Algorithm 1: Gradient Descent Algorithm for Training G-CASAE with Constructive Loss Function

Step 1: The data acquisition system collects the multivariable monitoring signals of the key components of the rotating machinery. Step 2: Prepare the SAE for fault diagnosis. Step 3: Set the parameters of SAE, including the number of neurons for each layer, the learning rate, and the maximum generation number or threshold for exit training. Step 4: Initialize all parameters of each layer $W,b$ to be learned by backpropagation. Step 5: Amplitude consistency and trend consistency are used to design the new SAE loss function for layer-by-layer feature extraction to extract the weak fault trend feature, which aims to enhance the feature extraction capability from the monitoring signals. Step 6: The well-learned features are fed into the classification layer, which is classified by the loss function constructed with amplitude distance consistency and orientation consistency. Step 7: Save the network model parameters. Step 8: Extraction and diagnosis of minor fault features using the trained model. Step 9: Output fault diagnosis results.