Update TO_Cal.py
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# -*- coding: utf-8 -*-
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"""
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Created on Thu Apr 23 15:08:01 2020
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@author: zzy
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Object: 存储TO计算过程所需的函数
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1. 所有函数均可jit
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2. 在调用时 选择在最外层封装jit 内层函数则将jit注释
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3. 对于部分确定的static variable 应采用numpy定义(仅限CPU)
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"""
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'''
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@ Copyright (c) 2022 by Zeyu Zhang, All Rights Reserved.
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@ Author : Zeyu Zhang
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@ Email : zhangzeyu_work@outlook.com
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@ Date : 2021-11-17 10:52:26
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@ LastEditTime : 2022-10-25 09:33:11
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@ FilePath : /ZZY_CODE/Env_JAX/IDRL/Linear_TO/TO_Cal.py
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@
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@ Description : 存储TO计算过程所需的函数
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@ Reference :
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'''
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import numpy as np
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import jax
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@ -26,90 +27,28 @@ config.update("jax_enable_x64", True)
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@partial(jax.jit, static_argnums=(5, 6, 7))
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def design_variable(x, design_area_indices, nondesign_area_indices, filter_kernal, filter_weight, beta_x, volfrac, projection=False):
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"""
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Parameters
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----------
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x : shape:[nely, nelx](2D) 经过reshape的NN输出
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design_area_indices : 设计域的单元编号索引
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nondesign_area_indices : 非设计域的单元编号索引
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filter_kernal : TOP88中的H 卷积过滤中的卷积核 计算影响域内每一个单元的权重
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filter_weight : TOP88中的HS 设计域内每一个单元的总权重 与网格划分同维度
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beta_x : Projection参数
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volfrac : 目标体积
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projection : 是否采用Projection
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Returns
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-------
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xPhys_1D : shape:[Total_ele](1D) 参与有限元计算的单元相对密度阵
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"""
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# density filtering 用在了转换之前 目前看也是有效果的
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x = filter(x, filter_kernal, filter_weight)
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x_1D = x.flatten(order='F')
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x_designed = design_and_volume_constraints(
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x_1D[design_area_indices], volfrac, beta_x)
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xPhys_1D = matrix_set_0(
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x_designed, design_area_indices, nondesign_area_indices)
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# 直接等于xPhys_1D 但尚需要在真实存在非设计域时验证
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# 原始方案
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# x_in = x[design_map_bool]
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# x_designed = design_and_volume_constraints(x_in, volfrac, beta_x) # x[design_map_bool]内含了一步matrix.flatten()
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# x_flat = matrix_set_0(x_designed, jnp.flatnonzero(design_map_bool, size=num_design_ele), Total_ele, num_nondesign_ele)
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# 因为x_designed内含flatten() 所以这里对应要复原 由于flatten时没有传入order='F' 这里也不能传入
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# xPhys = x_flat.reshape(x.shape)
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return xPhys_1D
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def projection(x, beta_TONR):
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"""
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实现projection 将[-z, z]的数值映射至(0, 1)
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目前
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原理 tanh能够将元素映射至(-1, 1) 因此 tanh_out * 0.5 + 0.5可以映射至(0, 1)
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注意 sigmoid(x) = 0.5 * tanh(0.5 * x) + 0.5
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Parameters
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----------
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x : 待映射的矩阵
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beta_TONR : projection函数斜率的控制参数
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Returns
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-------
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output : sigmoid/projection变换后的矩阵
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"""
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output = jnp.tanh(beta_TONR * 0.5 * x)*.5 + 0.5
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return output
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def logit(obj_V):
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"""
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根据obj_V确定sigmoid分母部分e ** (x-b)中 b搜索的初始上下界
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np.clip(a, a_min, a_max) 将a的取值截断在(a_min, a_max)内
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Parameters
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----------
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obj_V : 目标体积
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Returns
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-------
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"""
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p = jnp.clip(
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obj_V, 0, 1)
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return jnp.log(p) - jnp.log1p(-p) # p从-inf到inf p取0.5为0 以0.5为界限 大于小于符号相反 数值相同
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return jnp.log(p) - jnp.log1p(-p)
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# @partial(jax.jit, static_argnums=(1, 2))
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def design_and_volume_constraints(x, obj_V, beta_TONR):
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"""
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用来将神经网络的输出转化为满足设计约束 体积约束和projection的用于有限元计算的单元密度
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x_design = 1/(1 + e ** (x - b(x, obj_V)))
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Parameters
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----------
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x : 经过密度过滤后的单元相对密度阵
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obj_V : 目标体积.
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beta_TONR : Projection参数
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Returns
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-------
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x_design : 满足设计约束和体积约束的相对密度 向量形式
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"""
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def find_yita(y, x, beta):
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projection_out = projection(x + y, beta)
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volume_diff = jnp.mean(projection_out) - obj_V
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@ -118,28 +57,12 @@ def design_and_volume_constraints(x, obj_V, beta_TONR):
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upper_bound = logit(obj_V) - jl.stop_gradient(np.min(x))
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bisec = Bisection(optimality_fun=find_yita, lower=lower_bound, upper=upper_bound, tol=1e-12, maxiter=64, check_bracket=False)
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yita = bisec.run(x=x, beta=beta_TONR).params
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# yita = TPA.binary_search(find_yita, x, beta_TONR, lower_bound, upper_bound) # 自编二分法
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# 用来搜索yita的取值 由二分法获得 本质上这里和保体积projection搜索yita的过程完全相同
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# 实验和公式表明 在保体积projection和此处添加体积约束的sigmoid中 对yita的求解均是一个关于(x, obj_V)的函数
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# 其敏度必然要考虑
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x_design = projection(x + yita, beta_TONR)
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x_design = x_design + 0.00001
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return x_design
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def filter_define(design_map, filter_width):
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"""
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定义TO中过滤器的卷积核 权重等参数
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Parameters
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----------
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design_map : 设计域和非设计域定义矩阵
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filter_width : 过滤半径
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Returns
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-------
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filter_kernal : TOP88中的H 卷积过滤中的卷积核 计算影响域内每一个单元的权重
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filter_weight : TOP88中的HS 设计域内每一个单元的总权重 与网格划分同维度
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"""
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dy, dx = jnp.meshgrid(jnp.arange(-jnp.ceil(filter_width)+1, jnp.ceil(filter_width)),
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jnp.arange(-jnp.ceil(filter_width)+1, jnp.ceil(filter_width)))
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filter_kernal = jnp.maximum(0, filter_width - jnp.sqrt(dx ** 2 + dy ** 2))
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@ -149,17 +72,6 @@ def filter_define(design_map, filter_width):
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# @jax.jit
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def filter(matrixA, filter_kernal, filter_weight):
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"""
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Parameters
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----------
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matrixA : 待过滤的矩阵
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filter_kernal : TOP88中的H 卷积过滤中的卷积核 计算影响域内每一个单元的权重
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filter_weight : TOP88中的HS 设计域内每一个单元的总权重 与网格划分同维度
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Returns
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-------
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new_matrix : 过滤后的矩阵
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"""
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new_matrix = jss.convolve2d(matrixA, filter_kernal, 'same') / filter_weight
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return new_matrix
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@ -173,24 +85,6 @@ def inverse_permutation(indices):
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# @jax.jit
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def matrix_set_0(nonzero_values, nonzero_indices, zero_indices):
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"""
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补齐矩阵 对原始矩阵指定区域置0 可用于非设计域进行置0 以及节点位移添加指定节点的位移
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Parameters
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----------
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nonzero_values : 已存在数值的矩阵 如设计域的相对密度阵 freedofs对应的节点位移
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nonzero_indices : size=存在数值的个数 已存在数值矩阵对应的索引编号 如设计域对应的索引
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注意 这里为根据design_map自动生成的 是基于行展开编号的 仅用于此处计算 并非真正TO中的单元编号
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zero_indices : 矩阵中未存在数值的单元对应的索引编号
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origin_matrix_size : 原始矩阵元素个数 即包含设计域和非设计域
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zero_size : 矩阵中0元素的个数 代表非设计域的单元个数
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Returns
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-------
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new_matrix : 补齐后的矩阵
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"""
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# all_indices = np.arange(origin_matrix_size, dtype=jnp.int64)
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# zero_indices = jnp.setdiff1d(
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# all_indices, nonzero_indices, size=zero_size, assume_unique=True) # setdiff1d通常不支持jit 需要指定size
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index_map = inverse_permutation(
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jnp.concatenate([nonzero_indices, zero_indices]))
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u_values = jnp.concatenate([nonzero_values, jnp.zeros(len(zero_indices))])
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@ -200,19 +94,6 @@ def matrix_set_0(nonzero_values, nonzero_indices, zero_indices):
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@partial(jax.jit, static_argnums=(2, 3))
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def matrix_set_1(nonzero_values, nonzero_indices, origin_matrix_size, zero_size):
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"""
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补齐矩阵 对原始矩阵指定区域置1
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Parameters
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----------
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nonzero_values : 已存在数值的矩阵
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nonzero_indices : 已存在数值矩阵对应的索引编号
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origin_matrix_size : 原始矩阵元素个数 即包含设计域和非设计域
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zero_size : 矩阵中0元素的个数 代表非设计域的单元个数
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Returns
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-------
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new_matrix : 补齐后的矩阵
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"""
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all_indices = jnp.arange(origin_matrix_size, dtype=jnp.int64)
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zero_indices = jnp.setdiff1d(
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all_indices, nonzero_indices, size=zero_size, assume_unique=True)
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@ -225,29 +106,9 @@ def matrix_set_1(nonzero_values, nonzero_indices, origin_matrix_size, zero_size)
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@partial(jax.jit, static_argnums=(1, 2, 10))
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def objective(xPhys_1D, young, young_min, freedofs, fext, s_K_predefined, dispTD_predefined, idx, edofMat, ke, penal):
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"""
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Parameters
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----------
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xPhys_1D : shape:[Total_ele](1D) 参与有限元计算的相对密度
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young : 杨氏模量
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young_min : 弱单元的杨氏模量
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freedofs : 有限元的自由节点
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fext : Python中的1D矢量 外力
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s_K_predefined : 预定义的刚度阵
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dispTD_predefined : 预定义的位移阵
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idx : 刚度阵组装编号
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edofMat : shape:[Total_ele, 8](2D) 按照单元顺序存储每一个单元的自由度编号
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ke : 单元刚度阵 不考虑杨氏模量
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penal : 惩罚因子
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Returns
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-------
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obj : 目标函数输出 此处为结构的柔度
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"""
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# xPhys_1D = xPhys.T.flatten()
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disp = TO_FEA.FEA(young, young_min, ke, xPhys_1D, freedofs,
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penal, idx, fext, s_K_predefined, dispTD_predefined)
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obj = TO_Obj.compliance(young, young_min, ke,
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xPhys_1D, edofMat, penal, disp)
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# print('obj is running')
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return obj
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