unbanlanced_tension/auto_differentiation.py

# 利用自动微分计算
import datetime
from typing import List

import sympy
import data
import exp
import math
import main
import numpy as np

sympy.init_printing()
# h_i 悬点高差
# l_i 悬点档距
# _alpha 导线膨胀系数  1/°C
# _elastic 弹性系数 N/mm2
# _t_e 架线时考虑初伸长的降温，取正值。单位°C
# lambda_i 计算不平衡张力时导线比载 N/(m.mm)
# sigma_i 计算不平衡张力时最低点水平应力 单位N/mm2
# t_i 计算不平衡张力时导线温度 单位°C
# _lambda_m 导线架线时时导线比载 N/(m.mm)
# _sigma_m 导线架线时时最低点水平应力 单位N/mm2
# _t_m 导线架线时时导线温度 单位°C


loop_end = data.loop_end  # 最大循环次数
# 架线时的状态
# 取外过无风
string_length = data.string_length  # 串长 单位m
string_g = data.string_g  # 串重 单位N
t_m_data = data.t_m  # 导线架设时的气温。单位°C
t_e_data = data.t_e  # 架线时考虑初伸长的降温，取正值。单位°C
alpha_data = data.alpha  # 导线膨胀系数  1/°C
elastic_data = data.elastic  # 弹性系数 N/mm2
area_data = data.area  # 导线面积 mm2
lambda_m_data = data.lambda_m  # 导线比载 N/(m.mm)
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
span_count = data.span_count  # 几个档距
# n个档距,n-1个直线塔
h_array = data.h_array
l_array = data.l_array
t_data = data.t
conductor_n = data.conductor_n
lambda_i_array = data.lambda_i_array
# TODO: 暂时没考虑荷载变化
symbol_delta_l_i = exp.delta_li()
sigma_i = sympy.symbols("sigma_i")
d_delta_l_i_sigma_i = sympy.diff(symbol_delta_l_i, sigma_i)
fx_d_delta_l_i_sigma_i = exp.get_lambdify_d_delta_l_i_sigma_i(d_delta_l_i_sigma_i)
delta_Li__1 = sympy.symbols(
    "delta_Li:{span_count}".format(span_count=data.span_count - 1)
)
delta_Li = (
    *delta_Li__1,
    sympy.symbols("delta_Li_i"),
)
symbol_sigma_i1 = exp.fun_sigma_i1(delta_Li)
delta_Li_i = sympy.symbols("delta_Li_i")
d_sigma_i1_d_l_i = sympy.diff(symbol_sigma_i1, delta_Li_i)


fx_d_sigma_i1_d_l_i = exp.get_lambdify_d_sigma_i1_d_l_i(d_sigma_i1_d_l_i, delta_Li)


# 一共2n个变量，n个delta_Li，n个sigma_i
# 分 [
#     A B
#     C D
#     E1 E2
#   ]
# 6块


# B为dΔli/dσi
def evaluate_d_delta_l_i_sigma_i(val_delta_l_li, val_sigma_i):

    val_list = []
    for i in range(span_count):
        val = sympy.Float(
            fx_d_delta_l_i_sigma_i(
                val_delta_l_li[i],
                l_array[i],
                lambda_i_array[i],
                alpha_data,
                elastic_data,
                t_e_data,
                t_data,
                lambda_m_data,
                t_m_data,
                sigma_m_data,
                val_sigma_i[i],
                math.atan(h_array[i] / l_array[i]),
            )
        )
        # manual_val = exp.manual_diff_delta_li_sigma_i(
        #     h_array[i],
        #     l_array[i],
        #     lambda_m_data,
        #     lambda_i_array[i],
        #     val_sigma_i[i],
        #     sigma_m_data,
        #     alpha_data,
        #     t_data,
        #     t_e_data,
        #     t_m_data,
        #     elastic_data,
        # )
        # if math.fabs(val - manual_val) > 1e-5:
        #     raise Exception("d_delta_l_i_sigma_i 自动和手动微分不匹配")
        val_list.append(val)
    return val_list


# C为dσi1dΔli
# C只有n-1行
def evaluate_d_sigma_i1_d_delta_l_i(val_delta_l_li, val_sigma_i):

    row = []
    for i in range(span_count - 1):
        col = []
        for j in range(span_count):
            if i < j:
                col.append(0)
            else:
                _val_delta_l_li = list(val_delta_l_li)
                _val_delta_l_li[-1] = _val_delta_l_li[j]  # 把需要求导的Δlj放最后一个位置
                _val_delta_l_li[j] = 0
                # σi1的第i+1行至倒数第2行全部清0
                for k in range(i + 1, len(_val_delta_l_li) - 1):
                    _val_delta_l_li[k] = 0
                _val = sympy.Float(
                    fx_d_sigma_i1_d_l_i(
                        string_g / conductor_n,
                        area_data,
                        lambda_i_array[i],
                        lambda_i_array[i + 1],
                        val_sigma_i[i],
                        h_array[i],
                        h_array[i + 1],
                        l_array[i],
                        l_array[i + 1],
                        string_length,
                        val_sigma_i[i + 1],
                        math.atan(h_array[i] / l_array[i]),
                        math.atan(h_array[i + 1] / l_array[i + 1]),
                        *_val_delta_l_li
                    )
                )

                # manual_val = exp.manual_diff_sigma_i1_d_l_i(
                #     h_array[i],
                #     l_array[i],
                #     h_array[i + 1],
                #     l_array[i + 1],
                #     string_g / conductor_n,
                #     area_data,
                #     lambda_i_array[i],
                #     lambda_i_array[i + 1],
                #     val_sigma_i[i],
                #     string_length,
                #     math.fsum(val_delta_l_li[0 : i + 1]),
                # )
                # if math.fabs(manual_val - _val) > 1e-5:
                #     raise Exception("d_sigma_i1_delta_L_i 自动和手动微分不匹配")
                col.append(_val)
        row.append(col)
    return sympy.Matrix(row)


# D为dΔσi1dσi
# D只有n-1行
def evaluate_d_sigma_i1_d_delta_sigma_i(val_delta_li):
    row = []
    for i in range(span_count - 1):
        col = []
        for j in range(span_count):
            if i == j:
                sum_delta_li = math.fsum(val_delta_li)
                _val = -(
                    (
                        h_array[i] / l_array[i]
                        + ((string_g / conductor_n) ** 2 - sum_delta_li ** 2) ** 0.5
                    )
                    / (
                        ((string_g / conductor_n) ** 2 - sum_delta_li ** 2) ** 0.5
                        + h_array[i + 1] / l_array[i + 1]
                    )
                )
                col.append(_val)
                continue
            if i == j - 1:
                col.append(1)
                continue
            col.append(0)
        row.append(col)
    return sympy.Matrix(row)


def solve():
    starttime = datetime.datetime.now()
    # 初始化
    val_delta_li = [data.string_length / (span_count + 1) for _ in range(span_count)]
    val_sigma_i = [sigma_m_data for _ in range(span_count)]
    loop = 0
    while True:
        loop += 1
        # print("第{loop}次迭代".format(loop=loop))
        if loop >= 20:
            break
        # A为dΔli/dli
        M_A = sympy.eye(span_count)
        # B为dΔli/dσi
        M_B = sympy.diag(
            evaluate_d_delta_l_i_sigma_i(val_delta_li, val_sigma_i), unpack=True
        )
        # C为dΔσi1dli
        M_C = evaluate_d_sigma_i1_d_delta_l_i(val_delta_li, val_sigma_i)
        # D为dΔσi1dσi
        M_D = evaluate_d_sigma_i1_d_delta_sigma_i(val_delta_li)
        E1 = [1 for _ in range(span_count)]
        E2 = [0 for _ in range(span_count)]
        E = list(E1)
        E.extend(E2)
        M_E = sympy.Matrix([E])
        # 解方程
        A = sympy.Matrix([[M_A, M_B], [M_C, M_D], [M_E]])
        fx_delta_Li = []
        fx_sigma_i1 = []
        for i in range(span_count):
            fx_delta_Li.append(
                val_delta_li[i]
                - main.delta_li(
                    h_array[i],
                    l_array[i],
                    lambda_i_array[i],
                    alpha_data,
                    elastic_data,
                    t_e_data,
                    t_data,
                    val_sigma_i[i],
                    lambda_m_data,
                    t_m_data,
                    sigma_m_data,
                )
            )
            if i < span_count - 1:
                fx_sigma_i1.append(
                    val_sigma_i[i + 1]
                    - main.fun_sigma_i1(
                        area_data,
                        val_sigma_i[i],
                        math.fsum(val_delta_li[0 : i + 1]),
                        string_length,
                        string_g / conductor_n,
                        h_array[i],
                        l_array[i],
                        lambda_i_array[i],
                        h_array[i + 1],
                        l_array[i + 1],
                        lambda_i_array[i + 1],
                    )
                )
        fx_sum_Li = [math.fsum(val_delta_li)]
        b_list = []
        b_list.extend(fx_delta_Li)
        b_list.extend(fx_sigma_i1)
        b_list.extend(fx_sum_Li)
        AA = np.array(A.tolist(), dtype=np.float64)
        b = np.array(b_list, dtype=np.float64)
        x = np.linalg.solve(-AA, b)
        x_list = x
        # 强制要求等式满足
        abs_min: List[float] = [
            math.fabs(_x) for _x in [*x_list, *fx_delta_Li, *fx_sigma_i1]
        ]
        abs_min.sort()
        if abs_min[-1] < 1e-5:
            break
        # print("最大偏差{max_dx}".format(max_dx=abs_min[-1]))
        # 更新变量
        for i in range(span_count):
            val_delta_li[i] += x_list[i]
            val_sigma_i[i] += x_list[i + span_count]
    if loop >= loop_end:
        print("不收敛")
    else:
        print("经过{loop}次迭代收敛,最大偏差{bias}".format(loop=loop, bias=abs_min[-1]))
        # print(val_delta_li)
        # print(val_sigma_i)
        verify(val_delta_li, val_sigma_i)
        endtime = datetime.datetime.now()
        # print('执行时间{t}'.format(t=(endtime-starttime).microseconds/1000))
        pass


def verify(val_delta_li, val_sigma_i):
    main.verify(
        area_data,
        h_array,
        l_array,
        string_length,
        string_g / conductor_n,
        val_sigma_i,
        val_delta_li,
        lambda_i_array,
        t_data,
        alpha_data,
        elastic_data,
        t_e_data,
        lambda_m_data,
        t_m_data,
        sigma_m_data,
        1e-5,
    )


solve()

print("Finished.")