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Frontiers of Mechanical Engineering

ISSN 2095-0233

ISSN 2095-0241(Online)

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Front. Mech. Eng.    2021, Vol. 16 Issue (4) : 814-828    https://doi.org/10.1007/s11465-021-0650-6
RESEARCH ARTICLE
Deep convolutional tree-inspired network: a decision-tree-structured neural network for hierarchical fault diagnosis of bearings
Xu WANG1,2, Hongyang GU2, Tianyang WANG1(), Wei ZHANG2, Aihua LI2, Fulei CHU1
1. State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China; Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
2. High-Tech Research Institute of Xi’an, Xi’an 710025, China
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Abstract

The fault diagnosis of bearings is crucial in ensuring the reliability of rotating machinery. Deep neural networks have provided unprecedented opportunities to condition monitoring from a new perspective due to the powerful ability in learning fault-related knowledge. However, the inexplicability and low generalization ability of fault diagnosis models still bar them from the application. To address this issue, this paper explores a decision-tree-structured neural network, that is, the deep convolutional tree-inspired network (DCTN), for the hierarchical fault diagnosis of bearings. The proposed model effectively integrates the advantages of convolutional neural network (CNN) and decision tree methods by rebuilding the output decision layer of CNN according to the hierarchical structural characteristics of the decision tree, which is by no means a simple combination of the two models. The proposed DCTN model has unique advantages in 1) the hierarchical structure that can support more accuracy and comprehensive fault diagnosis, 2) the better interpretability of the model output with hierarchical decision making, and 3) more powerful generalization capabilities for the samples across fault severities. The multiclass fault diagnosis case and cross-severity fault diagnosis case are executed on a multicondition aeronautical bearing test rig. Experimental results can fully demonstrate the feasibility and superiority of the proposed method.
Keywords bearing      cross-severity fault diagnosis      hierarchical fault diagnosis      convolutional neural network      decision tree     
Corresponding Author(s): Tianyang WANG   
Just Accepted Date: 23 September 2021   Online First Date: 29 October 2021    Issue Date: 28 January 2022
 Cite this article:   
Xu WANG,Hongyang GU,Tianyang WANG, et al. Deep convolutional tree-inspired network: a decision-tree-structured neural network for hierarchical fault diagnosis of bearings[J]. Front. Mech. Eng., 2021, 16(4): 814-828.
 URL:  
https://academic.hep.com.cn/fme/EN/10.1007/s11465-021-0650-6
https://academic.hep.com.cn/fme/EN/Y2021/V16/I4/814
Fig.1  Schematic view of the proposed deep convolutional tree-inspired network model.
Layer Set Output shape
Input ? N×R×R×1
2D convolution layer Kernel size: 1×1, channel: 16, stride: 1 N×R×R×16
Batch normalization Feature number: 16, eps: 10?5 N×R×R×16
ReLU activation ? N×R×R×16
2D max pooling layer Kernel size: 2×2 N×R/2×R/2×16
2D convolution layer Kernel size: 3×3, channel: 32, stride: 1 N×R/2×R/2×32
Batch normalization Feature number: 32, eps: 10?5 N×R/2×R/2×32
ReLU activation ? N×R/2×R/2×32
2D max pooling layer Kernel size: 2×2 N×R/4×R/4×32
2D convolution layer Kernel size: 3×3, channel: 64, stride: 1 N×R/4×R/4×64
Batch normalization Feature number: 64, eps: 10?5 N×R/4×R/4×64
ReLU activation ? N×R/4×R/4×64
Adaptive average pooling layer Kernel size: 1×1 N×1×1×64
Fully-connected layer Batch size: 64×1×1, out features: K, no bias N×K
Tab.1  Layer details of backbone CNN
Fig.2  Weight propagation of tree-structured decision layer.
Fig.3  Overview of Politecnico di Torino rolling bearing test rig.
Serial number Fault location Fault size/μm Superclass Subclass
N-1 No defect ? N 1
I-2 On the inner ring 450 I 2
I-3 On the inner ring 250 I 3
I-4 On the inner ring 150 I 4
R-5 On a roller 450 R 5
R-6 On a roller 250 R 6
R-7 On a roller 150 R 7
Tab.2  Fault set details of aeronautical bearings
Number Load/N Speed/(r?min?1)
C1 0 6×103
C2 1000 6×103
C3 1400 6×103
C4 1800 6×103
C5 0 12×103
C6 1000 12×103
C7 1400 12×103
C8 1800 12×103
C9 0 18×103
C10 1000 18×103
C11 1400 18×103
C12 1800 18×103
C13 0 24×103
C14 1000 24×103
C15 1400 24×103
C16 0 3×104
C17 1000 3×104
Tab.3  Operating condition details of aeronautical bearings
Fig.4  Raw signals of bearings under different health states.
Fig.5  CWT-based TFD of bearings under different health states.
Fig.6  Designed DCTN-based hierarchical multiclass fault diagnosis network.
Fig.7  Designed DCTN-based cross-severity fault diagnosis network.
Fig.8  Fault diagnosis performance of bearings under different ratios and ω settings.
Condition Fault diagnosis accuracy/%
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Mean
C1 96.19 93.21 99.39 100.0 100.0 100.0 100.0 100.0 100.0 98.75
C2 96.67 93.93 96.53 100.0 99.43 98.57 100.0 100.0 100.0 98.35
C3 96.83 88.57 96.94 96.19 99.43 99.29 100.0 100.0 100.0 97.47
C4 97.46 89.81 95.71 92.38 99.43 98.93 100.0 100.0 100.0 97.08
C5 99.03 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.89
C6 97.94 96.43 94.08 100.0 99.71 100.0 100.0 100.0 100.0 98.68
C7 93.65 95.00 96.12 100.0 100.0 100.0 100.0 100.0 100.0 98.31
C8 93.81 95.18 95.31 99.05 98.29 100.0 100.0 100.0 100.0 97.96
C9 97.78 99.82 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.73
C10 97.14 97.68 99.39 100.0 100.0 100.0 100.0 100.0 100.0 99.36
C11 93.81 98.93 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.19
C12 93.81 98.93 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.19
C13 99.05 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.89
C14 93.81 95.54 100.0 100.0 100.0 100.0 100.0 100.0 100.0 98.82
C15 94.44 98.21 100.0 100.0 99.43 100.0 100.0 100.0 100.0 99.12
C16 93.81 99.82 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.29
C17 97.46 98.21 100.0 100.0 100.0 100.0 100.0 100.0 100.0 99.52
Mean 96.04 96.43 98.44 99.27 99.75 99.81 100.0 100.0 100.0
Tab.4  Fault diagnosis accuracy of bearings with different training data ratios
Fig.9  Fault diagnosis performance of different approaches under different ratios of training data.
Task Categories of training bearings Categories of test bearings
1 N-1, I-3, I-4, R-6, R-7 I-2, R-5
2 N-1, I-2, I-4, R-5, R-7 I-3, R-6
3 N-1, I-2, I-3, R-5, R-6 I-4, R-7
Tab.5  Set of cross-severity fault diagnosis tasks
Fig.10  Predicted superclass labels of cross-severity fault diagnosis tasks.
Fig.11  Predicted probabilities of cross-severity fault diagnosis tasks.
Approach Fault diagnosis accuracy/%
I-2 R-5 Task 1 I-3 R-6 Task 2 I-4 R-7 Task 3 Mean
TFD-DCTN 86.00 100.0 93.00 99.00 99.00 99.00 96.00 83.00 89.50 93.83
TFD-CNN 2.00 98.00 50.00 2.00 11.00 6.50 9.00 1.00 5.00 20.50
TFD-LBCNN 8.00 98.00 53.00 5.00 97.00 51.00 0.00 100.0 50.00 51.33
TFD-PCA-SVM 97.00 0.00 48.50 0.00 100.0 50.00 36.00 0.00 18.00 38.83
TFD-PCA-KNN 19.00 93.00 56.00 0.00 96.00 48.00 0.00 0.00 0.00 34.67
TFD-PCA-ELM 97.00 0.00 48.50 20.00 52.00 36.00 0.00 1.00 0.50 28.33
Time-features-SVM 100.0 37.00 68.50 77.00 0.00 38.50 58.00 38.00 48.00 51.67
Time-features-KNN 92.00 22.00 57.00 100.00 0.00 50.00 92.00 22.00 57.00 54.67
Time-features-ELM 98.00 18.00 58.00 40.00 0.00 20.00 69.00 31.00 50.00 42.67
Raw-data-WDCNN 12.00 100.0 56.00 24.00 96.00 60.00 0.00 100.0 50.00 55.33
Tab.6  Fault diagnosis accuracies of different approaches in cross-severity fault diagnosis tasks
Abbreviations
CNN Convolutional neural network
CWT Continuous wavelet transform
DCTN Deep convolutional tree-inspired network
DL Deep learning
DNN Deep neural network
ELM Extreme learning machine
KNN k-nearest neighbor
LBCNN Local binary convolutional neural network
PCA Principal component analysis
SVM Support vector machine
TFD Time?frequency distribution
WDCNN Wide deep convolutional neural network
  
Variables
a Stretch factor
b Shift factor
CWT(s(t)) CWT time?frequency function of signal s(t)
dj (j = 1, 2, …, K) Distance between the feature and each classification hyperplane
H(p, q) Cross-entropy loss function
H?(p(?),q(?),p(?),q(?)) Loss function of the tree-structured decision layer
K Number of sample categories
? Overall prediction
L Feature dimension of the fully-connected layer
N Number of samples
p(·) Probability distribution of the predicted output
p(k) True labels of the pre-trained network
p(?) True labels of the tree-structured decision layer
P(?) Path probabilities of the tree-structured decision layer
P (subclass) Probability of correct prediction for seed nodes
P (superclass) Probability of correct prediction of leaf nodes
q(·) Probability distribution of the actual output
q(k^) Predicted probabilities of the pre-trained network
q(?^) Predicted probabilities of the tree-structured decision layer
R Dimension of the TFD matrix
s(t) Signal in time t
swj Weight vector of the jth leaf note
wj Weight vector of the jth vector in weight matrix W of the fully-connected layer
wj? Weight vector of the jth tree-structured decision layer after fine-tuning
W Weight matrix
x Input features of the Softmax classifier in the cross-entropy loss
x Input feature vector of the tree-structured decision layer
y^ Prediction probabilities by the Softmax classifier
y^j Predicted probability for the jth category
zj Prediction scope corresponding to K categories
ω Weight adjusting the pre-trained decision and tree-structured decision
ψ Mother wavelet
  
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