算法特点贝叶斯不确定性量化将贝叶斯神经网络与物理信息神经网络结合提供预测结果的不确定性区间解决传统黑箱模型信任度低的问题自适应物理约束学习通过可学习物理权重参数动态平衡数据驱动与物理规律约束避免硬约束导致的模型僵化多分辨率特征自动融合时域RMS/峰值/峭度、频域多频段能量、小波域多分辨率分解特征自动加权融合算法步骤第一阶段智能特征提取振动信号自动分段2560点智能分割消除边界效应多尺度特征并行计算时域统计、频域能量、小波分解同步提取自适应特征融合根据退化阶段自动调整各特征权重第二阶段贝叶斯神经网络构建均值-方差双输出设计同时预测退化值和不确定性重参数化训练技巧实现高效贝叶斯推理训练速度提升3倍不确定性传播机制在预测过程中量化累积不确定性第三阶段物理约束智能融合自适应物理权重学习通过可学习参数动态调节物理约束强度柔性单调性约束一阶导数非负但允许±0.2的合理波动物理-数据损失平衡自动寻找最优约束平衡点第四阶段稳健训练优化稳定初始化策略Xavier初始化tanh激活防止梯度爆炸自适应学习率调度余弦退火配合早停机制防止过拟合梯度裁剪保护最大梯度范数限制为1.0保证训练稳定性第五阶段剩余寿命精准预测多步滚动预测从检查点开始逐步预测至阈值不确定性区间计算每次预测同步计算95%置信区间风险量化决策支持基于不确定性评估预测可靠性# Import necessary modules import os import time import scipy.io import scipy.stats import pywt from matplotlib import pyplot as plt import numpy as np import pandas as pd import torch import torch.nn as nn import torch.optim as optim import torch.nn.functional as F from sklearn.preprocessing import StandardScaler from matplotlib.patches import Rectangle print(PyTorch Version:, torch.__version__) # Load data files PHM_path PHM PHM_bearing_files [os.path.join(PHM_path, file) for file in os.listdir(PHM_path)] # Enhanced feature extraction def mat_to_arr_enhanced(file): Enhanced feature extraction h scipy.io.loadmat(file)[h].reshape(-1) h2 h.reshape(-1, 2560) # Basic features kurtosis np.array([scipy.stats.kurtosis(i) for i in h2]) rms np.array([np.mean(i**2)**0.5 for i in h2]) rms np.convolve(rms, [0.3, 0.4, 0.3], modesame) ma np.array([np.max(np.abs(i)) for i in h2]) # Time-frequency features wavelet_features [] for segment in h2: coeffs pywt.wavedec(segment, db4, level3) energies [np.sum(c**2) for c in coeffs] wavelet_features.append(energies) wavelet_features np.array(wavelet_features) # Frequency domain features freq_features [] for segment in h2: fft_vals np.abs(np.fft.rfft(segment)) freq_features.append([ np.sum(fft_vals[:10]), np.sum(fft_vals[10:50]), np.sum(fft_vals[50:]), np.argmax(fft_vals) ]) freq_features np.array(freq_features) # Combine features all_features np.concatenate([ rms.reshape(-1, 1), ma.reshape(-1, 1), kurtosis.reshape(-1, 1), wavelet_features, freq_features ], axis1) FPT int(len(h2)) * 1700 / 2560 print(fFault Progression Time (FPT): {FPT:.2f}, Feature Dimension: {all_features.shape}) return h, FPT, all_features # Bayesian Physics-Informed Neural Network (Bayesian PINN) class BayesianPINN(nn.Module): Bayesian Physics-Informed Neural Network with uncertainty quantification def __init__(self, input_dim1, hidden_dim32, dropout_rate0.3): super(BayesianPINN, self).__init__() self.input_dim input_dim self.hidden_dim hidden_dim # Network architecture for feature extraction self.feature_extractor nn.Sequential( nn.Linear(input_dim, hidden_dim), nn.Tanh(), nn.Dropout(dropout_rate), nn.Linear(hidden_dim, hidden_dim // 2), nn.Tanh(), nn.Dropout(dropout_rate) ) # Mean output layer self.mean_layer nn.Linear(hidden_dim // 2, 1) # Variance output layer (using softplus for positivity) self.logvar_layer nn.Sequential( nn.Linear(hidden_dim // 2, hidden_dim // 4), nn.Tanh(), nn.Linear(hidden_dim // 4, 1), nn.Softplus() ) # Physics constraint weight self.physics_weight nn.Parameter(torch.tensor(0.1)) # Initialize weights self._initialize_weights() print(fBayesian PINN: Hidden Layer{hidden_dim}, Dropout{dropout_rate})参考文章Uncertainty-Aware Bayesian PINN机械退化趋势预测Pytorch - 哥廷根数学学派的文章https://zhuanlan.zhihu.com/p/1999906972938544861工学博士担任《Mechanical System and Signal Processing》审稿专家担任《中国电机工程学报》优秀审稿专家《控制与决策》《系统工程与电子技术》《电力系统保护与控制》《宇航学报》等EI期刊审稿专家。擅长领域现代信号处理机器学习深度学习数字孪生时间序列分析设备缺陷检测、设备异常检测、设备智能故障诊断与健康管理PHM等。