
Citation: | WU Xiaochun, WEN Xin. Research on Health Stage Division of Switch Machine Based on Bray-Curtis Distance and Fisher Optimal Segmentation Method[J]. Chinese Journal of Electronics, 2023, 32(5): 955-962. DOI: 10.23919/cje.2022.00.250 |
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.
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.
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.
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 .
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.
Parameters | Formula |
STD | √1C∑Cc=1(F(c)−1C∑Cc=1F(c))2 |
KT | 1C∑Ci=1F(i)4σ4 |
P2P (W) | max(F)−min(F) |
SK | 1C∑Ci=1F(i)2σ2 |
RMS | √1C∑Cc=1F(c)2 |
CF | max(F)RMS |
Mean (W) | 1C∑Cc=1F(c) |
Var | 1C∑Cc=1(F(c)−1C∑Cc=1F(c))2 |
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
HC=∑f(i)g(j)(∑fp(i))1/p(∑gq(j))1/q |
(1) |
where
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.
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
HI=dij=∑mk=1|xik−xjk|∑mk=1xik+∑mk=1xjk |
(2) |
where
HI is obtained in the range of
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
Step 1: Set switch machine health index sample as
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
D(i,j)=∑ja=i|xa−xG| |
(3) |
where
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
e[p(n,k)]=∑kj=1D(ij,ij+1−1) |
(4) |
where
The error functions of the eight classification schemes from
f(k)=|e[p(n,k)]−e[p(n,k−1)]k−(k−1)| |
(5) |
where
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.
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.
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
4382 | 0.08 | 0.27 | 0.39 | 0.53 | 1.98 | −0.43 | 0.92 | 0.97 |
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.
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 |
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, HCC-RMS is HC value of RMS in the C section (conversion section) of switch machine power curve.
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 | – | – | – |
The switch machine characteristic parameter set is
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.
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
Tre(HI,n)=|n∑k=1(HIk−¯HI)(nk−¯n)|√n∑k=1(HIk−¯HI)2(nk−¯n)2 |
(6) |
where,
The results of the algorithm comparison are shown in Table 5.
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 |
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.
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
Set the number of parameter classification is
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) |
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
From Fig.6, It can be seen that the elbow point appears on the curve when
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 |
According to Table 6, when the number of health stages
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).
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.
[1] |
Z. W. Zhong, “Research on methods of health condition assessment and prediction of railway turnout,” Ph.D. Thesis, Beijing Jiaotong University, Beijing, China, 2019, pp.4–27. (in Chinese).
|
[2] |
L. M. Gao, Q. Y. Xu, F. Li, et al., “Research on degradation state of turnout equipment based on SOM-BP hybrid neural network,” China Railway Science, vol.41, no.3, pp.50–58, 2020. (in Chinese) DOI: 10.3969/j.issn.1001-4632.2020.03.06
|
[3] |
Y. X. Li, “Research on degradation model of turnout switch based on neural network,” Master Thesis, Beijing Jiaotong University, Beijing, China, 2020, pp.1–34. (in Chinese)
|
[4] |
A. Kampczyk and K. Dybeł, “The fundamental approach of the digital twin application in railway turnouts with innovative monitoring of weather conditions,” Sensors, vol.21, no.17, article no.5757, 2021. DOI: 10.3390/s21175757
|
[5] |
W. Z. Cheng, H. D. Wang, and Y. Liang, “Research on fault analysis and diagnosis monitoring system for railway turnout switch machine,” China Railway, no.7, pp.43–47, 2018. (in Chinese) DOI: 10.19549/j.issn.1001-683x.2018.07.043
|
[6] |
K. Zhang, “The railway turnout fault diagnosis algorithm based on BP neural network,” in Proceedings of 2014 IEEE International Conference on Control Science and Systems Engineering, Yantai, China, pp.135–138, 2014.
|
[7] |
J. Lee, H. Choi, D. Park, et al., “Fault detection and diagnosis of railway point machines by sound analysis,” Sensors, vol.16, no.4, article no.549, 2016. DOI: 10.3390/s16040549
|
[8] |
S. D. Bemment, R. M. Goodall, R. Dixon, et al., “Improving the reliability and availability of railway track switching by analysing historical failure data and introducing functionally redundant subsystems,” Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit, vol.232, no.5, pp.1407–1424, 2018. DOI: 10.1177/0954409717727879
|
[9] |
X. C. Wu and X. Chu, “Research on division of degradation stage of turnout equipment based on wavelet packet decomposition and GG fuzzy clustering,” Journal of the China Railway Society, vol.44, no.1, pp.79–85, 2022. DOI: 10.3969/j.issn.1001-8360.2022.01.011
|
[10] |
X. D. Qin, “ZYJ7 type electro-hydraulic turnout daily maintenance and troubleshooting points analysis,” Municipal Engineering, vol.7, no.1, pp.110–124, 2022.
|
[11] |
H. X. Lin and Y. Dong, “Signal centralized monitoring system,” in Principles and Engineering Applications of Signal Centralized Monitoring System, China Railway Publishing House, Beijing, China, pp.20–58, 2015 (in Chinese).
|
[12] |
Editorial Board, “ZYJ7 switch machine”, in Typical Case Analysis of Railway Signal Centralized Monitoring, China Railway Publishing House, Beijing, pp.20–67, 2020 (in Chinese).
|
[13] |
H. H. Wang and X. F. Shen, “New intra-pulse feature extraction approach of radar emitter signals,” Systems Engineering and Electronics, vol.31, no.4, pp.809–811, 2009. (in Chinese) DOI: 10.3321/j.issn:1001-506X.2009.04.019
|
[14] |
C. C. Xu, Q. S. Zhou, J. Y. Zhang, et al., “Radar emitter recognition based on ambiguity function features with derivative constraint on smoothing,” Acta Electronica Sinica, vol.46, no.7, pp.1663–1668, 2018. (in Chinese) DOI: 10.3969/j.issn.0372-2112.2018.07.018
|
[15] |
Y. J. Yuan, S. W. Chen, Z. X. Liu, et al., “Radar signal sorting method based on the symmetric Holder coefficients of high-order spectrum,” Journal of Signal Processing, vol.36, no.10, pp.1775–1783, 2020. (in Chinese) DOI: 10.16798/j.issn.1003-0530.2020.10.018
|
[16] |
Z. H. Zhao, L. H. Li, S. P. Yang, et al., “An unsupervised bearing health indicator and early fault detection method,” China Mechanical Engineering, vol.33, no.10, pp.1234–1243, 2022. (in Chinese) DOI: 10.3969/j.issn.1004-132X.2022.10.013
|
[17] |
X. X. Hu, R. Niu, and T. Tang, “Pre-processing of metro signaling equipment fault text based on fusion of lexical domain and semantic domain,” Journal of the China Railway Society, vol.43, no.2, pp.78–85, 2021. (in Chinese) DOI: 10.3969/j.issn.1001-8360.2021.02.010
|
[18] |
G. K. Hu and Q. T. Zhang, “An applicability comparison between two similarity coefficients to biological assemblage analysis,” Transactions of Oceanology and Limnology, no.4, pp.140–145, 2019. (in Chinese) DOI: 10.13984/j.cnki.cn37-1141.2019.04.017
|
[19] |
L. Liu, H. Wang, C. C. Lin, et al., “Vegetation and community changes of elm (Ulmus pumila) woodlands in northeastern China in 1983–2011,” Chinese Geographical Science, vol.23, no.3, pp.321–330, 2013. DOI: 10.1007/s11769-013-0607-8
|
[20] |
X. Zhang, “Analysis of health management of high speed railway speed-up switch,” Railway Signalling & Communication Engineering, vol.16, no.2, pp.80–83, 2019. (in Chinese) DOI: 10.3969/j.issn.1673-4440.2019.02.019
|
[21] |
Z. F. Wang, J. Q. Zhen, F. Z. Zhu, et al., “Quaternion kernel fisher discriminant analysis for feature-level multimodal biometric recognition,” Chinese Journal of Electronics, vol.29, no.6, pp.1085–1092, 2020. DOI: 10.1049/cje.2020.09.009
|
[22] |
H. J. Wang and P. L. Wu, “Flood season division based on fisher optimal partition method,” Yellow River, vol.37, no.8, pp.30–34, 2015. (in Chinese) DOI: 10.3969/j.issn.1000-1379.2015.08.009
|
[23] |
Y. Cao, P. Li, and Y. Z. Zhang, “Parallel processing algorithm for railway signal fault diagnosis data based on cloud computing,” Future Generation Computer Systems, vol.88, pp.279–283, 2018. DOI: 10.1016/j.future.2018.05.038
|
[24] |
F. Gao, J. Liu, X. G. Yang, et al., “Study on optimization of thermal key points for machine tools based on Fisher optimal segmentation method,” Chinese Journal of Scientific Instrument, vol.34, no.5, pp.1070–1075, 2013. (in Chinese) DOI: 10.3969/j.issn.0254-3087.2013.05.017
|
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Parameters | Formula |
STD | √1C∑Cc=1(F(c)−1C∑Cc=1F(c))2 |
KT | 1C∑Ci=1F(i)4σ4 |
P2P (W) | max(F)−min(F) |
SK | 1C∑Ci=1F(i)2σ2 |
RMS | √1C∑Cc=1F(c)2 |
CF | max(F)RMS |
Mean (W) | 1C∑Cc=1F(c) |
Var | 1C∑Cc=1(F(c)−1C∑Cc=1F(c))2 |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
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 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
4382 | 0.08 | 0.27 | 0.39 | 0.53 | 1.98 | −0.43 | 0.92 | 0.97 |
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 |
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 | – | – | – |
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 |
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) |
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 |