A method for predicting travel time reliability of urban rail transit network

Abstract

The present invention relates to the field of rail transit technology, and in particular, to a method for predicting the travel time reliability of an urban rail transit network, which comprises the following steps: 1. for a station OD pair with sufficient AFC data records, the travel time reliability of the station OD pair is calculated by a buffer time index; 2. the station OD features that affect the travel time reliability are clarified, multiple features are extracted, and a non-repeated two-factor variance analysis is used to determine whether there are statistically significant differences in these station OD features under different travel time reliability levels; 3. the sequential forward selection method is used to select the best input features for different operating periods from the station OD features to avoid feature redundancy, thereby accelerating the prediction and improving the prediction accuracy; 4. three machine learning models, namely support vector regression, multilayer perceptron regression and deep residual network, are used to predict the travel time reliability of the network during the morning, evening peak and off-peak periods, and determine the best prediction model for different operating periods. The present invention can better predict the travel time reliability of the urban rail transit network during different operating periods.

Description

Technical Field

[0001] The present invention relates to the field of rail transit technology, and in particular to a method for predicting the reliability of travel time of an urban rail transit network. Background Art

[0002] The rapidly developing urban rail transit network has provided convenience for passengers' travel, shortened their travel time, and effectively alleviated traffic congestion in large cities. However, train delays and cancellations frequently occur in urban rail transit operations, resulting in travel delays for passengers. At the same time, there is a large passenger demand during peak hours, and the travel time of passengers during peak hours is highly uncertain, so the reliability of their travel time is usually low. These unfavorable conditions have seriously restricted the improvement of the service level of urban rail transit and reduced passengers' travel satisfaction. As an important indicator for evaluating the quality of transportation services, travel time reliability has a great impact on passengers' travel experience and satisfaction. Therefore, predicting the travel time reliability of the urban rail transit network can not only help operators evaluate the efficiency and quality of transportation services, but also guide passengers to reasonably arrange their travel time and departure time to arrive at the destination station on time.

[0003] Commonly used travel time reliability indicators for transportation networks include: (1) buffer time index and planned travel time index; (2) on-time arrival probability; and (3) travel time standard deviation or travel time variation coefficient. With the development of new technologies, automatic gate charging (AFC) data, global positioning (GPS) data, and automatic vehicle location (AVL) data in transportation operations are becoming more and more abundant. These data record the travel time of passengers or the driving time of vehicles, so they can be directly used to calculate time reliability indicators to measure the travel time reliability of transportation networks.

[0004] The increase in the availability of traffic operation record data has made it easier for researchers to conduct research based on different types of operation data, thereby improving the level of traffic operation management. In the application research of rail transit AFC data, AFC data is widely used to predict passengers' route selection behavior, estimate passengers' walking speed and walking distance, estimate passengers' waiting time at the station, and estimate passengers' travel OD (origin station to destination station) matrix. AFC data records passengers' entry and exit time information, and can effectively calculate and predict the reliability of passengers' travel time on the urban rail transit network.

[0005] Analysis of domestic and foreign research shows that no existing research has used AFC data to predict the travel time reliability of urban rail transit networks. The passenger travel OD matrix of urban rail transit is usually a sparse matrix, and some station OD pairs may only have a few passengers' travel records in several days of operation. Accurately predicting travel time reliability requires sufficient passenger travel time data. Therefore, for some station OD pairs with fewer AFC data records, the travel time reliability of these OD pairs cannot be calculated based on AFC data. In addition, the travel time reliability of urban rail transit in different operating periods (morning and evening peaks and flat peaks) varies significantly, so travel time reliability prediction should be carried out for different operating periods. Summary of the invention

[0006] The present invention provides a method for predicting the reliability of travel time in an urban rail transit network, which can overcome certain defects of the prior art.

[0007] The present invention provides a method for predicting the reliability of travel time of an urban rail transit network, which comprises the following steps:

[0008] First, for the station OD pairs with sufficient AFC data records, the travel time reliability of the station OD pairs is calculated by the buffer time index;

[0009] Second, we identified the station OD characteristics that affect travel time reliability, extracted multiple station OD characteristics, and used unrepeated two-way ANOVA to determine whether there were statistically significant differences in these station OD characteristics at different travel time reliability levels;

[0010] Third, the sequential forward selection method is used to select the best input features for different operating periods to avoid feature redundancy, thereby reducing computational costs and improving prediction accuracy;

[0011] Fourth, three machine learning models, support vector regression, multilayer perceptron regression and deep residual network, are used to predict the travel time reliability between OD pairs and determine the optimal prediction model for different operating periods.

[0012] As a preference, the buffer time index is equal to the ratio of the buffer time to the average travel time, the buffer time is equal to the difference between the 95th percentile travel time and the average travel time, and the travel time reliability from station i to station j is expressed as R i,j , calculated as

[0013]

[0014] in, and They are the 95th percentile travel time and the average travel time from station i to station j, respectively.

[0015] Preferably, the AFC data records the ID of each ticket, and the travel time of each passenger is calculated by matching the ticket ID, thereby determining the travel time of passengers between stations OD; in step one, the reliability of travel time in three different operating periods, namely morning and evening peaks and off-peak hours, needs to be calculated respectively. For some station OD pairs with fewer AFC data records, the travel time reliability of these OD pairs cannot be accurately calculated based on the AFC data. Therefore, only when the number of AFC card swipes for entry and exit recorded by the station OD pair exceeds 100 times, the travel time reliability of the station OD pair is calculated based on the recorded card swipe data.

[0016] As a preferred method, in step 2, 20 features of the station OD pairs are extracted based on the shortest path between the OD pairs, and three different feature sets are obtained for the morning peak, evening peak and off-peak periods; in addition, the morning peak, evening peak and off-peak feature sets are combined to construct a mixed feature set; finally, the mean value is removed and divided by the standard deviation of the morning peak, evening peak, average peak and mixed feature set to obtain four feature sets.

[0017] Preferably, in step 2, a two-way ANOVA without repeated measurements is performed on the mixed feature set, the independent variables are the time period and travel time reliability level, and the dependent variable is the OD characteristic value; when dividing the travel time reliability level, the calculated buffer time indexes of all station OD pairs are arranged in ascending order and divided into 4 levels.

[0018] Preferably, in steps three and four, for each feature set, 30% of the data is used for feature selection and parameter adjustment, 50% of the data is used for model training, and the remaining 20% ​​of the data is used for testing; a 10-fold cross validation with random permutations is used to test accuracy.

[0019] Preferably, in step three, sequential forward selection is used to select features as input to avoid the curse of dimensionality; the sequential forward selection is encapsulated with a lasso estimator and 20-fold cross validation is performed, with mean absolute error regression loss as the evaluation parameter; the final feature set consists of station OD features that are repeatedly selected for more than 50% of the time; in addition, parameter adjustment is performed through random search of hyperparameters and 5-fold cross validation; this process is repeated 10 times, and the parameters with the most selection times are used as the final parameters.

[0020] As a preference, in step 4, support vector regression uses a Gaussian kernel with a regularization parameter equal to 1000. Support vector regression finds the most suitable fitting curve while tolerating a certain amount of error. The loss is calculated only when the absolute value of the error between the true value and the predicted value is greater than the threshold. The training sample set is represented by D = {(x1, y1),…, (x i ,y i ),…,(x m,y m )}, where x i and i are an input variable and an output variable respectively. The formula for support vector regression is:

[0021]

[0022] Among them, w and b are the model parameters to be determined, f(x i ) is the model output, C is a constant, l ∈ is an ∈-insensitive loss function; the loss function insensitive to ∈ is:

[0023]

[0024] Introducing the slack variable ξ i and To measure the deviation of training data outside the ∈ insensitive region, the support vector regression formula is rewritten as:

[0025]

[0026] subject to:

[0027] Therefore, after introducing the optimal constraint, the support vector regression optimization problem is transformed into a dual problem, and its solution is:

[0028]

[0029] Among them, κ(x,x i ) is a kernel function.

[0030] Preferably, in step 4, the multilayer perceptron uses three hidden layers, each layer has 100, 100 and 50 neurons respectively, and the multilayer perceptron is trained using adaptive moment estimation with an adaptive learning rate.

[0031] Preferably, in step 4, a deep residual network is used to build a model to select the features of station OD, and the deep residual network can solve the degradation problem of deep architecture; the features of all station ODs are input into a 1-D deep residual network, which consists of 14 convolutional layers, each of which is followed by a batch normalization layer (together forming a residual block); each of the first four convolutional layers has 32 filters with a kernel size of 9; each of the middle six convolutional layers has 64 filters with a kernel size of 6; the remaining four convolutional layers have 128 filters with a kernel size of 3; the stride of each convolutional layer is 1; skip connections are used for every two residual blocks; the residual map consists of a convolutional layer with a kernel size of 1 and a batch normalization layer; the last layer includes a fully connected layer and a linear layer; TensorFlow 2.7 is used to build a deep residual network model, and the mean absolute error percentage is used as the loss function and indicator for training.

[0032] The present invention can effectively predict the travel time reliability of the network in different time periods. The proposed method can not only be used to evaluate the service quality of urban rail transit, but also effectively guide passengers to reasonably arrange their travel time to arrive at the destination station on time. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a flow chart of a method for predicting the reliability of travel time of an urban rail transit network in an embodiment;

[0034] Figure 2 Schematic diagram of Chengdu subway network in 2016 in the embodiment;

[0035] Figure 3 Schematic diagram of the architecture of a 1-D deep residual network in an embodiment;

[0036] FIG4( a ) is a heat map of the station OD versus time reliability during the morning peak period in the embodiment;

[0037] FIG4( b ) is a heat map of the station OD versus time reliability during the evening peak period in the embodiment;

[0038] FIG4( c ) is a heat map of the time reliability of the station OD during the off-peak period in the embodiment. DETAILED DESCRIPTION

[0039] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention and are not intended to limit it.

[0040] Example

[0041] like Figure 1As shown, this embodiment provides a method for predicting the reliability of travel time of an urban rail transit network, which includes the following steps:

[0042] First, for OD pairs with sufficient AFC data records, the travel time reliability of OD pairs is calculated by the buffer time index;

[0043] Second, we identified the OD features that affect travel time reliability, extracted multiple OD features, and used unrepeated two-way ANOVA to determine whether there were statistically significant differences in the OD features of these stations at different travel time reliability levels;

[0044] Third, the sequential forward selection method is used to select the best input features for different operating periods to avoid feature redundancy, thereby reducing computational costs and improving prediction accuracy;

[0045] Fourth, three machine learning models, support vector regression, multilayer perceptron regression and deep residual network, are used to predict the travel time reliability between OD pairs and determine the optimal prediction model for different operating periods.

[0046] Calculation of travel time reliability

[0047] The buffer time index is equal to the ratio of the buffer time to the average travel time. The buffer time is equal to the difference between the 95th percentile travel time and the average travel time. The travel time reliability from station i to station j is expressed as R i,j , calculated as

[0048]

[0049] in, and They are the 95th percentile travel time and the average travel time from station i to station j, respectively.

[0050] Data processing

[0051] The travel time reliability prediction is carried out using the AFC data of Chengdu Metro Company shown in Table 1. This dataset includes the AFC data of all working days from June to October 2016. Figure 2 As shown, it consists of 81 stations and 4 lines.

[0052] Table 1 Information recorded by AFC

[0053]

[0054] The AFC data records the ID of each ticket and calculates the travel time of each passenger by matching the ticket ID, thereby determining the passenger travel time between all station ODs.

[0055] The travel time reliability varies significantly in different operating periods. Therefore, the travel time reliability of the morning and evening peaks and the off-peak period is calculated separately. In order to accurately reflect the actual fluctuation of travel time, sufficient travel time data is required to calculate the travel time reliability of the station OD pair. Therefore, in an operating period, only when the number of AFC card swipes for the station OD pair entering and exiting the station exceeds 100 times, the travel time reliability of the station OD pair in this period is calculated based on the AFC data.

[0056] Station OD feature extraction

[0057] In the rail transit network, most passengers take the shortest path between station OD pairs to travel on the network to shorten travel time. To this end, 20 station OD features that affect passenger travel time were analyzed and preliminarily determined, as shown in Table 2. Three different feature sets were obtained for the morning and evening peak and off-peak periods; in addition, the morning, evening peak and off-peak feature sets were combined to construct a mixed feature set; finally, four feature sets were obtained by removing the mean and dividing by the standard deviation of the morning, evening peak, average peak and mixed feature sets. Therefore, a total of 8 different feature sets were used as input data to evaluate the performance of the travel time reliability prediction model and to clarify whether standardization can improve the prediction performance of the model.

[0058] Table 2 Characteristics of station OD pairs

[0059]

[0060] Note: Load factor is the ratio of the passenger flow in the section to the section capacity.

[0061] Statistical analysis

[0062] In order to reveal whether there are statistically significant differences in station OD characteristics under different travel time reliability levels, a two-way ANOVA with mixed feature sets without repeated measurements was conducted, with the independent variables being time period and travel time reliability level, and the dependent variable being OD feature value; when dividing the travel time reliability level, the buffer time index of all calculated station OD pairs was arranged in order from small to large and divided into 4 levels. Since passenger flow is unevenly distributed in time and space, different time periods were analyzed to explore the impact of station OD characteristics, where the significance level was set to p<0.05.

[0063] Travel time reliability prediction

[0064] For each feature set, 30% of the data was used for feature selection and parameter adjustment, 50% of the data was used to train the model, and the remaining 20% ​​of the data was used for testing; a 10-fold cross validation with random permutations was used to test the accuracy.

[0065] Sequential forward selection was used to select features as input to avoid the curse of dimensionality; sequential forward selection was encapsulated with the lasso estimator and performed 20-fold cross validation with mean absolute error regression loss as the evaluation parameter; the final feature set consisted of station OD features with more than 50% repeated selections; in addition, random search of hyperparameters and 5-fold cross validation were used for parameter adjustment; for each model, this process was repeated 10 times, and the parameters with the most selections were taken as the final parameters.

[0066] Support vector regression and multilayer perceptron were used to predict travel time reliability. Support vector regression used a Gaussian kernel with a regularization parameter equal to 1000. The multilayer perceptron used three hidden layers with 100, 100, and 50 neurons in each layer, respectively. A rectified linear unit function was used and the L2 penalty parameter was set to 0.1. The multilayer perceptron was trained using adaptive moment estimation with an adaptive learning rate. Apart from these parameters, the default settings in scikit-learn 0.22 were used.

[0067] The deep residual network is used to build the model to select the features of station OD. The deep residual network can solve the degradation problem of deep architecture, such as Figure 3 As shown. The features of all station ODs are input into a 1-D deep residual network. The general network architecture used in the study consists of 14 convolutional layers, each followed by a batch normalization layer (together forming a residual block); each of the first four convolutional layers has 32 filters with a kernel size of 9; each of the middle six convolutional layers has 64 filters with a kernel size of 6; the remaining four convolutional layers have 128 filters with a kernel size of 3; the stride of each convolutional layer is 1; every two residual blocks use a skip connection; the residual map consists of a convolutional layer with a kernel size of 1 and a batch normalization layer; the last layer includes a fully connected layer and a linear layer; TensorFlow 2.7 is used to build a deep residual network model, and the mean absolute error percentage is used as the loss function and indicator for training.

[0068] Support Vector Regression

[0069] Support vector regression can find the most appropriate fitting curve while tolerating a certain amount of error. The loss is calculated only when the absolute value of the error between the true value and the predicted value is greater than the threshold. Support vector regression has good generalization ability and high prediction accuracy. The training sample set is represented by D = {(x1, y1),…, (x i ,y i ),…,(x m ,y m )}, where x i and iare an input variable and an output variable respectively. The formula for support vector regression is:

[0070]

[0071] Among them, w and b are the model parameters to be determined, f(x i ) is the model output, C is a constant, l ∈ is an ∈-insensitive loss function; the loss function insensitive to ∈ is:

[0072]

[0073] Introducing the slack variable ξ i and To measure the deviation of training data outside the ∈ insensitive region, the support vector regression formula is rewritten as:

[0074]

[0075] subject to:

[0076] Therefore, after introducing the optimal constraint, the support vector regression optimization problem is transformed into a dual problem, and its solution is:

[0077]

[0078] Among them, κ(x,x i ) is a kernel function.

[0079] Multi-layer Perceptron Regression

[0080] The multilayer perceptron is a class of fully connected feedforward artificial neural networks, which are used here to predict travel time reliability. The multilayer perceptron consists of an input layer, several hidden layers, and an output layer. Each layer contains some identical units, and each unit in the layer is connected to all units in the next layer. The units in the input layer use the value of the input vector, and a unit in the output layer returns the predicted value. Except for the units in the input layer, each unit uses a nonlinear activation function. This enables the multilayer perceptron to solve problems stochastically, thereby providing approximate solutions to extremely complex problems. The multilayer perceptron of this embodiment uses three hidden layers.

[0081] Travel time reliability calculation

[0082] Passenger travel time is obtained from the AFC data of 27 working days, and then the travel time reliability (i.e., buffer time index) of the station OD pair in different time periods is calculated. To ensure the accuracy of the travel time reliability calculation results, the travel time reliability of the station OD pair is calculated only when the AFC data recorded by the station OD pair exceeds 100. The travel time reliability heat maps between station OD pairs during the morning and evening peak and off-peak periods are shown in Figure 4(a), Figure 4(b), and Figure 4(c), respectively. The analysis results show that the buffer time index, which measures the travel time reliability, is higher during peak hours than during off-peak hours, and the travel time reliability during peak hours is lower.

[0083] Travel time reliability prediction

[0084] The station OD characteristics are analyzed, and according to the calculated travel time reliability results of the station OD pairs, the station OD characteristics are selected to predict the travel time reliability between station ODs.

[0085] Station OD feature analysis

[0086] Table 3 summarizes the two-way ANOVA results for the mixed feature set. Almost all station OD features, except features D, N, and T, show statistically significant differences across operating periods. The average train departure interval between station OD pairs shows significant differences across operating periods. In addition, all station OD features show statistically significant differences at different levels of travel time reliability. This finding suggests that these selected station OD features may be closely related to travel time reliability.

[0087] Table 3 Two-way ANOVA results of mixed feature sets - F value (P value), the significance level is set to p < 0.05

[0088]

[0089]

[0090] Some station OD features may be similar, so the sequential forward selection algorithm is used to reduce redundant features to avoid the curse of dimensionality. For the morning peak feature set, evening peak feature set, flat peak feature set and mixed feature set, the station OD features selected in each iteration are almost the same. In the mixed feature set, 11 features are selected during iteration: N, H, T, L1, L2, L3, and Period. When considering the period difference, the feature Period is the same and therefore not selected. N,H,T,L1,L2,L3,L mean ,L4, and The feature set selected as the morning peak is N,H,T,L1,L2,L3,Lmean ,L4,L5, and is selected as the feature set for the evening peak. Compared with the peak features, the 7 features that appear in both the morning and evening peaks, as well as L5, and was selected as the flat peak feature set. In addition, there was a huge difference in the number of times each feature was selected for each standardized feature set.

[0091] Travel time prediction for station OD pairs

[0092] The mean absolute percentage error (MAPE) and symmetric mean absolute percentage error (SMAPE) are used to evaluate the prediction performance of support vector regression, multilayer perceptron regression and deep residual network. MAPE and SMAPE are calculated by the following two formulas respectively. is a predicted value, and y i is a real value in Eq.

[0093]

[0094]

[0095] Table 4 lists the results of 10 iterations. According to Table 4, the best time reliability prediction model for different time periods is determined. For the prediction of travel time reliability during the morning peak, the deep residual network performs best, with a MAPE and SMAP of 11.389% and 11.088% respectively; for the prediction of travel time reliability during the evening peak, the support vector regression performs best, with a MAPE and SMAP of 6.150% and 6.347% respectively; for the prediction of travel time reliability during the off-peak period, the support vector regression performs best, with a MAPE and SMAPE of 6.847% and 7.171% respectively; when using a mixed feature set to predict the travel time reliability of all time periods, the deep residual network performs best, with a MAPE and SMAPE of 8.078% and 8.200% respectively. In addition, the standardized method of station OD feature preprocessing can further improve the prediction accuracy of some algorithms.

[0096] Table 4 Test MAPE and SMAPE for temporal reliability prediction using support vector regression, multilayer perceptron, and deep residual network (mean ± SD (minimum–maximum))

[0097]

[0098]

[0099] in conclusion

[0100] Predicting the travel time reliability of the urban rail transit network can not only guide passengers to arrive at the destination station on time, but also provide targeted suggestions for operators to improve the travel time reliability of the urban rail transit network. This embodiment uses a machine learning method based on AFC data to predict the travel time reliability of the urban rail transit network in different operating periods.

[0101] The method proposed in this embodiment uses the AFC data of 27 working days to predict the travel time reliability of Chengdu's urban rail transit network. AFC data is used to calculate the travel time reliability of station OD pairs. Based on the calculated time reliability of station OD pairs and the extracted station OD features, the travel time reliability of station OD pairs is predicted using a machine learning method. The research results show that although the AFC data of 27 working days are used to calculate the travel time reliability of station OD pairs, nearly 29.98% and 32.24% of station OD pairs cannot accurately calculate their time reliability due to the small amount of AFC data (less than 100 AFC records). The method of predicting the travel time reliability of the urban rail transit network based on AFC data can predict the time reliability of all station OD pairs, and the prediction results are effective and accurate, which has rarely been paid attention to in previous studies. According to the prediction results of different models, the optimal time reliability prediction model for different time periods is determined. For the prediction of travel time reliability during the morning peak, the deep residual network performs best; for the prediction of travel time reliability during the evening peak, the support vector regression performs best; for the prediction of travel time reliability during the off-peak period, the support vector regression performs best; when using a mixed feature set to predict the travel time reliability of all time periods, the deep residual network performs best. In addition, the standardized method of station OD feature preprocessing can further improve the prediction accuracy of the algorithm.

[0102] The above content schematically describes the present invention and its implementation methods, which are not restrictive. The drawings only show one implementation method of the present invention, and the actual structure is not limited thereto. Therefore, if a person skilled in the art is inspired by it and, without departing from the purpose of the present invention, designs a structure and an embodiment similar to the technical solution without creativity, they shall all fall within the protection scope of the present invention.

Claims

1. A method for predicting the reliability of travel time in an urban rail transit network, characterized in that: The following steps are involved: First, for the station OD pairs with sufficient AFC data records, the travel time reliability of the station OD pairs is calculated by the buffer time index; The buffer time index is equal to the ratio of the buffer time to the average travel time. The buffer time is equal to the difference between the 95th percentile travel time and the average travel time. The travel time reliability from station i to station j is expressed as R i,j , calculated as in, and are the 95th percentile travel time and average travel time from station i to station j respectively; AFC data records the ID of each ticket, and calculates the travel time of each passenger by matching the ticket ID, thereby determining the travel time of passengers between stations OD; in step 1, the reliability of travel time in the morning and evening peak and off-peak operating periods needs to be calculated respectively; for some station OD pairs with less AFC data records, the travel time reliability of these OD pairs cannot be accurately calculated based on AFC data; therefore, when the number of AFC card swipes for entry and exit recorded by the station OD pair exceeds 100, the travel time reliability of the station OD pair is calculated based on the recorded card swipe data; Second, we identified the station OD characteristics that affect travel time reliability, extracted multiple characteristics, and used unrepeated two-way ANOVA to determine whether there were statistically significant differences in these station OD characteristics at different travel time reliability levels; In step 2, 20 features of the station OD pairs were extracted according to the shortest path between the station OD pairs, and three different feature sets were obtained for the morning and evening peak and off-peak periods. In addition, the morning, evening peak and off-peak feature sets were combined to construct a mixed feature set. Finally, the mean value was removed and divided by the standard deviation of the morning peak, evening peak, average peak and mixed feature set to obtain four feature sets. In step 2, a two-way ANOVA without repeated measurements is performed on the mixed feature set, with the independent variables being the time period and travel time reliability level, and the dependent variable being the station OD feature value; when dividing the travel time reliability level, the buffer time indexes of all calculated station OD pairs are arranged in ascending order and divided equally into 4 levels; 3. Use the sequential forward selection method to select the best input features for different operating periods to avoid feature redundancy, thereby accelerating prediction and improving prediction accuracy; among them, N, H, T, L1, L2, L3, L mean , L4, and The feature set selected as the morning peak is N, H, T, L1, L2, L3, L mean , L4, L5, and are selected as the feature set for the evening peak; compared with the peak features, the 7 features that appear in both the morning and evening peaks, as well as L5, and Selected as the flat peak feature set; N represents the number of stations included in the shortest path between stations OD, H represents the average departure interval of trains on the shortest path between stations OD, T represents the average transfer time on the shortest path between stations OD, L1 represents the load factor of the first section on the shortest path between stations OD, and the load factor is the ratio of the passenger flow of the section to the capacity of the section, L2 represents the load factor of the last section on the shortest path between stations OD, L3 represents the average of L1 and L2, and L mean It represents the average load factor of the interval on the shortest path between stations OD, L4 represents the average load factor of the intervals except the first interval on the shortest path between stations OD, and L5 represents the average load factor of the intervals except the last interval on the shortest path between stations OD. express and The mean of represents the number of passengers boarding at station O per hour, represents the number of passengers getting off at station O per hour, It represents the number of passengers boarding at the transfer station per hour on the shortest route between stations OD. express and The mean of It represents the number of passengers getting off at the transfer station per hour on the shortest route between stations OD. represents the number of passengers getting off at station D per hour; In step 3, the sequential forward selection method is used to select features as input to avoid the curse of dimensionality; the sequential forward selection is encapsulated with the lasso estimator and 20-fold cross validation is performed, with the mean absolute error regression loss as the evaluation parameter; the final feature set consists of station OD features that are selected more than 50% repeatedly; in addition, parameter adjustment is performed through random search of hyperparameters and 5-fold cross validation; this process is repeated 10 times, and the parameters with the most selection times are used as the final parameters; Fourth, three machine learning models, support vector regression, multilayer perceptron regression and deep residual network, are used to predict the travel time reliability between station OD pairs and determine the optimal prediction model for different operating periods.

2. The method for predicting the reliability of travel time of an urban rail transit network according to claim 1, characterized in that: In steps 3 and 4, for each feature set, 30% of the data is used for feature selection and parameter adjustment, 50% of the data is used to train the model, and the remaining 20% ​​of the data is used for testing; a 10-fold cross validation with random permutations is used to test the accuracy.

3. The method for predicting the reliability of travel time of an urban rail transit network according to claim 2, characterized in that: In step 4, support vector regression uses a Gaussian kernel with a regularization parameter equal to 1000. Support vector regression finds the most suitable fitting curve while tolerating a certain amount of error. The loss is calculated only when the absolute value of the error between the true value and the predicted value is greater than the threshold. The training sample set is represented by D = {(x1, y1), ..., (x i ,y i ),…,(x m ,y m )}, where x i and i are an input variable and an output variable respectively. The formula for support vector regression is: Among them, w and b are the model parameters to be determined, f(x i ) is the model output, C is a constant, l ∈ is an ∈-insensitive loss function; the loss function insensitive to ∈ is: Introducing the slack variable ξ i and To measure the deviation of training data outside the ∈ insensitive region, the support vector regression formula is rewritten as: Therefore, after introducing the optimal constraint, the support vector regression optimization problem is transformed into a dual problem, and its solution is: Among them, K(x,x i ) is a kernel function.

4. The method for predicting the reliability of travel time of an urban rail transit network according to claim 3, characterized in that: In step 4, the multilayer perceptron uses three hidden layers with 100, 100, and 50 neurons in each layer, respectively, and the multilayer perceptron is trained using adaptive moment estimation with adaptive learning rate.

5. The method for predicting the reliability of travel time of an urban rail transit network according to claim 4, characterized in that: In step 4, a deep residual network is used to build a model to select the features of station OD. The deep residual network solves the degradation problem of the deep architecture. The features of all station ODs are input into the 1-D deep residual network, which consists of 14 convolutional layers, each of which is followed by a batch normalization layer, forming a residual block. Each of the first four convolutional layers has 32 filters with a kernel size of 9. Each of the middle six convolutional layers has 64 filters with a kernel size of 6. The remaining four convolutional layers have 128 filters with a kernel size of 3. The stride of each convolutional layer is 1. Skip connections are used for every two residual blocks. The residual map consists of a convolutional layer with a kernel size of 1 and a batch normalization layer. The last layer includes a fully connected layer and a linear layer. TensorFlow 2.7 is used to build a deep residual network model, which is trained using the root mean square attribute and the mean absolute error percentage as the loss function and indicator.

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