## 3 Proposed Integrated Deep Fault Recognizer
### Structure and Algorithm of Deep Fault Recognizer  
This study uses the SDAE based model as basis to propose a self-governed intelligent fault diagnosis method that can automatically mine fault features from original signals, classify different  
Figure 2: Process of SDAE training.  
fault conditions, and deal with the noises existing in raw signals. The original signals in this study refer to the measured data in the frequency domain, which is an advantage in presenting the distribution of constitutive components with discrete frequencies, as well as containing legible information about the health conditions of rotating machinery [40]. The successive flow chat of deep fault recognizer is presented in Figure 3.  
With the training set of the frequency spectra [_X, Y_], several DAs can be trained and stacked. After a stack of denoising DAs has been built, the highest level representation output is inputted to a stand-alone supervised training algorithm, such as a logistic regression layer (see Figure 4). This process yields a deep neural network to supervised learning. Figure 4 illustrated the structure of an SDAE based model, the length of each layer and number of layers of which will be different because of different tasks. To date, no validated method to immediately determine these parameters has been developed. Therefore, the grid search method was adopted to determine a suitable model structure based on the machine learning empirical analysis.  
For a neural network, training the model with gradient-based optimization technique as a back propagation method in a supervised manner is straightforward. However, to resolve the gradient missing problem occurring in a deep network, the greedy layer-wise learning algorithm is adopted to train this deep network. First, the network is pre-trained per layer in a bottom-up direction. The parameters are updated by a set of batches, and each batch comprises several samples. Thereafter, the parameters of the entire model can be fine-tuned with the back propagation method in a top-down direction.  
Figure 4: Architecture of SDAE.  
Figure 3: Flow chart of deep fault recognizer.  
In the pre-training process, SDAE can learn multiple nonlinear deformations and extract the main beneficial inherent features of the frequency spectra. Thereafter, the process of fine-tuning enables SDAE to obtain different information from the input to further promote the classification ability [41]. The whole training process of SDAE is described as Algorithm 1.  
```
Given training samples \(\{X,Y\}\), the number of data batch m, the number of hidden layers \(l\), Step 1: Pre-train the SDAE For \(j\) in \(l\): For \(i\) in \(m\): -Random Initialization for weight matrices and bias vectors \(\{W,b\}\). -Compute the output of the \(j\)th hidden layer and make it as the input of the \((j+1)\)th hidden layer. -Update encoding parameters \(\{W,b\}\) with the gradients computed from the loss function for the \((j+1)\)th hidden layer to minimize the loss function. Step 2: Fine-tune the whole network -Initial \(\{W,b\}\) with the pre-training result. For \(i\) in \(m\): -Use the BP method to compute the overall gradient of each batch and the optimization with the gradient-based optimization technique. -Fine-tune the \(\{W,b\}\) with the mean optimization of a batch by updating all the parameters of the network in a top-down direction.
```  
**Algorithm 1********Training deep fault recognizer