Mathematical Problems in Engineering

Mathematical Problems in Engineering / 2019 / Article

Research Article | Open Access

Volume 2019 |Article ID 6921975 |

Hong-bai Yang, Jiang-an Zhang, Lei-lei Chen, Hong-li Zhang, Shu-lin Liu, "Fault Diagnosis of Reciprocating Compressor Based on Convolutional Neural Networks with Multisource Raw Vibration Signals", Mathematical Problems in Engineering, vol. 2019, Article ID 6921975, 7 pages, 2019.

Fault Diagnosis of Reciprocating Compressor Based on Convolutional Neural Networks with Multisource Raw Vibration Signals

Academic Editor: Juan P. Amezquita-Sanchez
Received04 Mar 2019
Revised12 May 2019
Accepted10 Jun 2019
Published04 Jul 2019


Reciprocating compressors are widely used in petroleum industry. Due to containing complex nonlinear signal, it is difficult to extract the fault features from its vibration signals. This paper proposes a new method named Convolutional Neural Network based on Multisource Raw vibration signals (MSRCNN). The proposed method uses multisource raw vibration signals collected by several sensors as input and uses the designed CNN to operate both the feature extraction and classification. The gas valve signals of reciprocating compressor in different states are used as the experimental data. In order to test the effectiveness of the proposed method, it is compared with the traditional BP (Back-Propagation) neural network fault diagnosis method based on power spectrum energy and wavelet packet energy. In order to further test the antinoise performance of the proposed method, some noisy signals with different signal-to-noise ratios were constructed by adding white noise into sampled signals for testing. The results show that the MSRCNN model has higher fault recognition rate than the traditional methods. This indicates that the MSRCNN method not only has good fault recognition effect, but also has certain antinoise performance.

1. Introduction

Commonly, fault diagnosis involves two steps: feature extraction and fault decision. The fault feature is extracted from the raw signals, and then the fault diagnosis is performed by manual experience judgment or pattern recognition technology [113]. Common feature extraction techniques include time domain statistical analysis, Fourier spectrum analysis, wavelet transform, empirical mode decomposition (EMD), and other time-frequency analysis methods [1, 2, 5, 6]. Common pattern recognition classifiers could include k-nearest neighbor (KNN) [3], artificial neural network (ANN) [46], and support vector machine (SVM) [4, 811]. In order to improve the fault identification rate further, the multisensor fault signals are used to diagnose the device together. However, this will lead to new problems such as increased feature set dimensions and data redundancy. A feature selection step will be implemented to get rid of useless and insensitive features and reduce the dimensions for the sake of computational efficiency. Principal component analysis (PCA) is one of the common dimension reduction methods [3, 11].

As general machinery, reciprocating compressor is widely used in petroleum and petrochemical industries. A small fault in reciprocating compressor may cause serious issues in operation. Its fault diagnosis also uses traditional method—feature extraction adding pattern recognition [612]. Liu Shulin et al. [6] used wavelet packet energy of difficult frequency ranges and radial basis function (RBF) neural network to diagnose faults. Tang Youfu et al. [7] calculated the Lempel-Ziv complexity indexes and used back-propagation (BP) neural network to identify the failure of the reciprocating compressor valve. A fault diagnosis method for bearing fault of reciprocating compressor based on LMD multiscale entropy and SVM is proposed [8]. Wang Jindong et al. [9] applied compound fault diagnosis technique based on EMD-Information Entropy and SVM to fault diagnosis of reciprocating compressor bearings. Qi et al. [10], based on the pretrained dictionary by sparse code method, supposed that faults are recognized and classified by support vector machine (SVM). Liu et al. [11] proposed an integrated feature extraction method based on the variational mode decomposition (VMD) and multifractal detrended fluctuation analysis (MFDFA) for a fault diagnosis of a reciprocating compressor valve, and the faults were identified by pattern classifiers of BTSVM and CNN. The Teager–Kaiser energy operation (TKEO) is proposed to estimate the signal amplitude envelopes and statistical measures are used to extract characteristics of the valve conditions, while the deep belief networks (DBNs) are applied to classify the faults of compressor valves [12]. The above research has achieved certain results. But due to the complex structure of the reciprocating compressor, multisource nonlinear pulse signal [14], the existing feature extraction methods are difficult to capture the essential fault feature, which make the diagnostic effects not ideal.

After the deep learning convolutional neural network (CNN) was proposed [13], the recognition accuracy was significantly improved in many traditional pattern recognition tasks. CNN demonstrates its superior ability to deal with complex problems and attracts a large number of scholars to study its theory and application [15]. The implicit feature extraction capabilities of CNN make itself particularly attractive in the field of pattern recognition where feature analysis is difficult. Some researchers have attempted to exploit CNN for both feature extraction and pattern classification in mechanical equipment fault diagnosis [1627]. In these applications, some input of the CNN model is a 1-dimensional (1D) raw signal [1619], and some input of the CNN model is 2-dimensional (2D) data [2027]. In [16, 17] 1D vibration signal is used to diagnose the bearing. In [18] 1D motor current signal pair is applied to diagnose the fault of motor. In [19] a 1D vibration signal is applied to health monitoring of the mechanical structure. Papers of [2022] simply process the raw signals into a 2D raw signal to diagnose the bearing or the pump. In [2328] the time-frequency analysis of the raw signal is performed, and the 2-dimensional time-frequency image data is taken as the input of the CNN model.

Although the CNN method has achieved good results in many of the above-mentioned fault diagnosis fields, it is rarely seen in the fault diagnosis of reciprocating compressors at present. In this paper, a CNN model based on multisource raw vibration signals (MSRCNN) is proposed to diagnose the valve failure of reciprocating compressor. The multisource raw vibration signals are directly input in MSRCNN model. MRCNN has the following advantages: The multisource raw signals are 2D data themselves which are very suitable for CNNs; the existing feature extraction methods are difficult to capture the essential fault characteristics of reciprocating compressors, and MRSCNN works on raw temporal signals, without feature extraction or manual selection; more comprehensive fault information could be obtained through multiple sensors.

The remainder of this paper is organized as follows: Section 2 briefly introduces the structure and principle of CNN; Section 3 introduces the MSRCNN model based on multisensor vibration signals; Section 4 evaluates the effect of the proposed method through experiments by comparing it with other traditional methods. Section 5 gives some conclusions and present to the future work.

2. Overview of CNNs

CNNs are a typical deep learning model and are biologically inspired feed-forward ANNs that present a simple model for the mammalian visual cortex. They are now widely used and have become the de facto standard in many image and video recognition systems. Figure 1 illustrates a 2-D CNN model with an input layer accepting 28 × 28 pixel images [13, 18, 19]. Each convolution layer after the input layer alternates with the subsampling (pooling) layers which decimate propagated 2-D maps from the neurons of previous layer. Unlike handcrafted and fixed parameters of the 2-D filter kernels, in CNNs they are trained (optimized) by the BP algorithm. However, the kernel size and the subsampling factor that are set to 5 and 2 for illustration in Figure 1 are the two major parameters of the CNN. The input layer is only a passive layer which accepts an input image and assigns its (R,G,B) color channels as the feature maps of its three neurons. With forward propagation over sufficient number of subsampling layers, they are decimated to a scalar (1-D) at the output of the last subsampling layer. The following layers are identical to the hidden layers of a MLP, fully connected, and feed-forward networks. These so-called fully connected layers end up with the output layer that estimates the decision (classification) vector.

The convolutional layer of CNN is used to extract local features of the input neuron data. Each convolution layer is composed of multiple feature matrices. Each feature matrix is viewed as a plane. The corresponding convolution kernels are the same on each layer. They have the characteristics of rotation, displacement invariance, and weight sharing. The features can be learned in parallel. The number of free parameters is greatly reduced. The convolution kernels of different planes are different, and multiconvolution kernels make feature extraction more complete. The convolution operation is described as formula (1). is the input feature map, we use and to denote the weights and bias of the -th filter kernel in layer , respectively, is the input of the l-th layer, and is the output of the -th layer.

The pooling layer (P layer), also called the downsampling layer, merges similar features into one and reduces the parameters of the network. Pooling process can extract features with scale invariance and prevent data from overfitting. The polling transformation is described as follows (in formula (2)).where is the subsampling function and is the -th network multiplicative bias of the -th layer.

The last few layers are identical to the hidden layers of a MLP, fully connected, and feed-forward. These so-called fully connected layers end up with the output layer. Generally, the softmax classifier is used to solve the multiclassification problem.

At present, most CNN is used for a supervised mode. The training of CNN is similar to the traditional artificial neural networks training method. The back-propagation algorithm (BP) is used to transmit the error layer by layer, and the gradient descent method is used to adjust the parameters between the layers.

Convolution has three important ideas: sparse connectivity, parameter sharing, and equivariant representations. The sparse connectivity establishes the non-fully connected spatial relationship between the layers through the topology structure to reduce the number of training parameters. Weight sharing can effectively avoid the algorithm overfitting. Equivariant means that if the input changes, the output changes in the same way. Pooling helps to make the representation become approximately invariant to small translations of the input. CNN is very suitable for the processing and learning of massive data. It can effectively realize fault diagnosis and identification by extracting features layer by layer.

3. Proposed MSRCNN Model

In this study, fusing feature extraction and fault diagnosis of the reciprocating compressor, we propose a convolutional neural network (MSRCNN) model as shown in Figure 2, which uses the multisource raw vibration signals without prior feature extraction as input.

In this model, the input data is 10243 (3 sensors), and the kernel size is set to 33. The model parameters, including the number of layers and whether to use BatchNomalizarion, etc., were adjusted experimentally. Model is constructed by Python (a popular development language), using the Keras framework (the back end using Tensorflow). Keras framework can be used to build models quickly. After many trial adjustments, the MSRCNN model for fault diagnosis of reciprocating compressor adopts the network structure shown in Table 1, including 6 2-dimensional convolution (Conv2D) layers and 6 downsamplings (Max_pooling) layers, 6 BatchNormalization layers, 1 flat (Flatten) layer, and 3 fully connected (Dense) layers whose length is 196736, 4128, and 132, respectively. The BatchNormalization [28] layer is designed to reduce the shift of internal covariance and accelerate the training process of the deep network. The activation function uses the “ReLU” function, which overcomes the gradient disappearance problem and greatly speeds up the training. The full-connected layers operate data classification using “softmax” function.

Layer (type)Output ShapeParam #

input_1 (InputLayer)(None, 1024, 3, 1)0
conv1 (Conv2D)(None, 1024, 3, 8)80
bn1 (BatchNormalization)(None, 1024, 3, 8)32
activation_1 (Activation relu)(None, 1024, 3, 8)0
max_pool1 (MaxPooling2D)(None, 512, 3, 8)0
conv2 (Conv2D)(None, 512, 3, 16)3216
bn2 (BatchNormalization)(None, 512, 3, 16)64
activation_2 (Activation relu)(None, 512, 3, 16)0
max_pool2 (MaxPooling2D)(None, 256, 3, 16)0
conv3 (Conv2D)(None, 256, 3, 32)4640
bn3 (BatchNormalization)(None, 256, 3, 32)128
activation_3 (Activation relu)(None, 256, 3, 32)0
max_pool3 (MaxPooling2D)(None, 128, 3, 32)0
conv4 (Conv2D)(None, 128, 3, 64)2112
bn4 (BatchNormalization)(None, 128, 3, 64)256
activation_4 (Activation relu)(None, 128, 3, 64)0
conv5 (Conv2D)(None, 128, 3, 32)18464
bn5 (BatchNormalization)(None, 128, 3, 32)128
activation_5 (Activation relu)(None, 128, 3, 32)0
max_pool5 (MaxPooling2D)(None, 64, 3, 32)0
conv6 (Conv2D)(None, 64, 3, 16)4624
bn6 (BatchNormalization relu)(None, 64, 3, 16)64
activation_6 (Activation relu)(None, 64, 3, 16)0
max_pool6 (MaxPooling2D)(None, 32, 3, 16)0
flatten_1 (Flatten)(None, 1536)0
fc1 (Dense)(None, 128)196736
fc2 (Dense)(None, 32)4128
fc3 (Dense)(None, 4)132

4. Test and Verification

In order to get the effect of the convolutional neural network model on the fault diagnosis of reciprocating compressors, we design two experiments. The constructed MSRCNN model is applied to feature extraction and fault diagnosis of the multisource raw vibration signal and is compared with the commonly used power spectrum (+BP) method and the wavelet packet energy (+BP) method. The robustness of the MSRCNN model to noise is studied. The raw data unadded noise is used to train the MSRCNN model. Diagnostic tests were performed with different SNR data and the test results were compared with the wavelet packet energy (+BP) method.

Using the Daubechies-db16 wavelet packet and the compressor vibration signal is decomposed into three levels and 8 frequency bands. The BP network adopts a three-layer neural network structure. The first layer is the input layer. The second layer is the hidden layer, in which the sigmoid activation function is selected, and the number of hidden layer neurons is 10. The third layer is linear output layer, and the corresponding expected outputs are normal , less springs , gaps , and breaks .

4.1. Test Data Collection

The experimental data of the reciprocating compressor vibration was collected from the No. 1 working unit in the southern section of Daqing Natural Gas Company. In order to collect the vibration data under different conditions, the valves in 4 states including normal state, valve plate breakage, spring damage, and valve notch are installed in the secondary cylinder of No.1 working unit of Daqing Natural Gas Company. The gas valve is subjected to a fault simulation test. The secondary gas inlet pressure is 310 kPa, the outlet pressure is 1,040 kPa, the inlet temperature is 32°C, the outlet temperature is 104°C, the gas flow is 3,611 m3/h, and three acceleration sensors (X/Y/Z) are placed on the valve cover of the second-stage cylinder, as shown in Figure 3. The data collection system uses the INV-1021 program-controlled multifunction signal conditioner from Beijing Oriental Institute and the INV306U-6660 intelligent data collection and processing analyzer. The sampling frequency is 20 kHz. In the normal state 120,000 points are collected. In the other three valve states 80,000 points are collected for each state.

4.2. Training Sample and Test Sample Library Building

In order to obtain a large number of training and test samples, the data acquisition uses a partial overlap cutting method, as shown in Figure 4. The simulation experiments show that the quantity of training data will affect the correct rate of training. The training frames are more, and the diagnosis accuracy is higher. In this paper the step between sample frames is 10. Each sample is 1024 long, and a total of 5382 samples are collected. 70% of them were randomly selected as training samples and 30% as test samples.

For the power spectrum energy (+BP) method and the wavelet packet energy (+BP) method, there are four fault states: the normal state of the valve, the broken valve plate, the spring damage, and the gap of the valve plate. Each sample length is 1024 data items, and 78 samples in each state are, respectively, taken. The 55 samples (70%) in each state constitute the fault training samples (554=220 total), and the remaining 30% samples constitute the test samples of the model (234=92 total).

In order to get the fault recognition rates under different noise conditions, different signal-to-noise ratio Gaussian noise is added to the test samples to get the diagnosis accuracy.

4.3. Comparative Analysis of Test Results

Table 2 shows the comparison of the recognition rates of three fault diagnosis methods for the reciprocating compressor valve failure. From Table 2, the MSRCNN method based on the raw vibration signal has the highest recognition rate, which can reach 100% accuracy, which effectively identifies and diagnoses the reciprocating compressor valve faults.

power spectrum energy (+BP)wavelet packet energy (+BP)MSRCNN

Recognition rate60%87.27%100%

Table 3 compares fault diagnosis results between MSRCNN model and the three-layer wavelet packet energy (+BP) model under different noise intensities. Table 3 shows that the diagnostic rate of the MSRCNN method has a relatively high fault recognition rate under 4 kinds of test conditions. Under no-noise, the SNR of 50 dB and the SNR of 20 dB conditions, MSRCNN can all get 100% fault recognition rate. While SNR decreases to 10 dB, this model still reaches 90.2% recognition rate. In the contrast, the wavelet packet energy (+BP) method can achieve a test recognition rate of 87.27% under no-noise signals and 50 dB (less noise), but when the signal-to-noise ratio reaches 10 dB, the recognition rate is greatly reduced (40.91%) and the faults cannot be effectively identified.

SNRwavelet packet energy (+BP)MSRCNN

10 dB40.91%90.2%
20 dB75.45%100%
50 dB87.27%100%
no noise87.27%100%

5. Conclusions

The raw 2D vibration signal being directly applied as an input, MSRCNN model is constructed to perform reciprocating compressor fault diagnosis. Experiments were carried out using the compressor valve fault data samples obtained from the test bench, and MSRCNN method obtains higher fault recognition rate than power spectrum energy (+BP) method and the wavelet packet energy (+BP) method. The noise added fault signals with different SNRs were tested. The results showed that, for the tested compressor, MSRCNN model method has higher recognition rate than wavelet packet energy (+BP) method under the different signal-to-noise ratio conditions. Experiments indicate that MSRCNN not only has higher recognition effect, but also has certain antinoise performance.

At present, the focus of the article is the application of 2D data on CNN. The number of constructing model layers and each parameter are adjusted manually based on experiments. In the future, it is expected that further research can find out the inherent principle for model optimization.

Data Availability

The raw vibration data used in this paper are got from the cooperation enterprises project. There is confidentiality agreement. It can only be used by our research group and cannot be open to others.

Conflicts of Interest

The authors declare that they have no conflicts of interest.


This work was supported by the 2018 Shanghai Open University Research Project (KX1805), Shanghai Key Laboratory of Intelligent Manufacturing and Robotics (ZK1801), and National Natural Science Foundation of China (51575331).


  1. Z. P. Feng, M. Liang, and F. L. Chu, “Recent advances in time-frequency analysis methods for machinery fault diagnosis: a review with application examples,” Mechanical Systems and Signal Processing, vol. 38, no. 1, pp. 165–205, 2013. View at: Publisher Site | Google Scholar
  2. H. Y. Zhao, J. D. Wang, J. Lee, and L. Ying, “A compound interpolation envelope local mean decomposition and its application for fault diagnosis of reciprocating compressors,” Mechanical Systems and Signal Processing, vol. 110, pp. 273–295, 2018. View at: Publisher Site | Google Scholar
  3. D. H. Pandya, S. H. Upadhyay, and S. P. Harsha, “Fault diagnosis of rolling element bearing with intrinsic mode function of acoustic emission data using APF-KNN,” Expert Systems with Applications, vol. 40, no. 10, pp. 4137–4145, 2013. View at: Publisher Site | Google Scholar
  4. A. Hajnayeb, A. Ghasemloonia, S. Khadem, and M. Moradi, “Application and comparison of an ANN-based feature selection method and the genetic algorithm in gearbox fault diagnosis,” Expert Systems with Applications, vol. 38, no. 8, pp. 10205–10209, 2011. View at: Publisher Site | Google Scholar
  5. P. Potočnik and E. Govekar, “Semi-supervised vibration-based classification and condition monitoring of compressors,” Mechanical Systems and Signal Processing, vol. 93, pp. 51–65, 2017. View at: Publisher Site | Google Scholar
  6. S. L. Liu, J. Z. Zhang, M. Q. Xu et al., “Wavelet packet and neural network based approach for fault diagnosis of reciprocating compressors,” Oil Field Equipment, vol. 31, no. 5, pp. 1–3, 2002. View at: Google Scholar
  7. Y. F. Tang, S. L. Liu, Y. H. Liu et al., “Fault diagnosis based on nonlinear complexity measurefor reciprocating compressor,” Journal of Mechanical Engineering, vol. 48, no. 03, pp. 102–107, 2012. View at: Publisher Site | Google Scholar
  8. S. S. Yang, H. Zhou, H. Y. Zhao et al., “Fault diagnosis method for the bearing of reciprocating compressor based on LMD multiscale entropy and SVM,” Journal of Mechanical Transmission, vol. 39, no. 2, pp. 119–123, 2015. View at: Google Scholar
  9. J. D. Wang, M. Dai, F. F. Xia et al., “Fault diagnosis for reciprocating compressor bearings based on EMD-information entropy and SVM,” Fluid Machinery, vol. 42, no. 7, pp. 43–46, 2014. View at: Google Scholar
  10. G. Qi, Z. Zhu, K. Erqinhu, Y. Chen, Y. Chai, and J. Sun, “Fault-diagnosis for reciprocating compressors using big data and machine learning,” Simulation Modelling Practice and Theory, vol. 80, pp. 104–127, 2018. View at: Publisher Site | Google Scholar
  11. Y. Liu, J. Wang, Y. Li, H. Zhao, and S. Chen, “Feature extraction method based on VMD and MFDFA for fault diagnosis of reciprocating compressor valve,” Journal of Vibroengineering, vol. 19, no. 8, pp. 6007–6020, 2017. View at: Publisher Site | Google Scholar
  12. V. T. Tran, F. Althobiani, and A. Ball, “An approach to fault diagnosis of reciprocating compressor valves using Teager–Kaiser energy operator and deep belief networks,” Expert Systems with Applications, vol. 41, no. 9, pp. 4113–4122, 2014. View at: Publisher Site | Google Scholar
  13. A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” in Proceedings of the Conference on Neural Information Processing Systems, vol. 60, pp. 1097–1105, Lake Tahoe, Nev, USA, December 2012. View at: Google Scholar
  14. S. Xiao, S. Liu, F. Jiang, M. Song, and S. Cheng, “Nonlinear dynamic response of reciprocating compressor system with rub-impact fault caused by subsidence,” Journal of Vibration and Control, vol. 25, no. 11, pp. 1737–1751, 2019. View at: Publisher Site | Google Scholar
  15. H. Ren, J. F. Qu, Y. Chai, Q. Tang, and X. Ye, “Deep learning for fault diagnosis: the state of the art and challenge,” Control and Decision, vol. 32, no. 8, pp. 1345–1358, 2017. View at: Google Scholar
  16. L. Eren, “Bearing fault detection by one-dimensional convolutional neural networks,” Mathematical Problems in Engineering, vol. 2017, Article ID 8617315, 9 pages, 2017. View at: Publisher Site | Google Scholar
  17. W. Zhang, G. Peng, C. Li, Y. Chen, and Z. Zhang, “A new deep learning model for fault diagnosis with good anti-noise and domain adaptation ability on raw vibration signals,” Sensors, vol. 17, no. 2, 2017. View at: Google Scholar
  18. T. Ince, S. Kiranyaz, L. Eren, M. Askar, and M. Gabbouj, “Real-time motor fault detection by 1-D convolutional neural networks,” IEEE Transactions on Industrial Electronics, vol. 63, no. 11, pp. 7067–7075, 2016. View at: Publisher Site | Google Scholar
  19. O. Abdeljaber, O. Avci, S. Kiranyaz, M. Gabbouj, and D. J. Inman, “Real-time vibration-based structural damage detection using one-dimensional convolutional neural networks,” Journal of Sound and Vibration, vol. 388, pp. 154–170, 2017. View at: Publisher Site | Google Scholar
  20. W. Zhang, G. Peng, and C. Li, “Bearings fault diagnosis based on convolutional neural networks with 2-D representation of vibration signals as input,” in Proceedings of the 3rd International Conference on Mechatronics and Mechanical Engineering (ICMME '16), vol. 95, pp. 1–5, China, October 2016. View at: Google Scholar
  21. X. Guo, L. Chen, and C. Shen, “Hierarchical adaptive deep convolution neural network and its application to bearing fault diagnosis,” Measurement, vol. 93, pp. 490–502, 2016. View at: Publisher Site | Google Scholar
  22. L. Wen, X. Li, L. Gao, and Y. Zhang, “A new convolutional neural network-based data-driven fault diagnosis method,” IEEE Transactions on Industrial Electronics, vol. 65, no. 7, pp. 5990–5998, 2018. View at: Publisher Site | Google Scholar
  23. O. Janssens, V. Slavkovikj, B. Vervisch et al., “Convolutional neural network based fault detection for rotating machinery,” Journal of Sound and Vibration, vol. 377, pp. 331–345, 2016. View at: Publisher Site | Google Scholar
  24. S. Li, G. Liu, X. Tang, J. Lu, and J. Hu, “An ensemble deep convolutional neural network model with improved D-S evidence fusion for bearing fault diagnosis,” Sensors, vol. 17, no. 8, Article ID 1729, 2017. View at: Publisher Site | Google Scholar
  25. D. Verstraete, A. Ferrada, E. L. Droguett, V. Meruane, and M. Modarres, “Deep learning enabled fault diagnosis using time-frequency image analysis of rolling element bearings,” Shock and Vibration, vol. 2017, Article ID 5067651, 17 pages, 2017. View at: Publisher Site | Google Scholar
  26. M. Bach-Andersen, B. Rømer-Odgaard, and O. Winther, “Deep learning for automated drivetrain fault detection,” Wind Energy, vol. 21, no. 1, pp. 29–41, 2018. View at: Publisher Site | Google Scholar
  27. Z. Chen, C. Li, and R.-V. Sanchez, “Gearbox fault identification and classification with convolutional neural networks,” Shock and Vibration, vol. 2015, Article ID 390134, 10 pages, 2015. View at: Publisher Site | Google Scholar
  28. S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” in Proceedings of the 32nd International Conference on Machine Learning (ICML '15), pp. 448–456, July 2015. View at: Google Scholar

Copyright © 2019 Hong-bai Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

More related articles

 PDF Download Citation Citation
 Download other formatsMore
 Order printed copiesOrder

Related articles

Article of the Year Award: Outstanding research contributions of 2020, as selected by our Chief Editors. Read the winning articles.