Fault Diagnosis for Railway Point Machines Using VMD Multi-Scale Permutation Entropy and ReliefF Based on Vibration Signals

I.   Introduction

Railway plays an important part in passenger services and good transportation [1]–[7]. At present, most maintenance works are based on manual operation, urgently requiring the development and application of intelligent fault diagnosis methods [8]–[11]. Fault diagnosis has become one of the most important tasks in the engineering field [12]. It is the same for railway systems [13]–[16]. Especially, as one of the three outdoor equipment of the railway signaling system, railway point machines are used to provide routes for the trains. According to statistics, the faults of railway point machines account for 40% of the number of railway signaling system faults. Therefore, it is necessary to develop diagnosis method for railway point machines.

At present, the existing diagnosis works for railway point machines can be summarized as model-based methods, knowledge-based methods, and signal processing-based methods. 1) Model-based methods construct a model to characterize and reflect the switching mechanism of railway point machines for diagnosis [17], [18]. Though they can well address anomaly detection and fault diagnosis, it is difficult to acquire accurate model parameters in practice. 2) Knowledge-based methods use expert experience or knowledge and rules extracted from fault data to realize fault diagnosis [19]. However, the diagnosis rules were based on expert experience. 3) Signal processing-based methods provide an effective and intelligent way to realize fault diagnosis due to the developed signal processing technologies. For anomaly detection, the threshold-based method is the most commonly used method [20], [21]. Dynamic time warping is one of the popular methods to calculate the deviation and similarity between the given current curve and the nominal current curve [22], [23]. However, it can only detect abnormality, but not identify what fault occurs. Therefore, more intelligent fault diagnosis approaches are studied, such as some data-driven methods using different feature extraction and classification means [24]–[27]. These literatures mainly conduct research based on artificial extracted features. To realize automatic fault feature extraction, locally connected autoencoder was utilized for fault diagnosis [28]. However, most of the existing methods are on basis of analysis of motor current curve signals, which may have limited ability to characterize all mechanical faults. Recently, sound signals and vibration signals have been spreadly applied in the fault diagnosis field of mechanical equipment [29]–[33]. But in practice, sound signals are easily disturbed.

In view of the above literature review, this work aims to conduct diagnosis research based on vibration signals due to their higher anti-interference ability. In the past several decades, empirical mode decomposition (EMD) is widely used for processing nonstationary signals because it is an adaptive method [34]. However, it has some disadvantages, mode mixing and endpoint effect, etc. In 2014, variational mode decomposition (VMD), a novel processing method for nonstationary signals was proposed, which is based on strict mathematical derivation [35]. VMD has been verified as a more efficient tool in fault diagnosis of mechanical devices [36]. Thus VMD is adopted.

Permutation entropy (PE), as a simple and fast feature extraction method, can conveniently and accurately locate the moment when the system has a sudden change. Furthermore, multi-scale PE (MPE) can measure the complexity of time series from different time scales. Then feature selection is essential to reduce the redundant information to improve the diagnosis accuracy. Feature dimension reduction method mainly includes two categories: filter [37] and wrapper [38]. The former is simple, and can usually get good effect. Whereas the latter is more time-consuming. So filter method is utilized in this paper, where ReliefF is one of the preferable filter feature selection means [39].

Based on the above-mentioned methodology, this work presents a vibration signals-based fault diagnosis method. The main contributions are listed as follows. Vibration signal, a new monitoring mean, is introduced to conduct fault diagnosis for railway point machines. VMD, a more efficient tool is adopted to preprocess the nonstationary vibration signals. A feature extraction and selection method combining MPE and ReliefF is developed, which can greatly decrease feature dimension.

The rest of this paper is organized as follows. Section Ⅱ gives the setup and data descriptions. Section Ⅲ presents the methodology. Section Ⅳ shows results and comparisons. Section Ⅴ gives some conclusions.

II.   Setup and Data Descriptions

The used vibration signals in this work are acquired from Xi’an Railway Signals Co., Ltd. ZDJ9 railway point machine. An accelerometer sensor PCB 356A16_K is adopted to collect the vibration signals during switching process with a sampling frequency of 5.12 kHz. The throw rod is an important component to transmit the switching force of the railway point machines. Thus the accelerometer sensor is installed on the throw rod, as shown in Figure 1.

Figure  1.  Experiment setup.

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Vibration signals of total eight categories of working conditions (Conditions a–h) are acquired. Figure 2 gives their time-domain waveforms during reverse-normal process. And Table 1 shows the corresponding condition descriptions.

Figure  2.  Time-domain waveforms of vibration signals during reverse-normal process.

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Table  1.  Condition description

Condition	Description	Number
a	Smaller load than nominal load (3 kN)	60
b	Nominal load (4 kN)	57
c	Larger load than nominal load due to switching resistance (I) (5 kN)	60
d	Larger load than nominal load due to switching resistance (II) (6 kN)	39
e	The railway point machine slips due to obstacles	40
f	Indication circuit cannot be connected due to improper gap	60
g	No load (broken throw rod)	60
h	The railway point machine slips caused by insufficient friction of frictional clutch	60

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The detailed descriptions of different working conditions can be seen in our previous work [40]. Overall, though the time-domain waveforms under various working conditions are different, some of them show a certain similarity, such as Conditions a–d. Therefore, an efficient fault diagnosis method is urgently needed.

III.   Methodology

1   Proposed fault diagnosis approach

Given the literature review and the characteristics of the collected vibration signals, a fault diagnosis approach for railway point machines using VMD, MPE and ReliefF is developed. The framework is shown as Figure 3. First, VMD is adopted to realize stabilization preprocessing. Then, MPE features are applied to acquire efficient feature extraction contained in these modes. ReliefF is utilized for feature selection. Finally, support vector machine (SVM) is selected to realize fault diagnosis due to its superiority on classification of small sample.

Figure  3.  Framework of the presented approach.

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2   VMD

VMD is a new and adaptive signal processing method applying mathematical variational ideas. By iteratively searching for the optimal solution of the variational modes, constantly updating the modes $u_k$ and the central frequency $w_k$, several modes with a certain bandwidth can be obtained, so that these modes can best reconstruct the given input signal $f(t)$. Meanwhile, each mode is limited to an online estimated central frequency $w_k$. The decomposition model of VMD is constructed as

where $K$ presents the number of decomposed modes, $\delta (t)$ is the unit pulse function, j satisfies j² = 1, and * represents convolution operation.

The above constrained variational problem is transformed into a non-constrained one by introducing penalty factor $\alpha$ and Lagrange multiplier $\lambda$ as follows:

Combining the alternating direction multiplier method and the Fourier transform method, $u_k^{n + 1}$, $w_k^{n + 1}$, and $\lambda _k^{n + 1}$ are continuously updated iteratively and converted to the frequency domain. Finally, the qualified minimum function value of the varitional problem can be solved. The iterative formulas are as follows:

where $\tau$ is the noise tolerance parameter, $\hat{f} (w)$, $\hat{u} _k^n(w)$, $\hat{u} _i^n(w)$, and $\hat{\lambda } ^n(w)$ are the Fourier transform of $f(t)$, $u_k^n(t)$, $u_i^n(t)$, and $\lambda^n(t)$, respectively.

When $\sum\limits_k {\|\|\hat u_k^{n + 1} - \hat u_k^n\|\|_2^2} \/\|\|\hat u_k^n\|\| < \varepsilon ,{\kern 1pt} {\kern 1pt} \varepsilon > 0$ is satisfied, the iteration is ended to obtain the optimal modes.

3   MPE

Bandt et al. proposed PE [41], which reconstructs the sequence and then arranges it in ascending order. The complexity is measured by calculating the entropy value through the probability of occurrence of the arrangement pattern. The basic principle of MPE can be seen in our previous work [42].

4   ReliefF

For a given training set $S$, randomly select a sample $R$. Then search $k$ nearest samples with the same category to form the set $M$, and search $k$ nearest samples with other categories to form the set $H$. The weight of feature point $A$ is updated by

where $p(c)$ represents the probability that sample belongs to class $c$, ${\rm{diff}}(A, R, H_j)$ is an operator. For discrete variables, ${\rm{diff}}(A, R, H_j)$ is defined as

For continuous variables, ${\mathrm{diff}}(A, R, H_j)$ is defined as

where $R(A)$ and $H_j(A)$ represent the value of feature point $A$ in sample $R$ and $H_j$.

Repeat the above update steps for $m$ times, the weights of each feature point can be obtained.

5   SVM

Due to the applicability for small sample, SVM with radial basis function is utilized. The hyperparameters are optimized using particle swarm optimization [42].

IV.   Experiment Results and Comparison

This section gives the experiment results and comparison.

1   Feature extraction

Vibration signals of railway point machines are nonlinear and non-stationary. To realize stationary processing, VMD is adopted to process the vibration signals. In VMD, the penalty coefficient is selected as the default value 2000 [43], and modes’ number is selected as 14. Taking a vibration sample of Condition a during reverse-normal switching process as an example, its VMD results are given as Figure 4.

Figure  4.  VMD results of a vibration sample of Condition a during reverse-normal process.

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As can be seen from Figure 4, the vibration sample is decomposed into 14 modes. This paper only selects the first 12 modes for further studies.

Then, MPE extraction procedures are applied to the first 12 modes. Noted that the parameter embedding dimension has a great influence on the feature quality. Too small embedding dimension leads to too few types of permutation patterns, making it difficult to mine permutation information contained in the signals. However, too large embedding dimension leads to a significant increase in the time of extracting the permutation entropy. Combined, this paper set embedding dimension and time lag as 4 and 1, respectively [44]. Besides, coarse-grain scale factor also influences the feature quality. Similarly, too larger scale factor will result in time-consuming feature extraction process. In this paper, scale factor is set as 20. Therefore, for one sample, the feature dimension is $12\times 20$.

2   Feature selection

ReliefF is utilized for feature selection. The weights of the 240 feature points are given as Figure 5. It can be concluded that the weights of most fault feature points are greater than 0. According to statistics, the weights of 188 feature points are greater than 0. Thus they are selected as the optimal feature subset.

Figure  5.  Weights of feature points.

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3   Comparisons with different fault diagnosis methods

A total of 60% of the vibration samples are utilized as the training set. To demonstrate the superiority of the presented fault diagnosis approach, some different fault diagnosis approaches are utilized for comparisons: EMD+MPE: EMD for preprocessing and MPE for feature extraction, EMD+MPE+ReliefF: EMD for preprocessing, MPE for feature extraction and ReliefF for feature selection, VMD+MPE: VMD for preprocessing and MPE for feature extraction. The diagnosis results during reverse-normal process are given as Table 2 and Figure 6.

Table  2.  Diagnosis results during reverse-normal process

Condition	Number of test samples	Number of correctly detected samples
		EMD+MPE	EMD+MPE+ReliefF	VMD+MPE	Proposed method
a	24	17	24	24	24
b	23	10	18	23	23
c	24	7	20	24	24
d	16	5	11	16	16
e	16	9	15	14	16
f	24	8	19	24	24
g	24	18	23	24	24
h	24	10	21	24	24
Accuracy (%)		48.00	86.29	98.86	100.00

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Figure  6.  Confused matrix during reverse-normal process.

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From Table 2 and Figure 6, it can be concluded that EMD+MPE performs worst on fault diagnosis of railway point machines, with accuracy of 48%. By combining with ReliefF, EMD+MPE+ReliefF performs much better (86.29%), indicating the necessity of feature selection using ReliefF. Compared to EMD preprocessing method, VMD can much improve the diagnosis accuracy. For example, VMD+MPE realizes fault diagnosis of railway point machine with accuracy of 98.86%, much higher than EMD+MPE. By combing with ReliefF, the proposed method performs best, with accuracy of 100%. Besides, the diagnosis accuracy of each wording condition using the proposed method is the highest.

The diagnosis results during normal-reverse process are given as Table 3 and Figure 7.

Table  3.  Diagnosis results during normal-reverse process

Condition	Number of test samples	Number of correctly detected samples
		EMD+MPE	EMD+MPE+ReliefF	VMD+MPE	Proposed method
a	24	22	24	24	24
b	23	9	16	23	23
c	24	13	14	24	24
d	16	9	12	16	16
e	16	6	7	13	13
f	24	15	17	24	24
g	24	23	24	24	24
h	24	23	23	24	24
Accuracy (%)		68.57	78.29	98.29	98.29

 | Show Table

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Figure  7.  Confused matrix during normal-reverse process.

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The diagnosis result analysis of normal-reverse process is similar to that of reverse-normal process. Thus the analysis will not be repeated here.

4   Discussion

This paper aims to develop a novel vibration signal-based fault diagnosis approach for railway point machines. The effect of EMD preprocessing and VMD preprocessing are compared, which indicates VMD is more suitable for preprocessing the vibration signals of railway point machines. Feature selection is realized using ReliefF algorithm, which can further improve the fault diagnosis accuracy. It is noted that the diagnosis accuracy on reverse-normal process is higher than that of normal-reverse process, which may be caused by asymmetrical mechanical structure of railway point machines. Besides, the diagnosis accuracy of Condition e during normal-reverse process is a little lower than the other conditions, which will be our future studies.

V.   Conclusions

This work presents a novel vibration signal-based diagnosis approach for railway point machines. VMD is adopted for data preprocessing, which is verified as a more effective tool than EMD. Then the extracted MPE features are optimized by using ReliefF, which can greatly decrease feature dimension and improve fault diagnosis accuracy. By comparisons, the presented approach performs best on fault diagnosis of railway point machines during both switching processes. Vibration monitoring is one means that can conveniently applied to railway point machines due to its anti-interference performance and bringing no interference to railway point machines. This study provides the possibility of on-site application, which can help the maintenance staff realize fast fault diagnosis and location. Besides, this paper may also provide reference for other fault diagnosis fields.