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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

CN 11-5984/TH

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Front. Mech. Eng.    2021, Vol. 16 Issue (2) : 340-352    https://doi.org/10.1007/s11465-021-0629-3
RESEARCH ARTICLE
Multi-model ensemble deep learning method for intelligent fault diagnosis with high-dimensional samples
Xin ZHANG1, Tao HUANG1, Bo WU1, Youmin HU1(), Shuai HUANG1, Quan ZHOU2, Xi ZHANG1
1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
2. School of Mechanical and Electronic Engineering, Wuhan University of Technology, Wuhan 430070, China
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Abstract

Deep learning has achieved much success in mechanical intelligent fault diagnosis in recent years. However, many deep learning methods cannot fully extract fault information to recognize mechanical health states when processing high-dimensional samples. Therefore, a multi-model ensemble deep learning method based on deep convolutional neural network (DCNN) is proposed in this study to accomplish fault recognition of high-dimensional samples. First, several 1D DCNN models with different activation functions are trained through dimension reduction learning to obtain different fault features from high-dimensional samples. Second, the obtained features are constructed into 2D images with multiple channels through a conversion method. The integrated 2D feature images can effectively represent the fault characteristic contained in raw high-dimension vibration signals. Lastly, a 2D DCNN model with multi-layer convolution and pooling is used to automatically learn features from the 2D images and identify the fault mode of the mechanical equipment by adopting a softmax classifier. The proposed method, which is validated using the bearing public dataset of Case Western Reserve University, USA and a one-stage reduction gearbox dataset, has high recognition accuracy. Compared with other classical deep learning methods, the proposed fault diagnosis method has considerable improvements.
Keywords fault intelligent diagnosis      deep learning      deep convolutional neural network      high-dimensional samples     
Corresponding Author(s): Youmin HU   
Online First Date: 10 May 2021    Issue Date: 15 June 2021
 Cite this article:   
Xin ZHANG,Tao HUANG,Bo WU, et al. Multi-model ensemble deep learning method for intelligent fault diagnosis with high-dimensional samples[J]. Front. Mech. Eng., 2021, 16(2): 340-352.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0629-3
https://academic.hep.com.cn/fme/EN/Y2021/V16/I2/340
Fig.1  Typical architecture of 2D deep convolutional neural network.
Function Expression
relu f( x)={x, x≥00, x< 0
elu f(α, x)={ x, x≥0 α( ex –1)x , x <0
tanh f(x )=2/(1+exp(–2x))–1
Tab.1  Three different types of activation functions used in this study
Fig.2  Main procedure of the proposed multi-model ensemble deep learning method.
Layer Activation function
1st 1D DCNN 2nd 1D DCNN 3rd 1D DCNN 2D DCNN
input – – – –
conv1 relu elu tanh tanh
pool1 – – – –
conv2 relu elu tanh tanh
pool2 – – – –
conv3 relu elu tanh tanh
pool3 – – – –
FC1 – – – –
FC2 relu relu relu relu
output – – – –
Tab.2  Activation function settings of the four models
Layer 1D DCNN 2D DCNN
Parameter size Output size Parameter size Output size
input – 4096×1 – 32×32×3
conv1 8×1×4 4096×4 4×4×8 32×32×8
pool1 4×1 1024×4 2×2 16×16×8
conv2 4×1×8 1024×8 4×4×16 16×16×16
pool2 4×1 256×8 2×2 8×8×16
conv3 4×1×16 256×16 2×2×32 8×8×32
pool3 4×1 64×16 2×2 4×4×32
FC1 – 1024×1 – 512×1
FC2 1024×1024 1024×1 512×256 256×1
DR – 1024×1 – 256×1
output 1024×10 10×1 256×10 10×1
Tab.3  Details of the 1D DCNN and 2D DCNN models in case study 1
Fig.3  Training and validation accuracies/loss curves of the multi-model ensemble deep learning model: 1D DCNN using (a) relu, (b) elu, and (c) tanh; (d) 2D DCNN.
Fig.4  Visualization effect by t-SNE of the learned features under the test dataset: (a) 1D DCNN, (b) 2D DCNN, (c) DCAE, and (d) MMEDL.
Fig.5  Confusion matrices of the fault diagnosis results under the test dataset: (a) 1D DCNN, (b) 2D DCNN, (c) DCAE, and (d) MMEDL.
Fig.6  Composition of the monitoring platform.
Fig.7  Installation position of three triaxial sensors.
Gear type Teeth number Gear module/mm Teeth width/mm
Driving gear 50 2 20
Driven gear 80 2 20
Tab.4  Parameters of the experimental gears
Layer Parameter size Output size
input – 2048×1
conv1 8×1×4 2048×4
pool1 4×1 512×4
conv2 4×1×8 512×8
pool2 4×1 128×8
conv3 4×1×16 128×16
pool3 2×1 64×16
FC1 – 1024×1
FC2 1024×1024 1024×1
DR – 1024×1
output 1024×4 4×1
Tab.5  Details of the 1D DCNN models in case study 2
Fig.8  Fast Fourier transform results the four gear crack severities: (a) Non-crack, (b) 1/4 crack, (c) 1/2 crack, and (d) 3/4 crack.
Fig.9  (a) Training and validation accuracies and (b) loss curves of the 2D deep convolutional neural network in the proposed multi-model ensemble deep learning.
Fig.10  Accuracy comparison of the different methods under the multi-channel signals. DNN: Deep neural network; DBN: Deep belief network; DCNN: Deep convolutional neural network; MMEDL: Multi-model ensemble deep learning.
1D One-dimensional
2D Two-dimensional
conv Convolutional layer
CNN Convolutional neural network
DBN Deep belief network
DCAE Deep convolutional autoencoder
DCNN Deep convolutional neural network
DNN Deep neural network
DR Dropout layer
FC Fully-connected layer
IR Inner race fault state of the bearing in case study 1
MMEDL Multi-model ensemble deep learning
N Normal state of the bearing in case study 1
OR Outer race fault state of the bearing in case study 1
pool Max pooling layer
RE Rolling element fault state of the bearing in case study 1
SVM Support vector machine
t-SNE t-distributed stochastic neighbor embedding
b bias of the neurons in Eq. (1)
dk Length of the trainable filters in Eq. (1)
k Trainable filters in Eq. (1)
Lc Length of the gear crack in case study 2
Rc Radius of the root circle of the main driving wheel in case study 2
rh Radius of the center hole of the main driving wheel in case study 2
x Input of the convolution layer in Eq. (1)
s Nonlinear activation functions in Eq. (1)
  
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