A Deep-Learning-Based Fault Diagnosis Method of Industrial Bearings Using Multi-Source Information

Abstract

In recent years, the industrial motor bearing fault diagnosis method based on deep learning and multi-source information fusion has made some research progress, and research results show that the uncertainty of noise interference and signal measurement error has been improved to a certain extent. However, the multi-source heterogeneous information of industrial motor bearings not only improves the stability and fault tolerance of the bearing fault diagnosis model but also brings conflicts in information fusion. If the conflicts caused by multi-source information cannot be reasonably resolved, it will be difficult to make further judgments on the bearing faults of industrial motors. Therefore, solving the multi-source information conflict effectively while fully using the complementarity of bearing multi-source heterogeneous information is an urgent problem to be solved in developing industrial motor-bearing fault diagnosis technology. This paper proposes an industrial motor bearing fault diagnosis algorithm based on multi-local model decision conflict resolution (MLMF-CR) to fully integrate multi-source heterogeneous information and reasonably resolve multi-source information conflicts. After the initial characteristic signal selection and cleaning of the vibration and current signals of industrial motor bearings, the algorithm deeply excavates the characteristic information of the bearing signals in each fault state through the local fault diagnosis model based on the bidirectional long short-term memory network (Bi-LSTM) and forms a local diagnosis. After the decision is made, evidence theory is used for fusion. In addition, the high conflict situation that may occur in the process of decision-making fusion is also considered. To this end, the trust degree distribution is introduced to reduce information conflict. Specifically, according to the difference in the sensitivity and reliability of bearing faults under different operating environments or specific conditions, the degree of difference in faults is refined into balanced sensitivity and unbalanced sensitivity. When the fault sensitivity is balanced, the trust of different information sources is quantified by support and uncertainty. When the sensitivity is unbalanced, gray relational analysis is used to assign trust degrees to different information sources. The algorithm can effectively resolve the high degree of conflict in the decision-making fusion process while considering the complementarity of multi-source heterogeneous information. Experiments evaluate the effectiveness of the proposed method.

1. Introduction

With the fast development of industrial sensor networks and the automatic control theory, industrial automation based on machine vision is considered one of the most promising techniques to achieve industrial-parts looseness detection, product defect inspection, and other kinds of detection in modern industrial production and life [1]. Industrial motor as energy-driven equipment plays an important role in modern industry, which are expensive and mostly located at the core of large-scale production lines [2]. Once a failure occurs, it will damage the motor itself and directly affect other industrial equipment connected to it, which will cause problems in the entire industrial production process. In severe cases, it may cause safety accidents and major economic losses [3,4]. Industrial motors mainly consist of bearings, shafts, stators, rotors, and frames. Among them, industrial motor bearings, as one of the most critical components of industrial motors, play an important role in carrying the rotation of the main shaft, reducing the wear between the rotor and the stator support, and maintaining the rotation accuracy of the axis. According to statistics, the proportion of motor failures caused by damage to the bearing components is as high as 50%, much higher than the proportion of motor failures caused by other components [5]. Fault diagnosis technology for industrial motor bearings existed as early as the scale of industrial production but was limited by the level of science and technology at that time, the fault diagnosis of motor bearings mainly relied on the personal experience of maintenance personnel and the simple parameters of related instruments to make subjective decisions. It was not until the 1960s that due to the continuous development and progress of digital signal processing technology, computer technology, and pattern recognition technology, the fault diagnosis technology of industrial motor bearings was gradually improved and developed into a comprehensive system integrating a variety of modern science and technology [6,7,8,9].

Common fault diagnosis methods for industrial motor bearings can be roughly divided into fault diagnosis methods based on analytical models, fault diagnosis methods based on signal analysis [10,11,12,13,14,15], and fault diagnosis methods based on knowledge reasoning [16,17,18,19,20]. Although the bearing fault diagnosis method based on the analytical model can detect the fault in a short period of time, as the research object becomes more and more complex, the dependence of this method on the mathematical model also increases. In addition, the actual application process is often affected by several other factors such as modeling error, noise interference, and unknown input. Therefore, this type of method can no longer adapt to the complication trend of bearing fault diagnosis and is gradually being replaced by fault diagnosis methods based on signal analysis and knowledge reasoning. Although the bearing fault diagnosis method based on signal analysis can avoid the construction of complex mathematical analysis models, its diagnostic accuracy is excessively dependent on signal analysis and processing technology and manual feature selection, which increases the difficulty of feature selection and the uncertainty in the process of industrial motor bearing fault diagnosis to a certain extent. In addition, with the development of the industrial Internet, smart manufacturing information systems are faced with more uncertainties, dynamics, and complexity [21,22]. Hence, more efficient fault diagnosis methods are necessary. With the rapid development of related technologies, intelligent fault diagnosis methods have gradually replaced traditional ones. Algorithms based on knowledge reasoning have begun to emerge in the field of fault diagnosis, and the fault diagnosis technology of industrial motor bearings has also entered a new stage of development. The most representative one is the fault diagnosis method based on deep learning. This type of method does not need to extract fault features through complex signal analysis techniques. In addition, it can integrate adaptive feature extraction and intelligent fault identification in one model or system, which makes it more conducive to the practical application of industrial fault diagnosis [23,24,25,26]. In recent years, multi-source information fusion technology also plays an important role in the field of industrial motor bearing fault diagnosis. Various bearing fault diagnosis methods combined with information fusion technology have achieved relatively good results [27,28,29,30]. Multi-source information fusion technology breaks the limitations of traditional bearing fault diagnosis methods so that people no longer judge the operating status of industrial motor bearings based on a single type of sensor signal, which greatly reduces the uncertainty in fault diagnosis. Therefore, the fault diagnosis method based on deep learning and multi-source information fusion will be the future development trend of industrial motor bearing fault diagnosis technology.

Currently, most industrial motor bearing fault diagnosis methods are based on the diagnostic analysis of a single type of sensor signal, which has certain limitations. Due to the operating noise interference of the environment, the measurement error of the sensors, and other uncertain factors in the fault diagnosis process of industrial motor bearings, the bearing information collected only based on a single type of sensor may not fully reflect the operation of the bearing. In recent years, although the industrial motor bearing fault diagnosis method based on deep learning and multi-source information fusion has made some research progress and research results, the uncertainty of noise interference and signal measurement error has been improved to a certain extent, but there are still some problems need to be further studied. For instance, while improving the stability and fault tolerance of the bearing fault diagnosis model, the multi-source heterogeneous information of industrial motor bearings also brings conflicts in information fusion. If the conflicts caused by multi-source information cannot be reasonably resolved, making further judgments on industrial motor bearing failures will be difficult. Therefore, solving multi-source information conflicts while fully using the complementary of bearing multi-source heterogeneous information is one of the urgent problems to be solved in the development of industrial motor bearing fault diagnosis technology.

To fully integrate multi-source heterogeneous information and reasonably resolve multi-source information conflicts, an industrial motor bearing fault diagnosis algorithm based on multi-local model decision fusion conflict resolution (MLMF-CR) is proposed in this paper. After the initial characteristic signal selection and cleaning of the vibration and current signals of industrial motor bearings, the algorithm deeply excavates the bearing signals in the local fault diagnosis model based on Bidirectional Long Short-Term Memory Network (Bi-LSTM). The feature information of each fault state is fused with evidence theory after forming a local diagnosis decision. In addition, high-conflict situations that may occur during decision-making fusion are focused on consideration. To this end, the idea of trust distribution is introduced to reduce the degree of information conflict. Specifically, according to the differences in sensitivity and reliability of bearing faults in different operating environments or under specific conditions, the degree of difference in fault sensitivity is refined into two types: balanced sensitivity and unbalanced sensitivity. When the fault sensitivity is balanced, the trust of different information sources is quantified by support and uncertainty. When the sensitivity is unbalanced, gray relational analysis is used to assign trust degrees to different information sources. The algorithm can effectively resolve the high degree of conflict in the decision-making fusion process while considering the complementarity of multi-source heterogeneous information.

The following of this paper is organized as follows. Section 2 introduces the related work. Section 3 presents the proposed method. Section 4 describes the performance evaluation. Finally, we provide a conclusion to summarize this paper in Section 5. The abbreviations used in this paper are listed in

Table 1. The abbreviations used in this paper.

Abbreviation	Description
MLMF-CR	Multi-Local Model decision Fusion Conflict Resolution
Bi-LSTM	Bidirectional Long Short-Term Memory Network
EDM	Electrical discharge machining
F1	F1-score
ACC	Accuracy
P	Precision Recall
BHD	Balanced Homodyne Detection
TBIDF	Two-stage Bayesian inference decision fusion
FDB-IDS	Fault diagnosis algorithm based on improved D-S
S-LSTM	Fault diagnosis algorithm based on long-short term memory
	network on tree structures
DSNCR	D-S theory improved Yager D-S combination rule
ECACE	Improved Deng Yong conflict evidence combination method

.

2. Bearing Fault Diagnosis Method Based on Knowledge Reasoning

This section reviews the related work on the bearing fault diagnosis method based on knowledge reasoning. Currently, the bearing fault diagnosis method based on knowledge reasoning mainly includes the bearing fault diagnosis methods based on an expert system, the bearing fault diagnosis methods based on a support vector machine, and the bearing fault diagnosis methods based on deep learning.

2.1. The Fault Diagnosis Method Based on an Expert System

The fault diagnosis method based on an expert system, as the earliest intelligent diagnosis technology applied in the field of industrial motor bearing fault diagnosis, has the advantages of simple operation and short diagnosis time and also shows good logical reasoning in the process of partial bearing fault diagnosis and interpretation ability, but the expert system also has the limitation that it does not have the ability of autonomous learning. In particular, there are often problems of infinite expansion of rules in the knowledge base and compatibility problems between rules when faced with changing and complex operating conditions of industrial motor bearings.

2.2. The Fault Diagnosis Method Based on Support Vector

The identification performance of the industrial motor bearing fault diagnosis algorithm based on support vector machines depends to a certain extent on the setting of penalty coefficient and kernel function parameters. Still, there is no unified theory or standard for selecting support vector machine parameters. Currently, the core parameters of support vector machines are often determined by expert experience or cross-validation methods, which makes it difficult to obtain optimal parameter settings in the case of insufficient experience.

2.3. The Fault Diagnosis Method Based on Deep Learning

With the rise of machine learning, deep learning based on neural networks has also achieved rapid development and remarkable results in related fields such as fault diagnosis. Since the deep learning-based industrial motor bearing fault diagnosis method can adaptively extract the deep-level features of the bearing signal and has obvious advantages in nonlinear computing capabilities, optimization capabilities, maintaining the integrity of signal features, and mining the correlation between features, etc.; therefore, it has attracted extensive attention. How to fully integrate multi-source data information and use the intersectionality and complementary of multi-source data information to maximize the effectiveness of data is the most basic problem in data analysis and application. It is against this background that multi-source information fusion technology emerges and develops. In practical applications, the data information acquired by a single or single type of sensor often has certain ambiguity. The emergence of multi-source information fusion technology can effectively improve this situation. Multi-source information fusion technology combines the data collected by multiple sensors at different levels to obtain more abundant and complete data. The complex system structure and operating environment of industrial motor bearings make it inevitable that many uncertain factors will appear in the fault diagnosis process. Although with the development of deep learning and neural networks, fault diagnosis algorithms based on knowledge reasoning have reduced the uncertainty in the bearing diagnosis process to a certain extent, the problem of “knowledge acquisition bottleneck” still restricts the use of related fault diagnosis algorithms. Therefore, it is necessary to combine multi-source information fusion technology with bearing fault diagnosis technology and fuse the characteristic information of different types of sensors to reflect the real-time operating status of industrial motor bearings accurately.

3. Fault Diagnosis of Industrial Motor Bearings Based on Multi-Local Model Decision Conflict Resolution

In the actual industrial motor bearing fault diagnosis process, there are uncertain factors such as noise interference in the operating environment and sensor measurement error, so the industrial motor bearing information collected only based on a single type of sensor may not fully reflect the true state of the bearing which seriously affects the reliability and accuracy of diagnosis. Only by comprehensively utilizing the multi-source heterogeneous information of industrial motor bearings can the actual faults of the bearings be diagnosed more accurately. However, in some cases, due to the multi-source of bearing heterogeneous data, conflicts will occur in the process of information fusion when making full use of the complementarity of bearing multi-source heterogeneous information.

Based on the above reasons, this paper proposes MLMF-CR algorithm. The algorithm makes full use of the multi-source heterogeneous information of industrial motor bearings and constructs a multi-local fault diagnosis model based on Bi-LSTM to improve the accuracy of fault identification and training efficiency, which is helpful for practical industrial applications. In addition, since the D-S evidence theory cannot effectively integrate highly conflicting evidence, this paper proposes a decision-making conflict resolution strategy based on the sensitive difference of faults according to the sensitivity and reliability differences of different information sources to effectively resolve the conflicts in the process of decision-making fusion, which can improve the rationality and credibility of multi-local model decision fusion. In the following of this section, we first introduce the construction of multi-local fault diagnosis model based on Bi-LSTM. Then, we present the proposed decision conflict resolution method based on sensitive differences of multi-model fault.

3.1. Construction of Multi-Local Fault Diagnosis Model Based on Bi-LSTM

The structure of the multi-local fault diagnosis model based on Bi-LSTM proposed in this paper is shown in Figure 1. The multi-local fault diagnosis model based on Bi-LSTM firstly uses the noise reduction encoder to clean the vibration signal and current signal of the industrial motor bearing, respectively, to obtain the vibration reconstruction signal and the current reconstruction signal. Afterward, the reconstructed vibration signal and the reconstructed current signal are input into the local fault diagnosis model based on Bi-LSTM and the attention mechanism, and the characteristic information of the reconstructed signal in each fault state is deeply mined to form a local diagnosis decision. Finally, the local diagnostic decisions are fused using the D-S evidence theory to obtain the final diagnostic results.

3.1.1. Selection of Operating Characteristic Signals of Industrial Motor Bearings

When the industrial motor is running normally, the raceway of the inner ring of the bearing rotates around the main shaft, and the raceway of the outer ring of the bearing is stationary. The bearing retainer guides the rolling elements between the inner and outer raceway of the bearing and keeps them within the bearing to minimize wear and heat generation. When industrial motor bearings fail, it is usually accompanied by certain abnormal friction and vibration. Therefore, the vibration signals of industrial motor bearings often contain a large amount of fault information, and the analysis of bearing vibration signals is also one of the most widely used technical means at present. However, the vibration signal, as the external sensor signal of the industrial motor bearing, is easily affected by the resonance frequency of loose screws and different parts of the industrial motor, which is very likely to lead to wrong fault diagnosis results. When the fault happens on the industrial motor bearing, the motor air gap magnetic flux density distribution waveform will also be distorted. The distortion of the magnetic field in the motor will directly change the current at the outlet terminal, which will be effectively reflected in the current signal. In addition, the current signal is a built-in signal, which has the characteristics of convenient detection and strong anti-interference ability and can effectively supplement the failure or abnormal situation of the external signal of the bearing. Therefore, this paper captures more comprehensive bearing status information through the external vibration signal and built-in current signal of industrial motor bearings to achieve high-precision fault diagnosis. In addition, these two kinds of bearing signals have different statistical characteristics and physical properties, which can reflect the information of different directions and different physical fields of industrial motor bearings simultaneously. In this paper, the original vibration signal $V=(v_1,v_2,\dots ,v_t)$ and the original current signal $C=(c_1,c_2,\dots ,c_t)$ are collected respectively through the bearing vibration sensor and the current sensor, and input to the corresponding noise self-encoder to perform preliminary feature signal cleaning.

3.1.2. Bearing Timing Data Cleaning Based on Denoising Autoencoder

The data directly collected from the sensors of industrial motor bearings is extremely nonlinear, and the noise pollution brought by the operating environment to the bearing sample data makes it difficult to dig out the deep relationship in the data information during the fault diagnosis process. In response to the above problems, this section introduces the noise reduction autoencoder to perform preliminary cleaning on the bearing current and vibration signals of industrial motors. The denoising autoencoder first performs a certain degree of noise processing on the original data and then inputs the noised data into the encoder and decoder. The encoder eliminates the influence of noise according to the statistical characteristics of the data, while the decoder restores the detailed information and finally generates the reconstructed data. The specific structure of the noise reduction autoencoder is shown in Figure 2. Compared with traditional denoising methods, denoising autoencoders have more powerful functions of data representation, removing noise, and preventing overfitting. The most important thing is that the noise reduction self-encoder does not destroy the timing of the original industrial motor bearing data while eliminating noise. Therefore, the local diagnosis model based on Bi-LSTM and the attention mechanism can maximize the deep-level relationship of time series in the data information, effectively improving the generality and robustness of the model.

In the denoising autoencoder network, Gaussian noise processing is first performed on the original current data set C and vibration data set V to reconstruct the bearing sample data disturbed by noise. and obtain the input layer data $C_s$ and $V_s$ of the noise reduction autoencoder, which can be expressed as follows:

$$C_s=C+\alpha ,\alpha \in (0,{\delta }^2).$$

(1)

$$C_s|C\sim N(C,{\delta }^2,I).$$

(2)

$$V_s=V+\beta ,\beta \in (0,{\delta }^2).$$

(3)

$$V_s|V\sim N(V,{\delta }^2,I).$$

(4)

Afterward, the input layer data $C_s$ and $V_s$ are input into the autoencoder, and after being processed by the encoder $f_D$, the characteristic expressions $h_c$ and $h_v$ are obtained as:

$$h_c=f_D\left(C_s\right)=s(W_D·C_s+b),$$

(5)

$$h_v=f_D\left(V_s\right)=s(W_D·V_s+b),$$

(6)

where s is the encoder activation function, $W_D$ is the weight matrix, and b is the bias. Finally, the decoder g maps the feature expressions $h_c$ and $h_v$ to the output layer to obtain the reconstructed data $C_j$ and $V_j$ without noise, the expressions are as follows:

$$C_j=g\left(h_c\right)=o(Z·h_c+d).$$

(7)

$$V_j=g\left(h_v\right)=o(Z·h_v+d).$$

(8)

where o is the decoder activation function, Z is the weight matrix, and d is the bias.

3.1.3. Local Fault Diagnosis Model Based on Bi-LSTM

The fault diagnosis model based on Bi-LSTM is mainly composed of a feature extraction part, a feature optimization part, and a classification recognition part. The specific structure is shown in Figure 3. Among them, the feature extraction part includes a two-layer Bi-LSTM network, the feature optimization part consists of an attention mechanism layer, and the classification recognition part includes a fully connected layer and a classification layer.

The vibration and current data of industrial motor bearings studied in this paper are all one-dimensional time series. The collected data changes along the time axis, with obvious time series and periodic characteristics. The long-short-term memory network (LSTM) is stronger than the general neural network structure in acquiring and storing information and is especially suitable for memorizing and processing vibration and current data of industrial motor bearings. This is because the LSTM introduces the two concepts, i.e., the memory unit and candidate state, and the path of information transmission can be controlled through the gating mechanism, thereby realizing effective control of the information flow in the network and finally retaining task information as much as possible and filter redundant information. The specific structure of the LSTM memory unit is shown in Figure 4.

The information processing flow of the long short-term memory network is to first use the external state $h_{t-1}$ at the previous moment and the input $x_t$ at the current moment to calculate the input gate $i_t$, the forgetting gate $f_t$, the output gate $l_t$ and the candidate state $C_t^{\prime }$, as shown in the Equations (9)–(12).

$$i_t=\varphi [{\beta }_i·(h_{t-1},x_t)+{\psi }_i].$$

(9)

$$f_t=\varphi [{\beta }_f·(h_{t-1},x_t)+{\psi }_f].$$

(10)

$$l_t=\varphi [{\beta }_l·(h_{t-1},x_t)+{\psi }_l].$$

(11)

$$C_t^{{}^{\prime }}=tanh[{\beta }_c·(h_{t-1},x_t)+{\psi }_c].$$

(12)

where the $\varphi$ is activation function, and ${\beta }_i$, ${\beta }_f$, ${\beta }_l$, ${\beta }_c$ represent the weighting matrix of the input gate, forget gate, output gate, and memory unit, respectively. After that, the information to be forgotten is determined by the forget gate and the internal state at the previous moment, and new candidate value information is generated by the input gate and the candidate state. The two work together to update the internal memory unit, which can be expressed as follows.

$$C_t=f_t{C}_{t-1}+i_t{C}_t^{\prime }.$$

(13)

The output of the LSTM network is determined by the output gate and the internal state. The output gate filters the information of the internal state and then passes it to the external state through an activation function, which can be expressed as follows:

$$h_t=l_{t}tanh\left(C_t\right).$$

(14)

The bidirectional long short-term memory network (Bi-LSTM) is developed based on the LSTM network. The Bi-LSTM network is composed of two independent LSTM networks. The data information enters different LSTM networks through the forward channel, and the reverse channel, respectively, and then the two LSTM networks output the extracted forward and reverse features together. Since the Bi-LSTM network has a special structure and makes up for the time-reversal feature part ignored by the traditional unidirectional LSTM network, it can more comprehensively obtain the time-series characteristics of relevant information data. Compared with other deep neural networks, the Bi-LSTM network has more obvious advantages in processing time series data and is currently one of the most suitable ways to process time series data of industrial motor bearings. In addition, the Bi-LSTM network has the ability of adaptive feature extraction and the ability to process high-dimensional nonlinear data so that it can directly use the time-domain vibration data and time-domain current data to make the end-to-end intelligent diagnosis of bearing operating status. Therefore, we use the Bi-LSTM network to perform adaptive feature extraction on the bearing time-domain vibration data and current data. In the proposed method, after preliminary cleaning of the bearing time-domain vibration data and current data through the noise reduction autoencoder, the obtained reconstructed current sensor data and reconstructed vibration sensor data are input into the Bi-LSTM network in parallel for forward and reverse bidirectional operations, deeply mine the feature information of the signal in each fault state and deepen the level of time series feature extraction. The hidden layer features obtained by Bi-LSTM layer conversion are:

$$D=(d_1,d_2,d_3,\dots ,d_n).$$

(15)

Due to the long-term operation of industrial motor bearings in a complex environment and variable working conditions, the original monitoring data characteristics of the bearings in different periods have obvious time-varying differences, which seriously affects the feature extraction efficiency of motor bearing signals using the Bi-LSTM network for industrial applications. To improve the problem that the Bi-LSTM network is susceptible to insensitive features and maximize the use of the extracted relevant features, we introduce an attention mechanism based on the Bi-LSTM network. Features are screened and optimized to highlight the contribution and importance of key features to the results of fault identification and classification by using it. In this way, more robust deep features can be obtained, and the training efficiency of the neural network can be improved to a certain extent, laying a good foundation for realizing high precision bearing fault diagnosis. The specific construction process of the attention mechanism for adaptive dynamic feature weighted fusion can be expressed as follows:

$$R=F_A(W_s{d}_i+e).$$

(16)

$${\lambda }_i=\frac{exp\left(R_i\right)}{\sum exp\left(R_k\right)}.$$

(17)

$$m=\sum {\lambda }_i{d}_i.$$

(18)

where R is the attention scoring function, ${\lambda }_i$ represents the attention weight coefficient, $F_A$ represents the activation function, m is the feature expression obtained after weighted fusion, $d_i$ represents the hidden layer state corresponding to the input sequence, e represents the bias, and $W_s$ represents the variable weight matrix. Then, the fully connected layer accepts the feature vector m output by the attention mechanism layer. Its forward propagation formula is as follows:

$$T=p(Wm+k).$$

(19)

where T is the output of the fully connected layer, p is the activation function of the fully connected layer, and m is the output of the attention mechanism layer. Finally, as shown in the equation below, the fully connected layer realizes the feature space transformation through weighted calculation and then inputs the classification layer to realize the output U of the predicted target category.

$$U=WT+k.$$

(20)

3.1.4. Multi-Local Model Decision Fusion under Conflict-Free Conditions

Due to various objective or subjective reasons, the local diagnosis results formed by the multi-part model may be inconsistent, making it difficult to make a further comprehensive diagnosis of the fault conditions of industrial motor bearings. Hence, it is necessary to introduce decision-level information fusion technology that is used as a support to integrate the diagnosis results of multiple local diagnosis models to obtain more comprehensive and accurate fusion diagnosis results. The emergence of decision-level information fusion technology has greatly improved the uncertainty situation in industrial motor bearing fault diagnosis. Bayesian reasoning and evidence theory are typical decision fusion algorithms. Bayesian reasoning is an earlier method used to deal with the uncertainty mentioned above problems, but because the theory itself obeys the principle of additivity, the theory cannot properly deal with the uncertainty problems caused by “unknown situations”. D-S evidence theory is developed based on Bayesian theory, further improves the description of probability point estimation, redefines the representation method of uncertain information, and specifically uses the form of “confidence interval estimation” to describe uncertain information, making the reasoning mechanism more concise, the reasoning process more rigorous, and the uncertainty measurement more flexible. For this reason, we apply the classic D-S evidence theory in multi-source information fusion technology to the fault diagnosis of industrial motor bearings. Specifically, we use the classic D-S evidence theory to fuse two local diagnosis results and take the fusion result as the final fault diagnosis conclusion. The basic process of applying the classic D-S evidence theory for decision fusion is mainly divided into the following steps:

(1) Construct the identification framework and evidence of the global fusion system for the local diagnosis stage: According to all fault types of industrial motor bearings, an identification framework for decision fusion fault diagnosis is constructed $\theta =\{A_1,A_2,A_3,\dots ,A_n\}$, where $A_n$ represents the n-th bearing fault type. Afterward, according to the output of the two local diagnostic models based on Bi-LSTM, the evidence based on the recognition framework is constructed as $\theta =\{E_1,E_2\}$ to determine the corresponding elements of different evidence.

(2) Determine the basic probability assignment of each evidence and the reliability interval under the action of a single evidence: In this paper, the basic probability assignment $\{m_1\left(A_1\right),m_1\left(A_2\right),m_1\left(A_3\right),\dots ,m_1\left(A_n\right)\}$ and $\{m_2\left(A_1\right),m_2\left(A_2\right),m_2\left(A_3\right),\dots ,m_2\left(A_n\right)\}$ is constructed while the reliability interval under the action of every single evidence $\{[Be{l}_{11},P{l}_{11}],[Be{l}_{12},P{l}_{12}],[Be{l}_{13},P{l}_{13}],\dots ,[Be{l}_{1n},P{l}_{1n}]\}$ and $\{[Be{l}_{21},P{l}_{21}],[Be{l}_{22},P{l}_{22}],$$[Be{l}_{23},P{l}_{23}],\dots ,[Be{l}_{2n},P{l}_{2n}]\}$ is calculated mainly based on the diagnosis results of the multi-local diagnosis model.

(3) Determining the basic probability assignment and reliability interval under the joint action of multiple evidence. The composition rule of classical D-S evidence theory can be expressed as:

$$m\left(A_i\right)=m_1\left(A_i\right)\oplus m_2\left(A_i\right)=\frac{{\sum }_{A_x\bigcap A_y=A_i}{m}_1\left(A_x\right)m_2\left(A_y\right)}{K},$$

(21)

where ⊕ is an orthogonal sum operator, and K is called a normalization constant or conflict coefficient, which indicates the degree of conflict between pieces of evidence. The normalization constant increases with the degree of conflict. Carry out fusion reasoning according to the above D-S evidence theory combination rules, and calculate the basic probability function $\{m\left(A_1\right),m\left(A_2\right),m\left(A_3\right),\dots ,m\left(A_n\right)\}$ under the joint action of two evidence and reliability interval $[Bel,Pl]$.

(4) Get the final diagnosis result according to the corresponding decision rules: After calculating the reliability interval under the combined effect of the two evidence (local diagnostic models), according to the maximum trust decision rule, absolute support decision rule, and uncertainty limit decision rule of D-S evidence theory, the corresponding diagnostic conclusions of the elements in each evidence are made. The maximum trust decision rule, the absolute support decision rule, and the uncertainty limit decision rule can be expressed as:

$$\left\{\begin{array}{c}Bel\left(A\right)=max\left\{Bel\left(A_n\right)\right\}\hfill \\ Bel\left(A\right)-Pl\left(A\right)>a\hfill \\ m\left(\theta \right)<b\hfill \end{array}\right.$$

(22)

where A is the fault type of fusion diagnosis, and n is the number of bearing fault types. In addition, a and b are the parameters that are greater than 0.

3.2. Decision Conflict Resolution Method Based on Sensitive Differences of Multi-Model Fault

Since the decision fusion method of the classic D-S evidence assumes that multi-source heterogeneous information or multi-local models in complex environments have the same sensitivity and reliability, unreasonable or wrong fusion results are often obtained when highly conflicting evidence is fused. In this paper, the local decision-making generated by the local fault diagnosis model is used to construct the basic probability assignment, which greatly reduces the possibility of high-level fusion conflicts. Although the possibility of highly conflicting evidence is low, it is aimed at situations where local diagnostic results may be highly conflicting or completely contradictory. We improve the decision fusion method based on the classic D-S evidence theory. First, according to the difference in fault sensitivity of industrial motor bearings in different working environments, the degree of fault sensitivity difference is specifically refined into balanced and unbalanced types. In addition, the idea of trust degree distribution is introduced. In the two cases, the information source or evidence with relatively high fault sensitivity is given a greater trust degree, and the information source or evidence with relatively low fault sensitivity is given a lower trust degree. Finally, the basic probability assignment of each piece of evidence is reconstructed to highlight and improve the influence and role of information sources or evidence with high fault sensitivity in the entire decision fusion and weaken and reduce the influence and role of information sources or evidence with low fault sensitivity in the entire decision fusion.

3.2.1. Sensitivity Analysis of Bearing Faults in Different Environments

During long-term research and practice, scholars in related fields have found that under different environments or certain operating conditions, the fault data collected by different types of sensors at the same time as industrial bearings show obvious differences in sensitivity. For example, motor bearings can be classified into two types according to the installation location, namely, bearings installed inside the motor (inner bearings) and bearings installed outside the motor (external bearings). When the external bearing of the motor fails, the current signal will have a large attenuation in the process of transmission along the transmission system. In addition, it is easy to be overlapped by the interference generated during the operation. Hence, the effect of fault diagnosis based on the vibration sensor signal at this time should be better than that based on the current sensor signal. Due to the different physical properties of the vibration signal and the current signal itself, it is more effective to use the current signal to detect bearing faults for faults with low characteristic frequencies. Bearing fault diagnosis is more sensitive for the acoustic sensor signal than the vibration sensor signal because the vibration signal generated at low speed is covered by strong background noise, making the components of the vibration signal too complex. In addition, through the research on the position of the measuring point of the industrial motor bearing sensor network, it can be known that when the bearing fails, the sensor signals at different positions will change, but the degree of change is different. Data collected by sensors at some locations may vary significantly, while data collected by sensors at other locations may vary slightly. Based on the above analysis, when a high degree of evidence conflict or contradiction occurs in the industrial motor bearing fault diagnosis process, it is unreasonable to directly adopt the fusion rule of “same default information source sensitivity” in the classic D-S evidence theory. Because of the above problems, we combine the idea of evidence trust degree distribution with the degree of sensitivity difference between evidence and improve the classic D-S evidence theory so that the basic probability assignment of highly conflicting evidence is more in line with the actual situation. In the following, the degree of sensitivity difference between conflicting evidence is subdivided and discussed into two categories: balanced sensitivity of faults and unbalanced sensitivity of faults.

3.2.2. Multi-Local Model Conflict Resolution under the Condition of Balanced Fault Sensitivity

In the actual fault diagnosis process of industrial motor bearings, if a high degree of conflict occurs during the decision fusion of multi-local models, then the combination rules of the classic D-S evidence theory will no longer apply. This section introduces the idea of trust distribution for the high-level decision-making conflicts that occur under fault-like sensitivity balance. While using information entropy to quantify the uncertainty of high-level conflict evidence, it also calculates the high support value of conflicting evidence. According to the information entropy value and support value of each highly conflicting evidence, the corresponding trust degree is assigned to it. The basic probability assignment of each conflicting piece of evidence is reconstructed to obtain a more reasonable and accurate fusion diagnosis result. Entropy is used in statistical physics to measure the singularity and unity of a defined state, that is, to quantify the degree of chaos in some material system. However, information data has typical statistical characteristics, and in information theory, it is believed that random interference will inevitably exist in the process of information transmission. Therefore, some valuable information data can be regarded as a mathematical set, and the uncertainty of this set is like the degree of disorder of the microscopic state in statistical physics. Information entropy can also be used to measure the degree of disorder of information data. If the information entropy of a certain information data is larger, it indicates that the degree of disorder of the information data itself is higher. On the contrary, if the information entropy of a certain information data is smaller, it indicates that the degree of disorder of the information data itself is lower.

As a special kind of information, evidence can also reflect its degree of “uncertainty” through information entropy. The higher the information entropy value of the evidence, the greater the corresponding evidence uncertainty, and the relationship between the two is proportional. Conversely, the lower the information entropy value of the evidence, the smaller the corresponding evidence uncertainty. In the process of multi-local model decision fusion, although the information entropy of evidence can reflect the amount of information contained in the evidence, it is unreasonable to assign the trust degree of evidence only based on the uncertainty of the evidence. This may lead to an increase in the weight of evidence that has errors during fusion, affecting the accuracy and credibility of the fusion results. The evidence support degree reflects the evidence’s effect on decision-making and the agreement between the local decision-making results corresponding to the evidence and the actual situation. The greater the support degree of the evidence, the more consistent the decision fusion result corresponding to the evidence is with the actual situation. The smaller the support degree of the evidence, the more the decision fusion result corresponding to the evidence deviates from the actual situation. Therefore, this section comprehensively considers evidence support and uncertainty to jointly determine the trust distribution of high-conflict evidence.

Given the recognition framework $\theta =\{A_1,A_2,A_3,\dots ,A_n\}$, two evidence (local diagnostic models) generate evidence $E_{1n}=E_{11},E_{12},E_{13},\dots ,E_{1N}$ and $E_{2n}=E_{21},E_{22},E_{23},\dots ,$$E_{2N}$. Assume $m_{1n}$ and $m_{2n}$ are the basic probability assignments corresponding to $E_{1n}$ and $E_{2n}$, respectively. Then, the information entropy $H_i$ of the i-th evidence is defined as:

$$H_i=-\sum m_{in}{log}_2{m}_{in}.$$

(23)

$$h_i=\frac{{\left(H_i\right)}^{-1}}{\sum {\left(H_i\right)}^{-1}}.$$

(24)

The additive theorem in probability is introduced to calculate the support degree of two evidence for element (i.e., fault type) $A_n$. After the support of all fault types is calculated, it is normalized to get $Z\left(A_n\right)$, that is, the support value of the two evidence bodies for $A_n$. Its expression is as follows:

$$\begin{array}{c}\hfill O\left(A_1\right)=m_1\left(A_1\right)+m_2\left(A_1\right)-m_1\left(A_1\right)m_2\left(A_1\right).\\ \hfill O\left(A_2\right)=m_1\left(A_2\right)+m_2\left(A_2\right)-m_1\left(A_2\right)m_2\left(A_2\right).\\ \hfill O\left(A_3\right)=m_1\left(A_3\right)+m_2\left(A_3\right)-m_1\left(A_3\right)m_2\left(A_3\right).\\ \hfill \dots \\ \hfill O\left(A_n\right)=m_1\left(A_n\right)+m_2\left(A_n\right)-m_1\left(A_n\right)m_2\left(A_n\right).\end{array}$$

(25)

$$Z\left(A_n\right)=\frac{O\left(A_n\right)}{\sum O\left(A_n\right)}.$$

(26)

$O\left(A_n\right)$ reflects the degree of support of the two evidence for fault type $A_n$. Finally, the information entropy value and support value of the evidence are integrated to construct the trust distribution formula of element $A_n$, as shown below:

$$W_{A_n}=\frac{Z\left(A_n\right)+h_i{m}_{in}}{2}.$$

(27)

Among them, $W_{A_n}$ comprehensively reflects the degree of recognition of the element $A_n$ by the two evidence bodies. Therefore, this paper uses it as the basic probability assignment for reconstruction.

3.2.3. Conflict Resolution of Multi-Local Models under the Condition of Non-Equilibrium Fault Sensitivity

Due to differences in actual working environments, operating conditions, motor loads, sensor types, and installation locations for industrial motor bearings, the sensitivity of each fault type will likely show a corresponding imbalance, that is, the fault sensitivity non-equilibrium situation. Aiming at the high decision-making conflicts that occur under the condition of unbalanced fault sensitivity, this section first compares the fitting differences between the bearing conflict data samples and the standard reference samples through the gray correlation analysis technology. Then determine the optimal average correlation degree of the bearing data according to the trust degree of each high conflict evidence. Finally, reconstruct the basic probability assignment of each conflict evidence. In this way, the conflict between evidence can be reduced, and the credibility and rationality of multi-local model decision fusion can be improved. In essence, gray relational analysis transforms the infinite convergence problem into an approximate convergence problem; transforms the infinite space problem into a finite sequence problem to solve; replaces the continuous concept with discrete data. Specifically, the gray relational analysis describes the variable information in the system through mathematical theory, quantitatively analyzes the development and change of the system, and compares the correlation similarity of the internal components of the system. In addition, gray relational analysis has no hard and fast rules for the value and law of variable information and is applicable to most analysis scenarios.

In this section, the gray relational analysis is used to take the spatial type of information as the mathematical benchmark, and the gray relational axiom is used as the principle to express the fitting degree between the bearing conflict data sample and the standard reference sample in numerical form. The closer the fitting degree between samples is, the greater the degree of correlation between them is, the higher the sensitivity is, and the corresponding distribution coefficient of trust degree is also greater. The conflict resolution process of multi-local models under the condition of unbalanced fault sensitivity is as follows:

(1) Assume that the recognition framework $\theta =\{A_1,A_2,A_3,\dots ,A_n\}$ is known, where n is the number of fault types. Taking the evidence $E_1$ as an example, when a high degree of conflict occurs, the bearing data sample X corresponding to the evidence $E_1$ is:

$$X=(x_1,x_2,x_3,\dots ,x_p),$$

(28)

where p is the sequence length of the bearing samples. The standard samples Y of each fault category corresponding to the evidence $E_1$ are expressed as follows:

$$\begin{array}{c}\hfill Y_1=(y_{11}.y_{21},y_{31},\dots ,y_{p1}).\\ \hfill Y_2=(y_{12}.y_{22},y_{32},\dots ,y_{p2}).\\ \hfill Y_3=(y_{13}.y_{23},y_{33},\dots ,y_{p3}).\\ \hfill \dots \\ \hfill Y_n=(y_{1n}.y_{2n},y_{3n},\dots ,y_{pn}).\end{array}$$

(29)

(2) Calculate the gray correlation degree between the conflict samples and each fault standard sample. Taking the calculation of the gray correlation degree between the conflict sample X and the standard sample $Y_1$ of the fault type 1 as an example, the gray correlation coefficient is:

$${ϵ}_1=\frac{{\Delta }_{min}+\mu {\Delta }_{max}}{|x_p-y_{p1}|+\mu {\Delta }_{max}}.$$

(30)

$${\Delta }_{min}=min|x_d-y_{e1}|,d=1,2,3,\dots ,p\mathrm{and}e=1,2,3,\dots ,p.$$

(31)

$${\Delta }_{max}=max|x_r-y_{s1}|,r=1,2,3,\dots ,p\mathrm{and}s=1,2,3,\dots ,p.$$

(32)

where $\mu$ is the resolution coefficient, which is used to weaken the distortion caused by the maximum absolute difference in the analysis process to show the difference of the gray correlation coefficient more objectively, and its value is determined in advance according to expert experience, $\mu \in (0,1)$. The average correlation $r_1$ between the conflict sample X and the standard sample $Y_1$ is:

$$r_1=\frac{\sum {ϵ}_{p1}}{p}.$$

(33)

Similarly, the average degree of correlation between the conflict sample X and the standard sample $Y_n$ of other fault types can be obtained by repeating the above calculation process.

(3) Sort all the average correlation degrees corresponding to the evidence $E_1$ in ascending (or descending) order and take the average correlation degree with the largest value as the optimal average correlation degree of this evidence. Similarly, the optimal average correlation degree of other evidence bodies also can be calculated.

(4) After normalizing the optimal average correlation degree of all evidence bodies, the trust distribution coefficient $f_i$ corresponding to each conflicting evidence can be obtained. Afterward, the basic probability assignment under the joint action of different evidence can be obtained through the following formula:

$$m=\sum f_i{r}_i.$$

(34)

where m represents the basic probability assignment corresponding to evidence i after the weighted average, and $r_i$ is the local diagnosis result corresponding to evidence i when the multi-local model decision conflicts.

(5) Finally, fusion is carried out according to the fusion rules of evidence theory, so as to obtain the final fusion diagnosis result.

4. Performance Evaluation

In this section, the rationality and effectiveness of the MLMF-CR algorithm are verified by the experimental data collected by the motor bearing platform. Among them, the analysis and comparison of the complementarity of multi-source and heterogeneous information of bearings, the effectiveness of multi-part model decision fusion, and the conflict resolution performance of the multi-part model are emphasized. In the following of this section, we first introduce the experimental platform. Then, we present the performance metrics. Next, we evaluate the performance in the complementarity of multi-source heterogeneous information, the effectiveness of decision fusion of multiple partial models, and the conflict resolution of the multi-part model.

4.1. Experimental Platform

The experiments are carried out based on the PT700 motor bearing platform as shown in Figure 5. The experimental platform is mainly composed of a three-phase asynchronous AC motor, a parallel gearbox, a bearing assembly, a coupling, a frequency converter, an oil level gauge, and an electromagnetic powder brake for changing loads. Considering the advantages and characteristics of different information sources of bearings and the complementarity between multi-source heterogeneous information of bearings. The vibration acceleration sensor is installed in the experimental platform as an external sensor, and the current sensor is used as a built-in sensor. In addition, the type of rolling bearing placed in the experimental platform is UC206, and the contact angle of the rolling element of the bearing is 0 degrees. To simulate the working state of the faulty bearing and consider the independence of different fault data of the bearing, the electrical discharge machining (EDM) technology was used in the experiment to process local single-point damage on the UC206 bearing artificially. The locations of local single-point damage are respectively located on the bearing’s outer ring and inner ring, and the damage diameter is 0.3 mm, as shown in Figure 6. Thereby simulating three different bearing operating states: normal operating state, inner ring fault state, and outer ring fault state.

The vibration datasets of the bearing and current datasets are collected synchronously through the VAL-DC29, and VAL-DC25 signal acquisition and analyzers under the condition that the motor speed and load are fixed at 1500 rpm and 0 hp, respectively. The operating state of the bearing is constantly changing. The number of data samples under different bearing operating conditions was balanced during the data collection process. The bearing data set is divided into a training set and a test set at a ratio of 7:3. The training set is used to train a fault diagnosis model. The test set is used to evaluate the relevant performance of the model. Among them, the number of samples in the training set is 1680, and the number of samples in the test set is 720. To ensure that the collected current and vibration data samples include the periodic characteristics and fault information characteristics of one revolution of the bearing, the number of sampling points for one revolution under test as the number of sampling points contained in one sample in the experiment. According to the calculation of the transmission ratio formula and the highest analysis frequency formula, it is finally obtained that the bearing can sample about 512 points per revolution; that is, every 512 continuous sampling points are selected as an experimental sample. The details related to data collection are summarized in

Table 2. Details related to data collection.

Bearing Operating States	Normal, Inner Ring Fault, Outer Ring Fault
The speed and the load of the motor	Fixed to 1500 rpm and 0 hp
The condition of the motor	Constantly changing among normal, inner ring fault, and outer ring fault.
Data Status Distribution	Equalization
The equipment for collecting vibration and current datasets	VAL-DC29 and VAL-SC25.
The ratio of the numbers of training and test samples	7:3
The numbers of training and test samples	1680 and 720
The number of sampling data in one sample	The number of sampling points for one revolution of the bearing, i.e., 512 sampling points

.

Figure 7 shows the time-domain waveform of the vibration signal and current signal per unit sample length under the normal bearing state, the fault state of inner and outer rings.

4.2. Experimental Settings and Performance Metrics

The local fault diagnosis model used in the experiments mainly includes a noise reduction encoder, a Bi-LSTM overlay layer with an activation function of tanh, an attention mechanism layer, a fully connected layer with an activation function of Tanh, and an activation function of SoftMax classification layer. Among them, the noise reduction encoder first adds Gaussian noise with a mean value of 0 and a variance of 0.15 to the original signal and then obtains a reconstructed signal through encoding and decoding, then outputs it to the first Bi-LSTM layer. The output of the LSTM forward layer and reverse layer in the first Bi-LSTM layer is used as the input of the second Bi-LSTM forward layer and reverse layer, and the two Bi-LSTM layers jointly complete the feature extraction of the bearing data. Then the extracted features are input into the attention mechanism layer, and the attention weight coefficient is calculated. Finally, the weight coefficient is combined with the vector to obtain the final feature expression. The fully connected layer accepts the output feature vector of the attention mechanism layer. After realizing the feature space conversion of the bearing feature, the classification layer realizes the output of the predicted target state category. The number of Bi-LSTM units is 64, and the number of neurons in the fully connected layer is 32. In addition, a dropout operation with a parameter of 0.25 is set in the fully connected layer, which only takes effect during the training process to prevent the network from memorizing or overfitting the training data. The batch size is set to 64, the learning rate is adjust dynamically. Specifically, Adam optimization algorithm with learning rate adaptive function is used. The optimization algorithm is derived from adaptive moment estimation, which is different from the traditional stochastic gradient descent. The optimization algorithm adaptively corrects the first-order moment and second-order moment estimates of different parameter gradients through the loss function and the bias correction mechanism built into the algorithm. The learning rate of each iteration has a relatively definite range after bias correction, which may ensure the stability of related parameters. The initial learning rate of the multi-local model is set to 0.001.

For the typical multi-category classification problem of industrial motor bearing fault diagnosis, commonly used performance evaluation indicators include Accuracy (ACC), Precision, Recall (P), and F1-Score (F1). ACC indicates the proportion of all data samples that are correctly classified, which can be expressed as follows:

$$ACC=\frac{TP+TN}{TP+TN+FP+FN},$$

(35)

where $TP$ represents the number of positive samples that are correctly identified, $FN$ represents the number of positive samples that are falsely detected as negative samples, $TN$ represents the number of negative samples that are correctly recognized, and $FP$ represents the number of negative samples that are falsely detected as positive samples. Precision P represents the proportion of samples predicted as faults that are correctly identified as faulty classes, which can be expressed as follows:

$$P=\frac{TP}{TP+FP}.$$

(36)

The recall rate R represents the proportion of all fault samples that are correctly identified as fault categories, which can be expressed as follows:

$$R=\frac{TP}{TP+FN}.$$

(37)

F1-Score $F1$ is the harmonic mean of precision P and recall R. F1-Score is positively correlated with the performance of the algorithm. The larger the value, the better the performance of the algorithm. The value range of F1 is between 0 and 1, which can be expressed as follows:

$$FI=\frac{2\times P\times R}{P+R}.$$

(38)

Usually, the F1-Score indicator is mostly used in binary classification problems. To measure the comprehensive performance of the MLMF-CR algorithm in dealing with multi-classification problems such as fault diagnosis, the traditional F1-Score indicator is expanded in this paper. Each time a bearing data sample category (bearing operating status) is selected as the positive class, the rest of the bearing data sample categories (bearing operating status) are used as the negative class. Then the precision and recall rate of different types of data samples are calculated. Hence, the F1-Score index of each data sample category can be obtained by Equation (38).

In summary, it can be found that the fault diagnosis accuracy index is the ratio of the number of correctly identified data samples to the total number of data samples, which can reflect the effective recognition degree of the fault diagnosis algorithm. The F1-Score index not only fully shows the comprehensive performance of the fault diagnosis algorithm, but also reflects the performance of the algorithm under different operating conditions of the bearing. Therefore, the fault diagnosis and recognition accuracy and F1-Score index are used as the performance metrics in this paper.

4.3. Performance Evaluation in the Complementarity of Multi-Source Heterogeneous Information

To evaluate the complementarity among multi-source heterogeneous information of industrial motor bearings and the influence of multi-source heterogeneous information on the performance of the fault diagnosis model, the synchronously collected bearing vibration signal and current signal data are respectively input into the local fault diagnosis model based on Bi-LSTM and denoted them as Bi-LSTM-V algorithm and Bi-LSTM-C algorithm. The Bi-LSTM-V and Bi-LSTM-C algorithms are set as comparison algorithms. To control a single variable, the training hyperparameters of the local fault diagnosis model and the number of neurons in each network layer are kept consistent. The experiments are repeated several times to reduce the impact of experimental contingency on fault diagnosis accuracy.

Figure 8 shows the fault diagnosis accuracy of the Bi-LSTM-V, Bi-LSTM-C, and MLMF-CR algorithms. The MLMF-CR algorithm proposed in this paper has obvious advantages in fault diagnosis accuracy than the other two algorithms. In the six times of experiments, the fault diagnosis accuracy of the MLMF-CR algorithm far exceeds that of the Bi-LSTM-V and the Bi-LSTM-C algorithms, which shows that compared with single-source information, multi-source heterogeneous information of bearings has more comprehensive and state information and is more helpful for bearing fault diagnosis. It is worth noting that the average fault diagnosis accuracy rates of the MLMF-CR, the Bi-LSTM-V, and Bi-LSTM-C algorithms are 98.58%, 96.43%, and 94.85%, respectively. Although the average fault diagnosis accuracy of the Bi-LSTM-V and Bi-LSTM-C algorithms is far lower than that of the proposed algorithm in this paper, they can achieve good results, which shows that the fault diagnosis model based on Bi-LSTM can still carry out effective fault identification when the input is single information source data. In addition, it can also be seen that when the Bi-LSTM-C algorithm is used for bearing fault diagnosis, its fault diagnosis accuracy index is lower than that of the Bi-LSTM-V algorithm. This may be because the test bearing of the experimental platform used in the experiments is installed outside the motor. At this time, the current source signal is more likely to be affected by factors such as its generation mechanism and propagation path, which leads to the higher accuracy of the state identification results based on vibration source data. When the vibration data and current data of the bearing are comprehensively used for fault diagnosis, the fault diagnosis accuracy rate of a single experiment and the average fault diagnosis accuracy rate are improved, which also confirms from the side that the bearing vibration data (external sensor data) and current data (built-in sensor data) has a certain complementary effect.

Figure 9 shows the F1-Score index of the algorithm under different bearing conditions. Among them, the F1-Score index of the proposed MLMF-CR algorithm is better than that of the Bi-LSTM-C and Bi-LSTM-V algorithms, regardless of the status of the bearing. Moreover, the F1-Score index change fluctuation is also relatively small in the proposed algorithm under the different operating statuses of the bearing, which fully demonstrates that the MLMF-CR algorithm has relatively excellent comprehensive performance. The Bi-LSTM-V algorithm has also achieved relatively satisfactory results regarding F1-Score indicators, and the index changes in different status are relatively stable. In contrast, the F1-Score index of the Bi-LSTM-C algorithm fluctuates greatly under different bearing status conditions, and the F1-Score index value under different operating states is also weaker than the other two algorithms. In summary, the numerical results demonstrate the importance of multi-source heterogeneous monitoring data for bearing fault diagnosis.

4.4. Performance Evaluation in the Effectiveness of Decision Fusion of Multiple Partial Models

To verify the validity of the effectiveness of the proposed MLMF-CR algorithm, we select three comparison methods from the feature-level information fusion fault diagnosis methods, the decision-level information fusion fault diagnosis methods, and the data splicing-level information fusion fault diagnosis methods, respectively. The three comparison algorithms are the feature fusion fault diagnosis algorithm based on two-stage Bayesian inference decision fusion (TBIDF), the decision fusion fault diagnosis algorithm based on improved D-S (FDB-IDS), and the data fusion fault diagnosis algorithm based on a long-short term memory network on tree structures (S-LSTM).

Figure 10 and Figure 11 show the fault diagnosis accuracy and the F1-Score indicators of different fault diagnosis algorithms. It can be seen from the numerical results that the proposed MLMF-CR algorithm can achieve the highest fault diagnosis accuracy and the F1-Score while the TBIDF, the FDB-IDS, and the S-LSTM algorithms all have different levels of lacking in fault identification accuracy and F1-Score indicators. Among them, the TBIDF algorithm is superior to the FDB-IDS algorithm and the S-LSTM algorithm regarding fault diagnosis accuracy and the F1-Score index in most of the experiments. The highest and lowest recognition accuracy of the TBIDF algorithm in multiple experiments is 98.75% and 96.36%, respectively. However, the TBIDF algorithm still has some uncertainties in feature selection and feature fusion, which may impact the final fault diagnosis results. At the same time, in the feature selection and fusion process, some effective state information may be deleted by mistake, leading to a decline in the fusion accuracy. The reasons described above make the TBIDF algorithm have high requirements for the preprocessing of the initial data, which is not as good as the applicability of the proposed algorithm in the industrial operating environment. The fault diagnosis accuracy of the FDB-IDS algorithm in different experiments exceeds 95.13%. In addition, the F1-Score index under different operating statuses also maintains a relatively stable level, illustrating the effectiveness of decision-making fusion to a certain extent. However, the algorithm did not fully consider the timing characteristics of bearing data and the actual background of industrial big data. It directly selects BP neural network, RBF neural network, etc., to build local diagnostic modules, resulting in poor algorithm performance when dealing with large-scale training samples. The S-LSTM algorithm performs generally in terms of fault identification accuracy and F1-Score. The F1-Score values under different operating statuses are 97.14%, 94.14%, and 93.22%, respectively, which show that the fluctuation range under different statuses is relatively obvious. The S-LSTM algorithm combines the bearing vibration and current signals into a fusion signal as the input of the LSTM network. Although such a data splicing and fusion method can minimize the loss of information, it also reduces the fault tolerance of the algorithm and affects the accuracy of fault identification to a certain extent. In addition, the bearing operating state data at a certain moment is related to the state at the previous moment and the state at the subsequent moment. However, the LSTM network ignores the correlation characteristics of the bearing time series data in the time reverse part, which is one of the reasons why the performance of the S-LSTM is not as good as our proposed algorithm.

In addition, the time cost required by different algorithms to complete fault diagnosis is also considered, e.g., the operating efficiency of each algorithm. Since the test time of each fault diagnosis algorithm is relatively short, if the test time is selected as the evaluation index of the algorithm, it will not be able to accurately show the actual operating efficiency of each algorithm. Hence, the training time is used as the main index for evaluating the operating efficiency of the algorithms. The training time of the TBIDF, FDB-IDS, S-LSTM and MLMF-CR algorithms is shown in Figure 12. It can be seen from Figure 12 that the proposed MLMF-CR and FDB-IDS algorithms are relatively faster training speeds because they adopt a distributed processing framework and can analyze and process the vibration data and current data of the bearing in parallel. The S-LSTM algorithm adopts the fusion method of data splicing, directly combining the bearing vibration and current signals into a fusion signal as input. Hence, the training time of the algorithm is far longer than that of the other three algorithms. In addition, although the FDB-IDS algorithm is slightly stronger than the MLMF-CR algorithm in model training time, considering various factors such as the accuracy of fault identification, F1-Score, and comprehensive performance of each algorithm, the proposed MLMF-CR algorithm still has more advantages in the field of industrial motor bearing fault diagnosis.

4.5. Performance Evaluation in the Conflict Resolution of the Multi-Part Model

A high degree of conflict occurs when the classic D-S evidence theory is adopted by the multi-local model for decision fusion of the 179 groups of basic probability assignment. In this subsection, we will take this as an example to analyze and evaluate the decision-conflict resolution performance of the multi-local model.

The evidence 1 and 2 belong to the same identification framework, and their corresponding basic assignment functions are $m_1$ and $m_2$. Evidence 1 is constructed according to the local diagnosis model of the input vibration data, and evidence 2 is constructed according to the local diagnosis model of the input current data. The basic assignment function $m_i$ of each evidence when a high degree of conflict occurs is shown in

Table 3. The basic assignment function $m_i$ of each evidence when there is a high degree of conflict.

Evidence	${\mathit{m}}_{\mathit{i}}$ (Normal Status)	${\mathit{m}}_{\mathit{i}}$ (Inner Ring Fault)	${\mathit{m}}_{\mathit{i}}$ (Outer Ring Fault)
Evidence 1	$9.9984777 \times {10}^{-1}$	$4.4219062 \times {10}^{-11}$	$1.5215934 \times {10}^{-4}$
Evidence 2	$7.2511165 \times {10}^{-13}$	$9.8507023\times {10}^{-1}$	$1.4929717 \times {10}^{-2}$

. It can be obtained that the normalization constant (conflict coefficient) k between the two conflicting pieces of evidence is 0.999 by calculation, indicating that a high degree of conflict occurred in the process of decision-making fusion. At this time, if the classic D-S evidence theory is used for decision fusion, the final fusion diagnosis result is the outer ring fault. However, it can be seen from Table 3 that the basic probability assignments of the outer ring fault status of different evidence are much smaller than the basic probability assignments of the other two operating states of the bearing. That is, the outer ring fault for two evidence bodies is less likely to occur simultaneously. The classic D-S evidence theory did not support the proposition that the belief is more in line with common sense but chose to believe the proposition with the smallest basic probability assignment.

This subsection first analyzes the specific model of the tested bearing and the actual operating environment and then determines the fault category’s sensitive difference type. Since the motor bearings tested in the experiment are installed outside the motor, the current signal will have a large attenuation in the transmission process along the transmission system, which leads to a higher reliability of the fault diagnosis based on the vibration sensor signal than that based on the current confidence in fault diagnosis of sensor signals. Based on the above analysis, the bearing operation described in this subsection conforms to the unbalanced type of bearing fault sensitivity. Therefore, following the multi-local conflict resolution strategy under unbalanced fault sensitivity, the trust degree distribution is introduced. The average optimal correlation degree of the vibration and current data of the 179 groups of bearings is calculated according to the Formulas (30)–(33), respectively. After normalization processing, the trust degree distribution coefficients $f_1$ and $f_2$ corresponding to highly conflicting evidence 1 and evidence 2 can be obtained as 0.651 and 0.349. Finally, the basic probability assignment $m_{12}$ (MLMF-CR) under the joint action of the two evidence bodies is reconstructed by Formula (34). The newly constructed basic probability assignments are $6.5090089 \times {10}^{-1}$, $3.4378952 \times {10}^{-1}$, $5.30952103 \times {10}^{-3}$.

Figure 13 shows the comparison of the basic probability assignment before and after assigning the trust degree, where $m_{12}$ (D-S) represents the basic probability assignment after the fusion of the two evidence bodies using the classic D-S evidence theory. Compared with the basic probability assignment before assigning the trust degree, the reconstructed basic probability assignment $m_{12}$ (MLMF-CR) is more in accord with the actual situation. In addition, according to the multi-local model conflict resolution strategy proposed in this paper, the final fusion diagnosis result is normal, and the diagnosis result is consistent with the actual running status of the bearing, which shows that the multi-part model conflict resolution strategy proposed in this paper is reasonable and effective.

The classic D-S theory improved Yager D-S combination rule (DSNCR), and the improved Deng Yong conflict evidence combination method (ECACE) are used as comparison algorithms to fuse the local diagnostic decisions (basic probability assignment) generated by the two local models. The misjudgment rate of each comparison algorithm is shown in Figure 14. The results show that the misjudgment rate of the MLMF-CR algorithm is much lower than that of the three comparison algorithms.

In addition, the operation efficiency of the fusion algorithm is considered comprehensively. The fusion time of D-S evidence theory, DSNCR algorithm, ECACE algorithm, and MLMF-CR algorithm is 0.0026 s, 0.000717 s, 0.109 s, and 0.271 s, respectively. Compared with the other three fusion algorithms, the MLMF-CR algorithm does not have an advantage in terms of fusion time. This is because the decision conflict resolution strategy not only considers the statistical characteristics of the data sample itself but also comprehensively considers and analyzes the difference in sensitivity of bearing faults in the actual operating environment, resulting in relatively high computational costs.

5. Conclusions

In this paper, we proposed an industrial motor bearing fault diagnosis algorithm based on multi-local model decision fusion conflict resolution (MLMF-CR) to fully integrate multi-source heterogeneous information and reasonably resolve multi-source information conflicts. The proposed method is based on Bi-LSTM and first uses the noise reduction encoder to clean the vibration signal and current signal of the industrial motor bearing, respectively, to obtain the vibration reconstruction signal and the current reconstruction signal. Afterward, the reconstructed vibration signal and the reconstructed current signal are input into the local fault diagnosis model based on Bi-LSTM and the attention mechanism, and the characteristic information of the reconstructed signal in each fault state is deeply mined to form a local diagnosis decision. Finally, the local diagnostic decisions are fused using the D-S evidence theory to obtain the final diagnostic results. Performance in accuracy, PI score, training time, and the false positive rate was evaluated by experiments, which showed the superiority of the proposed method. However, there are still some points that could be improved. Several of the directions are listed as follows and will be further developed in our future work. First, more evaluation indicators may be considered to increase the objectivity of the results. Second, in the actual production process, for some special industrial motor platforms, such as centrifugal pumps, cryogenic pumps, mine hoisting motors, etc., their bearing signal duration is usually short, or the monitoring conditions are relatively harsh, so that the bearing sensor can only collect a small amount of sample data. When the bearing fault diagnosis method based on deep learning and information fusion is directly adopted, it will lead to overfitting problems in the model training process, which will seriously affect the recognition accuracy of the fault diagnosis model. Maintaining the accuracy of bearing fault diagnosis and recognition under the condition of small samples is another critical issue facing the development of industrial motor bearing fault diagnosis technology.