A detection method for the impact of rainfall on the train journey time of high-speed railway networks

Abstract

The present invention relates to the technical field of high-speed railways, and specifically relates to a detection method for the impact of rainfall on the travel time of trains in a high-speed railway network, including the following steps: S1. Data collection: Collect the historical operation data of trains in the high-speed railway network, including the departure time, arrival time, stopping stations, and delay time of each train, and collect rainfall data near the stations in relevant regions; S2. Data preprocessing: Remove outliers, missing values, and incorrect data to ensure the accuracy and integrity of the data, and match the train operation data with the rainfall data according to time and location for subsequent analysis; S3. Impact analysis: Use the Markov chain Monte Carlo method based on kernel density estimation to quantify the average delay duration experienced by trains passing through each station under rainfall conditions, and further analyze the impact on the travel time of trains in the high-speed railway network under the spatio-temporal difference of rainfall. This method can perform detection and analysis quickly and accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of high - speed railways, and specifically relates to a method for detecting the influence of rainfall on the travel time of trains in a high - speed railway network. Background Art

[0002] High - speed railways play an important role in social and economic development and passenger travel. However, the travel time of high - speed trains is affected under rainfall conditions. The existing technology cannot quickly analyze the specific degree of its influence and the differences in influence under different spatio - temporal scenarios, lacking a theoretical basis for formulating train emergency measures and inspection plans under such conditions. Therefore, a reasonable detection and analysis method is needed to solve the above problems. Summary of the Invention

[0003] Aiming at the problems in the existing technology, the present invention provides a method for detecting the influence of rainfall on the travel time of trains in a high - speed railway network.

[0004] The technical solution adopted by the present invention to solve its technical problems is as follows: A method for detecting the influence of rainfall on the travel time of trains in a high - speed railway network, including the following steps:

[0005] S1. Data collection: Collect the historical operation data of trains in the high - speed railway network, including the departure time, arrival time, stopping stations, and delay time of each train, and collect the rainfall data near the stations in the relevant areas, including rainfall intensity and rainfall duration;

[0006] S2. Data pre - processing: Remove outliers, missing values, and error data to ensure the accuracy and integrity of the data, and match the train operation data with the rainfall data according to time and location for subsequent analysis;

[0007] S3. Influence analysis: Using the historical delay data of trains at a certain station under rainfall conditions, through the method of kernel density estimation, determine the probability density curve of the train delay time when rainfall occurs at this station; then, based on the Markov chain Monte Carlo method, quantitatively obtain the ergodic mean after sampling convergence under this density curve, so as to be used as the average delay duration when the train passes through this station under rainfall conditions, which reveals the influence of rainfall on the travel time of trains in different regions;

[0008] S4. Set different rainfall spatio - temporal scenarios, determine the running paths of each train in the network through the heap - optimized Dijkstra algorithm, consider the trains passing through the rainfall area during the research period being affected, and further analyze the number of affected trains in the high - speed railway network under each scenario, as well as the average delay degree and fluctuation degree of the travel time of all trains;

[0009] S5. Detection and Policy Recommendations: Taking the Yangtze River Economic Belt as an example, three different research areas are divided, and the proposed method is used to calculate the delay impact degree and fluctuation impact degree of rainfall on the train travel time of the high-speed railway network in the three different research areas respectively. After that, for the research area with the greatest impact degree, different rainfall occurrence time periods are set, and the impact of rainfall scenarios in different time periods on the train travel time in the network is further analyzed. The detection results can identify the areas and time periods with greater impact degree to quantify the impact of rainfall on train operation. Applying the detected impact results to the operation management and dispatching decision-making of high-speed railways helps to early warn and respond to train delays that may be brought by rainfall, and put forward targeted optimization measures to reduce the impact of rainfall on train travel time.

[0010] Advantages of the present invention:

[0011] First, the present invention can effectively detect the areas and time periods where rainfall has a greater impact on the train travel time of the high-speed railway network. The embodiment shows that the eastern research area can have a greater impact on the train travel time under rainfall conditions. This is related to the strong train flow between stations in the eastern region. At the same time, due to the departure time characteristics and planned travel time characteristics of trains in the network, rainfall occurring in the eastern research area between 6:00 - 12:00 and 18:00 - 21:00 will have a strong impact. Therefore, the present invention can fully detect the impact of rainfall on the train travel time of the high-speed railway network.

[0012] Second, the present invention can provide a reference for the emergency measures of high-speed railway hubs and stations adjacent to areas prone to rainfall, and can also provide a theoretical basis for traffic planners and operation managers, enabling them to formulate flexible emergency plans according to the spatio-temporal differences of delay impacts and reasonably arrange the safety inspection tasks of facilities and equipment in different time periods. Description of the Drawings

[0013] The present invention will be further described below with reference to the drawings and embodiments.

[0014] Figure 1 It is a detection framework diagram of the impact of rainfall on the train travel time of the high-speed railway network;

[0015] Figure 2 It is an example diagram of constructing a high-speed railway network by the method;

[0016] Figure 3 It is a sampling schematic diagram of the Markov chain Monte Carlo method;

[0017] Figure 4 It is a schematic diagram of the research area in Embodiment 2;

[0018] Figure 5Schematic diagram of train delay simulation sampling passing through Shanghai station under rainfall conditions. Detailed implementation manners

[0019] To enable those skilled in the art to better understand the solution of this application, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of this application. Obviously, the described embodiments are only a part of the embodiments of this application, rather than all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of this application.

[0020] It should be noted that the terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data used can be interchanged under appropriate circumstances so as to implement the embodiments of this application described herein. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device including a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0021] The present invention will be further described below in conjunction with the accompanying drawings.

[0022] Embodiment 1, a method for detecting the impact of rainfall on the travel time of trains in a high-speed railway network, comprising the following steps:

[0023] S1. Data collection: Collect historical operation data of trains in the high-speed railway network, including the departure time, arrival time, stopping stations, and delay time of each train, and collect rainfall data near the stations in the relevant area, including rainfall intensity and rainfall duration;

[0024] S2. Data preprocessing: Remove outliers, missing values, and error data to ensure the accuracy and integrity of the data, and match the train operation data and rainfall data according to time and location for subsequent analysis;

[0025] S3. Impact analysis: Using the historical delay data of trains at a certain station under rainfall conditions, determine the probability density curve of the train delay time when rainfall occurs at this station through the method of kernel density estimation; then, based on the Markov chain Monte Carlo method, quantify and obtain the ergodic mean after sampling convergence under this density curve, so as to be used as the average delay duration when the train passes through this station under rainfall conditions, which reveals the impact of rainfall conditions on the travel time of trains in different regions;

[0026] S4. Set different rainfall spatio-temporal scenarios, determine the operation paths of each train in the network through the heap-optimized Dijkstra algorithm, considering that the trains passing through the rainfall area during the research period are affected, and further analyze the number of affected trains in the high-speed railway network under each scenario, as well as the average delay degree and fluctuation degree of the travel time of all trains.

[0027] S5. Detection and policy recommendations: Taking the Yangtze River Economic Belt as an example, divide it into three different research regions, and use the proposed method to calculate the delay impact degree and fluctuation impact degree of rainfall on the travel time of trains in the high-speed railway network in the three different research regions respectively. Then, for the research region with the greatest impact degree, set different rainfall occurrence time periods, and further analyze the impact of rainfall scenarios at different time periods in this region on the travel time of trains in the network. The detection results can identify the regions and time periods with greater impact degrees to quantify the impact of rainfall on train operation. Applying the detected impact results to the operation management and dispatching decision-making of high-speed railways helps to early warn and respond to train delays that may be brought by rainfall, and propose targeted optimization measures to reduce the impact of rainfall on the travel time of trains.

[0028] Embodiment 2. A method for detecting the impact of rainfall on the travel time of trains in a high-speed railway network:

[0029] The proposed framework can obtain the travel time of trains under different rainfall scenarios and calculate the corresponding reliability indicators. Specifically, the framework consists of three parts:

[0030] Obtain the shortest paths of all trains in the high-speed railway network. According to the physical connection attributes of the railway, construct an undirected weighted network with distance as the weight; for all trains in the network, use the heap-optimized Dijkstra algorithm to obtain their shortest paths.

[0031] Calculate the travel time of all trains under different spatio-temporal scenarios. Set rainfall to occur in different regions and times, obtain the delay time of affected trains through the Markov chain Monte Carlo method based on kernel density estimation, then calculate the stopping time and operation time of each train, and finally sum them up to obtain the travel time of the train.

[0032] Finally, use the results obtained in the previous step to calculate the reliability indicators of the travel time of trains in the high-speed railway network under different scenarios, and conduct differential analysis according to different regions and time periods when rainfall occurs, so as to detect the time and space scenarios with greater impact.

[0033] The Space-L method is adopted to construct the high-speed railway network. High-speed trains usually operate in pairs and in opposite directions. Therefore, the high-speed railway network can be represented as an undirected weighted network G=(V, E, W), where V represents the set of stations, E represents the set of edges connecting adjacent stations, and W represents the set of distance weights of the edges. When a city has multiple high-speed railway stations, they are considered to be merged into one station, and the shortest distance between the stations is used as the edge weight. Figure 2 is a simple example graph. In addition, this method considers determining the train operation path based on the shortest operation distance. Since the constructed high-speed railway network belongs to an undirected weighted network and the distance weights are always non-negative, the heap-optimized Dijkstra algorithm is used to obtain the shortest path of the train.

[0034] Normally, the time T for train i to complete a passenger transportation task i should be composed of the operation time T i running and the stop time T i dwell , that is, T i =T i running +T i dwell . Among them, T i running represents the total operation time of train i, and T i dwell represents the total stop time of train i. Before introducing the composition of the travel time of the affected trains in case of rainfall, corresponding reasonable assumptions need to be made: that is, if a train passes through a station within the rainfall area, it is considered that the train is affected by rainfall and a delay occurs (because it is impossible to accurately know at which position on the section the train is affected by rainfall, but it can be determined that the train takes deceleration measures due to rainfall before and after passing through the event station). Thus, the travel time of the train affected by rainfall is T i '=T i +T i delay . Among them, T i delay represents the delay time suffered by train i, and its value is the total delay time suffered by train i when passing through each station within the rainfall area.

[0035] In most cases, a train needs to pass through and stop at multiple stations when completing a passenger transportation task. Correspondingly, the running time and stop time of train i should also be obtained by summing the operation time of each section and the stop time of passing through each station:

[0036]

[0037] Among them, k is the constituent section of the shortest path of train i, and K i is the set of sections, and d k is the length of section k, v is the running speed of the train; q is the station that train i passes through in the shortest path, and Q i is the set of passing stations, represents the dwell time of train i at station q. In special cases, if the starting station and the terminal station are directly connected, the dwell time T of the train i dwell is set to 0.

[0038] In reality, the impact of rainfall in different regions on trains varies, which is related to factors such as the geological conditions, line equipment, and train operation speed in this region. Therefore, it is considered to separately quantify the delay impact caused by rainfall at each research station on trains. For the above considerations, this method uses the Markov chain Monte Carlo method based on kernel density estimation to complete this quantification process: First, use kernel density estimation (KDE) to obtain the probability density curve of different delays caused by trains under historical rainfall conditions at the research station; then, use the Markov chain Monte Carlo method (MCMC) to simulate and sample the delay time values; finally, after the Markov chain reaches the convergence condition, calculate the traversal mean of the delay time as the delay impact caused by rainfall at this research station on trains.

[0039] Specifically, the principle of kernel density estimation can be summarized as follows: Assume there is a set of sample observations x i =[x1, x2, x3, … x n , and there is a kernel function around each sample point. For a certain point x on the coordinate axis, the kernel density estimation value at x is obtained by summing the values of the kernel functions of each sample point at x, and it is inversely proportional to the distance from x to each sample point. The kernel density estimation value is shown in Equation 3:

[0040]

[0041] Among them, n is the number of samples; h is the bandwidth, which affects the smoothness of the estimation; represents the kernel function, which determines the probability density weight of the sample point x i at x. Considering that the target distribution to be fitted is a normal distribution, the optimal bandwidth h obtained by minimizing the integrated mean square error is shown in Equation 4:

[0042] h = 1.06σn -1 / 5 (4)

[0043] Among them, σ is the sample standard deviation, and n is the number of samples. For the kernel function K(u), common kernel functions include Gaussian kernel, Epanechnikov kernel, tricube kernel, etc. In order to better fit the data distribution at the boundary, this method considers using the tricube kernel as the kernel function, as shown in Equation 5:

[0044]

[0045] Among them, I(·) is the indicator function. If the condition in the parentheses is true, the value is 1; otherwise, the value is 0.

[0046] After obtaining the probability density curves of different delay times when the train passes through the rainfall site, it is hoped to perform large-scale sampling within the density curves to obtain the average delay suffered by the train when passing through during rainfall at this research site. The present invention uses the Markov chain Monte Carlo method, regards the sampling operation as a Markov process, and the sampling result as the state in the Markov chain. By constructing a rule similar to the state transition matrix, the result after n samplings approximately follows the kernel density estimation curve. As Figure 3 shown, assume that the kernel density estimation curve is f(x), and the initial state is S0. According to the proposed normal distribution function G(S0,σ), the alternative state S1 is determined. If the state S1 meets the preset rule, the proposed normal distribution function becomes G(S1,σ) and is used for the next sampling; otherwise, no change is made. Repeat the above steps to make the sampling result finally converge to the target distribution function f(x). The detailed balance condition can achieve the above rule, and it is a sufficient condition for the stationary distribution. Assume that π is the converged stationary distribution (i.e., the kernel density estimation curve), then the detailed balance condition can be expressed by Equation 6:

[0047] π i ·A(j|i)=π j ·A(i|j) (6)

[0048] In the formula, π i represents the probability of being in state S i under the stationary distribution, and A(j|i) represents the transition from state S i to S jThe probability. To satisfy the detailed balance condition, the Metropolis-Hasting algorithm [1] provides a solution that satisfies the above equation ([1] Hastings WK. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 1970; 57(1): 97-109. https: / / doi.org / 10.1093 / biomet / 57.1.97.) as shown in Equation 7:

[0049]

[0050] In the formula, α represents the sampling acceptance rate; f(i) represents the probability density value of the kernel density estimation curve at state S i ; G(j|i) represents the probability of extracting S i from the proposed normal distribution function with mean S j . Specifically, after obtaining the alternative state S j , calculate the corresponding acceptance rate α and generate a random number u between 0 and 1. Finally, determine whether to accept the state transition according to Equation 8:

[0051]

[0052] Through the Metropolis-Hasting algorithm, we can perform sampling under the detailed balance condition. Assuming that it follows the target distribution after n samplings, then the mean of the kernel density estimation curve can be obtained from the ergodic theorem, that is, the mean delay suffered by the train when passing through during rainfall at the research site:

[0053]

[0054] In the formula, E is the mean delay suffered by the train, and g(k) is the result of the k-th sampling (m > k > n). Assuming that the delay time generated when train i passes through rainfall site r is E r , then the delay time of train i is as shown in Equation 10:

[0055]

[0056] where R i is the set of rainfall sites passed by.

[0057] The content of the train journey time reliability index of the high-speed railway network is as follows:

[0058] To reasonably quantify the impact of rainfall on the travel time reliability of high-speed railway networks, this paper proposes a Delay Index (DI) and a Fluctuation Index (FI) to calculate the average delay impact and travel time fluctuation impact on trains in the network. Specifically, DI is obtained by averaging the travel time delay rates (delay time divided by travel distance) of all trains in the network, as shown in Equation 11:

[0059]

[0060] where N represents the total number of trains operating in the network during the study period, d i represents the operating mileage of train i, and DI represents the average delay time per unit distance of train operation in the network. The larger its value, the greater the average delay degree of trains caused by rainfall. FI reflects the proportion of delay time relative to the normal travel time and is obtained by averaging the travel time volatility rates (delay time divided by normal travel time) of all trains in the network, as shown in Equation 12:

[0061]

[0062] where FI is called the Fluctuation Index. The larger its value, the greater the travel time fluctuation degree of trains under the influence of rainfall.

[0063] To reasonably analyze the impact of rainfall on the travel time reliability of high-speed railway networks, this embodiment selects three study areas in the east, central, and west as the occurrence locations of rainfall events. As Figure 4 shown, the three selected areas are located in the Yangtze River Delta Urban Agglomeration, the Middle Yangtze River Urban Agglomeration, and the Chengdu-Chongqing Urban Agglomeration, which are the economic and cultural centers of the regions and have strong high-speed railway passenger flow connections. The train operation data and station area rainfall data used in this embodiment are from the dataset published by Zhang et al [2] ([2]Zhang D, Peng Y, Xu Y, Du C, Zhang Y, Wang N, Chong Y, Wang H, Wu D, Liu J, Zhang H, Lu L, Liu J. A high-speed railway network dataset from train operation records and weather data, Figshare, v4; 2021. https: / / doi.org / 10.6084 / m9.figshare.15087882.v4.) on the Figshare website (https: / / figshare.com / ). The operation data of G-series high-speed trains on October 15, 2019, were extracted for analysis. After simplification, a total of 2043 train OD data were obtained.

[0064] Calculate the running time, stop time, and delay time affected by rainfall for each train on the shortest path. Among them, it is relatively easy to obtain the running time, which can be calculated using Equation 1. Therefore, the calculation of the stop time and delay time will be described in detail.

[0065] Affected by the passenger flow intensity and the conditions of facilities and equipment, the stop times of trains at different stations vary greatly. Therefore, in this embodiment, the dataset published by Zhang et al. [2] ([2]Zhang D, Peng Y, Xu Y, Du C, Zhang Y, Wang N, Chong Y, Wang H, Wu D, Liu J, Zhang H, Lu L, Liu J. A high-speed railway network dataset from train operation records and weather data, Figshare, v4; 2021. https: / / doi.org / 10.6084 / m9.figshare.15087882.v4.) is used to quantify the average stop time of trains passing through each station through the historical operation data of trains. The calculation results are arranged in ascending order as shown in Table 1. According to the average stop time mean results in Table 1, the total stop time of each train can be calculated using Equation 2.

[0066] Table 1 Average stop time of trains at each station

[0067]

[0068]

[0069] Regarding the delay time of each train under rainfall conditions, the embodiment calculates the average delay of trains passing through each station in three research regions. Taking the Shanghai station as an example, first, the train data with delay durations ranging from 5 minutes to 30 minutes under rainfall conditions (including light rain, light to moderate rain, moderate rain, showers) was extracted, totaling 871 pieces. As Figure 5As shown, the probability density curve of the delay time was obtained using the kernel density estimation method, and 15,000 simulation samplings were carried out by the Markov chain Monte Carlo method. Finally, the ergodic mean of 9.6 min was calculated according to Equation 9 as the average delay caused by rainfall at the Shanghai station to the trains. Similarly, the quantification results of the remaining stations in the study area are given in Table 2. According to the average train delay results in Table 2, the total delay time of each train can be calculated using Equation 10.

[0070] Table 2 Average delay time of trains passing through each station in the study area under rainfall conditions.

[0071]

[0072] Assuming that rainfall events occur in three study areas respectively, the spatial differences in the impact of rainfall on the train travel time of the high-speed railway network can be analyzed. Similarly, this method still uses 2,043 train OD data on October 15, 2019 for analysis, and all trains originating from, passing through, and terminating at rainfall stations will be affected by delays. Table 3 gives the relevant numerical calculation results of the impact caused by rainfall in different study areas. Generally speaking, the number of trains affected by rainfall in the eastern study area is the largest, but the affected range is small; the number of trains affected in the central and western regions is small, but the affected range is wider. From the perspective of the impact degree, the calculation results of DI and FI in the eastern study area are the largest under the event, indicating that the impact degree of rainfall on the train travel time of the high-speed railway network in this area is the largest: when rainfall occurs, the trains in the network are delayed by 17.64 min per 1,000 km of operation on average and the actual travel time increases by 7.19% compared with the planned travel time. On the contrary, the impact of rainfall on the train travel time of the high-speed railway network in the central and western study areas is relatively small, and the calculation results of DI and FI do not exceed 5 min / 1,000 km and 2% respectively.

[0073] Table 3 Quantification results of the impact caused by rainfall in different study areas

[0074]

[0075] Divide the time period from 6:00 to 24:00 into 6 time intervals, and count the train OD within each time interval on October 15, 2019 and the trains passing through the eastern research area within each time interval. Further, the calculation results of the delay impacts caused by rainfall within each time interval are given, as shown in Table 4. It can be seen that during the afternoon time interval (12:00 - 18:00), the number of trains affected by rainfall is relatively large, but the average operating mileage of the affected trains is relatively short; on the contrary, if rainfall occurs during the morning and night time intervals (6:00 - 9:00 and 21:00 - 24:00), the average operating mileage of the affected trains is relatively long. In addition, there are significant differences in the degree of impact of rainfall occurring in different time intervals on the train travel time reliability of the high - speed railway network. The calculation results of DI and FI seem to be positively correlated with the proportion of the number of affected trains to the total number of trains. If rainfall occurs within 6:00 - 12:00 and 18:00 - 21:00, the calculation results of DI and FI are relatively large, and it can be considered that rainfall occurring in these time intervals will have a greater delay impact on the trains in the network; on the contrary, if rainfall occurs within 21:00 - 24:00, the degree of delay and the degree of travel time fluctuation of the trains in the network are the smallest.

[0076] Table 4 Quantification results of the impacts caused by rainfall in different time intervals in the eastern research area

[0077]

[0078] To reasonably detect the impact of rainfall on the train travel time of the high - speed railway network, this method proposes a statistical evaluation method considering train operation characteristics and station heterogeneity, which can calculate the delay situation and travel time fluctuation situation of trains under different spatio - temporal rainfall scenarios. Using the real high - speed railway train operation data, an example analysis of the proposed method is carried out, and the detection results of the impact of rainfall on the train travel time of the high - speed railway network in different research areas and times are obtained.

[0079] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A detection method for the impact of rainfall on the train travel time of a high-speed railway network, characterized in that, It includes the following steps: S1. Data collection: Collect the historical operation data of trains on the high-speed railway network, including the departure time, arrival time, stopping stations, and delay time of each train, and collect the rainfall data near the stations in the relevant areas, including rainfall intensity and rainfall duration; S2. Data preprocessing: Remove outliers, missing values, and incorrect data to ensure the accuracy and integrity of the data, and match the train operation data with the rainfall data according to time and location for subsequent analysis; S3. Impact analysis: Use the historical delay data of trains at a certain station under rainfall conditions, and through the method of kernel density estimation, determine the probability density curve of the train delay time when rainfall occurs at this station; then, based on the Markov chain Monte Carlo method, quantify and obtain the ergodic mean after sampling convergence under this density curve, so as to serve as the average delay duration suffered by the train passing through this station under rainfall conditions, which reveals the impact of rainfall on the train travel time in different regions; S4. Set different rainfall spatio-temporal scenarios, determine the operation paths of each train in the network through the heap-optimized Dijkstra algorithm, and consider the impact on the trains passing through the rainfall area during the research period, so as to analyze the number of affected trains in the high-speed railway network under each scenario and the average delay degree and fluctuation degree of the travel time of all trains; S5. Detection and suggestions: Divide three different research areas, and use the proposed method to calculate the delay impact degree and fluctuation impact degree on the train travel time of the high-speed railway network when rainfall occurs in the three different research areas respectively; then, for the research area with the greatest impact degree, set different rainfall occurrence time periods and analyze the impact of rainfall scenarios at different times in this area on the train travel time in the network; The detection results can identify the areas and time periods with greater impact degrees to quantify the impact of rainfall on train operation; Applying the detected impact results to the operation management and dispatching decisions of high-speed railways helps to early warn and respond to train delays that may be brought by rainfall, and put forward targeted optimization measures to reduce the impact of rainfall on train travel time.

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