【EI+Scopus+Google Scholar三平台护航】2025年8-9月智能融合:计算建模、人工智能与物联网、机械制造与智能控制以及人工智能与数字化管理等领域的创新之旅
import numpy as np
from scipy.sparse import lil_matrix
from scipy.sparse.linalg import spsolve
def finite_element_analysis(elements, nodes, E, A, forces, boundaries):
"""
简单的有限元分析,计算杆系结构的位移。
:param elements: 元素连接关系,列表,每个元素包含节点索引对 (node_i, node_j)
:param nodes: 节点坐标,列表,每个节点为 (x, y)
:param E: 材料弹性模量,浮点数
:param A: 截面面积,浮点数
:param forces: 节点荷载,字典,键为节点索引,值为 (Fx, Fy)
:param boundaries: 边界条件,字典,键为节点索引,值为 (ux, uy) 约束
:return: 节点位移,字典,键为节点索引,值为 (ux, uy)
"""
num_nodes = len(nodes)
num_elements = len(elements)
dof_per_node = 2 # 每个节点有两个自由度(x, y)
total_dof = num_nodes * dof_per_node
# 初始化刚度矩阵和荷载向量
K = lil_matrix((total_dof, total_dof))
F = np.zeros(total_dof)
# 组装刚度矩阵
for elem in elements:
node_i, node_j = elem
x_i, y_i = nodes[node_i]
x_j, y_j = nodes[node_j]
L = np.sqrt((x_j - x_i)**2 + (y_j - y_i)**2)
cos = (x_j - x_i) / L
sin = (y_j - y_i) / L
# 单元刚度矩阵(局部坐标系)
k_local = (E * A / L) * np.array([[1, 0, -1, 0],
[0, 0, 0, 0],
[-1, 0, 1, 0],
[0, 0, 0, 0]])
# 转换到全局坐标系
T = np.array([[cos, sin, 0, 0],
[-sin, cos, 0, 0],
[0, 0, cos, sin],
[0, 0, -sin, cos]])
k_global = T.T @ k_local @ T
# 组装到总刚度矩阵
dof = [node_i*2, node_i*2+1, node_j*2, node_j*2+1]
for i in range(4):
for j in range(4):
K[dof[i], dof[j]] += k_global[i, j]
# 应用力荷载
for node, force in forces.items():
F[node*2] += force[0]
F[node*2+1] += force[1]
# 应用边界条件
fixed_dof = []
for node, boundary in boundaries.items():
if boundary[0] == 0:
fixed_dof.append(node*2)
if boundary[1] == 0:
fixed_dof.append(node*2+1)
# 将固定自由度的行和列置零,对角线置一
for dof in fixed_dof:
K[dof, :] = 0
K[:, dof] = 0
K[dof, dof] = 1
F[dof] = 0
# 转换为 CSC 格式求解
K = K.tocsc()
U = spsolve(K, F)
# 整理结果
displacements = {}
for node in range(num_nodes):
displacements[node] = (U[node*2], U[node*2+1])
return displacements
import numpy as np
from tensorflow.keras.models import Model
from tensorflow.keras.layers import Input, Embedding, Flatten, Concatenate, Dense, Dot
def create_recommendation_model(num_users, num_items, embedding_dim=50):
"""
创建一个基于矩阵分解的深度学习推荐系统模型。
:param num_users: 用户数量
:param num_items: 商品数量
:param embedding_dim: 嵌入维度
:return: Keras 模型
"""
# 用户输入和嵌入
user_input = Input(shape=(1,))
user_embedding = Embedding(num_users, embedding_dim)(user_input)
user_vec = Flatten()(user_embedding)
# 商品输入和嵌入
item_input = Input(shape=(1,))
item_embedding = Embedding(num_items, embedding_dim)(item_input)
item_vec = Flatten()(item_embedding)
# 点积和 Concatenate
dot_product = Dot(axes=1)([user_vec, item_vec])
concat = Concatenate()([user_vec, item_vec])
dense = Dense(128, activation='relu')(concat)
dense = Dense(64, activation='relu')(dense)
output = Dense(1)(dense) # 预测评分
model = Model(inputs=[user_input, item_input], outputs=output)
model.compile(optimizer='adam', loss='mse')
return model
# 示例:训练推荐系统模型
num_users = 1000
num_items = 500
embedding_dim = 32
# 生成模拟数据
users = np.random.randint(0, num_users, size=10000)
items = np.random.randint(0, num_items, size=10000)
ratings = np.random.randint(1, 6, size=10000).astype(np.float32)
# 创建模型
model = create_recommendation_model(num_users, num_items, embedding_dim)
# 训练模型
model.fit([users, items], ratings, epochs=5, batch_size=64, validation_split=0.2)
import numpy as np
def genetic_algorithm_optimization(objective_func, bounds, pop_size=50, generations=100, mutation_rate=0.01):
"""
遗传算法优化函数。
:param objective_func: 目标函数(最小化)
:param bounds: 参数边界,列表,每个元素为 (min, max)
:param pop_size: 种群大小
:param generations: 代数
:param mutation_rate: 变异率
:return: 最优解
"""
n_vars = len(bounds)
# 初始化种群
pop = np.random.rand(pop_size, n_vars)
for i in range(n_vars):
pop[:, i] = bounds[i][0] + pop[:, i] * (bounds[i][1] - bounds[i][0])
for _ in range(generations):
# 计算适应度
fitness = np.array([objective_func(ind) for ind in pop])
# 选择操作(轮盘赌选择)
fitness -= np.min(fitness) # 确保非负
fitness += 1e-6 # 避免除以零
selection_prob = fitness / np.sum(fitness)
selected_indices = np.random.choice(range(pop_size), size=pop_size, p=selection_prob)
selected_pop = pop[selected_indices]
# 交叉操作(单点交叉)
offspring = np.copy(selected_pop)
for i in range(0, pop_size, 2):
if np.random.rand() < 0.8: # 交叉率
cross_point = np.random.randint(1, n_vars)
offspring[i, :cross_point] = selected_pop[i+1, :cross_point]
offspring[i+1, cross_point:] = selected_pop[i, cross_point:]
# 变异操作
for i in range(pop_size):
if np.random.rand() < mutation_rate:
mut_gene = np.random.randint(n_vars)
offspring[i, mut_gene] += np.random.normal(0, 0.1)
# 边界检查
offspring[i, mut_gene] = np.clip(offspring[i, mut_gene], bounds[mut_gene][0], bounds[mut_gene][1])
# 更新种群
pop = offspring
# 找到最优个体
fitness = np.array([objective_func(ind) for ind in pop])
best_idx = np.argmin(fitness)
return pop[best_idx]
# 示例:机械结构重量最小化优化
def structural_weight(x):
# 简化的结构重量计算函数
return (x[0]**2 + x[1]**2) * 10 + x[2]**3 # 参数为尺寸参数
bounds = [(0.1, 1.0), (0.1, 1.0), (0.5, 2.0)] # 各参数的范围
optimal_solution = genetic_algorithm_optimization(structural_weight, bounds)
print("最优结构尺寸参数:", optimal_solution)
import numpy as np
import gym
from gym import spaces
class BusinessProcessEnv(gym.Env):
"""
业务流程优化环境。
"""
def __init__(self):
super(BusinessProcessEnv, self).__init__()
# 定义动作空间和状态空间
self.action_space = spaces.Discrete(3) # 0: 加快速度, 1: 保持, 2: 减慢速度
self.observation_space = spaces.Box(low=0, high=1, shape=(4,), dtype=np.float32)
# 初始化状态
self.state = np.array([0.5, 0.2, 0.3, 0.1]) # [流程时间, 成本, 质量, 客户满意度]
self.target = np.array([0.2, 0.1, 0.4, 0.5]) # 目标状态
def step(self, action):
# 根据动作更新状态
if action == 0: # 加快速度
self.state[0] *= 0.9
self.state[1] *= 1.1
self.state[2] *= 0.95
self.state[3] *= 0.9
elif action == 1: # 保持
self.state[0] *= 0.98
self.state[1] *= 0.98
self.state[2] *= 1.0
self.state[3] *= 1.0
elif action == 2: # 减慢速度
self.state[0] *= 1.1
self.state[1] *= 0.9
self.state[2] *= 1.05
self.state[3] *= 1.1
# 计算奖励(与目标状态的距离)
reward = -np.sum((self.state - self.target)**2)
# 判断是否完成
done = np.allclose(self.state, self.target, atol=0.05)
return self.state, reward, done, {}
def reset(self):
# 重置环境
self.state = np.array([0.5, 0.2, 0.3, 0.1])
return self.state
# 示例:使用简单的 Q-learning 进行业务流程优化
env = BusinessProcessEnv()
q_table = np.random.rand(env.observation_space.shape[0], env.action_space.n)
learning_rate = 0.1
discount_factor = 0.99
episodes = 1000
for episode in range(episodes):
state = env.reset()
done = False
while not done:
# 选择动作(简单策略:随机选择)
action = np.random.choice([0, 1, 2])
next_state, reward, done, _ = env.step(action)
# 更新 Q 表
q_table[int(state[0] * 10), action] = q_table[int(state[0] * 10), action] + learning_rate * (
reward + discount_factor * np.max(q_table[int(next_state[0] * 10), :]) - q_table[int(state[0] * 10), action]
)
state = next_state
print("优化后的 Q 表:", q_table)