为了加快速度，将symbol公式lambdify成普通python函数
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@ -60,25 +60,9 @@ 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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def get_lambdify_d_delta_l_i_sigma_i(_d_delta_l_i_sigma_i):
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(
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delta_l_i,
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l_i,
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@ -108,46 +92,37 @@ def evaluate_d_delta_l_i_sigma_i(val_delta_l_li, val_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_data),
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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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manual_val = exp.manual_diff_delta_li_sigma_i(
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h_array[i],
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l_array[i],
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lambda_m_data,
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lambda_i_array[i],
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val_sigma_i[i],
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sigma_m_data,
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alpha_data,
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t_data,
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t_e_data,
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t_m_data,
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elastic_data,
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)
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if math.fabs(val - manual_val) > 1e-5:
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raise Exception("d_delta_l_i_sigma_i 自动和手动微分不匹配")
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val_list.append(val)
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return val_list
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return sympy.lambdify(
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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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_d_delta_l_i_sigma_i,
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)
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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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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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def get_lambdify_d_sigma_i1_d_l_i(_d_sigma_i1_d_l_i):
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(
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G_i,
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A,
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@ -179,6 +154,84 @@ def evaluate_d_sigma_i1_d_delta_l_i(val_delta_l_li, val_sigma_i):
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beta_i1,
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"""
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)
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return sympy.lambdify(
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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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*delta_Li,
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),
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_d_sigma_i1_d_l_i,
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)
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fx_d_sigma_i1_d_l_i = get_lambdify_d_sigma_i1_d_l_i(d_sigma_i1_d_l_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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val_list = []
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for i in range(span_count):
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val = sympy.Float(
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fx_d_delta_l_i_sigma_i(
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val_delta_l_li[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_data,
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t_e_data,
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t_data,
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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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val_sigma_i[i],
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math.atan(h_array[i] / l_array[i]),
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)
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)
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manual_val = exp.manual_diff_delta_li_sigma_i(
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h_array[i],
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l_array[i],
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lambda_m_data,
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lambda_i_array[i],
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val_sigma_i[i],
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sigma_m_data,
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alpha_data,
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t_data,
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t_e_data,
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t_m_data,
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elastic_data,
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)
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if math.fabs(val - manual_val) > 1e-5:
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raise Exception("d_delta_l_i_sigma_i 自动和手动微分不匹配")
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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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row = []
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for i in range(span_count - 1):
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col = []
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@ -186,36 +239,31 @@ def evaluate_d_sigma_i1_d_delta_l_i(val_delta_l_li, val_sigma_i):
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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_data),
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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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_val = sympy.Float(
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fx_d_sigma_i1_d_l_i(
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string_g / conductor_n,
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area_data,
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lambda_i_array[i],
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lambda_i_array[i + 1],
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val_sigma_i[i],
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h_array[i],
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h_array[i + 1],
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l_array[i],
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l_array[i + 1],
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string_length,
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val_sigma_i[i + 1],
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math.atan(h_array[i] / l_array[i]),
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math.atan(h_array[i + 1] / l_array[i + 1]),
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*_val_delta_l_li
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)
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)
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manual_val = exp.manual_diff_sigma_i1_d_l_i(
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h_array[i],
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l_array[i],
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@ -267,11 +315,11 @@ 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 = [0.1 for _ in range(span_count)]
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val_delta_li = [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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# val_sigma_i = [sigma_m_data for _ in range(span_count)]
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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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val_sigma_i = [sigma_m_data for _ in range(span_count)]
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loop = 0
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while True:
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@ -360,10 +408,10 @@ def solve():
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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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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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abs_min.sort()
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if abs_min[-1] < 1e-6:
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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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@ -373,9 +421,9 @@ 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(loop)
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print(val_delta_li)
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print(val_sigma_i)
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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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2
data.py
2
data.py
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@ -24,7 +24,7 @@ lambda_i_array = [
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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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span_count = 9 # 几个档距
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span_count = 10 # 几个档距
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# n个档距,n-1个直线塔
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h_array = [
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0,
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12
main.py
12
main.py
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@ -132,10 +132,10 @@ def cal_loop():
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b_i += _delta_l_i
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length_i = string_length
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g_i = string_g / data.conductor_n
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h_i1 = h_array[i + 1]
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l_i1 = l_array[i + 1]
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if i < span_count - 1:
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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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try:
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sigma_i1 = fun_sigma_i1(
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area,
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@ -257,10 +257,10 @@ def verify(
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print("!!!应力等式不满足")
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return
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print("等式满足。")
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print('sigma')
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print(sigma_array)
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print('delta_li')
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print(delta_l_i_array)
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# print('sigma')
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# print(sigma_array)
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# print('delta_li')
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# print(delta_l_i_array)
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if __name__ == "__main__":
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