## 4 Proposed Fault Diagnosis Algorithm
Figure 6 shows the wavelet packet tree that the red lines highlight the frequency bands directions with 50 Hz in deeper levels when the sampling rate is 2000 Hz. Fourier analysis of the reconstructed signal was performed to find the sub-band with maximum value using the MATLAB(r) command line. Therefore, various features can be extracted exactly from the fault-related sub-frequency band of the WPT-based signal decomposition. Figure 4: Architecture of the proposed system. Figure 5: Wavelet packet signature analysis (WPSA)-based algorithm. Figure 6: WPSA-based algorithm. Finally, the statistical parameter of wavelet packet coefficients together with the slip speed are the input vector to the classifier for decision making approach to examine the effect of load variations and fault severity. To evaluate the effectiveness of proposed method, a NN-based approach is developed in the MATLAB environment. The algorithm is proposed to configure the best decision-making solution. WPSA is used for the feature extraction which gives distinguishable signatures from stator current signal in a specific frequency band. In the experimental setup, the left affected frequency is considered \(f_{brb}=(1-2s)f_{s}\) to discern the healthy and faulty condition and fault severity. The related depths and nodes of the WP tree constitute of most appropriate frequency range is arranged to cover various load illustrated in Table 2.  
Feature vector, which is one of the most significant parameters to design an appropriate neural network, was innovated by features extracted from statistical parameters of WPC. In order to check the learning ability and classification accuracy of MLP-NN classifier, 75% of data (60 samples among all 80 samples in each load condition) are tagged as training data. In this study, the leave-one-out (LOO) method has been applied for available train data. The algorithm trains the network 60 times. Each time, one out of the 60 available inputs is excluded and used for testing the performance of the constructed MLP-based classifier. The proposed NN is trained on various datasets and later validated carefully based on the second dataset (25% = 20 remained samples in each load condition), which is tagged for final testing as to ensure a completely independent test set. Figure 7 schematically demonstrates wavelet packet coefficients of raw signal and their relevant standard deviation as one of the feature vectors of neural network. The statistical parameter of wavelet packet coefficients together with the slip speed are the input vector to the classifier for decision making approach to examine the effect of load variations and fault severity. As it can be seen, four three-layer MLP networks are dedicated to four assorted load range (80%, 50%, 35% and 10% of full load), each with 13 neurons in their hidden layers. MLP network structure, which is a feed-forward neural network (FFNN), has found an immeasurable popularity in neural network and has been frequently exploited in machine condition monitoring applications. Furthermore, to diminish the training time and accelerate the convergence of neural network in real-world applications, specifically fault detection and classification procedure, it is preferred to use a small-sized and fixed-dimension vector for training purposes. Therefore, in this study, by preparing the finite-dimension input vectors from all classes under investigation, the utilized classification approach with FFNN structure was employed as the base of severity assessment. The mean sum of squares of the network errors is a typical performance function for feedforward networks which is defined as:  
\[mse=\frac{1}{N}\sum_{i=1}^{N}(e_{i})^{2}\]  
where, \(e_{i}=t_{i}-y_{i}\), error is desired output \(t\) minus actual outputs \(y\).