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.
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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
- a :
-
Stretch factor
- b :
-
Shift factor
- CWT(s(t)):
-
CWT time-frequency function of signal s(t)
- d j (j = i, 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
- ℓ :
-
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(ℓ):
-
True labels of the tree-structured decision layer
- P(ℓ):
-
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
- \(q\left({\hat k} \right)\) :
-
Predicted probabilities of the pre-trained network
- \(q\left({\hat \ell} \right)\) :
-
Predicted probabilities of the tree-structured decision layer
- R :
-
Dimension of the TFD matrix
- s(t):
-
Signal in time t
- sw j :
-
Weight vector of the jth leaf note
- w j :
-
Weight vector of the jth vector in weight matrix W of the fully-connected layer
- w*j :
-
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
- \(\bf{\hat y}\) :
-
Prediction probabilities by the Softmax classifier
- \({\bf{\hat y}}_j\) :
-
Predicted probability for the jth category
- z j :
-
Prediction scope corresponding to K categories
- ω :
-
Weight adjusting the pre-trained decision and tree-structured decision
- ψ :
-
Mother wavelet
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Acknowledgements
The authors declare that they have no competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. The work was supported by the National Key R&D Program of China (Grant No. 2020YFB2007700), the National Natural Science Foundation of China (Grant No. 51975309), the State Key Laboratory of Tribology Initiative Research Program, China (Grant No. SKLT2020D21), and the Natural Science Foundation of Shaanxi Province, China (Grant No. 2019JQ-712).
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Wang, X., Gu, H., Wang, T. et al. Deep convolutional tree-inspired network: a decision-tree-structured neural network for hierarchical fault diagnosis of bearings. Front. Mech. Eng. 16, 814–828 (2021). https://doi.org/10.1007/s11465-021-0650-6
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DOI: https://doi.org/10.1007/s11465-021-0650-6