Vibration-Based Fault Diagnosis for Railway Point Machines Using VMD and Multiscale Fluctuation-Based Dispersion Entropy

I.   Introduction

Fault diagnosis and health monitoring are a hot topic in various fields [1]-[6]. In recent years, China’s railways, especially high-speed railways, have developed rapidly. With the advantages of fast speed, large transportation capacity, low energy consumption and less limited by natural conditions, railway transportation plays an important role in China’s passenger and freight transportation and promotes the development of the national economy [7]-[11]. However, due to the high speed and high density of railway, especially for high-speed railway, once an accident occurs, the consequences will be unimaginable [12]-[15]. Therefore, the fault diagnosis of railway signal equipment has attracted more and more attention [16], [17].

As one of the major outdoor basic equipment of signal equipment, railway point machines are closely related to railway transportation safety. No matter in the static condition of no train passing or the dynamic condition of train passing, the railway point machine shall lock the movable part of the rail at the specified position. Over the years, failures of railway point machines account for about 40% of the total failures of railway train control system [18]. At present, the maintenance and repair of railway point machines are mainly by manual regular investigation during skylights, which consumes a lot of human and material resources [19]. Therefore, exploring and developing the intelligent fault diagnosis method of railway point machines is an important issue to ensure the safe operation of railway signaling system.

Aimed at fault diagnosis for railway point machines, many scholars all over the world have carried out a lot of research works. These works are mainly based on motor voltage and current curves, which can be summarized as the following categories: statistical analysis-based methods, threshold-based methods, expert systems, model-based methods, and signal processing-based methods. Statistical analysis-based methods mainly analyze the historical fault data to obtain the importance degree ranking of different kinds of faults. The commonly used method is fault tree analysis [20]. Through statistical analysis of historical fault data and fault causes, the importance degrees of faults and their causes are ranked, which can provide guidance for onsite maintenance to some extent. But the confirmation of fault modes still needs manual troubleshooting. Threshold-based methods calculate the deviation between the given data and standard data (usually motor current curve), and set a deviation threshold to judge whether there is a fault. The commonly used method is dynamic time warping [21], [22]. This kind of method is suitable for anomaly detection. However, the setting of threshold requires expert experience. Besides, it cannot realize fault location. In order to enhance the intelligence of fault diagnosis methods of railway point machines, expert systems are introduced. For example, Atamuradov et al. proposed a remote monitoring system using expert systems [23]. However, expert systems require lots of knowledge of domain experts. Thus, the diagnosis results are influenced by subjective factors. There are only a few model-based fault diagnosis methods for railway point machines because the railway point machine is a very complicated system and the accurate model parameters are difficult to obtain [24]. Signal processing-based methods can well address the existing problems of the above-mentioned methods due to developed signal processing technologies, including time-domain analysis, frequency-domain analysis, and time-frequency analysis [25]-[28]. The existing fault diagnosis methods of railway point machines mainly carry out studies on voltage or current curves. Especially, sound signals have been used for contactless fault diagnosis of railway point machines [29], [30]. Though only a few works based on sound signals are done, it provides a new idea for fault diagnosis of railway point machines. However, sound signals are easily affected by external interference, such as bird calls. To address this issue, this paper aims to develop an intelligent fault diagnosis method for railway point machines based on vibration signals by taking advantage of vibration signals’ stronger anti-interference ability than sound signals.

Vibration signals of mechanical equipment are usually non-stationary. To preprocess non-stationary signals, some methods are developed, of which empirical mode decomposition (EMD) is one of the preferable means. EMD can decompose the raw signal into several intrinsic mode functions by a screening process [31], [32]. Though it has been widely used, it has the disadvantages of mode mixing, which affects the preprocessing effect [33]. It is noted that variational mode decomposition (VMD) has been proposed in 2014 [34]. It is developed based on mathematical derivation, which can well address the problem of mode mixing existing in EMD [35], [36]. Thus, VMD is adopted to preprocess the vibration signals of railway point machines in this paper.

Entropy is one of the most powerful tools to evaluate the complexity of signals [37]. Existing entropy, including sample entropy [38], [39], fuzzy entropy [40], [41], permutation entropy [42], etc. have been widely used to characterize the complexity of signals. Table 1 gives some up-to-date entropy-based fault diagnosis methods.

Table  1.  Some up-to-date entropy-based fault diagnosis methods

Years	Methods	Works
2016, 2018	Sample entropy	[31], [32]
2017	Fuzzy entropy	[33], [34]
2018	Permutation entropy	[35]
2019	Multiscale dispersion entropy	[36]

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However, sample entropy and fuzzy entropy are time-consuming. Though permutation entropy is faster than sample entropy and fuzzy entropy, it cannot fully mine the complexity of signals. Though the recently proposed multiscale dispersion entropy can increase the reliability of complexity measures, it does consider the relative rather than absolute values. Multiscale fluctuation-based dispersion entropy (MFDE), developed from multiscale dispersion entropy, can address the problem [43].

Feature selection is also one of the most important steps to realize high-accuracy fault diagnosis. The extracted features are high-dimensional and redundant, which may reduce the diagnosis accuracy. The existing feature selection methods for railway point machines are usually one-stage feature selection using Fisher discrimination [44], principal component analysis [45], or linear discriminant analysis [46]. However, the single feature selection method is difficult to eliminate the redundant information of multi-dimensional features comprehensively. Considering the effectiveness, this paper aims to propose a two-stage feature selection method based on Fisher discrimination and ReliefF.

The main contributions of this paper are summarized as follows. First, a feature extraction method combining VMD and MFDE is developed, which is verified a more effective tool compared with EMD and MFDE. Then, a two-stage feature selection method based on Fisher discrimination and ReliefF is proposed, which is more powerful than single-stage feature selection method, indicating it can eliminate redundant information among multi-dimensional features more effectively. Besides, it is a try to use new means for fault diagnosis on railway point machines.

The remaining parts of this paper are organized as follows. Section II shows the experiment setup and data description. Section III detailedly represents the proposed intelligent fault diagnosis method. Section VI gives the experiment results analysis and discussions. Section V concludes this paper.

II.   Experiment Setup and Data Description

Sound signals used in this paper were collected from a fully operational Type ZDJ9 point machine in Xi’an Railway Signal Co., Ltd, Shaanxi Province, which is one of the most commonly used types in the railway system. The inside view of ZDJ9 point machine is illustrated in Figure 1. The ZDJ9 point machine is composed of motor, retarder, ball screw, switch circuit controller, throw rod, indication rod, locking system and so on. When three-phase voltage (380 V) is given, the motor starts to work which marks the switching process starts. After the unlocking process, the ball screw starts to move, which renders the throw rod and indication rod begin to move. In the switching process, the switch circuit controller cuts position indication circuit, simultaneously turns on the switch control circuit. When the switching process finishes, the switch circuit controller cuts the switch control circuit, simultaneously turns on the indication circuit of the opposite position.

Figure  1.  The inside view of ZDJ9 point machine.

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Accelerometer sensor PCB 356A16_K is used to collect the vibration signals during switching process with a sampling frequency of 5.12 kHz. Total 8 kinds and 436 samples are acquired. The time-domain waveforms are shown in Figure 2, and the data description is given in Table 2.

Figure  2.  Time-domain waveforms of 8 kinds of working conditions during reverse-normal switching process (from accelerometer sensor).

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It can be seen from Figure 2 that the time-domain waveforms of the first four working conditions with different load forces are very similar. When the switching process starts, the indication circuit is cut off, and the movable contact is driven into the fixed contact, which is reflected as the first pulse. Then, the ball screw moves, rendering the throw rod and indication rod move. When the switching process finishes, the switch control circuit is cut off by the switch circuit controller, and the indication circuit is turned on through the movable contact driving into the fixed contact, which is reflected as the pulse at the end of the vibration signals. When there are obstacles between the switch rail and stock rail, the railway point machine will idle (working condition-e). For working condition-f, when the switching process finishes, the indication circuit cannot be turned on because of an improper gap. The movable contact cannot be driven into the fixed contact. Thus the pulse amplitude at the end is smaller. When the throw rod is broken, the switching process consumes less time (working condition-g). When the friction of the frictional clutch is insufficient, the switching process cannot finish (working condition-h).

Table  2.  Data description (The working conditions letter code corresponds to the sub-graph number of the same letter in Figure 2)

Working conditions	Description
a	The load is too small (3 kN)
b	Nominal load (4 kN)
c	The load is too large (I) (5 kN)
d	The load is too large (II) (6 kN)
e	The switching process cannot be finished due to obstacles
f	Improper gap leading indication circuit cannot be connected
g	No load (broken throw rod)
h	Insufficient friction of frictional clutch leading slipping

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III.   Methods

1   Proposed intelligent fault diagnosis method

This part represents the proposed intelligent fault diagnosis method for railway point machines based on vibration signals, shown as Figure 3. First, VMD is used to preprocess the non-stationary vibration signals. A series of modes can be obtained. Then, the MFDE features of the modes are extracted. To select the optimal features, a two-stage feature selection method based on Fisher discrimination and ReliefF is proposed. Fisher discrimination is used to preselect the MFDE features, and the feature dimension can be greatly reduced. Then ReliefF is utilized to further eliminate redundant information of the preselected features. Finally, support vector machine (SVM) is used for diagnosis due to its applicability to small-sample data.

Figure  3.  Proposed intelligent fault diagnosis method.

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2   VMD

VMD is a signal decomposition algorithm with variable scale based on Wiener filtering and variational idea. The signal is decomposed into several modes by adaptive decomposition. The alternating direction multiplier method is used to iteratively solve the center frequency of each mode, so as to demodulate each mode to the corresponding fundamental frequency band. Different from the recursive decomposition of EMD, VMD is a signal decomposition process under the constraints of variational model. It has a complete theoretical basis and is widely used in the field of complex signal analysis [47], [48]. To ensure the minimum sum of the bandwidth of the center frequency, the corresponding constraint expression is

where $\{ {u_k}\} = \{ {u_1},\;{u_2},\; \ldots ,\;{u_K}\}$ is the $K$ modes, $\{ {w_k}\} = \{ {w_1},\;{w_2},\; \ldots ,\;{w_K}\}$ is the corresponding center frequencies, $f$ is the original signal.

Lagrange multiplication operator is introduced to transform the constraint problem into an unconstrained problem. The corresponding augmented Lagrange expression is as

where $\alpha$ is the second penalty factor, $\lambda$ is the Lagrange multipliers. Modes and center frequency are updated by

where $\hat f(w)$, $\hat u_i(w)$, $\hat \lambda(w)$ and $\hat u_k^{n+1}(w)$ represent Fourier transforms of $f(t)$, $u_i(t)$, $\lambda (t)$ and $u_k^{n+1}(w)$, respectively.

3   MFDE

MFDE is developed based on coarse-grain process and fluctuation-based dispersion entropy [49]. The main idea of coarse-grain process is to separate the signal $x(j)$ using non-overlapping windows, which is defined as

where $l$ is the coarse-grain factor, $N$ is the length of $x(j)$. Then, the fluctuation-based dispersion entropy of each $y^l(i)$ can be calculated, making up MFDE.

The main steps of fluctuation-based dispersion entropy are as follows: First, $x(j)$ are mapped to $c$ classes with integer indices from 1 to $c$ using normal cumulative distribution function (NCDF), as

where $\sigma$ and $\mu$ are the standard deviation and mean of time series $x(j)$. $z_j^c = {\rm{round}}(c \cdot {u_j} + 0.5)$ is used assign each $\mu _j$ an integer from 1 to $c$.

Then, time series $z_i^{m,c}$ are defined using embedding dimension $m-1$ and time lag $d$ by $z_i^{m,c}=\{ z_i^c, z_{i + d}^c, \ldots, z_{i + (m - 1)d}^c\}$, $i = 1,2, \ldots ,N - (m - 1)d$. Each $z_i^{m,c}$ is mapped to a fluctuation-based dispersion pattern ${\pi _{{v_0}{v_1} \ldots {v_{m - 1}}}}$, where ${v_1} = z_i^c,\, z_{i + d}^c = {v_1}, \ldots,{v_{m - 1}} = z_{i + (m - 1)d}^c$. The number of possible fluctuation-based dispersion patterns is equal to ${(2c - 1)^{m - 1}}$. Count the number of each pattern as $({N_1},{N_2}, \ldots, {N_{{{(2c - 1)}^{m - 1}}}})$. The relative frequency of each pattern is obtained as

Finally, according to the definition of Shannon entropy, the fluctuation-based dispersion entropy can be obtained as

4   Fisher discrimination

Fisher criterion requires that the difference between multiple classes should be as large as possible, while the difference within each class should be small, which can be reflected using discrimination function value. The larger the discriminant function value, the better the feature discrimination effect. The detailed description of Fisher discrimination can be seen in our previous work [11].

5   ReliefF

ReliefF algorithm is an extension of Relief algorithm to solve multi-class problems. The basic idea of ReliefF algorithm is: randomly select a sample $R$ from training set $D$, then find $k$-nearest neighbor sample $H$ from samples of the same class as $R$, find $k$-nearest neighbor sample $M$ from samples of different classes from $R$, and finally update the feature weight according to the following formula:

where $W(A)$ is the feature weight of feature $A$, $m$, $p(c)$, $M_j(c)$ are the iteration number, prior probability of class $c$, $j$-th nearest neighbor sample in class $c$, respectively. ${\rm{diff}}()$ is an operator defined as

where $D_i[A]$ and $H_j[A]$ represent the feature $A$ in sample $D_i$ and $H_j$, respectively.

6   SVM

SVM is a machine learning method based on statistical learning theory. It is considered to be the most effective method to solve small sample and nonlinear issue. It can map the sample data into high-dimensional space through kernel function for linear regression. The commonly used kernel function is radial basis function (RBF). Thus SVM with RBF kernel function is used in this paper.

IV.   Results and Discussion

This section gives experiment results and discussions.

1   Feature extraction

First, VMD is utilized to preprocess the raw vibration signals for stabilization processing. The decomposition results of an example of working condition-a of reverse-normal switching process are given as Figure 4.

Figure  4.  Decomposition results of a sample using VMD (refer to Figure 2(a)).

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It can be seen that the modes contained in the raw vibration signal can be obtained. Then, the MFDE features can be extracted from these modes. During MFDE extraction process, the parameters are important for features’ quality. Coarse-grain scale factor is an important parameter. Too small coarse-grain scale factor is difficult to mine all information contained in signals. Whereas too large coarse-grain scale factor will lead to a significant increase of computing time. On balance, coarse-grain scale factor is set as 20. Class number $c$ usually takes an integer between 4 and 8. In this paper, $c$ is set as 5. Embedding dimension and time lag are set as 4 and 1, respectively. The first 12 modes are used for feature extraction. Finally, a $12\times 20$ feature matrix can be obtained. Thus, the feature dimension is 240.

2   Two-stage feature selection

Too high feature dimension will lead to ineffective fault diagnosis. The existing single feature selection method cannot eliminate the redundancy information contained in original features completely. In this paper, a two-stage feature selection method combining Fisher discrimination and ReliefF is proposed. The discrimination function values of a sample are given in Figure 5.

Figure  5.  Discrimination function values of a sample.

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After feature preselection process using Fisher discrimination, we use 80 feature points with high discrimination function values for the second-stage selection. Their weights calculated using ReliefF is given as Figure 6. It can be seen from Figure 6 that most weights of the feature points are larger than 0, indicating the effectiveness of feature preselection using Fisher discrimination to some extent. Finally, we select 35 feature points with the largest weights as the optimal features.

Figure  6.  Weights of a sample using ReliefF.

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3   Comparison with other fault diagnosis methods

The vibration samples are randomly divided into training set and test set by the ratio of 6:4. To demonstrate the effectiveness of the proposed preprocessing method and two-stage feature selection method, some methods are used as comparisons: Method1 (EMD preprocessing with two-stage feature selection), Method2 (VMD preprocessing with Fisher discrimination), and Method3 (VMD preprocessing with ReliefF). The identification results and confusion matrix of reverse-normal switching process are shown in Table 3 and Figure 7.

Table  3.  Identification results of reverse-normal switching process

Type	Traning samples	Test samples	Number of correctly identified samples
			Method1	Method2	Method3	Method4 (proposed method)
a	36	24	24	24	24	24
b	34	23	19	22	23	23
c	36	24	23	24	24	24
d	23	16	16	16	16	16
e	24	16	16	15	14	16
f	36	24	23	24	24	24
g	36	24	24	24	24	24
h	36	24	24	24	23	24
Accuracy (%)			96.57	98.86	98.29	100

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Figure  7.  Confusion matrix of reverse-normal switching process.

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From Table 3 and Figure 7, it can be concluded that the proposed method performs best on the fault diagnosis of railway point machines with an accuracy of 100%. Compared with the proposed method, Method1 performs worst, indicating the superiority of VMD preprocessing method. Besides, the performance of Method2 and Method3 is worse than that of the proposed method, demonstrating the effectiveness and feasibility of the two-stage feature selection method. Therefore, by combining Fisher discrimination and ReliefF, the proposed two-stage feature selection method performs better than any of them. By comparison analysis, the proposed method combining VMD and two-stage feature selection method performs best on each working condition, indicating its feasibility and superiority.

The identification results and confusion matrix of normal-reverse switching process are shown in Table 4 and Figure 8, respectively. The analysis conclusion is the same for the normal-reverse switching process. Overall, the fault diagnosis accuracy of the proposed method reaches the highest. Detailed analysis is not given here.

Table  4.  Identification results of normal-reverse switching process

Type	Traning samples	Test samples	Number of correctly identified samples
			Method1	Method2	Method3	Method4 (proposed method)
a	36	24	23	24	24	24
b	35	23	22	23	23	23
c	36	24	23	21	24	23
d	24	16	16	16	16	16
e	24	16	15	8	11	11
f	36	24	20	24	24	24
g	35	24	24	24	24	24
h	36	24	24	24	23	24
Accuracy (%)			95.43	93.71	96.57	96.57

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4   Discussions

This paper aims to propose an intelligent fault diagnosis method for railway point machines based on new means (vibration signals) due to its good anti-interference characteristics. Two data preprocessing methods (EMD and VMD) are compared. The experiment results show the superiority of VMD. Besides, a two-stage feature selection method combining Fisher discrimination and ReliefF is proposed, which is a more powerful tool for feature selection. The fault diagnosis accuracies of both normal-reverse and reverse-normal switching processes reach the highest by comparison experiments, indicating its superiority. However, it is noted that the identification accuracy of working condition-e of normal-reverse switching process is a little lower than that of reverse-normal switching process, which may be caused by the structural asymmetry of the ZDJ9 railway point machine. In the future, more studies will be done to improve the identification accuracy of working condition-e of normal-reverse switching process.

Figure  8.  Confusion matrix of normal-reverse switching process.

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V.   Conclusion

This paper proposes a novel vibration signal-based intelligent fault diagnosis method for railway point machines. VMD is used to preprocess the non-stationary vibration signals, which is verified as a more powerful tool than EMD. A two-stage feature selection method by combining Fisher discrimination and ReliefF is developed, which can significantly improve fault diagnosis accuracy of railway point machines. By applying the two-stage feature selection method, the feature dimension can be significantly reduced from 240 to 35. Experiment comparisons with different processing method and single feature selection method verify the superiority and effectiveness of the proposed method. The satisfying diagnosis accuracy of two switching processes reach 100% and 96.57%, respectively. The presented method provides a new idea for fault diagnosis for railway point machines. Besides, it can also provide references for other mechanical fault diagnosis fields.