Article
WDA: An Improved Wasserstein Distance-Based Transfer
Learning Fault Diagnosis Method
Zhiyu Zhu
1,2
, Lanzhi Wang
3
, Gaoliang Peng
1,
* and Sijue Li
1
Citation: Zhu, Z.; Wang, L.; Peng, G.;
Li, S. WDA: An Improved
Wasserstein Distance-Based Transfer
Learning Fault Diagnosis Method.
Sensors 2021, 21, 4394. https://
doi.org/10.3390/s21134394
Academic Editors: Kim Phuc Tran,
Athanasios Rakitzis and Khanh T.
P. Nguyen
Received: 12 June 2021
Accepted: 23 June 2021
Published: 26 June 2021
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4.0/).
1
State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China;
zhiyuzhu2-c@my.cityu.edu.hk (Z.Z.); lisijue@hit.edu.cn (S.L.)
2
The Department of Computer Science, City University of Hong Kong, Hong Kong
3
Beijing Institute of Aerospace Launch Technology, Beijing 100076, China; bluewill-926@163.com
* Correspondence: pgl7782@hit.edu.cn
Abstract:
With the growth of computing power, deep learning methods have recently been widely
used in machine fault diagnosis. In order to realize highly efficient diagnosis accuracy, people need
to know the detailed health condition of collected signals from equipment. However, in the actual
situation, it is costly and time-consuming to close down machines and inspect components. This
seriously impedes the practical application of data-driven diagnosis. In comparison, the full-labeled
machine signals from test rigs or online datasets can be achieved easily, which is helpful for the
diagnosis of real equipment. Thus, we introduced an improved Wasserstein distance-based transfer
learning method (WDA), which learns transferable features between labeled and unlabeled signals
from different forms of equipment. In WDA, Wasserstein distance with cosine similarity is applied to
narrow the gap between signals collected from different machines. Meanwhile, we use the Kuhn–
Munkres algorithm to calculate the Wasserstein distance. In order to further verify the proposed
method, we developed a set of case studies, including two different mechanical parts, five transfer
scenarios, and eight transfer learning fault diagnosis experiments. WDA reached an average accuracy
of 93.72% in bearing fault diagnosis and 84.84% in ball screw fault diagnosis, which greatly surpasses
state-of-the-art transfer learning fault diagnosis methods. In addition, comprehensive analysis and
feature visualization are also presented.
Keywords:
intelligent bearing fault diagnosis; Wasserstein distance; convolutional neural network;
domain adaptive ability; Kuhn–Munkres algorithm
1. Introduction
With the rise of machine learning, especially deep learning, more and more data-
driven algorithms have been proposed and applied successfully in different fields in the
last few years [
1
–
3
]. Similarly, data-driven methods are increasingly suggested to deal
with problems in the field of machine health monitoring [
4
], which has great importance in
modern industry.
For example, Atoui et al. [
5
] presented Bayesian network for fault detection and
diagnosis, Rajakarunakaran S et al. [
6
] proposed artificial neural networks (ANN) for the
fault detection of the centrifugal pumping system, and Ivan et al. [
7
] suggested a novel
weighted adaptive recursive fault diagnosis method based on principal component analysis
(PCA) to reduce the false alarm rate in processing monitoring schemes. Recently, as deep
learning is rapidly developing, artificial intelligence methods are considered to handle the
fault detection and classification in rolling bearing elements, e.g., autoencoders [
8
] and
convolutional neural networks (CNN). Li et al. [
9
] proposed a bearing defect diagnosis
technique based on a fully connected winner-take-all autoencoder. Jafar Zarei [
10
] proposed
a pattern recognition technique for fault diagnosis of induction motor bearings via utilizing
the artificial multilayer perceptron neural networks. Olivier Janssens et al. [
11
] introduced
feature learning means for condition monitoring based on convolutional neural networks
Sensors 2021, 21, 4394. https://doi.org/10.3390/s21134394 https://www.mdpi.com/journal/sensors
