import numpy as np import pandas as pd

读取训练数据

data = pd.read_excel('C题.xlsx') X = data[['接收距离（cm）', '热风速度(r/min)']].values y = data[['厚度mm', '孔隙率（%）', '压缩回弹性率（%）']].values

定义激活函数（sigmoid函数）

def sigmoid(x): return 1 / (1 + np.exp(-x))

定义激活函数的导数

def sigmoid_derivative(x): return x * (1 - x)

初始化权重和偏置

np.random.seed(0) weights1 = 2 * np.random.random((2, 4)) - 1 weights2 = 2 * np.random.random((4, 3)) - 1 bias1 = np.zeros((1, 4)) bias2 = np.zeros((1, 3))

定义训练迭代次数和学习率

epochs = 10000 learning_rate = 0.1

训练模型

for i in range(epochs): # 前向传播 layer1_output = sigmoid(np.dot(X, weights1) + bias1) layer2_output = sigmoid(np.dot(layer1_output, weights2) + bias2)

# 计算误差
layer2_error = y - layer2_output
if i % 1000 == 0:
    print('Error after', i, 'epochs:', np.mean(np.abs(layer2_error)))

# 反向传播
layer2_delta = layer2_error * sigmoid_derivative(layer2_output)
layer1_error = layer2_delta.dot(weights2.T)
layer1_delta = layer1_error * sigmoid_derivative(layer1_output)

# 更新权重和偏置
weights2 += layer1_output.T.dot(layer2_delta) * learning_rate
bias2 += np.sum(layer2_delta, axis=0, keepdims=True) * learning_rate
weights1 += X.T.dot(layer1_delta) * learning_rate
bias1 += np.sum(layer1_delta, axis=0, keepdims=True) * learning_rate

保存模型

import pickle model = { 'weights1': weights1, 'weights2': weights2, 'bias1': bias1, 'bias2': bias2 } with open('model.pkl', 'wb') as file: pickle.dump(model, file)

测试模型

test_data = pd.read_excel('C题.xlsx') X_test = data[['接收距离（cm）', '热风速度(r/min)']].values y_true = data[['厚度mm', '孔隙率（%）', '压缩回弹性率（%）']].values

layer1_output_test = sigmoid(np.dot(X_test, weights1) + bias1) layer2_output_test = sigmoid(np.dot(layer1_output_test, weights2) + bias2)

print('Predicted Output:', layer2_output_test) print('True Output:', y_true)

加载模型

with open('model.pkl', 'rb') as file: model = pickle.load(file)

weights1 = model['weights1'] weights2 = model['weights2'] bias1 = model['bias1'] bias2 = model['bias2']

使用加载的模型进行预测

X_test = data[['接收距离（cm）', '热风速度(r/min)']].values layer1_output_test = sigmoid(np.dot(X_test, weights1) + bias1) layer2_output_test = sigmoid(np.dot(layer1_output_test, weights2) + bias2)

print('Predicted Output:', layer2_output_test) print('True Output:', y_true)