## 3 Fault Diagnosis
### Current New Fault Diagnosis Algorithm
#### 3.2.1 Intelligent FD Methods Using Deep Learning Theories  
Deep learning, also known as deep neural networks (DNN), employs deep hierarchical architectures (sparse auto-encoder (SAE), deep belief networks (DBN), convolutional neural network (CNN)) with multiple neural layers to extracts the information features automatically, and further realize the mapping between learned features and output results. SAE is an unsupervised learning method. By constructing a self-encoder structure to obtain the transform output that can approximate the input signal, the model can obtain the internal characteristics of data without labels or a small number of labels after training, which can be used to study the sample missing or imbalance in fault diagnosis. DBN solves the global optimization problem of multilayer networks by layer by layer training. Reasonable initial values and weights are selected for the whole network structure, and then the optimal solution of the network can be obtained by fine-tuning the parameters. SAE was developed as a monitoring model to realize the FD of the air compressors [115]. DBN was applied to diagnose gearboxes and bearings [116]. The following will briefly introduce CNN and its process of realizing MSAE fault diagnosis.  
The structure of CNN is divided into 2-dimensional and 1-dimensional diagnostic models. Because 1D CNN can directly process 1D signals such as vibration signals, it is widely used in fault diagnosis of rolling bearings, motors, hydraulic pumps, and other equipment. [PERSON] et al. proposed a motor fault diagnosis system based on 1D CNN as shown in Figure 7, which fused the feature extraction and classification in the traditional fault detection methods into a single module [117]. The forward propagation from convolution layer \(l-1\) to current neuron input layer \(l\) can be expressed as  
\[x_{k}^{l}=b_{k}^{l}+\sum_{i=1}^{N_{l-1}}conv1D\left(w_{ik}^{l-1},s_{i}^{l-1}\right) \tag{18}\]  
where \(x_{k}^{l}\) is the input, \(b_{k}^{l}\) is a scalar bias of the \(k\) th neuron at the layer \(l\), and \(s_{i}^{l-1}\) is the output of the \(i\) th neuron at the layer \(l-1\), \(w_{ik}^{l-1}\) is the kernel. Use the input \(x_{k}^{l}\) to calculate the intermediate output \(y_{k}^{l}\), which can be written as  
\[y_{k}^{l}=f\left(x_{k}^{l}\right)\text{ }and\text{ }s_{k}^{l}=y_{k}^{l}\downarrow ss \tag{19}\]  
where \(s_{k}^{l}\) is the output of the neuron and \(\downarrow ss\) represents the down-sampling operation with the factor \(ss\). This method is directly applicable to the real-time data for a single equipment like a marine motor, so there is no need for a separate feature extraction algorithm, which makes the system more efficient in speed and hardware. This method is also applicable to the FD of MSAE by directly extracting signals from the ship end database.  
Diagnosis models based on the CNN method can directly capture the shift variant properties and learn features from measurement parameters from MSAE without preprocessing to obtain the corresponding characteristics. Furthermore, due to the shared weight method, the training data of the diagnostic model could be reduced, which is helpful to accelerate the convergence speed and prevent over-fitting. Like other deep learning methods, CNN also needs sufficient labeled samples to train the model to improve diagnostic efficiency.