Modeling of Journal Bearings for Wear Diagnosis and Its Verification Using SVM

Recently, deterioration of infrastructure facilities has become problem. To reduce inspection costs, wear diagnosis of journal bearings in operating conditions using machine learning has been studied. However, constructing a highly accurate machine learning model requires training data, and it may be difficult to conduct numerous tests depending on the application. In this study, a mathematical model of a rotor system for wear diagnosis of journal bearings was developed, and the vibration data was obtained when the clearance changed due to wear. Then, changes in the features used for condition monitoring were examined. Furthermore, the important features for wear diagnosis were selected and SVM models were constructed to verify the mathematical model.


INTRODUCTION
Recently, the aging infrastructure facilities has become problems.These facilities include rotating machinery such as pumps.In rotating machinery, journal bearing is used to support the rotating shaft and reduce the vibration, and bearing may be worn in some rotating condition.So regular inspections on facilities are required.However, the inspections tend to involve disassembly of equipment, which incurs time and cost.To reduce such costs, wear diagnosis of journal bearing by condition monitoring is required.
Research on condition monitoring of journal bearings using machine learning has been investigated actively in recent years.Alves, Daniel, Castro, Machado, Cavalca, Gecgel, Dias, and Ekwaro-Osire (2020) built a mathematical model to simulate the failure conditions of journal bearings.A neural network algorithm was trained using the data generated by the simulation to diagnose the condition of the journal bearings.König, Sous, Chaib, and Jacobs (2021) measured the acoustic emission signals in experiment.The measured signals and a neural network were used to diagnose the wear of journal bearings.
The building of machine learning model generally requires training data.However, for some machines, it may be difficult to conduct tests many times and obtain enough number of training data because the tests take a very long time.Therefore, if reliable data can be generated using a mathematical model that represents the wear of journal bearing, it is possible to predict the approximate wear of journal bearing without collecting data by the tests, even when the design of other parts of the bearing or operating conditions are changed.These are significant advantages in reducing costs for condition monitoring and diagnosis of mechanical systems.However, to our best knowledge, evaluation of the features for the wear diagnosis of journal bearing using both experiment and simulation has not been done.In this paper, a mathematical model for wear diagnosis of a journal bearing is constructed, and the features obtained from the simulation data and the experimental data are compared and evaluated.Then, an SVM model trained with the simulation data is used to diagnose wear of the journal bearing from the experimental data.

Experimental apparatus and Methods
The experimental apparatus used in this paper is shown in Figure 1 and its schematic diagram is shown in Figure 2.  The journal bearing was set in water containing slurry with a concentration of 1000 ppm.This experimental apparatus was operated for 1600 hours at a rotational speed of 500 rpm to develop wear on the journal bearing.Then, the horizontal () and vertical () displacements of the shaft during operation were regularly measured at a sampling frequency of 1000 Hz for 30 seconds.Among the measured data, 12 measurement data up to the point before peeling occurred were used.To increase the number of data, each data was divided into three 10-second data sets for a total of 36 data sets.
The operation was stopped less frequently than the displacement measurements, and the wear of the journal bearing was measured.The wear was measured in the  and  directions at three axial locations.

Simulation assuming wear of journal bearing
A horizontal rotating shaft model with two disks is shown in Figure 3.The equation of motion for the horizontal rotating shaft model (Figure 3) is shown in Eq. ( 1).
where   is the contact force at the journal bearing,   is a random excitation force considering the effect of slurry water at the journal bearing, and   is the fluid force.  is obtained by integrating the pressure distribution in the journal bearing.This pressure distribution is derived by solving the Reynolds equation in Eq. ( 2) The oil film thickness () is defined by Eq. (3).
In this paper, wear development was expressed as an increase in clearance   .In practice, the stator bore of journal bearing is no longer a perfect circle due to wear, and the amount of wear is not uniform in the axial direction.Therefore, this model is very approximate.The clearance is varied from 1.0 to 1.6 times the design value by 0.1 increments, and time history displacement data was obtained by simulation.The range of the clearance size in the simulation corresponds to the average value of the amount of wear in the experiment, just prior to peeling.Considering that the excitation force is random, the time history displacement data was obtained five times for each clearance case.
The parameters used in the simulations are listed in Table 1.

Analysis and selection of features
From both the experimental and simulation data, the features commonly used in condition monitoring are obtained (Caesarendra, & Tjahjowidodo, 2017), (Li, Dong, & Yuan, 1999).Average and coefficient of variation (CV) of each of RMS value, kurtosis, and skewness of displacements in  and  directions, and 1~4th order discrete wavelet transforms (DWT) in each direction, a total of 20 features were obtained.
The features used in this paper are listed in Table 2.
Goto, Inoue, Hori, Yabui, Katayama, Tomimatsu and Heya (2023) used these features for fault diagnosis of journal bearing and showed their effectiveness.Then, SVM models were built using the features of the experimental and simulation data respectively and interpreted.To build each SVM model, the first 9 data, which were in the early stages of wear, were used as normal, and the last 9 data, which were after wear development, were used as abnormal training data.The rest of the data in the middle part were used as test data.
The Fisher Score (Sun, Wang, Ding, Xu, & Lin, 2021) and Wrapper method (Maldonado & Weber, 2009) were used for interpretation, and the features are arranged in order of importance for diagnosis.Some of the features, listed in order of importance for both the experiment and simulation, are shown in Table 3 3, there were no feature which were common to both the experiment and simulation.Therefore, among the features shown in Table 3, the features which show the same trend of change relative to the wear development were considered to be essentially important.As a result, the CV of the kurtosis of the  displacement was selected.
In the following, only the CV of the kurtosis of the  displacement is used to diagnose the experimental data.

SVM model training based on simulation data
The SVM model was built using the CV of the kurtosis of the  displacement obtained from the simulation data as training data.As in section 3.1, among the simulation data, the first 9 data, which were in the early stages of wear, were used as normal, and the last 9 data, which were after wear development, were used as abnormal training data.

Validation of experimental data with SVM model
Using the SVM model trained on the simulation data, wear diagnosis of the journal bearing in the experimental data was conducted.Results of the diagnosis using all features and using only the CV of the kurtosis of the  displacement are shown in Figure 4.When all the features were used, the wear condition of the journal bearing even in the early stages of wear was diagnosed as abnormal.On the other hand, when only the CV of the kurtosis of the  displacement was used, the initial stage of wear was correctly diagnosed as normal and after wear developing as abnormal.

CONCLUSION
In this paper, the important features for diagnosis were compared for experimental and simulated data.Then, the feature showing same trend in both the experimental and simulation data was chosen, and the wear diagnosis was demonstrated for the experimental data using the SVM model learned by the simulation data.The following conclusions are obtained: Among the features for diagnosis, the CV of the kurtosis of the  displacement indicated the same trend for both the experimental and simulation data.
The wear of journal bearing was not predicted by SVM model which used all features in its training.However, it was diagnosed correctly when the CV of the kurtosis of the  displacement was used.
In the future, multiple experiments will be conducted using the same experimental apparatus to verify the reproducibility of changes in the features due to the wear development.In addition, the model will be improved by considering the shape change of the journal bearing, and the effect of this on the features will be evaluated.

Figure 2 .
Figure 2. Schematic diagram of the experimental apparatus.

Figure 3 .
Figure 3. Horizontal rotating shaft model with two disks.

Figure 4 .
Figure 4. Evaluation of experimental data using SVM model and wear diagnosis of the journal bearing -Comparison of results for difference in selected features.

Table 1 .
. Parameters of the mathematical model.