# Distilling the Knowledge of Multiscale Densely Connected Deep Networks in Mechanical Intelligent Diagnosis

Authors: Xiaochuan Wang; Aiguo Chen; Liang Zhang; Yi Gu; Mang Xu; Haoyuan Yan
Journal: Wireless Communications and Mobile Computing
 (2021)

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## Abstract

At present, deep neural network (DNN) technology is often used in intelligent diagnosis research. However, the huge amount of calculation of DNN makes it difficult to apply in industrial practice. In this paper, an advanced multiscale dense connection deep network MSDC-NET is designed. A well-designed multiscale parallel branch module is used in the network. This module can greatly improve the acceptance domain of MSDC-NET, so as to learn useful information from input samples more effectively. Based on the inspiration of Densely Connected Convolutional Networks, MSDC-NET designed a similar dense connection technology, so that the model will not have the problem of gradient vanishing because of the deep network. The experimental data of MSDC-NET on MFPT, SEU, and Pu datasets show that our method has higher performance than other latest technologies. At the same time, we carried out knowledge distillation based on the high-precision classification level of MSDC-NET, which makes the diagnosis ability and robustness of the lightweight CNN model improve significantly.


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## Body

## 1. Introduction

The mechanical equipment in modern industry often needs to work in the complex environment of high temperature, fatigue, and heavy load for a long time, which may cause incalculable production accidents and economic property losses. At present, most enterprises use the way of manual supervision, which consumes a lot of human and material resources. Since mechanical failures are often not so obvious, only technicians with professional knowledge can be sure to judge mechanical failures. As a mature unsupervised system, intelligent diagnosis can solve this problem for related enterprises. The traditional intelligent diagnosis method mainly uses a machine learning algorithm to classify the feature data from the sensor signal. For example, Zhang et al. used support vector machine (SVM) to identify the working state of bearing [1]; Banerjee and Das used SVM fusion multisensor signal to detect motor fault [2]; Bugharbee and Trendafilova used the nearest neighbor classifier to identify faults [3]; Keskes et al. studied the method of feature extraction using stationary wavelet packet transform, and support vector machine (SVM) is applied to rotor fault classification. [4]; Mustafa et al. proposed that the spectrum analysis method be used in feature extraction and SVM be used to detect mechanical faults. [5]. However, the signal obtained by sensor needs complex feature extraction, which is difficult to achieve instantaneity, and depends on professional knowledge and relevant experience.With the rapid development of deep learning (DL) technology in many fields, researchers have begun to use some DL-based technologies to achieve intelligent diagnosis, such as Multilayer Perceptron (MLP) [6], Deep Belief-Net (DBN) [7], Convolutional Neural Net (CNN) [8], Autoencoder-Net (AE) [9], and Recurrent Neural Network (RNN) [10]. The MLP model is a very simple perceptron model. The knowledge it can learn is very scarce, and it has been rarely used at present. As a probabilistic generation model relative to the traditional discriminant model, DBN is composed of multiple restricted Boltzmann machine layers; Shao et al. proposed to use the optimized DBN model to diagnose rolling bearings [11]; Tamilselvan and Wang proposed a DBN model for engine fault diagnosis [12]. The improvement of the CNN model is mainly in two directions. One is to use different input types, such as two-dimensional images [13], infrared thermal images [14], vibration spectrum images [15], and time-frequency images [16]. Another direction is to improve the structure of CNN model, such as combining the CNN with Generative Adversarial Network (GAN [17]) to generate more new labeled samples [18, 19]. Janssens et al. proposed a CNN model to classify the faults of rotating machinery [20]. Recently, some researchers use transfer learning [21, 22] combined with the CNN to obtain the prior knowledge of the original dataset [23–25]. The AE model is composed of multiple automatic encoders, and there are two common extended models, such as denoising AE (DAE) [26] and compression AE (CAE) [27]. The advantage of DAE is that it can learn useful information from damaged data, and CAE learns more stable feature representations through penalty items. The latest AE model also combines with the GAN network to generate labeled samples [28–30] and also embeds the semisupervised learning method into the VAE model [31, 32]. The Recurrent Neural Network has no advantage in classification, and it is more commonly used in mechanical life prediction.So as to evaluate the effectiveness and fairness of the model, our experiment is carried out in the benchmark code base proposed by Zhao et al. [33]. They conducted a comprehensive benchmark study on the realization of intelligent diagnosis based on the DL model. The study evaluated the intelligent diagnosis performance of nine commonly used models on nine publicly available datasets. The nine models include three encoder models, such as AE, DAE, and CAE, including the MLP model and CNN model and two advanced deep classification networks AlexNet [34], ResNet18 [35], and finally include an LSTM [36] model. The results of these studies show the significant advantages of DL in intelligent diagnosis, especially the models that have outstanding performance in other classification problems such as ResNet18, which also have good results when transplanted to intelligent diagnosis. However, the scale of these deep classification networks is very large, and the computing power of the equipment is relatively high. How to improve the accuracy of model intelligent diagnosis in different accuracy requirements and equipment environment is a worthy research direction.The main target of our method is to use a new and powerful deep classification network as the powerful model to guide the lightweight model to realize mechanical intelligent diagnosis. Therefore, our main contribution can be outlined in two aspects:(1)
We designed a new multiscale densely connected deep network MSDC-NET, and the experimental results of five comparison algorithms on three types of datasets show that the model has higher superiority(2)
We innovatively use the knowledge distillation technology in the mechanical intelligent diagnosis subject, which makes the classification accuracy of the lightweight CNN model significantly improve and provides an effective solution to achieve the highest level of diagnosis in the case of limited computing powerThe experiments in this paper are carried out on the open MFPT bearing dataset (https://mfpt.org/fault-data-sets/), Pu bearing dataset (https://mb.uni-paderborn.de/kat/forschung/datacenter/bearing-datacenter/), and SEU transmission dataset (https://github.com/cathysiyu/Mechanical-datasets).The rest of the paper is arranged as follows: Section2 retrospects the related work of deep classification network and knowledge distillation technology, and then in Section 3, we introduce our MSDC-NET model, knowledge distillation process, and its algorithm in detail. After that, the experimental results obtained on three common datasets are discussed and analyzed in Section 4. Finally, the article is summarized in the Section 5.


## 2. Related Work

### 2.1. Deep Convolution Network

The CNN, which was proposed in 1997, is a classification network for processing labeled data. It can transfer, extract, and learn information through convolution and pool operations. AlexNet won the championship in the 2012 ImageNet competition, and the ResNet proposed in 2016 has surpassed human classification accuracy for the first time.The CNN model is generally composed of a convolution layer, pooling layer (maximum pooling layer, average pooling layer), and fully connected layer. We often use the convolution layer and maximum pooling layer with a step size of 2 to learn features and finally classify features through full connection layer.The convolution layer operation is equivalent to the multiplication of inputx and convolution kernel w, which is then represented by the activation function mapping:(1)hkl=ϕwkl⋅x+bkl,where ϕ is the convolution operator, hkl is the output of convolution operation, k is the k-th convolution kernel, l is the l-th layer, and wkl and bkl are the weight and bias.The purpose of maximum pooling layer is to learn the most essential knowledge in the local acceptance domain, focus on texture information, and reduce the bias of estimation mean caused by convolution layer parameter error. The purpose of average pooling layer is to consider the characteristics of step size, focus on the background information, and reduce the estimation variance.As the number of layers of CNN tends to be deeper, the problem of model degradation may arise, and jump connection technology is often used to avoid gradient disappearance. Meanwhile, the multiscale technology widely used in CV field can also be transplanted into the CNN to improve the receptive field of network model.


### 2.2. Distilling the Knowledge

In the industrial application, in addition to the requirement that the model should have as high a prediction level as possible, it is also expected that the expenditure of the model should be as small as possible, so that the deployment needs the least computing resources (computing power, storage space) and has a lower delay. Knowledge distillation [37] is a solution to this problem. First, we need a powerful and effective pretraining model (T-Model), then train a lightweight model (S-Model) from scratch and pass on the knowledge contained in a T-Model to an S-Model during the training process.The above process of knowledge transfer only requires that the “SoftMax” output distribution of S-Model and T-Model under a given input be fully closed.(2)qi=expzi/TEMP∑jexpzj/TEMP,where qi is the output distribution of S-Model, zi is the calculated probability for each class in S-Model, and TEMP is a parameter usually set to 1. When TEMP becomes larger, we get a softer output. For cross-entropy loss, the gradient for a logit of S-Model is as follows:(3)∂C∂zi=1TEMPqi−pi=1TEMPezi/TEMP∑jezj/TEMP−eci/TEMP∑jecj/TEMP,where pi is the output distribution of the T-Model, ci is the calculated probability for each class in the T-Model, and when x tends to 0, it is equivalent to infinitesimal with ex−1. Easy to know, when TEMP is sufficiently large, there are(4)∂C∂zi≈1TEMP1+zi/TEMPN+∑jzj/TEMP−1+ci/TEMPN+∑jcj/TEMP.Suppose that every sample has Logits with zero mean, that is∑jzj=∑jcj=0, then:(5)∂C∂zi≈1NTEMP2zi−ci.


## 2.1. Deep Convolution Network

The CNN, which was proposed in 1997, is a classification network for processing labeled data. It can transfer, extract, and learn information through convolution and pool operations. AlexNet won the championship in the 2012 ImageNet competition, and the ResNet proposed in 2016 has surpassed human classification accuracy for the first time.The CNN model is generally composed of a convolution layer, pooling layer (maximum pooling layer, average pooling layer), and fully connected layer. We often use the convolution layer and maximum pooling layer with a step size of 2 to learn features and finally classify features through full connection layer.The convolution layer operation is equivalent to the multiplication of inputx and convolution kernel w, which is then represented by the activation function mapping:(1)hkl=ϕwkl⋅x+bkl,where ϕ is the convolution operator, hkl is the output of convolution operation, k is the k-th convolution kernel, l is the l-th layer, and wkl and bkl are the weight and bias.The purpose of maximum pooling layer is to learn the most essential knowledge in the local acceptance domain, focus on texture information, and reduce the bias of estimation mean caused by convolution layer parameter error. The purpose of average pooling layer is to consider the characteristics of step size, focus on the background information, and reduce the estimation variance.As the number of layers of CNN tends to be deeper, the problem of model degradation may arise, and jump connection technology is often used to avoid gradient disappearance. Meanwhile, the multiscale technology widely used in CV field can also be transplanted into the CNN to improve the receptive field of network model.


## 2.2. Distilling the Knowledge

In the industrial application, in addition to the requirement that the model should have as high a prediction level as possible, it is also expected that the expenditure of the model should be as small as possible, so that the deployment needs the least computing resources (computing power, storage space) and has a lower delay. Knowledge distillation [37] is a solution to this problem. First, we need a powerful and effective pretraining model (T-Model), then train a lightweight model (S-Model) from scratch and pass on the knowledge contained in a T-Model to an S-Model during the training process.The above process of knowledge transfer only requires that the “SoftMax” output distribution of S-Model and T-Model under a given input be fully closed.(2)qi=expzi/TEMP∑jexpzj/TEMP,where qi is the output distribution of S-Model, zi is the calculated probability for each class in S-Model, and TEMP is a parameter usually set to 1. When TEMP becomes larger, we get a softer output. For cross-entropy loss, the gradient for a logit of S-Model is as follows:(3)∂C∂zi=1TEMPqi−pi=1TEMPezi/TEMP∑jezj/TEMP−eci/TEMP∑jecj/TEMP,where pi is the output distribution of the T-Model, ci is the calculated probability for each class in the T-Model, and when x tends to 0, it is equivalent to infinitesimal with ex−1. Easy to know, when TEMP is sufficiently large, there are(4)∂C∂zi≈1TEMP1+zi/TEMPN+∑jzj/TEMP−1+ci/TEMPN+∑jcj/TEMP.Suppose that every sample has Logits with zero mean, that is∑jzj=∑jcj=0, then:(5)∂C∂zi≈1NTEMP2zi−ci.


## 3. Our Proposed Method

### 3.1. The Composition of the Blocks

To ensure the performance of the model, we have carefully designed the neural network modules shown in Figures1–3, through the stacking of these modules constituting the final MSDC-NET.Figure 1
The construction of a Go_Down cell.Figure 2
The construction of a DS cell.Figure 3
The construction of an MS_Block cell.Go_Down cell is proposed to achieve a similar dense connection effect, which can maximize the retention of the original lore of the previous data, and realize the superposition of the previous and subsequent feature maps in the channel dimension. The “times” represents the multiple relationship of the size of the previous and subsequent feature maps. After “times” max pooling, the dimension of the feature map will be reduced to 1/times of the original size.DS cell is proposed for downsampling of the feature map, which is implemented by convolution operation (the parameters are as follows:stride=2 and kernel_size=3×3). The dimension of the input data will be decreased by half, and the number of channels will be doubled.MS_Block cell draws on the idea of inception cell [38], in which 3×3 and 5×5 convolution kernels are used for multiscale learning feature map, and average pooling and maximum pooling are used to extract useful information from multiple angles. After the multibranch network structure has learned the input data, a complete feature map of each branch superimposed and fused in the channel dimension will be obtained, and then, this feature map will be placed in the MSDC network to continue learning.


### 3.2. The Structure of MSDC-NET

For the purpose of get a high-precision Teacher-Model, we integrated the most prevalent multiscale and dense connection technology to advance a split-new deep classification network MSDC-NET. It is made up of our carefully designed stack of various modules. Taking the input data size AB as an example, five MS_Block cells are set in the model to realize multiscale and multiangle learning sample data information. At the same time, five DS cells are set for downsampling, and the size of the top feature map is AC. In practical applications, we can adjust the network model reasonably according to the input data size. When the input data is large, more stacking blocks can be set, and on the contrary, the number of layers can be set fewer.However, only through the one-way propagation of this order often fails to achieve a good classification effect, because the deep network will forget and lose a lot of previous knowledge and information. We need a unique cascade operation to fuse the same resolution features of different stages in the channel dimension, so we designed a technology similar to dense connection. The implementation of this technology relies on Go_Down cell, through which we save the output feature map of each MS_Block cell. The feature maps obtained by Go_Down of different “times” can be merged with the small feature map of matching size later, which is able to speed up the convergence of the network model, while improving the robustness of the model and avoiding problems such as gradient disappearance.The structure of the MSDC-NET model we proposed is shown in Figure4. The main road after the data sample enters the model is the green one-way line. A network training procedure using reasonable and effective loss function is crucial; the output l~ is obtained from the top-level feature graph through Adaptive AvgPool and FC layers. If the class label of data sample is l, the loss function of model training is as follows:(6)lossCrossentropy=−∑i=1nllogl~+1−llog1−l~.Figure 4
The structure of the MSDC-NET.Since the quantity of layers of the DNN is relatively deep, the useful information contained in the first data entering the network and the first feature map may be forgotten and lost. We borrowed the idea of DenseNet [39] in the MSDC-NET model and, after the foregoing features of FIG different sizes corresponding to multiples by scaling Go_Down cell extract, then merged them with the feature maps of the back of the network. And we let them influence the training process of the network to varying degrees according to the set weights.Finally, the category of input data is forecasted by the following formula:(7)labelx=argmaxl~.


### 3.3. CNN after Knowledge Distillation

We use the simple CNN model shown in Figure5. With the input by way of multiple stacked Conv layers and Pool layers, it enters the classifier to obtain the final output.Figure 5
The structure of the CNN.The model contains only 4 convolutional layers in total, with a very simple structure and very low requirements on the computing power and storage of the deployed equipment, so it is suitable to run in the industrial environment.


### 3.4. Algorithm Details

In Section2, we describe the process of knowledge distillation in detail. After knowledge distillation, the CNN model can obtain loss_soft according to formula (5). (In the experiment, we set T as 10 according to the relevant literature.)(8)loss_soft=1NT2zi−vi.According to the previous formula (6) of MSDC-NET, we can get loss_hard as follows:(9)loss_hard=−∑i=1nllogl~+1−llog1−l~.Finally, the total loss function of knowledge distillation process is (whereω is the weight of loss_hard)(10)loss=ω∗loss_hard+loss_soft.As shown in Figure6, after the Teacher-Model is divided by the temperature parameter T, the soft label is obtained through the “SoftMax” transformation, and the value in the label is between 0 and 1. The larger the temperature parameter T, the softer the distribution. On the contrary, it is easy to introduce unnecessary noise and amplify the probability of misclassification. We need to make sure that the correct predicted contribution is made in the Teacher-Model, so set T to a larger value. The real label in the sample is converted to a one-hot vector and used as a hard label. The total loss is the weighted sum of the cross entropy of the soft label and the predicted value and the cross entropy of the hard label and the predicted value. If the value of ω is smaller, it indicates that more attention is paid to the contribution of Teacher-Model; on the contrary, let the Student-Model pay more attention to the identification of difficult samples. Therefore, the higher the classification accuracy of the teacher model, the more conducive to student model learning samples. Our specific algorithm is reflected in Algorithm 1.Algorithm 1: Process of MSDC-NET (or CNN) for fault classification
Input: Sample X, Sample category, Test samplex~Step1: The training process of the MSDC- NET model:1) Processing sample input data:Unify the sample data X into the same segmentation method, input type and input size, and finally we get the input as (x, y).2) Train the MSDC-NET model:Train MSDC-NET through the processed training data, and the objective function (6) as:minloss=−∑i=1nllogl~+1−llog1−l~Step2: The training process of the CNN model:1) Processing sample input data:2) Train the CNN model:Train CNN through the processed training data, and the objective function (10) asminloss=ω∗loss_hard+loss_softStep3: Fault classification1) Output of MSDC-NET (or CNN):Input the test data samplex~ into the pre-trained model (MSDC-NET or CNN) to get the output y~.2) Category determinationAfter obtaining the outputy~ of the model (MSDC-NET or CNN), use Formula (7) to predict the category of the test sample:labelx~=argmaxy~Output: Predict the category of input xFigure 6
Flow chart of knowledge distillation technology.


## 3.1. The Composition of the Blocks

To ensure the performance of the model, we have carefully designed the neural network modules shown in Figures1–3, through the stacking of these modules constituting the final MSDC-NET.Figure 1
The construction of a Go_Down cell.Figure 2
The construction of a DS cell.Figure 3
The construction of an MS_Block cell.Go_Down cell is proposed to achieve a similar dense connection effect, which can maximize the retention of the original lore of the previous data, and realize the superposition of the previous and subsequent feature maps in the channel dimension. The “times” represents the multiple relationship of the size of the previous and subsequent feature maps. After “times” max pooling, the dimension of the feature map will be reduced to 1/times of the original size.DS cell is proposed for downsampling of the feature map, which is implemented by convolution operation (the parameters are as follows:stride=2 and kernel_size=3×3). The dimension of the input data will be decreased by half, and the number of channels will be doubled.MS_Block cell draws on the idea of inception cell [38], in which 3×3 and 5×5 convolution kernels are used for multiscale learning feature map, and average pooling and maximum pooling are used to extract useful information from multiple angles. After the multibranch network structure has learned the input data, a complete feature map of each branch superimposed and fused in the channel dimension will be obtained, and then, this feature map will be placed in the MSDC network to continue learning.


## 3.2. The Structure of MSDC-NET

For the purpose of get a high-precision Teacher-Model, we integrated the most prevalent multiscale and dense connection technology to advance a split-new deep classification network MSDC-NET. It is made up of our carefully designed stack of various modules. Taking the input data size AB as an example, five MS_Block cells are set in the model to realize multiscale and multiangle learning sample data information. At the same time, five DS cells are set for downsampling, and the size of the top feature map is AC. In practical applications, we can adjust the network model reasonably according to the input data size. When the input data is large, more stacking blocks can be set, and on the contrary, the number of layers can be set fewer.However, only through the one-way propagation of this order often fails to achieve a good classification effect, because the deep network will forget and lose a lot of previous knowledge and information. We need a unique cascade operation to fuse the same resolution features of different stages in the channel dimension, so we designed a technology similar to dense connection. The implementation of this technology relies on Go_Down cell, through which we save the output feature map of each MS_Block cell. The feature maps obtained by Go_Down of different “times” can be merged with the small feature map of matching size later, which is able to speed up the convergence of the network model, while improving the robustness of the model and avoiding problems such as gradient disappearance.The structure of the MSDC-NET model we proposed is shown in Figure4. The main road after the data sample enters the model is the green one-way line. A network training procedure using reasonable and effective loss function is crucial; the output l~ is obtained from the top-level feature graph through Adaptive AvgPool and FC layers. If the class label of data sample is l, the loss function of model training is as follows:(6)lossCrossentropy=−∑i=1nllogl~+1−llog1−l~.Figure 4
The structure of the MSDC-NET.Since the quantity of layers of the DNN is relatively deep, the useful information contained in the first data entering the network and the first feature map may be forgotten and lost. We borrowed the idea of DenseNet [39] in the MSDC-NET model and, after the foregoing features of FIG different sizes corresponding to multiples by scaling Go_Down cell extract, then merged them with the feature maps of the back of the network. And we let them influence the training process of the network to varying degrees according to the set weights.Finally, the category of input data is forecasted by the following formula:(7)labelx=argmaxl~.


## 3.3. CNN after Knowledge Distillation

We use the simple CNN model shown in Figure5. With the input by way of multiple stacked Conv layers and Pool layers, it enters the classifier to obtain the final output.Figure 5
The structure of the CNN.The model contains only 4 convolutional layers in total, with a very simple structure and very low requirements on the computing power and storage of the deployed equipment, so it is suitable to run in the industrial environment.


## 3.4. Algorithm Details

In Section2, we describe the process of knowledge distillation in detail. After knowledge distillation, the CNN model can obtain loss_soft according to formula (5). (In the experiment, we set T as 10 according to the relevant literature.)(8)loss_soft=1NT2zi−vi.According to the previous formula (6) of MSDC-NET, we can get loss_hard as follows:(9)loss_hard=−∑i=1nllogl~+1−llog1−l~.Finally, the total loss function of knowledge distillation process is (whereω is the weight of loss_hard)(10)loss=ω∗loss_hard+loss_soft.As shown in Figure6, after the Teacher-Model is divided by the temperature parameter T, the soft label is obtained through the “SoftMax” transformation, and the value in the label is between 0 and 1. The larger the temperature parameter T, the softer the distribution. On the contrary, it is easy to introduce unnecessary noise and amplify the probability of misclassification. We need to make sure that the correct predicted contribution is made in the Teacher-Model, so set T to a larger value. The real label in the sample is converted to a one-hot vector and used as a hard label. The total loss is the weighted sum of the cross entropy of the soft label and the predicted value and the cross entropy of the hard label and the predicted value. If the value of ω is smaller, it indicates that more attention is paid to the contribution of Teacher-Model; on the contrary, let the Student-Model pay more attention to the identification of difficult samples. Therefore, the higher the classification accuracy of the teacher model, the more conducive to student model learning samples. Our specific algorithm is reflected in Algorithm 1.Algorithm 1: Process of MSDC-NET (or CNN) for fault classification
Input: Sample X, Sample category, Test samplex~Step1: The training process of the MSDC- NET model:1) Processing sample input data:Unify the sample data X into the same segmentation method, input type and input size, and finally we get the input as (x, y).2) Train the MSDC-NET model:Train MSDC-NET through the processed training data, and the objective function (6) as:minloss=−∑i=1nllogl~+1−llog1−l~Step2: The training process of the CNN model:1) Processing sample input data:2) Train the CNN model:Train CNN through the processed training data, and the objective function (10) asminloss=ω∗loss_hard+loss_softStep3: Fault classification1) Output of MSDC-NET (or CNN):Input the test data samplex~ into the pre-trained model (MSDC-NET or CNN) to get the output y~.2) Category determinationAfter obtaining the outputy~ of the model (MSDC-NET or CNN), use Formula (7) to predict the category of the test sample:labelx~=argmaxy~Output: Predict the category of input xFigure 6
Flow chart of knowledge distillation technology.


## 4. Experiment and Discussion

### 4.1. Datasets

#### 4.1.1. PU Bearing Dataset

There are 21 categories, including 6 undamaged bearings, 12 damaged bearings, and 14 actual damaged bearings caused by an accelerated life test. The details are shown in Table1.Table 1
Fault classification of PU dataset.
CodeFault mode: descriptionK001Health state: launched 50 hours in advanceK002Health state: launched 19 hours in advanceK003Health state: launched 1 hours in advanceK004Health state: launched 5 hours in advanceK005Health state: launched 10 hours in advanceK006Health state: launched 16 hours in advanceKA01Outer ring: man-made damage caused by EDM (Level 1)KA03Outer ring: man-made damage caused by electric engraver (Level 2)KA05Outer ring: man-made damage caused by electric engraver (Level 1)KA06Outer ring: man-made damage caused by electric engraver (Level 2)KA07Outer ring: man-made damage caused by drilling (Level 1)KA08Outer ring: man-made damage caused by drilling (Level 2)KA09Outer ring: man-made damage caused by drilling (Level 2)KI01Inner ring: man-made damage caused by EDM (Level 1)KI03Inner ring: man-made damage caused by electric engraver (Level 1)KI05Inner ring: man-made damage caused by electric engraver (Level 1)KI07Inner ring: man-made damage caused by electric engraver (Level 2)KI08Inner ring: man-made damage caused by electric engraver (Level 2)KA04Outer ring: damage caused by fatigue and pitting (single point and single damage and Level 1)KA15Outer ring: damage caused by plastic deform and indentation (single point and single damage and Level 1)KA16Outer ring: damage caused by fatigue and pitting (single point and repetitive damage and Level 2)KA22Outer ring: damage caused by fatigue and pitting (single point and single damage and Level1)KA30Outer ring: damage caused by plastic deform and indentation (distributed and repetitive damage and Level 1)KB23Outer ring, inner ring: damage caused by fatigue and pitting (single point and multiple damage and Level 2)KB24Outer ring, inner ring: damage caused by fatigue and pitting (distributed and multiple damage and Level 3)KB27Outer ring, inner ring: damage caused by fatigue and pitting (distributed and multiple damage and Level 1)KI04Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level1)KI14Inner ring: damage caused by fatigue and pitting (singlepoint+multipledamage+Level1)KI16Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level3)KI17Inner ring: damage caused by fatigue and pitting (singlepoint+repetitivedamage+Level1)KI18Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level2)KI21Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level1)


#### 4.1.2. MFPT Bearing Dataset

There are 15 categories, according to different loads, one healthy bearing and fourteen faulty bearings. The fault classification is displayed in Table2. The four values in the Description are load, input shaft speed, sampling rate, and duration.Table 2
Fault classification of MFPT dataset.
CategoryDescriptionCategoryDescriptionHealth state270 lb, 25 Hz, 97656 sps,6 s//Outer ring 125 lb, 25 Hz, 48828 sps, 3 sInner ring 125 lb, 25 Hz, 48828 sps, 3 sOuter ring 250 lb, 25 Hz, 48828 sps, 3 sInner ring 250 lb, 25 Hz, 48828 sps, 3 sOuter ring 3100 lb, 25 Hz, 48828 sps, 3 sInner ring 3100 lb, 25 Hz, 48828 sps, 3 sOuter ring 4150 lb, 25 Hz, 48828 sps, 3 sInner ring 4150 lb, 25 Hz, 48828 sps, 3 sOuter ring 5200 lb, 25 Hz, 48828 sps, 3 sInner ring 5200 lb, 25 Hz, 48828 sps, 3 sOuter ring 6250 lb, 25 Hz, 48828 sps, 3 sInner ring 6250 lb, 25 Hz, 48828 sps, 3 sOuter ring 7300 lb, 25 Hz, 48828 sps, 3 sInner ring 7300 lb, 25 Hz, 48828 sps, 3 s


#### 4.1.3. SEU Gearbox Dataset

There are 20 categories, including inner ring, outer ring, and rolling element in different states. In each file, we use the second line of eight vibration signals. Details are shown in Table3.Table 3
Fault classification of SEU dataset.
SortFault mode (RS-LC:20 Hz-0 V)SortFault mode (RS-LC:3 Hz-2 V)1Health gear11Health gear2Health bearing12Health bearing3Chipped tooth13Chipped tooth4Inner ring14Inner ring5Missing tooth15Missing tooth6Outer ring16Outer ring7Root fault17Root fault8Inner+outerrings18Inner+outerrings9Surface fault19Surface fault10Rolling element20Rolling element


### 4.2. Data Split

There are two common data segmentation methods in mechanical intelligent diagnosis. One is the stochastic segmentation strategy, and the other is the time sort segmentation of datasets. The random segmentation strategy may cause data overlap between two sets, resulting in the risk of test leakage, and the final test accuracy cannot be used as a basis for fair evaluation of model performance. Industrial data are generally continuous, which may contain time-dependent knowledge information. Therefore, in order to evaluate the scientific and retain the useful information in the dataset as much as possible, we adopt the strategy of dividing the dataset according to the time sort (Figure7). The last 20% of the time series data is used for testing, and the rest is used for training.Figure 7
Data split according to time sequences.


### 4.3. Input Types

In mechanical intelligent diagnosis, signal processing methods are often used to map sample data to other domains. These methods include converted into time domain (TD), converted into frequency domain (FD), converted into time-frequency domain (TFD), converted into slice image (SI), and converted into wavelet domain (WD). The benchmark study of Zhao et al. [33] showed that FD and TFD can achieve higher accuracy, so we finally used TFD to complete the experiment.(11)xiSTFT=STFTxi,i=1,2,⋯,N.InsideSTFT⋅ is to convert xi into TFD.TFD is to perform short-time Fourier transform (STFT) on each specimen, and the Hanning window length is 64. Since the CNN model requires a larger 2D size to extract features, the final signal size is adjusted to330×330.


### 4.4. Training Details

During model training, we used the Adam optimizer. Some parameters of model training are as follows:learningrate=0.001 and batchsize=8 (due to the device limitation). Each model is trained and tested alternately during training, and a total of 100 epochs are experienced. All comparison models and MSDC-NET are trained and fairly compared under the open source code framework proposed by Zhao et al. [33], and the data enhancement method provided in the code framework is adopted. All work is performed on the device equipped with E5-2640 V4 @ CPU and 12G GeForce RTX 2080 Ti GPU. The device system is Ubuntu 16.04, the running environment is Python 3.6, and the Pytorch1.4 library is used.We have done the optimization experiment on the SEU gearbox dataset for the value ofω between 0 and 1. It is able to deduce from Figure 8 that as ω increases, the performance of the CNN model will tend to the performance without knowledge distillation; classification accuracy showed a downward trend, which also shows the effectiveness of knowledge distillation technology from the side, so we set ω to 0 in the subsequent comparative experiments.Figure 8
The influence of differentω on the model.


### 4.5. Evaluating Indexes

In our research process, the comprehensive accuracy (Acc) is used to fairly assess the capability of the algorithm. With the purpose of avoiding the impact of the fluctuation of DNN model in training, we repeat each experiment 10 times. Finally, we take the average Acc and the maximum Acc as the assessment indexes, the average Acc is the average of 10 times of Acc, and the maximum Acc is the maximum of 10 times of Acc.


### 4.6. MSDC-NET Experimental Results

For each algorithm, we completed 10 tests on the corresponding dataset in the same environment. The achievement of the highest predicted Acc is recorded in Figure9, and then, the achievement of the average predicted Acc of 10 times is recorded in Figure 10. From the overall view of these two figures, our algorithm reached the first-rate capability. The LSTM algorithm does not perform well on classification problems, and the average test Acc is between 85% and 90%.Figure 9
Maximum prediction accuracy graph of MSDC-NET and five contrast algorithms on three datasets.Figure 10
Average prediction accuracy graph of MSDC-NET and five contrast algorithms on three datasets.Compared with those on other datasets, the capability of the AE network on the SEU dataset is significantly not the same, which shows that the AE network has higher requirements for datasets. The classification ability of the simple CNN network is relatively poor without knowledge distillation, ranging from 75 to 85. The test Acc of DNN is relatively high, the test Acc of AlexNet is between 95 and 100, the test Acc of ResNet18 is between 98 and 100, and the test Acc of our MSDC-NET is between 98 and 100. From the comparison chart of average test Acc, our method is 1.27%, 3.55%, and 1.12% higher than ResNet18, which is the best algorithm in comparison. In the maximum test Acc diagram, our method is 0.54%, 0.77%, and 0.48% higher than ResNet18. Meanwhile, it is a surprise that our MSDC-NET has achieved 100% results on SEU gearbox dataset for 10 times, which reflects the powerful classification ability and robustness of our algorithm and will not produce serious over fitting phenomenon due to the deep network layers.


### 4.7. CNN Experimental Results after Knowledge Distillation

We distill the knowledge of MSDC-NET according to the algorithm in Figure6, so that the classification Acc of the CNN model is significantly improved without any change in the internal structure. As can be seen in Figure 11, contrasted with the original CNN, the average test Acc of CNN_D after knowledge distillation is 5.98%, 3.29%, and 7.24% higher on the three datasets. The maximum test Acc is 4.91%, 3.19%, and 6.55% higher, respectively. The average test Acc of CNN_D even exceeds the maximum test Acc of the original CNN. CNN_D has the most obvious improvement on the SEU gearbox dataset, which is comparable to the deep neural classification network AlexNet shown in Figure 10. Due to the problems of MFPT dataset itself, the effect of knowledge distillation is not obvious, but it has also been improved.Figure 11
Map of average and maximum classification accuracy of original CNN and knowledge distilled CNN_D on three datasets.


## 4.1. Datasets

### 4.1.1. PU Bearing Dataset

There are 21 categories, including 6 undamaged bearings, 12 damaged bearings, and 14 actual damaged bearings caused by an accelerated life test. The details are shown in Table1.Table 1
Fault classification of PU dataset.
CodeFault mode: descriptionK001Health state: launched 50 hours in advanceK002Health state: launched 19 hours in advanceK003Health state: launched 1 hours in advanceK004Health state: launched 5 hours in advanceK005Health state: launched 10 hours in advanceK006Health state: launched 16 hours in advanceKA01Outer ring: man-made damage caused by EDM (Level 1)KA03Outer ring: man-made damage caused by electric engraver (Level 2)KA05Outer ring: man-made damage caused by electric engraver (Level 1)KA06Outer ring: man-made damage caused by electric engraver (Level 2)KA07Outer ring: man-made damage caused by drilling (Level 1)KA08Outer ring: man-made damage caused by drilling (Level 2)KA09Outer ring: man-made damage caused by drilling (Level 2)KI01Inner ring: man-made damage caused by EDM (Level 1)KI03Inner ring: man-made damage caused by electric engraver (Level 1)KI05Inner ring: man-made damage caused by electric engraver (Level 1)KI07Inner ring: man-made damage caused by electric engraver (Level 2)KI08Inner ring: man-made damage caused by electric engraver (Level 2)KA04Outer ring: damage caused by fatigue and pitting (single point and single damage and Level 1)KA15Outer ring: damage caused by plastic deform and indentation (single point and single damage and Level 1)KA16Outer ring: damage caused by fatigue and pitting (single point and repetitive damage and Level 2)KA22Outer ring: damage caused by fatigue and pitting (single point and single damage and Level1)KA30Outer ring: damage caused by plastic deform and indentation (distributed and repetitive damage and Level 1)KB23Outer ring, inner ring: damage caused by fatigue and pitting (single point and multiple damage and Level 2)KB24Outer ring, inner ring: damage caused by fatigue and pitting (distributed and multiple damage and Level 3)KB27Outer ring, inner ring: damage caused by fatigue and pitting (distributed and multiple damage and Level 1)KI04Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level1)KI14Inner ring: damage caused by fatigue and pitting (singlepoint+multipledamage+Level1)KI16Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level3)KI17Inner ring: damage caused by fatigue and pitting (singlepoint+repetitivedamage+Level1)KI18Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level2)KI21Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level1)


### 4.1.2. MFPT Bearing Dataset

There are 15 categories, according to different loads, one healthy bearing and fourteen faulty bearings. The fault classification is displayed in Table2. The four values in the Description are load, input shaft speed, sampling rate, and duration.Table 2
Fault classification of MFPT dataset.
CategoryDescriptionCategoryDescriptionHealth state270 lb, 25 Hz, 97656 sps,6 s//Outer ring 125 lb, 25 Hz, 48828 sps, 3 sInner ring 125 lb, 25 Hz, 48828 sps, 3 sOuter ring 250 lb, 25 Hz, 48828 sps, 3 sInner ring 250 lb, 25 Hz, 48828 sps, 3 sOuter ring 3100 lb, 25 Hz, 48828 sps, 3 sInner ring 3100 lb, 25 Hz, 48828 sps, 3 sOuter ring 4150 lb, 25 Hz, 48828 sps, 3 sInner ring 4150 lb, 25 Hz, 48828 sps, 3 sOuter ring 5200 lb, 25 Hz, 48828 sps, 3 sInner ring 5200 lb, 25 Hz, 48828 sps, 3 sOuter ring 6250 lb, 25 Hz, 48828 sps, 3 sInner ring 6250 lb, 25 Hz, 48828 sps, 3 sOuter ring 7300 lb, 25 Hz, 48828 sps, 3 sInner ring 7300 lb, 25 Hz, 48828 sps, 3 s


### 4.1.3. SEU Gearbox Dataset

There are 20 categories, including inner ring, outer ring, and rolling element in different states. In each file, we use the second line of eight vibration signals. Details are shown in Table3.Table 3
Fault classification of SEU dataset.
SortFault mode (RS-LC:20 Hz-0 V)SortFault mode (RS-LC:3 Hz-2 V)1Health gear11Health gear2Health bearing12Health bearing3Chipped tooth13Chipped tooth4Inner ring14Inner ring5Missing tooth15Missing tooth6Outer ring16Outer ring7Root fault17Root fault8Inner+outerrings18Inner+outerrings9Surface fault19Surface fault10Rolling element20Rolling element


## 4.1.1. PU Bearing Dataset

There are 21 categories, including 6 undamaged bearings, 12 damaged bearings, and 14 actual damaged bearings caused by an accelerated life test. The details are shown in Table1.Table 1
Fault classification of PU dataset.
CodeFault mode: descriptionK001Health state: launched 50 hours in advanceK002Health state: launched 19 hours in advanceK003Health state: launched 1 hours in advanceK004Health state: launched 5 hours in advanceK005Health state: launched 10 hours in advanceK006Health state: launched 16 hours in advanceKA01Outer ring: man-made damage caused by EDM (Level 1)KA03Outer ring: man-made damage caused by electric engraver (Level 2)KA05Outer ring: man-made damage caused by electric engraver (Level 1)KA06Outer ring: man-made damage caused by electric engraver (Level 2)KA07Outer ring: man-made damage caused by drilling (Level 1)KA08Outer ring: man-made damage caused by drilling (Level 2)KA09Outer ring: man-made damage caused by drilling (Level 2)KI01Inner ring: man-made damage caused by EDM (Level 1)KI03Inner ring: man-made damage caused by electric engraver (Level 1)KI05Inner ring: man-made damage caused by electric engraver (Level 1)KI07Inner ring: man-made damage caused by electric engraver (Level 2)KI08Inner ring: man-made damage caused by electric engraver (Level 2)KA04Outer ring: damage caused by fatigue and pitting (single point and single damage and Level 1)KA15Outer ring: damage caused by plastic deform and indentation (single point and single damage and Level 1)KA16Outer ring: damage caused by fatigue and pitting (single point and repetitive damage and Level 2)KA22Outer ring: damage caused by fatigue and pitting (single point and single damage and Level1)KA30Outer ring: damage caused by plastic deform and indentation (distributed and repetitive damage and Level 1)KB23Outer ring, inner ring: damage caused by fatigue and pitting (single point and multiple damage and Level 2)KB24Outer ring, inner ring: damage caused by fatigue and pitting (distributed and multiple damage and Level 3)KB27Outer ring, inner ring: damage caused by fatigue and pitting (distributed and multiple damage and Level 1)KI04Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level1)KI14Inner ring: damage caused by fatigue and pitting (singlepoint+multipledamage+Level1)KI16Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level3)KI17Inner ring: damage caused by fatigue and pitting (singlepoint+repetitivedamage+Level1)KI18Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level2)KI21Inner ring: damage caused by fatigue and pitting (singlepoint+singledamage+Level1)


## 4.1.2. MFPT Bearing Dataset

There are 15 categories, according to different loads, one healthy bearing and fourteen faulty bearings. The fault classification is displayed in Table2. The four values in the Description are load, input shaft speed, sampling rate, and duration.Table 2
Fault classification of MFPT dataset.
CategoryDescriptionCategoryDescriptionHealth state270 lb, 25 Hz, 97656 sps,6 s//Outer ring 125 lb, 25 Hz, 48828 sps, 3 sInner ring 125 lb, 25 Hz, 48828 sps, 3 sOuter ring 250 lb, 25 Hz, 48828 sps, 3 sInner ring 250 lb, 25 Hz, 48828 sps, 3 sOuter ring 3100 lb, 25 Hz, 48828 sps, 3 sInner ring 3100 lb, 25 Hz, 48828 sps, 3 sOuter ring 4150 lb, 25 Hz, 48828 sps, 3 sInner ring 4150 lb, 25 Hz, 48828 sps, 3 sOuter ring 5200 lb, 25 Hz, 48828 sps, 3 sInner ring 5200 lb, 25 Hz, 48828 sps, 3 sOuter ring 6250 lb, 25 Hz, 48828 sps, 3 sInner ring 6250 lb, 25 Hz, 48828 sps, 3 sOuter ring 7300 lb, 25 Hz, 48828 sps, 3 sInner ring 7300 lb, 25 Hz, 48828 sps, 3 s


## 4.1.3. SEU Gearbox Dataset

There are 20 categories, including inner ring, outer ring, and rolling element in different states. In each file, we use the second line of eight vibration signals. Details are shown in Table3.Table 3
Fault classification of SEU dataset.
SortFault mode (RS-LC:20 Hz-0 V)SortFault mode (RS-LC:3 Hz-2 V)1Health gear11Health gear2Health bearing12Health bearing3Chipped tooth13Chipped tooth4Inner ring14Inner ring5Missing tooth15Missing tooth6Outer ring16Outer ring7Root fault17Root fault8Inner+outerrings18Inner+outerrings9Surface fault19Surface fault10Rolling element20Rolling element


## 4.2. Data Split

There are two common data segmentation methods in mechanical intelligent diagnosis. One is the stochastic segmentation strategy, and the other is the time sort segmentation of datasets. The random segmentation strategy may cause data overlap between two sets, resulting in the risk of test leakage, and the final test accuracy cannot be used as a basis for fair evaluation of model performance. Industrial data are generally continuous, which may contain time-dependent knowledge information. Therefore, in order to evaluate the scientific and retain the useful information in the dataset as much as possible, we adopt the strategy of dividing the dataset according to the time sort (Figure7). The last 20% of the time series data is used for testing, and the rest is used for training.Figure 7
Data split according to time sequences.


## 4.3. Input Types

In mechanical intelligent diagnosis, signal processing methods are often used to map sample data to other domains. These methods include converted into time domain (TD), converted into frequency domain (FD), converted into time-frequency domain (TFD), converted into slice image (SI), and converted into wavelet domain (WD). The benchmark study of Zhao et al. [33] showed that FD and TFD can achieve higher accuracy, so we finally used TFD to complete the experiment.(11)xiSTFT=STFTxi,i=1,2,⋯,N.InsideSTFT⋅ is to convert xi into TFD.TFD is to perform short-time Fourier transform (STFT) on each specimen, and the Hanning window length is 64. Since the CNN model requires a larger 2D size to extract features, the final signal size is adjusted to330×330.


## 4.4. Training Details

During model training, we used the Adam optimizer. Some parameters of model training are as follows:learningrate=0.001 and batchsize=8 (due to the device limitation). Each model is trained and tested alternately during training, and a total of 100 epochs are experienced. All comparison models and MSDC-NET are trained and fairly compared under the open source code framework proposed by Zhao et al. [33], and the data enhancement method provided in the code framework is adopted. All work is performed on the device equipped with E5-2640 V4 @ CPU and 12G GeForce RTX 2080 Ti GPU. The device system is Ubuntu 16.04, the running environment is Python 3.6, and the Pytorch1.4 library is used.We have done the optimization experiment on the SEU gearbox dataset for the value ofω between 0 and 1. It is able to deduce from Figure 8 that as ω increases, the performance of the CNN model will tend to the performance without knowledge distillation; classification accuracy showed a downward trend, which also shows the effectiveness of knowledge distillation technology from the side, so we set ω to 0 in the subsequent comparative experiments.Figure 8
The influence of differentω on the model.


## 4.5. Evaluating Indexes

In our research process, the comprehensive accuracy (Acc) is used to fairly assess the capability of the algorithm. With the purpose of avoiding the impact of the fluctuation of DNN model in training, we repeat each experiment 10 times. Finally, we take the average Acc and the maximum Acc as the assessment indexes, the average Acc is the average of 10 times of Acc, and the maximum Acc is the maximum of 10 times of Acc.


## 4.6. MSDC-NET Experimental Results

For each algorithm, we completed 10 tests on the corresponding dataset in the same environment. The achievement of the highest predicted Acc is recorded in Figure9, and then, the achievement of the average predicted Acc of 10 times is recorded in Figure 10. From the overall view of these two figures, our algorithm reached the first-rate capability. The LSTM algorithm does not perform well on classification problems, and the average test Acc is between 85% and 90%.Figure 9
Maximum prediction accuracy graph of MSDC-NET and five contrast algorithms on three datasets.Figure 10
Average prediction accuracy graph of MSDC-NET and five contrast algorithms on three datasets.Compared with those on other datasets, the capability of the AE network on the SEU dataset is significantly not the same, which shows that the AE network has higher requirements for datasets. The classification ability of the simple CNN network is relatively poor without knowledge distillation, ranging from 75 to 85. The test Acc of DNN is relatively high, the test Acc of AlexNet is between 95 and 100, the test Acc of ResNet18 is between 98 and 100, and the test Acc of our MSDC-NET is between 98 and 100. From the comparison chart of average test Acc, our method is 1.27%, 3.55%, and 1.12% higher than ResNet18, which is the best algorithm in comparison. In the maximum test Acc diagram, our method is 0.54%, 0.77%, and 0.48% higher than ResNet18. Meanwhile, it is a surprise that our MSDC-NET has achieved 100% results on SEU gearbox dataset for 10 times, which reflects the powerful classification ability and robustness of our algorithm and will not produce serious over fitting phenomenon due to the deep network layers.


## 4.7. CNN Experimental Results after Knowledge Distillation

We distill the knowledge of MSDC-NET according to the algorithm in Figure6, so that the classification Acc of the CNN model is significantly improved without any change in the internal structure. As can be seen in Figure 11, contrasted with the original CNN, the average test Acc of CNN_D after knowledge distillation is 5.98%, 3.29%, and 7.24% higher on the three datasets. The maximum test Acc is 4.91%, 3.19%, and 6.55% higher, respectively. The average test Acc of CNN_D even exceeds the maximum test Acc of the original CNN. CNN_D has the most obvious improvement on the SEU gearbox dataset, which is comparable to the deep neural classification network AlexNet shown in Figure 10. Due to the problems of MFPT dataset itself, the effect of knowledge distillation is not obvious, but it has also been improved.Figure 11
Map of average and maximum classification accuracy of original CNN and knowledge distilled CNN_D on three datasets.


## 5. Conclusion

In this paper, we created a new MSDC-NET, which is derived from several typical deep convolutional neural network structures, combined with the most advanced multiscale and jump connection technologies. Experimental results on several datasets show that our MSDC-NET has a more prominent classification level than other latest research. At the same time, we found that knowledge of distillation technology in the diagnosis of intelligent mechanical issue is effective, and the classification accuracy of small CNN model after knowledge distillation is significantly improved. Next, we will further study the knowledge distillation technology, improve the diagnostic accuracy of the CNN model after knowledge distillation, and verify the portability and reliability of the related technology in the direction of mechanical intelligence prediction.



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*Source: 4319074-2021-07-07.xml*