11450


FACTA UNIVERSITATIS  
Series: Mechanical Engineering  
https://doi.org/10.22190/FUME230425027Z 

© 2020 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND 

Original scientific paper 

CONDITION MONITORING OF ROLLER BEARING USING 

ENHANCED DEMPSTER-SHAFER EVIDENCE THEORY 

Xingtong Zhu, Minchuan Huang, Ke Chen 

School of computer science, Guangdong University of Petrochemical Technology, 

Maoming, China 

Abstract. According to the generalized Jaccard coefficient and false degree, an 

improved approach is proposed by incorporating Dempster-Shafer proofs for 

determining the level of confidence in the evidence. It also determines the weight of proof 

in terms of trust and falsity. Then, the base probability of the original evidence is 

weighted and averaged, followed by the adoption of the combined Dempster's 

compositional rule. It is evident that the above combination can be applied in condition 

monitoring of bearings up to rupture. Firstly, the supporting vibration signal is 

decomposed by applying the empirical mode decomposition, empirical wavelet 

transformation and variational mode decomposition approaches. All the vectors of the 

fault characteristic are extracted by combining the sample entropy. Then, the fault 

probability is obtained by performing preliminary diagnosis using the relevance vector 

machine, where the obtained preliminary diagnostic result is considered as the primary 

probability of the Dempster-Shafer evidence theory. Finally, it is revealed that an 

accurate diagnosis could be achieved by performing fusion using the enhanced evidence 

combination method. Specifically, the accuracies of the initial condition monitoring 

based on the EMD, EWT and VMD sample entropies and RVM were found to be 97.5%, 

98.75% and 95%, respectively. The closeness and high values of these accuracies show 

that the selected methods are valid. The obtained condition monitoring results show that 

the relevance vector machine combined with the Dempster-Shafer evidence could 

enhance the efficiency. This theory has the least error and better reliability in supporting 

failure diagnosis. 

Key words: Evidence combination, Generalized Jaccard coefficient, Falsity, Bearing 

Condition monitoring, Dempster-Shafer (D-S) 

                                                           
Received: April 25, 2023 / Accepted August 11, 2023 
Corresponding author: Minchuan Huang  

School of Computer Science, Guangdong University of Petrochemical Technology, No. 139, Guandu 2nd Road, 

Maoming City, Guangdong Province: 525000, China  
E-mail: h0912259520@163.com 



2 X. ZHU, M. HUANG, K. CHEN 

1. INTRODUCTION 

A bearing is an important part of rotational components of a machine. The failure of 

the bearing affects the performance of the machine, leading to power loss, more wear and 

tear of the machine components, and even to break down of the machine. Since every 

bearing usually remains around 30% defective, the vibration signals generated from 

bearings should be monitored continuously. Timely identification and maintenance of 

bearing defects can ensure the safety of machine components and production personnel. 

The research on the diagnosis of bearing defects has practical importance to consider the 

general operations of rotating machine components and safety of operators. 

The Dempster-Shafer (D-S) evidence theory [1-3] uses both upper and lower limit 

probabilities in solving multivalued mapping problems, thus leading to be an inaccurate 

reasoning theory.  Such study is initiated from the Dempster-Shafer evidence theory [1,2]. 

It is supposed to be an effective method in handling uncertain information, and widely used 

in information merging, decision-making and many other areas [4-7]. 

The performance can be enhanced by combining evidences using an average rule. 

Average the base probability distribution value and use the Dempster combination rules 

for the N-1 combination [8]. The credibility of evidences is first obtained by measuring the 

closeness error between them through the Jousselme distance function as per the Murphy's 

method [9]. Then, the weightage of evidence is determined by combining the average 

credibility as per the Dempster's combination rule [9]. 

In this article, a combined method is presented for proving conflict by using the 

generalized Jaccard coefficient [10-12]. The objective of the present work is to replace the 

Jousselme distance with the generalized Jaccard coefficient [11]. Both the generalized 

Jaccard coefficient and Jousselme distance are measures of the distance between two sets 

of evidence in the Dempster-Shafer theory. However, the generalized Jaccard coefficient 

is considered superior to the Jousselme distance in several ways: (a) Handles the empty 

set: The Jousselme distance cannot handle the empty set, which means it is not well-defined 

when one of the sets is empty. On the other hand, the generalized Jaccard coefficient can 

handle the empty set and provide a meaningful result in such cases. (b) Reflects 

uncertainty: The Jousselme distance does not reflect the uncertainty associated with 

evidence. In contrast, the generalized Jaccard coefficient can reflect the degree of 

uncertainty in the evidence, which is important in applications where the evidence may be 

ambiguous. (c) Considers negative evidence: The Jousselme distance does not consider 

negative evidence, which may be useful in some applications. The generalized Jaccard 

coefficient can handle both positive and negative evidence, allowing for a more 

comprehensive analysis of the evidence. (d) Consistent with probability theory: The 

generalized Jaccard coefficient is consistent with probability theory, which means it 

satisfies the axioms of probability. This property is important for applications where a 

probability-like interpretation of evidence is desired. For these reasons, the generalized 

Jaccard coefficient is considered superior to the Jousselme distance in several ways, 

making it a more versatile and reliable measure of distance between sets of evidence in the 

Dempster-Shafer theory. Song et al. [13] proposed a method of combining evidences based 

on their levels of confidence with falsity. 

An accelerated single-value thresholding (ASVT) method was considered in [14] for 

estimating missing values in large scale problems, which was more efficient than a single-

value thresholding (SVT) method. A three-step process was proposed in [15] by combining 



 Condition Monitoring of Roller Bearing using Enhanced Dempster-Shafer Evidence Theory 3 

the weighted conflicting evidence with the credibility and uncertainty data of evidence 

considered according to the Hellinger distance along with the belief entropy. An extended 

version of the evidence theory was proposed in [16], with the application to monitor the 

position of gas pressure in a gas pressure regulation station, for dynamic fusion of time 

domain information by combining the time decay factor with the relative conflict factor. 

An innovative evidential correlation coefficient (ECC) was proposed in [17] for 

decision making in measuring the conflict distance of a belief function by satisfying various 

criteria, such as symmetry, non-negativity, insensitivity, boundedness, and extreme 

consistencies. A combined method of conflict proving, called as the automatic K-means 

encoder (AE-K means), was proposed in [18], where a composite credibility defined based 

on an automatic encoder and similarity of evidence integrates both direct and indirect data 

about the evidence for efficiently obtaining detail data by reducing the involvement of other 

factors. The D-S evidence theory is used in condition monitoring as an uncertainty 

algorithm because of its certain benefits. 

The back propagation (BP) neural network, widely used as the primary method to 

enhance the vector machine and radial basis function, was used in [19] for preliminary 

diagnosis, where three preliminary diagnosis results were combined using an improved D-

S evidence theory. A new weighted evidence fusion method was proposed in [20,21] for 

monitoring bearing conditions.  

In [22], features from vibration signals were extracted by using a multi-dimensional 

feature extraction method that combines entropy feature, Holder coefficient feature and 

improved generalized box dimension feature; followed by the calculation of the basic belief 

distribution using the gray correlation algorithm; and finally patterns of defects were 

recognized by merging the basic belief distribution using the Yager method. 

In [23], an enhanced fusion method of the Dempster-Shafer theory of proof was 

presented for adjusting sensor weights, as per the diagnostic accuracy of different sensor 

data, by using the kappa coefficient as the closeness error between evidences. The reader 

is also referred to a recent review by Hakim et al. [24]. 

It is observed that there is no universally recognized method for combining evidences. 

Hence, researchers focus on improving such methods based on the D-S evidence theory. 

Since the weight distribution of the existing evidence is not reasonable enough, more 

importance should be given to effective methods for combining conflicting evidences. In 

this article, a method of combining evidences is proposed based on the generalized Jaccard 

coefficient and false degree, and its effectiveness is demonstrated by diagnosing failure of 

bearings. 

The aim of the study is to propose an improved approach for condition monitoring of 

bearings up to rupture using the Dempster-Shafer evidence theory and to demonstrate its 

effectiveness in achieving accurate diagnosis. This paper is written to present a novel 

approach for condition monitoring of bearings that incorporates the Dempster-Shafer 

evidence theory and to provide evidence of its efficiency in supporting failure diagnosis. 

The difference of the present submitted paper from the previous works is the incorporation 

of the Dempster-Shafer evidence theory for determining the level of confidence in the 

evidence and weighting the base probability of the original evidence, followed by the 

adoption of the combined Dempster's compositional rule. This approach is shown to 

enhance the efficiency, have the least error, and better reliability in supporting failure 

diagnosis. 



4 X. ZHU, M. HUANG, K. CHEN 

2. IMPROVING DEMPSTER-SHAFER (D-S) EVIDENCE THEORY 

The Bayesian method, generalized by using the D-S evidence theory, is primarily a 

mathematical method to cope up with uncertainty by using the Bayesian conditional 

probability theory. The method needs to know the likelihood probability of a problem in 

advance. In this case, the D-S evidence theory is more adoptable in handling uncertain data, 

which can express the uncertainty of a problem without knowing its likelihood probability 

a priori. In the D-S identification framework, a set of incompatible proposals provide many 

possible answers, among which one might be the right answer. The concept of "basic 

probability distribution (BPA)" refers to a subset of the recognition framework and the 

degree of confidence for each proposal. If the event criteria are met, then the value of the 

impossible event of the corresponding base probability distribution becomes 0. m(ϕ)=0 

indicates 0 value of the probability distribution for the impossible event. It is described in 

the confidence function as the total probability corresponding to each subassembly in 𝐴. 
The likelihood function, which represents the uncertainty measure, sums up all the 

subassemblies BPA that intersect A and the expression of non-repudiation confidence in 

A. In the Trust space [Bel(A), pl(A)], Bel(A) represents the lower limit function, and pl(A) 

represents the upper limit function. 

 ∑ 𝑚(𝐴) = 1𝐴⊆Θ  (1) 

 Bel: 2Θ → [0,1] (2) 

 Bel(𝐴) = ∑ 𝑚(𝐵)  (∀𝐴 ⊂ 𝑃)𝐵⊂𝐴  (3) 

 pl(𝐴) = 1 − Bel(�̅�) = ∑ 𝑚(𝐵) − ∑ 𝑚(𝐵) = ∑ 𝑚(𝐵)𝐵∩𝐴≠𝜙𝐵⊂�̅�𝐵⊂𝑃  (4) 

2.1 Dempster Composition Rules 

For ∀ A ⊆ Θ, the rule given by the Dempster combination of two different mass 
functions 𝑚1 and 𝑚2 is defined on Θ: K as the conflict coefficient. If there are 𝑛 finite 
functions for masses m1, m2,…Mn defined on Θ, then their Dempster combination rules can 
be expressed as follows: 

 𝑚1⨁𝑚2(𝐴) =
1

𝐾
∑ 𝑚1𝐵∩𝐶=𝐴 (𝐵) ∙ 𝑚2(𝐶) (5) 

 (𝑚1⨁𝑚2 ⊕∙∙∙ ⨁𝑚𝑛)(𝐴) =
1

𝐾
∑ 𝑚1(𝐴1) ∙ 𝑚2(𝐴2) ∙∙∙ 𝑚𝑛(𝐴𝑛)𝐴1∩𝐴2∩∙∙∙∩𝐴𝑛=𝐴  (6) 

𝐾 = ∑ 𝑚1(𝐴1) ∙ 𝑚2(𝐴2)𝐴1∩∙∙∙∩𝐴2≠𝜙 ∙∙∙ 𝑚𝑛(𝐴𝑛) = 1 − ∑ 𝑚1(𝐴1) ∙ 𝑚2(𝐴2)𝐴1∩∙∙∙∩𝐴2=𝜙 ∙∙∙ 𝑚𝑛(𝐴𝑛) (7) 

2.2 Evidence Combining Method Based on Generalized Jaccard Factor and False 

Degree 

The generalized Jaccard coefficient, also referred to as the Tanimoto coefficient, is a 

method of measuring similarity, e.g., the similarities of evidences. In this paper, a method 

is proposed for combining evidences based on the generalized Jaccard coefficient and false 

degree. The important points of this method are described below. 

 Input the base probabilities of 𝑛 evidences. 
 Calculate the generalized Jaccard coefficient of proof using the following formula: 



 Condition Monitoring of Roller Bearing using Enhanced Dempster-Shafer Evidence Theory 5 

 sim(𝑚1, 𝑚2) =
∑ 𝑚1

𝑛
𝑖=1 (𝐴𝑖)∙𝑚2(𝐴𝑖)

∑ 𝑚1(𝐴𝑖)
2𝑛

𝑖=1 +∑ 𝑚2(𝐴𝑖)
2−∑ 𝑚1(𝐴1)∙𝑚2(𝐴𝑖)

𝑛
𝑖=1

𝑛
𝑖=1

 (8) 

 Calculate the trust between evidences as follows: 

 crd𝑖 =
sup (𝑚𝑖)

∑ sup (𝑚𝑖)
𝑛
𝑖=1

 ;    where, sup(𝑚𝑖 ) = ∑ sim(𝑚𝑖 , 𝑚𝑗 )
𝑛
𝑗=1,𝑗≠𝑖  (9) 

 Calculate the falsehood between evidences using the falsification formula of 
evidence. The false degree of evidence is a measure of evidence conflict as proposed 

by Schubert [25]. It is determined according to the conflict coefficient of evidence 

as expressed by Eq. (10), where K0 is the global conflict system and Ki is the conflict 

coefficient between the remaining evidences except mi. The false degree vector of 

evidence has n elements, m1,m2,m3,…,mn . 

 𝐹(𝑚𝑖 ) =
𝐾0−𝐾𝑖

1−𝐾𝑖
;       where, 𝐹 = [𝐹(𝑚1), 𝐹(𝑚2),∙∙∙ 𝐹(𝑚𝑛 )]

𝑇  (10) 

 The degree of trust and falsehood of evidence are obtained by using the following 
weight coefficient: 

 𝑤𝑖 = crd𝑖 + 1 − 𝐹(𝑚𝑖 ) (11) 

  The weight coefficient is normalized as follows: 

 𝑤𝑖̅̅ ̅ =
𝑤𝑖

∑ 𝑤𝑖
𝑛
𝑖=1

  (12) 

 After weighting the base probabilities of all the evidences using the normalized 
weight coefficient, calculate the average value as follows: 

 MAE = ∑ (crd𝑖 × 𝑚𝑖)
𝑛
𝑖=1  (13) 

 Combine weighted average BPA for (𝑛-1) times using the Dempster synthesis rule. 

3. NUMERICAL EXAMPLE 

In this paper, we take an example from the efficient combination approach of 

conflicting evidences for generating data, and set the identification framework as 

Θ={f1,f2,f3}. In this case, five evidences are involved in the probability distribution, which 
are given below.  

E1: 𝑚1(𝑓1) = 0.50, 𝑚1(𝑓2) = 0.2, 𝑚1(𝑓3) = 0.30 

E2: 𝑚2(𝑓1) = 0.00, 𝑚2(𝑓2) = 0.9, 𝑚2(𝑓3) = 0.10 

E3: 𝑚3(𝑓1) = 0.55, 𝑚3(𝑓2) = 0.1, 𝑚3(𝑓3) = 0.35 

E4: 𝑚4(𝑓1) = 0.55, 𝑚4(𝑓2) = 0.1, 𝑚4(𝑓3) = 0.35 

E5: 𝑚5(𝑓1) = 0.55, 𝑚5(𝑓2) = 0.1, 𝑚5(𝑓3) = 0.35 

Table 1 shows the comparison of the methods used to synthesize evidences. 



6 X. ZHU, M. HUANG, K. CHEN 

Table 1 Comparison of methods used in evidence synthesis. 

Item 𝑚(𝑓1) 𝑚(𝑓2) 𝑚(𝑓3) 
Bisht and Kumar [2] 0.0000 0.1228 0.8772 

Deng [10] 0.7958 0.0932 0.1110 

Song [13] 0.9636 0.0109 0.0255 

Present methodology 0.9703 0.0048 0.0249 

4. BEARING CONDITION MONITORING 

The proposed D-S evidence theory method for condition monitoring of bearings 

includes two main steps: construction of evidence body and combining evidences.  

4.1 Condition Monitoring Model Based on Enhanced D-S Evidence Theory 

Data of the vibration signals of rolling contact bearings is used for monitoring bearing 

conditions. Direct extraction of effective information affects the accuracy of condition 

monitoring. In order to avoid this problem, inaccurate signals are filtered out by using a 

single-signal decomposition method. In this paper, the empirical mode decomposition 

(EMD), empirical wavelet transformation (EWT) and variable mode decomposition 

(VMD) approaches are used for this purpose. The characteristic information of rolling 

contact bearings is extracted from their signals generated due to vibration by combining 

the sample entropies using the relevance vector machine (RVM). This information is used 

for enhancing the preliminary diagnosis by improving the evidence theory. Figure 1 depicts 

the structure of the diagnosis model. Specifically, calculations of sample entropy are 

performed for each of the three methods, followed by mRVM fault diagnosis. Thereafter, 

fusion diagnosis was carried out on the basis of the improved D-S evidence theory. Finally, 

the final diagnosis results are extracted based on the decision rules. 

 

Fig. 1 Methodology for condition monitoring of bearings by using enhanced D-S 

evidence theory 

Collect the vibration signal of rolling bearing

mRVM fault diagnosis

EMD

Calculate sample entropy

Fusion Diagnosis Based on Improved D-S Evidence Theory

Output final diagnosis results according to decision rules

Calculate sample entropy Calculate sample entropy

mRVM fault diagnosis mRVM fault diagnosis

EWT VMD



 Condition Monitoring of Roller Bearing using Enhanced Dempster-Shafer Evidence Theory 7 

4.2 Diagnosis of Condition Monitoring Mode 

The condition monitoring mode is diagnosed in the following steps:  

 Collection of vibration signal of rolling contact bearing. The vibration signals of 
the inner race, outer race and rolling element in both fault and normal states are 

collected by an acceleration sensor. 

 Feature extraction. The wavelet packet, empirical mode decomposition, and 
VMD approaches are used for calculating the sample entropy of signal 

components by suppressing their vibration signals. 

 Probability is determined by performing preliminary diagnosis using the 
correlation vector machine. 

 The input of evidence fusion is obtained in the form of fault probability by 
performing preliminary diagnosis using RVM, and then the evidence 

combination method based on similarity and falsehood is used to fuse the 

evidence bodies, so as to obtain the fused probability and finally to complete the 

condition monitoring. 

5. EXPERIMENT AND RESULT ANALYSIS 

The data used in this work was derived from the Bearing Data Center of Case Western 

Reserve University, United States [26]. The schematic of the test bench used for collecting 

experimental data is shown in Figure 2, which is mainly composed of a 1.5KW motor, a 

decoder and a power tester. The drive-end of the motor is equipped with a bearing (model: 

SKF6205), and the fan-end is also equipped with another bearing (model: SKF6203).  

The vibration signal of the rolling contact bearing is measured using an acceleration 

sensor, which is installed at the drive-end of the motor. The measurement includes the 

vibration signals of the inner race, outer race and rolling element in both fault and normal 

states. In this experiment, 2048 sample data points were collected, including 100 samples 

of vibration signals for each bearing state.  

 

Fig. 2 Schematic of the experimental bearing test rig. 

5.1 Collection of Vibration Data of Rolling Contact Bearing 

The bearing data used in this paper is the vibration data acquired by the acceleration 

sensor positioned at the drive-end of the motor. Data is collected in different states, 

including the normal state (NC), IRF, ORF and RBF. The experimental data reveals that 

the combination of RVM and D-S evidence theory could more precisely complete the 

condition monitoring of the rolling contact bearing. Figure 3 shows the amplitude of the 

acceleration signals.  

Tenque 
Sensor/Decode 

Power Test Meter
1.5KW[2-HP]

Electric MotorElectionic 
Conroter

Bearing test rig used for the experimentData



8 X. ZHU, M. HUANG, K. CHEN 

 

Fig. 3 Experimental data of amplitude of vibration of (a) IRF (b) ORF and (c) RBF. (d) 

Vibration signal under normal condition 

5.2 Feature Extraction 

After breaking down the vibration signal by the EMD, EWT and VMD approaches, the 

sample entropy of the signal component is computed. Then, three characteristic subspaces 

are constructed as the input of the correlation vector.  

Figures 4 to 6 show the waveforms of the component signals of the faulty inner race 

decomposed by the EMD, EWT and VMD methods.  

The sample entropies corresponding to the component signals obtained by the EMD, 

EWT and VMD decomposition methods, as shown in Figures 4-6, are [0.5728, 0.5814, 

0.3126, 0.1925, 0.0633], [0.4603, 0.5997, 0.3063, 0.2776, 0.4518] and [0.5902, 0.5938, 

0.5663, 0.1034, 0.4921], respectively. 



 Condition Monitoring of Roller Bearing using Enhanced Dempster-Shafer Evidence Theory 9 

 

Fig. 4 Transformed waveforms of the original signals obtained by EMD method 

 

Fig. 5 Transformed waveforms of the original signals obtained by EWT method 



10 X. ZHU, M. HUANG, K. CHEN 

 

Fig. 6 Transformed waveforms of the original signals obtained by VMD method 

5.3 Preliminary Diagnosis Results by Vector Machine 

For the purpose of diagnosis, the output probability is obtained by using the relevance 

vector machine. Tables 2 to 4 present the preliminary condition monitoring results for few 

test samples obtained by the RVM method.  

Table 2 Results of EMD sample entropy and RVM condition monitoring  

Test 

sample 

No 

Rolling 

element 

failure 

probability 

Failure 

probability 

of inner 

ring 

Failure 

probability 

of outer 

ring 

Normal 

state 

probability 

Test 

label 

Actual 

label 

1 0.9981 0.0000 0.0013 0.0006 1 1 

3 0.3573 0.0412 0.0002 0.6012 4 1 

4 0.9906 0.0000 0.0062 0.0032 1 1 

14 0.9785 0.0000 0.0027 0.0189 1 1 

17 0.9582 0.0000 0.0000 0.0418 1 1 

19 0.9830 0.0000 0.0168 0.0001 1 1 

43 0.5485 0.0000 0.4351 0.0164 1 3 

56 0.0408 0.0001 0.9480 0.0112 3 3 

 

It can be seen that the rolling element failure probability in Tables 2 and 3 appear to be 

approximately inverse to the failure probabilities of the outer and inner rings, respectively, 



 Condition Monitoring of Roller Bearing using Enhanced Dempster-Shafer Evidence Theory 11 

while no correlation was observed in Table 4. These preliminary results are useful in 

elucidating the observations in the next sub-section and Table 5. 

Table 3 Results of EWT sample entropy and RVM condition monitoring  

Test 

sample 

No 

Rolling 

element 

failure 

probability 

Failure 

probability 

of inner ring 

Failure 

probability 

of outer ring 

Normal state 

probability 

Test 

label 

Actual 

label 

1 0.9160 0.0834 0.0006 0.0000 1 1 

3 0.7632 0.2368 0.0000 0.0000 1 1 

4 0.4653 0.5315 0.0032 0.0000 2 1 

14 0.8586 0.1176 0.0000 0.0238 1 1 

17 0.9920 0.0079 0.0000 0.0001 1 1 

19 0.9745 0.0255 0.0000 0.0001 1 1 

43 0.0000 0.0012 0.9983 0.0006 3 3 

56 0.0002 0.0036 0.9962 0.0000 3 3 

Table 4 Results of VMD sample entropy and RVM condition monitoring  

Test 

sample 

No 

Rolling 

element 

failure 

probability 

Failure 

probability 

of inner 

ring 

Failure 

probability 

of outer 

ring 

Normal state 

probability 

Test 

label 

Actual 

label 

1 0.9996 0.0003 0.0001 0.0000 1 1 

3 0.9982 0.0000 0.0018 0.0000 1 1 

4 0.9998 0.0000 0.0002 0.0000 1 1 

14 0.1517 0.0001 0.8482 0.0000 3 1 

17 0.4605 0.5260 0.0135 0.0000 2 1 

19 0.0551 0.5337 0.4112 0.0000 2 1 

43 0.0018 0.1450 0.8531 0.0000 3 3 

56 0.4336 0.1355 0.4309 0.0000 1 3 

5.4 Final Diagnosis Results by Improved Evidence Combination Method for 
Fusion 

Preliminary diagnosis is performed by RVM, where the failure probability is obtained 

as the evidence. The final diagnosis is performed by the method based on the combination 

of the generalized Jaccard coefficient and false degree, where each evidence body is fused 

to obtain the probability to be used in condition monitoring. Table 5 shows the evidence of 

this combination method, and the results of the combined evidences are shown in Tables 

2-4. 

A total of 80 test samples were considered in this experiment, 20 samples in each state. 

The accuracies of the initial condition monitoring based on the EMD, EWT and VMD 

sample entropies and RVM were found to be 97.5%, 98.75% and 95%, respectively. Finally, 

the enhanced D-S evidence combination procedure was employed for fusion to complete 

the diagnosis. 

 



12 X. ZHU, M. HUANG, K. CHEN 

Table 5 Condition monitoring results obtained by the proposed fusion method  

Test 

sample 

No 

Rolling 

element 

failure 

probability 

Failure 

probability 

of inner ring 

Failure 

probability 

of outer 

ring 

Normal state 

probability 

Test 

label 

Actual 

label 

1 1.0000 0.0000 0.0000 0.0000 1 1 

3 0.9954 0.0018 0.0000 0.0028 1 1 

4 0.9982 0.0018 0.0000 0.0000 1 1 

14 0.9993 0.0002 0.0005 0.0000 1 1 

17 0.9979 0.0021 0.0000 0.0000 1 1 

19 0.9999 0.0000 0.0000 0.0000 1 1 

43 0.0025 0.0003 0.9972 0.0000 3 3 

56 0.0018 0.0000 0.9982 0.0000 3 3 

6. CONCLUSION 

In this paper, taking rolling contact bearing as the object, bearing fault features are 

studied by different methods, and then the relevant vector machine is used to determine the 

probability. Finally, the types of faults are identified by using an improved method based 

on the D-S evidence theory for fusion, which does not figure out the fundamental 

probability distribution. The probability obtained by RVM is applied as the BPA value, 

and then the enhanced evidence combination method is applied to diagnose the bearing 

fault. Compared with a single method, the diagnosis of the proposed method was found 

more accurate and reliable. 

In conclusion, the proposed approach that incorporates Dempster-Shafer proofs for 

determining the level of confidence in evidence and determining the weight of proof in 

terms of trust and falsity has shown promising results in condition monitoring of bearings 

up to rupture. The combination of the relevance vector machine and the enhanced evidence 

combination method based on the generalized Jaccard coefficient and false degree has 

enhanced the efficiency and achieved accurate diagnosis with the least error and better 

reliability in supporting failure diagnosis. The experiment's results on 80 test samples with 

different states have shown high accuracies of the initial condition monitoring based on the 

EMD, EWT, and VMD sample entropies and RVM. Finally, the enhanced D-S evidence 

combination procedure was employed for fusion to complete the diagnosis. Overall, this 

approach provides a new perspective for condition monitoring that can improve the 

diagnosis and reliability of the system. 

Acknowledgement: This work was supported by the Guangdong Basic and Applied Basic Research 
Foundation (Grant No. 2018A030307038), Projects of PhDs’ Start-up Research of GDUPT (Grant 

No. BS-XJ2022000501), National Natural Science Foundation of China (Grant 62073090), and the 

Key research platform and project of universities in Guangdong Province (2020zdzx3038). We would 

like to thank the Guangdong University of Petrochemical Technology. Project Number: 2019rc076 

(702-519186, 702-71013303119, 702-72100003102, 702-72200010122, 702-72200010358). 



 Condition Monitoring of Roller Bearing using Enhanced Dempster-Shafer Evidence Theory 13 

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