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if i < span_count - 1:
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fx_sigma_i1.append(
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val_sigma_i[i + 1]
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- main.fun_sigma_i1(
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area,
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val_sigma_i[i],
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math.fsum(val_delta_li[0 : i + 1]),
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string_length,
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string_g / conductor_n,
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h_array[i],
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l_array[i],
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lambda_i_array[i],
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h_array[i + 1],
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l_array[i + 1],
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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 = list(x)[0]
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abs_min = [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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print("最大偏差{max_dx}".format(max_dx=abs_min[-1]))
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# 更新变量
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for i in range(span_count):
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val_delta_li[i] += x_list[i]
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val_sigma_i[i] += x_list[i + span_count]
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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(loop)
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print(val_delta_li)
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print(val_sigma_i)
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solve()
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print("Finished.")
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