Research on Health Stage Division of Switch Machine Based on Bray-Curtis Distance and Fisher Optimal Segmentation Method

I.   Introduction

As one of the three basic equipments of Chinese railway signaling system, switch machine equipment plays the role of switching and locking turnouts, thus its health status is related to the efficiency and safety of railway traffic, and in case of failure, it will have incalculable consequences. With the rapid development of China’s railway industry, the railway signal monitoring system has collected a large amount of real-time monitoring data, which contains information about health status of switch machine. How to use these monitoring data to realize health management of switch machine is of great significance to meet requirements of preventive maintenance of equipment and ensure the efficiency of driving.

In recent years, scholars have made many achievements in the research of switch machine health management. Zhong [1] proposed methods for turnout switch machine fault detection and health management based on vector machine description, which can effectively evaluate health status of turnout switch machine. Gao et al. [2] proposed the use of self organizing map (SOM) and back propagation (BP) hybrid neural network to classify and identify the degradation state of turnout switch machine. Li [3] proposed to use neural network to evaluate the state of turnout switch machine and predict its life. Kampczyk et al. [4] applied digital twin technology to railway turnouts by monitoring temperature and atmospheric conditions to achieve real-time mastery of turnout switch machine health status. Cheng et al. [5] established the fault rule through data analysis and fault feature extraction, and studied a complete data acquisition system based on the turnout switch machine. Zhang [6] analyzed the characteristics of each stage of the action curve and used BP neural network algorithm to diagnose the fault of turnout switch machine. Lee et al. [7] proposed a fault diagnosis method based on the change of sound converted by the turnout switch machine. Bemment et al. [8] designed a simple dynamic reference model using historical operation data for fault diagnosis of turnout switch machine.

However, these studies did not give a segmentation interval for health or degradation state of the switch machine, and could not accurately correspond to each health stage of switch machine. In order to solve these problems, this paper divides the health stages of railway ZYJ7 switch machine based on Bray-Curtis distance and Fisher optimal segmentation. The main contributions and innovations of this work are as follows:

1) In this paper, a new data feature screening method is proposed, that is, the Holder coefficient method is used to screen the feature parameters of switch machine. Compared with traditional feature parameter screening methods, Holdr coefficient method is more suitable for high-dimensional data, which can mine and screen feature parameters with greater correlation with the health status of switch machine, and sort them.

2) The Bray-Curtis distance algorithm is used to calculate the health index of switch machine and digitize the status of the switch machine equipment. Compared with the traditional algorithm, this method can capture the degradation characteristics of switch machine more accurately and detect the degradation information of the equipment earlier.

3) In this paper, we propose a new method to divide the state of switch machine, that is, Fisher optimal segmentation is used to divide the health stage of switch machine. This method can calculate the health index value of each health stage of switch machine, and provide data support for the division of the health stage of switch machine.

II.   Basic Theory

In this paper, health stage of switch machine is divided into three main parts, the spceific process is as follows:

1) Feature selection. Switch machine power curve is divided into 5 stages, and 8 time-domain features of each stage are extracted for a total of 40-dimensional feature parameters. The first 15-dimensional feature parameters with the highest correlation with switch machine state are selected as the final parameter set using Holder coefficients.

2) Calculation health index. The Bray-Curtis distance is used to calculate switch machine health index curve and compare algorithm results with Frechet distance and Euclidean distance.

3) Health stage division of switch machine. The Fisher optimal segmentation method is used to divide the health index (HI) curve of switch machine, determine the optimal partitioning scheme, i.e., the optimal number of health stages, and determine health index interval for each health stage.

1   ZYJ7 switch machine

ZYJ7 switch machine was born to meet the requirements of speed turnout in 1998 [9], [10], which has changed the electric or pneumatic transmission mode of switch machine and adopted the electro-hydraulic transmission mode to convert hydraulic energy into mechanical energy to realize the traction of turnout. ZYJ7 switch machine has fast switching speed and high response efficiency, and is widely used in high-speed line sections in China. Therefore, ZYJ7 electro-hydraulic switch machine is adopted as the object of this paper. Fig.1 shows the schematic diagram of the ZYJ7 switch machine.

Figure  1.  ZYJ7 switch machine.

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2   Feature extraction and screening

For ZYJ7 switch machine research and maintenance means generally rely on relevant data in microcomputer monitoring system, such as: current, voltage and power. The current curve can reflect situation of most switch machine during operation, due to the use of three-phase motors, current curve cannot accurately reflect the resistance encountered during switch machine action in time, while power curve of switch machine is strongly influenced by resistance and can reflect moving push-pull force of turnout tip-rail in real time [11], the power data of ZYJ7 switch machine is selected in this paper as the basis for analyzing its health status.

Power curve duration of standard ZYJ7 switch machine is generally less than 9 s [12], and the power curve can be divided into five stages: A–E. A stands for starting stage, B for unlocking stage, C for conversion stage, D for locked stage, and E for indicating stage [12]. The specific division schematic is shown in Fig.2 .

Figure  2.  Power curve of ZYJ7 switch machine.

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Switch machine power curve is a typical time series, time-domain features can better represent characteristics of the whole curve. In this paper, power curve is divided into five stages, and 8 time-domain features of each stage are extracted, with a total of 40-dimensional data, are extracted as the initial feature parameter set. The feature parameter names and calculation formulas are shown in Table 1.

Table  1.  Equations for the 8 time-domain characteristic parameters

Parameters	Formula
STD	$\sqrt{\frac{1}{C}{ {\sum }_{c=1}^{C}{(F(c)-\frac{1}{C}{{\sum }_{c=1}^{C}F(c)})}^{2} } }$
KT	$\dfrac{ {\frac{1}{C}\sum\nolimits_{i = 1}^C {F{ {(i)}^4} } } }{ { {\sigma ^4} } }$
P2P (W)	$\max (F) - {\text{min} }(F)$
SK	$\dfrac{ {\frac{1}{C}\sum\nolimits_{i = 1}^C {F{ {(i)}^2} } } }{ { {\sigma ^2} } }$
RMS	$\sqrt {\frac{1}{C}\sum\nolimits_{c = 1}^C {F(c)} {}^2}$
CF	$\frac{ {{\rm{max}}(F)} }{ {{\rm{RMS}}} }$
Mean (W)	$\frac{1}{C}\sum\nolimits_{c = 1}^C {F(c)}$
Var	$\frac{1}{C}\sum\nolimits_{c = 1}^C { { {(F(c) - \frac{1}{C}\sum\nolimits_{c = 1}^C {F(c)} )}^2} }$

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Too many dimensions of the initial feature parameter set are not conducive to the subsequent algorithm input and will affect the accuracy of algorithm results. In this paper, Holder coefficient method is used to screen switch machine feature parameters to achieve data dimensionality reduction.

Holder coefficient is evolved from the Holder inequality [13]–[15], which can be used to characterize magnitude of the correlation between two functions, defined and described as follows: let $f(i)$ and $g(j)$ be two one-dimensional sequences of positive signals $\{ i = 1,2, \ldots ,N,\,j = 1,2,\ldots ,N \}$, and the Holder coefficient between the two sequences is defined as

where $f(i)$ is set as a sequence of time domain characteristic parameters, $g(j)$ is set as a sequence of standard power curves, $p,q > 1$ and satisfying $\frac{1}{p}+\frac{1}{q} =1$, and $0 \lt {\rm{HC}} \lt 1$.

The larger HC value indicates the higher correlation between characteristic parameter and standard power curve. The HC values of 40-dimensional characteristic parameters are solved, and the top 15-dimensional characteristic parameters are determined as the final characteristic parameter set for switch machine health assessment according to size ranking.

3   Calculating health index

Switch machine health index is deviation value between measured condition and standard condition, which can characterize current health state of switch machine. In this paper, Bray-Curtis distance is used to calculate switch machine health index.

Bray-Curtis distance is a common metric used in biology to calculate similarity between two biomes based on species composition [16]–[19], which can characterize not only the degree of difference between species, but also the abundance of species [20]. The calculation formula is

where $x_{ik}$ is the $i$-th feature of the standard power curve of switch machine, $x_{jk}$ is the $j$-th feature of the measured power curve of the switch machine, $m$ is the number of feature parameters, $m=15$ according to the previous.

HI is obtained in the range of $[0,1]$, the larger Bray-Curtis distance value, i.e., the larger HI value, the greater difference between actual condition of switch machine and standard health condition, and the poorer health condition of switch machine; conversely, the smaller HI value, the better health condition of switch machine. HI curve of switch machine is obtained by calculating one HI value for each action of switch machine and so on, the degradation trend of switch machine can be visualized according to fluctuation of the curve.

4   Delineation of health stages

Health index curve of switch machine can only roughly determine current state of switch machine, and the key problem to be solved is how to divide health state of the equipment and how to give interval and threshold value between health states. Since the degradation process of switch machine is irreversible, health index is also an irreversible sequence. For health life cycle of switch machine, HI curves are divided using Fisher optimal segmentation method to determine a scheme for dividing health stages of switch machine [21]–[24]. Fisher optimal segmentation method, which evolved from Fisher criterion, is a mathematical clustering algorithm for optimally segmenting ordered samples [22]–[24]. For $n$ samples, there are $2^{n-1}$ segmentation methods for their segmentation. Fisher optimal segmentation method consider that there exists a segmentation method that can make data within each segment group have the least difference and the most similar characteristics, while difference between groups is the greatest and the most obvious, and this segmentation method is called the optimal segmentation for this sample, and uses this characteristic to determine the optimal segmentation scheme for health stages of switch machine, specific process is as follows.

Step 1: Set switch machine health index sample as $X=[x_1, x_2, \ldots, x_n ]$, total $n$ sample data, in order to prevent the switch machine health stages from being divided too much, which makes the differences within stages not obvious, and increases workload. In this paper, the maximum number of health stages for switch machine is 8, i.e., there are eight segmentation schemes: $k=1,2,\ldots, 8$.

Step 2: Fisher optimal segmentation uses diameter of the class to indicate the degree of variation in the group, if diameter is smaller, it indicates that variation in the group is smaller and data is more concentrated. A class contain samples of $p = \{ x_{i},x_{i + 1},\ldots x_{j}\}$,define the diameter as

where $x_{G}$ is the median, $x_a$ is the $a$-th sample, $i\le n$, $j\le n$.

Diameter of each group in the eight classification schemes from k = 1 to 8 was obtained based on the formula.

Step 3: Error function is usually used to measure goodness of the classification results, and error function is defined as the sum of diameters of each category. The formula is

where $p(n,k)$ is classification of the optimal segmentation and$k$is the number of segments to be segmented.

The error functions of the eight classification schemes from $k=1$ to 8 were calculated. The final optimal segmentation scheme is determined by considering two aspects: firstly, by plotting the curve of error function $e[p(n,k)]$ with the change of classification number $k$, and taking the value of $k$ corresponding to the more obvious change of this curve as the most suitable classification number; secondly, calculating absolute value of slope $f(k)$ of this curve at each classification point. Then $f(k)$-$k$ curve is plotted. The larger the $f(k)$, the better the $k$ classification is than the $k-1$ classification, and classification number $k$ that makes $f(k)$ the maximum is generally taken as the optimal classification number. $f(k)$ is calculated by the following formula:

where $e[p(n,k)]$ is error functions, $k$ is classification number, $n$ is sample data, $n=4382$.

Step 4: After determining the health stage of switch machine, HI interval and threshold value for each health stage of switch machine can be determined by obtaining HI value corresponding to divided division points.

III.   Experimental Validation

1   Holder coefficient extraction and screening of feature parameters

In this paper, 4382 sets of power data of ZYJ7 switch machine in Changsha Electric Section are used, among which the first 4094 motions are normal fault-free data of switch machine. Firstly, feature extraction is performed on power curve of switch machine divided into five segments, and 8 time-domain features of each segment are extracted, totaling 40-dimensional data. The feature parameters of some sample sequences are shown in Table 2.

Table  2.  Partial sample sequence characteristic parameters

Sample	A: Starting stage
	Var	STD	Mean	RMS	CF	KT	SK	P2P
1	1.29	1.13	1.52	1.89	1.79	−1.58	0.12	3.35
2	1.32	1.15	1.54	1.88	1.74	−1.57	0.10	3.35
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
4382	1.29	1.14	1.52	1.90	1.78	−1.43	0.12	3.36
	B: Unlocking stage
1	0.15	0.39	1.84	1.88	1.30	−1.33	−0.11	1.17
2	0.14	0.38	1.82	1.88	1.26	−1.56	−0.10	1.19
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
4382	0.15	0.41	1.85	1.88	1.31	−1.41	−0.10	1.20
	C: Conversion stage
1	0.01	0.05	1.39	1.39	1.05	−0.87	−0.57	0.16
2	0.01	0.04	1.54	1.23	1.12	−0.77	−0.62	0.13
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
4382	0.009	0.04	1.31	1.35	1.01	−0.88	−0.61	0.16
	D: Locked stage
1	0.01	0.12	1.31	1.32	1.08	0.65	−1.32	0.35
2	0.02	0.14	1.57	1.48	1.14	0.78	−1.33	0.41
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
4382	0.01	0.14	1.31	1.38	1.28	0.63	−1.18	0.39
	E: Indicating stage
1	0.09	0.30	0.32	0.44	2.19	−0.46	0.81	0.93
2	0.08	0.34	0.30	0.39	1.84	−0.57	0.80	0.88
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$
4382	0.08	0.27	0.39	0.53	1.98	−0.43	0.92	0.97

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Holder coefficient method was used to filter 15 dimensions from the 40-dimensional characteristic parameters obtained. The standard power curve is collected 165 data, set as series S₁, accordingly a certain characteristic parameter of 165 groups of power curve is extracted, such as the variance of selected 165 groups of power curve, set as series S₂. the magnitude of the correlation of these two series is solved according to Holder coefficient formula, expressed as HC value. The results of solving HC value for the 40-dimensional characteristic parameter are shown in Table 3.

Table  3.  HC values of 40-dimensional characteristic parameters of switch machine

A: Starting stage
Var	STD	Mean	RMS	CF	KT	SK	P2P
0.5744	0.5753	0.6277	0.5934	0.6549	0.6059	0.7365	0.7403
B: Unlocking stage
0.7304	0.6128	0.6422	0.6301	0.5904	0.5789	0.5826	0.7869
C: Conversion stage
0.7466	0.6278	0.8546	0.8831	0.8201	0.6031	0.7011	0.7869
D: Locked stage
0.6983	0.6302	0.6757	0.6029	0.5844	0.5933	0.5848	0.6342
E: Indicating stage
0.6401	0.6302	0.6972	0.6029	0.5844	0.5970	0.6733	0.6434

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After sorting the 40-dimensional HC values, the top 15-dimensional feature parameters were selected as the final parameter set, i.e., these 15-dimensional feature parameters are the ones with the greatest correlation with switch machine power curve and the greatest influence on switch machine state. The finalized 15-dimensional parameters and their ranking are shown in Table 4. For example, HC_C-RMS is HC value of RMS in the C section (conversion section) of switch machine power curve.

Table  4.  Ranking table of HC values of 15-dimensional characteristic parameters of switch machine

Serial number	Characteristic parameters	HC		Serial number	Characteristic parameters	HC
1	HCC-RMS	0.8831		9	HCC-SK	0.7011
2	HCC-Mean	0.8546		10	HCD-VAR	0.6983
3	HCC-CF	0.8201		11	HCE-Mean	0.6972
4	HCC-P2P	0.7869		12	HCD-Mean	0.6757
5	HCC-VAR	0.7466		13	HCE-SK	0.6733
6	HCA-P2P	0.7403		14	HCA-CF	0.6549
7	HCA-SK	0.7365		15	HCE-P2P	0.6434
8	HCB-VAR	0.7304		–	–	–

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2   Bray-Curtis distance calculation of switch machine health index

The switch machine characteristic parameter set is $15\times 4382$ sets of data, and Bray-Curtis distance algorithm is used as the input of switch machine characteristic parameter set to calculate health index that can characterize the change of switch machine health status. The obtained health index curves of 4382 sets of switch machine are shown in Fig.3.

Figure  3.  Bray-Curtis distance calculation for switch machine HI.

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To verify the validity of calculating health index curve of switch machine using Bray-Curtis distance, Frechet distance and Euclidean distance were chosen as the comparison algorithms, and health index curve calculated by Frechet distance and Euclidean distance algorithms are shown in Figs.4 and 5.

Figure  4.  Frechet distance calculation for switch machine HI.

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Figure  5.  Euclidean distance calculation switch machine HI.

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Through the preliminary observation of the health index curves of switch machine under the three algorithms, it can be seen that the health index of switch machine is significantly reduced when the switch machine is converted for about 2500 times, indicating that the health status of switch machine during this period has improved compared with that before. This is because the “self-healing” phenomenon of switch machine, a mechanical equipment, will degrade the equipment due to the mutual running-in of its internal mechanical components at the initial stage of equipment operation, after a period of running-in of devices, the equipment will be in a relatively healthy state for a short time. Later, due to the rising utilization rate, the switch machine will begin to deteriorate more seriously until it fails. The health index curve of switch machine in the figure rises sharply when switch machine is converted for about 4000 times, indicating that health status of switch machine is not good at this time. Combined with the aforementioned switch machine failure after 4094 times of conversion, it is proved that the health index curve obtained by the algorithm can truly reflect actual health status of switch machine.

By comparing Figs.3, 4 and 5, it can be seen that health index curve calculated by Bray-Curtis distance is smoother than other algorithms, and the overall degradation trend of switch machine is more clear, with less large fluctuations, which conforms to the irreversible characteristics of switch machine degradation.

To further verify the effectiveness of the algorithm, curve Tendency, Robustness, and Runtime are used to evaluate the experimental results. Tendency can evaluate the correlation between health indexs and transfor-mation sequence $n$. The formula is shown as

where, $n$ is the switch machine conversion sequence, that is, $n=4382$, ${\rm{HI}}_k$ is the $k$th health index, $\overline{HI}$ is the mean value of health indicators, and $n_k$ is the $k$th conversion sequence, $\overline{n}$ is the mean value of the conversion sequence.

The results of the algorithm comparison are shown in Table 5.

Table  5.  Comparison of the effect of algorithms to calculate the health index of switch machine

Projects	Tendency	Robustness	Runtime
Bray-Curtis distance	0.767	0.810	1.6 s
Euclidean distance	0.544	0.565	2.4 s
Frechet distance	0.732	0.782	2.1 s

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Table 5 shows that the health index of switch machine calculated by Bray-Curtis distance is 0.223 higher than European distance and 0.035 higher than Frechet distance in terms of algorithm curve tendency; In terms of algorithm robustness, it is 0.245 higher than Euclidean distance and 0.028 higher than Frechet distance; In terms of running time, Bray-Curtis distance is 0.85 s faster than European distance and 0.53 s faster than Frechet distance. It can be seen that Bray-Curtis distance has a better performance in calculating the health index of the switch machine, and can better reflect the whole process of the deterioration of the health state of the switch machine.

3   Fisher optimal segmentation based division of health stage

Take the obtained health index curve as the object of dividing the health stage of switch machine, that is, use Fisher optimal segmentation to classify 4094 groups of normal and fault free health index data of switch machine, and select the optimal classification from eight classifications, that is, the optimal number of health stages. The optimal classification method is determined from two aspects: first, the error function image of each classification scheme is drawn, and the $k$-value corresponding to the elbow in the image is the optimal classification; Secondly, the slope $f(k)$ of the error function image is calculated. the larger the slope is, the better $k$ classification is than $k-1$ classification.

Set the number of parameter classification is $k=1, 2,\ldots, 8$. When $k=2$, there are ${{\rm{C}}}_{n-1}^{k-1}={{\rm{C}}}_{4093}^{1}=4093$ classification methods for 4094 groups of data, that is, the number of algorithm iterations is 4093; and when $k=8$, there are ${{\rm{C}}}_{n-1}^{k-1}={{\rm{C}}}_{4093}^{7}=3.799 \times {10}^{21}$ classification methods for 4094 groups of data, that is, the number of algorithm iterations is $3.799 \times {10}^{21}$. The classification of eight classification schemes and their error functions and slopes $f(k)$ are shown in Table 6.

Table  6.  Health stage division scheme of switch machine

k	Error function	f(k)	Classification
1	–	–	(1,4094)
2	45.34	–	(1,589) (589,4094)
3	17.43	27.91	(1,589) (589,3248) (3248,4094)
4	9.27	8.16	(1,589) (589,2442) (2442,3248) (3248,4094)
5	7.66	1.61	(1,589) (589,1297) (1297,2442) (2442,3248) (3248,4094)
6	5.42	2.42	(1,589) (589,1297) (1297,2442) (2442,3248) (3248,3657) (3657,4094)
7	4.37	1.05	(1,589) (589,1297) (1297,2075) (2075,2442) (2442,3248) (3248,3657) (3657,4094)
8	3.28	1.09	(1,589) (589,1297) (1297,1944) (1944,2075) (2075,2442) (2442,3248) (3248,3657) (3657,4094)

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It can be seen from Table 6 that with increase of classification number k, the error function and slope show a decreasing trend. In order to further determine the optimal classification number, a image of error function and classification number $k$ is drawn as shown in Fig.6.

Figure  6.  Plot of error function with the number of classifications k.

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From Fig.6, It can be seen that the elbow point appears on the curve when $k$ equals 3, which indicates that after exceeding 3, error function no longer decreases much when $k$ increases further. Secondly, comparing the $f(k)$ values of each classification point, the $f(k)$ value is the largest when $k=3$. Therefore, the optimal number of segments for the health stage of switch machine is determined as 3, which is defined as health level I, health level II, and health level III, corresponding to description of switch machine state in each stage are shown in Table 7.

Table  7.  Operating status of switch machine in health stage

Health stage	Operating status description
Health I	Very good running condition, very low possibility of failure
Health II	General operating condition, can perform the work content more accurately, need to carry out preventive maintenance
Health III	Poor operating condition, the possibility of failure is very high, need to be repaired as soon as possible

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According to Table 6, when the number of health stages $k=3$, the classification is (1,589) (589,3248) (3248,4094), which corresponds to the health index curve. The final switch machine health stage division diagram is shown in Fig.7.

Figure  7.  Schematic diagram of the health stages of the switch machine.

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In Fig.7, it is determined that the dividing points of each health stage are 589 and 3248, that is, the switch machine enters the next health stage when it has converted 589 and 3248 times, and the corresponding health index are 0.088789 and 0.20381, that is, the health level I segmentation threshold is 0.088789, and the health level I interval is (0,0.088789); The threshold value of health level II segmentation is 0.20381, and the health level II interval is (0.088789,0.20381); The switch machine 4094 starts to fail, the corresponding health index is 0.33094, and the corresponding HI interval of the failure state is (0.33094,1).

IV.   Conclusions

This paper combines the current railway development situation and proposes a method of dividing the health state stages of switch machine based on Bray-Curtis distance and Fisher optimal segmentation for the serious problem of equipment degradation of switch machine. The following conclusions are drawn:

1) The switch machine power characteristic parameters screened by Holder coefficients can better characterize switch machine state, and the effective data dimensionality reduction is achieved by screening 15 dimensions from 40 dimensions of characteristic parameters.

2) The health index extracted by Bray-Curtis distance can effectively represent the change of the health status of the switch machine. Compared with the European distance and Frechet distance, the health index extracted by Bray Curtis distance has increased by 0.223 and 0.035 in tendency, 0.245 and 0.028 in robustness, and has shorter running time and more efficient algorithm.

3) The Fisher optimal segmentation method can be used to divide the healthy state stages of switch machine, and the health index intervals of each state can be clearly given. The classification effect is good, and it can more accurately correspond to the healthy state of the switch machine.

At present, the main data of this method is the power data of the switch machine in microcomputer monitoring system, which is one of the main bases for judging the state of switch machine equipment. In fact, there are other factors that may affect the collected data of switch machine.such as temperature, humidity, etc. The uncertainty of the equipment operating environment will bring more interference factors to switch machine status judgment. Therefore, it is necessary to consider other environmental interference factors in the future switch machine status assessment to make decision support suitable for on-site maintenance.