Citation: Ye, H.; Wu, P.; Huo, Y.;
Wang, X.; He, Y.; Zhang, X.; Gao, J.
Bearing Fault Diagnosis Based on
Randomized Fisher Discriminant
Analysis. Sensors 2022, 22, 8093.
https://doi.org/10.3390/s22218093
Academic Editors: Kim Phuc Tran,
Athanasios Rakitzis and Khanh T. P.
Nguyen
Received: 8 September 2022
Accepted: 19 October 2022
Published: 22 October 2022
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Article
Bearing Fault Diagnosis Based on Randomized Fisher
Discriminant Analysis
Hejun Ye
1
, Ping Wu
1,2,
*, Yifei Huo
1
, Xuemei Wang
1
, Yuchen He
2
, Xujie Zhang
3
and Jinfeng Gao
1
1
School of Information Science and Engineering, Zhejiang Sci-Tech University, Hangzhou 310018, China
2
Key Laboratory of Intelligent Manufacturing Quality Big Data Tracing and Analysis of Zhejiang Province,
China Jiliang University, Hangzhou 310018, China
3
College of Control Science and Engineering, Zhejiang University, Hangzhou 310058, China
* Correspondence: pingwu@zstu.edu.cn
Abstract:
In this paper, a novel randomized Fisher discriminant analysis (RFDA) based bearing fault
diagnosis method is proposed. First, several representative time-domain features are extracted from
the raw vibration signals. Second, linear Fisher discriminant analysis (FDA) is extended to nonlinear
FDA named RFDA by introducing the random feature map to deal with the non-linearity issue.
Specifically, the extracted time-domain features data are mapped onto a high-dimensional space
using the random feature map function rather than kernel functions. Third, the time-domain features
are fed into the built RFDA model to extract the discriminant features for diagnosis. Moreover, a
Bayesian inference is employed to identify the class of the collected vibration signals to diagnose the
bearing status. The proposed method uses random Fourier features to approximate the kernel matrix
in the kernel Fisher discriminant analysis. Through employing randomized Fisher discriminant
analysis, the nonlinearity issue is dealt with, and the computational burden is remarkably reduced
compared to the kernel Fisher discriminant analysis (KFDA). To illustrate the superior performance of
the proposed RFDA-based bearing fault diagnosis method, comparative experiments are conducted
on two widely used datasets, the Case Western Reserve University (CWRU) bearing dataset and the
Paderborn University (PU) bearing dataset. For the CWRU dataset, the computation time of RFDA
is much shorter than KFDA, while the accuracy rate reaches the same level of KFDA. For the PU
dataset, the accuracy rate of RFDA is slightly higher than KFDA, and the computation time is only
44.14% of KFDA.
Keywords: bearing; fault diagnosis; random Fourier feature; Fisher discriminant analysis
1. Introduction
Bearings are an essential and key part that is widely used in modern rotating ma-
chinery. As a vital component, the occurrence of bearing faults will result in significant
breakdown time, increasing maintenance costs, and even jeopardizing casualties. There-
fore, it is critical to precisely and quickly diagnose the bearing status [
1
–
3
]. To explore
the bearing status, a variety of signals are collected and used, such as acoustic signals [
4
],
vibration signals [
5
], and current signals [
6
]. Among them, the vibration signals contain
abundant fault energy information, and the data acquisition of bearing vibration signals
does not require complex equipment and professionals.
Therefore, the vibration signal is popularly used to monitor the bearing status. Bear-
ing fault diagnosis techniques via vibration signals can be generally categorized into
two classes, including signal-analysis-based and data-driven methods. Regarding the
signal-analysis-based method, the raw vibration signals are firstly analyzed using signal
processing methods such as time-domain analysis [
7
,
8
], frequency-domain analysis [
9
]
and time–frequency-domain analysis [
10
]. Afterward, the bearing status is determined by
features extracted from different domains using expert knowledge.
Sensors 2022, 22, 8093. https://doi.org/10.3390/s22218093 https://www.mdpi.com/journal/sensors
