算法特点将黎曼流形理论转化为可训练的神经网络正则化项解决高维特征空间几何结构保持难题防止模型塌陷通过余弦相似度矩阵保持退化轨迹的局部平滑性相似退化状态的特征在黎曼流形上保持接近黎曼正则化保持特征空间的几何结构物理约束确保退化趋势符合实际物理规律算法步骤第一阶段多尺度特征智能提取振动信号自适应分割2560点智能分段消除随机噪声干扰滑动平均平滑凸显退化趋势退化特征全息计算时域统计特征RMS、峰值、峭度捕捉异常频域能量特征多频段能量分布识别故障类型小波多分辨率特征冲击特征精确定位第二阶段黎曼流形智能建模特征空间黎曼度量构建提取网络中间层特征作为黎曼流形基计算特征向量的余弦相似度矩阵流形几何一致性约束在特征流形上施加局部平滑约束保持相邻退化状态的特征相似性第三阶段物理规律智能融合退化过程物理建模一阶导数非负性约束单调退化允许±0.2的合理波动范围自适应约束权重学习黎曼正则化权重自学习物理约束权重自调节第四阶段高效稳定训练稳定收敛策略Xavier初始化Tanh激活函数AdamW优化器余弦退火学习率智能早停机制150轮耐心监测自动保存最佳模型第五阶段RUL预测流形空间外推预测在黎曼流形上进行多步预测考虑流形几何结构的外推修正可视化退化轨迹与预测路径对比故障时间置信区间展示# Riemannian Geometry Constrained PINN class RiemannianConstrainedPINN(nn.Module): Riemannian Geometry Constrained Physics-Informed Neural Network def __init__(self, input_dim1, hidden_dim32, dropout_rate0.3): super(RiemannianConstrainedPINN, self).__init__() self.input_dim input_dim self.hidden_dim hidden_dim # Network architecture self.network 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), nn.Linear(hidden_dim // 2, 1) ) # Riemannian regularization parameter self.riemannian_weight nn.Parameter(torch.tensor(0.1)) # Physics constraint weight self.physics_weight nn.Parameter(torch.tensor(0.1)) # Initialize weights self._initialize_weights() print(fRiemannian Constrained PINN: Hidden Layer{hidden_dim}, Dropout{dropout_rate}) def _initialize_weights(self): Stable initialization for m in self.modules(): if isinstance(m, nn.Linear): nn.init.xavier_uniform_(m.weight, gainnn.init.calculate_gain(tanh)) if m.bias is not None: nn.init.constant_(m.bias, 0) def forward(self, x): Forward propagation output self.network(x) # Apply output limits output torch.sigmoid(output) * 3.0 return output.squeeze(-1) def riemannian_loss(self, x): Riemannian geometry constraint loss if len(x) 2: return torch.tensor(0.0, devicex.device) # Get intermediate features from network features self.network[:-1](x) # Features before last layer # Calculate Riemannian metric (cosine similarity matrix) features_norm F.normalize(features, p2, dim1) similarity_matrix torch.mm(features_norm, features_norm.t()) # Riemannian loss: maximize local consistency riemannian_loss torch.mean(1.0 - similarity_matrix) * 0.01 return riemannian_loss参考文章Riemann-Geometry 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/1999943345863161346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。