A train operation adjustment method based on initial delay classification and mode deduction

Abstract

This application discloses a train operation adjustment method based on initial delay classification and pattern deduction, relating to the field of aerospace engineering measurement. The method includes: S1, constructing a multi-dimensional evaluation index system for train delays; S2, using a clustering algorithm to classify train delay sequences into four delay patterns and obtaining the evolutionary characteristics of these patterns; S3, constructing an initial delay impact index prediction model; S4, establishing train motion equations, quantitatively analyzing train behavior characteristics under different delay patterns, and constructing a multi-objective optimization model based on these characteristics; S5, combining the initial delay impact index prediction model and the multi-objective optimization model to adjust train operation. This application integrates the prediction model and the multi-objective optimization model for dynamic calculation of train timetables, achieving accurate generation and real-time adjustment of delayed train operation strategies, thus improving the intelligence and flexibility of railway scheduling.

Description

Technical Field

[0001] This application relates to the field of train delay prediction, and in particular to a train operation adjustment method based on initial delay classification and pattern deduction. Background Technology

[0002] With the rapid expansion of my country's high-speed railway network, train punctuality has become one of the core indicators for measuring the quality of railway transportation services, directly affecting passenger travel experience and the overall operational efficiency of the network. However, in actual operation, due to multiple uncertainties such as equipment failure, extreme weather, and increased scheduling complexity, initial train delays occur frequently. Furthermore, through mechanisms such as inter-train tracking and competition for station resources, cascading delays are triggered, creating a chain reaction that severely restricts the railway system's transportation capacity and service stability.

[0003] In current railway train control systems, the traditional CTCS-3 level system adopts a quasi-moving block mode, relying on fixed block sections for tracking interval control. This results in insufficient adjustment flexibility and difficulty in quickly responding to dynamic changes caused by delay propagation. Dispatchers often rely on experience for manual adjustments, leading to high decision-making delays and limited optimization effects due to information asymmetry. While existing research has conducted analysis of delay causes and prediction of single indicators, it has significant limitations: firstly, it lacks a systematic classification and evolutionary mechanism analysis of delay patterns, making it impossible to accurately identify the propagation characteristics of different delay scenarios; secondly, single-objective optimization strategies struggle to balance safety constraints, operational efficiency, and passenger comfort, and are not fully adapted to the moving block technology characteristics of the next-generation CTCS-4 level train control system, thus failing to meet the actual needs of intelligent dispatching.

[0004] Furthermore, delay data suffers from uneven distribution and complex propagation paths. Traditional machine learning models lack accuracy in predicting multi-dimensional delay impact indicators, while the static control method of train tracking intervals further limits the improvement of line throughput capacity. Therefore, how to construct a scientific delay pattern classification system based on actual operational data, achieve accurate prediction of delay impact indicators, and propose a multi-objective collaborative optimization train operation adjustment strategy in conjunction with advanced train control technology has become a key technical bottleneck in solving the problem of delay propagation in high-speed railways and improving the system's robustness and intelligence. Summary of the Invention

[0005] In view of this, this application provides a real-time trajectory estimation method for launch vehicles based on adaptive adjustment of angular measurement accuracy, which aims to solve the problem of decreased trajectory position estimation accuracy caused by changes in angular measurement accuracy due to coordinate transformation during trajectory estimation, especially during the high elevation angle working period of the observation station, where existing methods show a significant deterioration in trajectory position estimation accuracy.

[0006] A train operation adjustment method based on initial delay classification and pattern deduction includes: S1. Based on the delay propagation mechanism, construct a multi-dimensional evaluation index system for train delays; The multi-dimensional evaluation index system includes: initial delay time, number of affected trains, and total delay impact time; S2. Based on the multidimensional evaluation index system, a clustering algorithm is used to divide the train delay sequence into four types of delay patterns, and the evolution characteristics of the delay patterns are obtained. The evolutionary features include: the transition probability features between late-arrival modes and the propagation path features; S3. Construct an initial prediction model for the impact of late arrivals by combining the multidimensional evaluation index system and the evolutionary characteristics. It is used to predict the delay impact index corresponding to each delay pattern in the acquired train time map based on real-time train operation data, and obtain the delay impact index prediction result. S4. By establishing train motion equations, the train behavior characteristics under different delay modes are quantitatively analyzed, and a multi-objective optimization model is constructed based on the train behavior characteristics. The multi-objective optimization model is used to generate delayed train operation strategies. S5. Combine the initial delay impact index prediction model and the multi-objective optimization model to calculate the train operation diagram at the current sampling time, obtain the corresponding delayed train operation strategy, and adjust the train operation according to the current delayed train operation strategy.

[0007] In one possible technical solution, the transition probability feature between late-delay modes in S2 is calculated as follows: ; —The transition probability from pattern i to pattern j; —The frequency of switching from late arrival mode i to late arrival mode j; —The sum of the frequencies of transitions from late-arrival mode i to all possible states; S={A,B,C,D} — Set of late-delay patterns; —Late-delay pattern index; A-A type delay mode, used to represent minor delay scenarios; B-B class delay mode is used to represent medium delay scenarios; C-C class delay mode, used to represent severe delay scenarios; D-D class delay mode is used to represent extreme delay scenarios.

[0008] In one possible technical solution, the initial delay impact index prediction model in S3 includes: The input module is used to process the initial late arrival index data through at least one multi-dimensional CNN combination to obtain preprocessed data; The feature extraction module is used to extract spatial features from the preprocessed data by stacking multiple convolutional and pooling layers; The sequence learning module is used to generate temporal features by combining a bidirectional long short-term memory neural network layer and a regularization layer to serialize the spatial features. An attention module is used to calculate the attention weights of the time features through an attention mechanism; The prediction module is used to perform non-linear calculations on the attention weights obtained by the attention module through the fully connected layer and the output layer to obtain the final prediction result.

[0009] In one possible technical solution, the convolutional neural network in the feature extraction module includes: Convolutional layers are used to extract local features from input data; Pooling layers are used to sample the obtained local features and output high-order abstract feature maps; A fully connected layer is used to combine and transform the high-order abstract feature map to output the spatial features.

[0010] In one possible technical solution, the bidirectional long short-term memory neural network includes: Two parallel LSTM units are used to process the spatial features from both forward and backward directions to obtain the generated temporal features. ; The two parallel LSTM units include a forward LSTM network and a reverse LSTM network. Forward LSTM networks process sequence features sequentially to obtain forward information. ; The inverse LSTM network processes sequence features in reverse chronological order to obtain inverse information. ; Combining the aforementioned positive information and the reverse information Perform element-wise addition of vectors to generate time features. ; ; Among them, ⊕ — vector element-wise addition operation, used for summing the forward and reverse output components.

[0011] In one possible technical solution, the step of calculating the attention weights of the temporal features using an attention mechanism includes: Attention scores are obtained by using input data features or output data features from the previous layer. , ; in, —Attention score; —The weight of the attention mechanism; —Bias in attention mechanisms; —Input data features or previous layer output data features; pass The function normalizes the attention score, and then normalizes the attention score. Convert to probability distribution form , ; Based on probability distribution form The value vector v is weighted and summed to generate the final attention value SH. .

[0012] In one possible technical solution, S4 establishes precise train motion equations to quantitatively analyze train behavior characteristics under different delay modes, including: A longitudinal dynamics model of the train is constructed based on a single-mass point model. ; ; ; —Overall quality of the train; t—the point in time when the train departs; —Slewing mass coefficient, used to reflect the equivalent mass effect of rotating parts of a train; —The instantaneous speed of the train at time t; —The spatial coordinates of the train at time t; —Output control force, representing the net external force applied to the train; —Characterizes the resultant resistance force acting on the train at time t.

[0013] In one possible technical solution, a multi-objective optimization model is constructed in S4 based on the train behavior characteristics. The multi-objective optimization model is used to minimize the variable part of the initial delay impact index. The multi-objective optimization model is as follows: ; in, —Initial delay time calculation model; —Affects the train number calculation model; —Affects the total time calculation model.

[0014] In one possible technical solution, the constraints of the multi-objective optimization model include: Security constraints; ; ; ; in, —The maximum permissible operating speed of this line; —The actual position of train i-1 at time t; —The actual position of train i at time t; Comfort constraints: ; ; ; —The average comfort function of train i, with a threshold of ; —The rate of change of acceleration of train i at time t; —Gaussian evaluation model width coefficient; —The center position of the width of the Gaussian evaluation model; —The acceleration of train i at time t.

[0015] In one possible technical solution, in step S4, which is used to generate the delayed train operation strategy, Step 1: Solve the multi-objective optimization model using the NSGA-II algorithm and output the Pareto optimal solution set; represent the Pareto optimal solution set as a decision matrix, and perform weighted standardization on the decision matrix to obtain the standardized weight matrix; Step 2: Determine the ideal solution Z+ and the negative ideal solution Z- based on the standardized weight matrix; Step 3: Calculate the distances from each solution to the ideal point and the negative ideal point based on the ideal solution Z+ and the negative ideal solution Z-; Step 4: Calculate the relative proximity index C for each solution based on the distances from each solution to the ideal point and the negative ideal point. i Based on proximity index C iObtain the priority order of the solutions in the Pareto solution set.

[0016] This application provides a train operation adjustment method based on initial delay classification and pattern deduction, which has the following technical advantages compared with the prior art: Construct a multi-dimensional evaluation index system for initial delay time, number of affected trains, and total delay impact time. This system breaks through the limitations of traditional single indicators, comprehensively quantifies the chain propagation effect of delays, and solves the problem of incomplete representation of delay impact. Based on clustering algorithms, four types of late-delay patterns are divided and the transition probability and propagation path evolution features are extracted to achieve refined classification of late-delay scenarios and accurate identification of propagation patterns, thus solving the bottleneck of traditional methods that lack systematic late-delay pattern classification. By integrating multidimensional indicators and evolutionary features to construct a prediction model, and combining real-time train operation data, the impact of delays can be accurately predicted, thus solving the problem of low prediction accuracy of traditional machine learning models for complex delay data. The train motion equations are established to quantify the behavioral characteristics, and a multi-objective optimization model is constructed to take into account operating efficiency, driving safety and passenger comfort, and to adapt to the characteristics of CTCS-4 level moving block technology, thus solving the problems of traditional single-objective optimization and poor technology adaptability. By integrating prediction and optimization models to dynamically calculate and generate operating strategies, train operation can be adjusted in real time and accurately, replacing manual experience-based scheduling and solving the problems of insufficient adjustment flexibility and high delay in manual decision-making in the CTCS-3 level system. The entire approach upgrades train delay control from experience-based, static, and singular methods to intelligent, dynamic, and multi-objective methods, effectively suppressing the chain reaction of delays and improving the railway system's anti-interference capabilities and overall network operational efficiency. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a train operation adjustment method based on initial delay classification and pattern deduction provided in an embodiment of this application; Figure 2 This is a block diagram of the initial delay impact index prediction model provided in the embodiments of this application; Figure 3 This is a schematic diagram of the initial delay impact index provided in the embodiments of this application; Figure 4This is a diagram illustrating the K-Means clustering results provided in the embodiments of this application. Figure 5 This is a schematic diagram of the propagation path of late-delay mode A provided in the embodiments of this application; Figure 6 This is a schematic diagram of the propagation path of late-delay mode B provided in the embodiments of this application; Figure 7 This is a schematic diagram of the propagation path of late-delay mode C provided in the embodiments of this application; Figure 8 This is a schematic diagram of the propagation path of late-delay mode D provided in the embodiments of this application; Figure 9 This is a diagram illustrating the training process of the CNN-BiLSTM-AM model provided in the embodiments of this application; Figure 10 This is a graph showing the loss function of the CNN-BiLSTM-AM model provided in the embodiments of this application. Figure 11 This is a comparison chart of initial delay predictions provided in the embodiments of this application; Figure 12 This is a comparison chart of the predicted number of trains affected, provided in the embodiments of this application. Figure 13 This is a comparison chart of the total impact time prediction provided in the embodiments of this application; Figure 14 This is a flowchart of the NSGA-II genetic algorithm provided in the embodiments of this application; Figure 15 This is the initial delay time box plot provided in the embodiments of this application; Figure 16 This is a diagram showing the influence of train number and carriage line in the embodiments of this application. Detailed Implementation

[0019] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] like Figure 1As shown, a train operation adjustment method based on initial delay classification and pattern deduction is proposed. The method constructs a multi-dimensional evaluation index system based on the delay propagation mechanism, including initial delay time, number of affected trains, and total delay impact time. This breaks through the limitations of single-index analysis in existing studies and achieves a comprehensive and quantitative characterization of the impact of train delays. By combining late-delay pattern segmentation and evolutionary feature analysis with clustering algorithms, the propagation patterns of different late-delay scenarios can be accurately identified, solving the problem that traditional methods cannot systematically classify late-delay patterns. By integrating predictive and multi-objective optimization models for dynamic calculation of train timetables, the system enables precise generation and real-time adjustment of delayed train operation strategies. It is compatible with the moving block technology characteristics of the CTCS-4 level train control system, enhancing the intelligence and flexibility of railway dispatching. This solves the problems of insufficient adjustment flexibility and high delays in manual dispatching decisions inherent in the traditional CTCS-3 level system, including: S1. Based on the delay propagation mechanism, construct a multi-dimensional evaluation index system for train delays; The multi-dimensional evaluation index system includes: initial delay time, number of affected trains, and total delay impact time; Specifically, high-speed trains encounter too many unpredictable factors during their journey, making train delays highly complex and potentially leading to delays. Based on the different causes of delays, train delays can be divided into two main categories: initial delays and consequential delays. A diagram illustrating the impact indicators of initial delays, based on initial delays and consequential delays, is shown below. Figure 3 As shown; With the station to Taking train operation within a section as an example, by observing the deviation between the actual train running line (red line in the diagram) and the planned running line (black line in the diagram), the propagation mechanism of train delays can be identified. Let... , , , As a group of adjacent trains, For trains running on schedule. When the first train... Duration of occurrence: After the initial delay, in order to ensure the minimum safe tracking interval between trains, the subsequent three trains ( , , Delays occur sequentially. In this scenario, the number of affected trains includes one initially delayed train and three subsequently delayed trains. The total delay impact time is determined by the delay time of each train in the sequence (…). , , , It consists of the sum of ) .

[0022] S2. Based on the multidimensional evaluation index system, a clustering algorithm is used to divide the train delay sequence into four types of delay patterns, and the evolution characteristics of the delay patterns are obtained. For example, based on a system analysis of multi-angle evaluation indicators, this application uses the K-means algorithm to classify train delay sequences into patterns.

[0023] The system of multi-angle evaluation indicators is used to analyze the clustering algorithm by combining the CH index (Calinski-Harabasz Index, CHI), silhouette coefficient (SC), and SD validity index (S_Dbw Index, SDI) to obtain the optimal solution of the clustering algorithm and its parameters. The Calinski-Harabasz index (CH index) is one of the indicators used in cluster analysis to evaluate the clustering effect. Its purpose is to measure the compactness and segregation of clusters and help evaluate the quality of clustering.

[0024] The silhouette coefficient measures the density of each point within the same cluster, i.e., the similarity of the point to other points in the same cluster and the distance to the nearest neighbor cluster, to determine the reasonableness of clustering. The silhouette coefficient value ranges from -1 to 1. A silhouette coefficient of 1 means that the data point is very well-suited to its own cluster and far away from other clusters; 0 indicates that the data point is located on the boundary between two clusters; a negative value indicates that the data point has been misclassified into another cluster.

[0025] The SD validity index is an internal evaluation metric used to assess the quality of clustering results, primarily considering cluster compactness and separation. It combines the distribution of data points within clusters with the separability of data between clusters to select the optimal number of clusters or to validate the effectiveness of clustering algorithms.

[0026] Through systematic analysis of the aforementioned multi-angle evaluation indicators, the K-means algorithm used in this application shows that when K=4, the CH index reaches a local peak, indicating that the inter-cluster separation and intra-cluster compactness are optimally balanced. The global silhouette coefficient (SC) value is higher than other candidate cluster configurations, reflecting a high confidence level in the clustering membership of the samples. The S_Dbw index exhibits a minimum value when K=4, verifying the optimal overall compactness and separability of the clustering structure. Furthermore, through engineering feasibility analysis, when the number of clusters exceeds 4, the increase in the SC value slows down and cluster fragmentation occurs, indicating that excessive subdivision will reduce the interpretability of the pattern.

[0027] The four clustering patterns effectively cover typical train delay propagation scenarios (such as point-based delays, chain-like propagation, and regional spread), meeting the actual application needs of railway dispatching. By comprehensively considering the clustering effectiveness index and engineering application value, the optimal number of clusters was determined to be 4.

[0028] For example, the K-means clustering algorithm in this study was implemented using Python 3.11, with the core computation performed by the K-Means module of the scikit-learn 1.4.1 library. The hardware environment consisted of a server with a 12th Gen Intel(R) Core(TM) i7-12700H processor (20 cores, 2.3GHz) and 16GB of DDR4 memory. The K-Means clustering results were obtained using Python, as shown in the image. Figure 4 As shown.

[0029] The number of delayed trains in different categories are as follows: 3786 in delay pattern A, 1638 in pattern B, 669 in pattern C, and 429 in pattern D, with a relatively even distribution. Based on the clustering, a delay classification system can be constructed, yielding the ranges of the four delay patterns and their initial delay impact indicators, as shown in Table 1: Initial Delay Indicator Ranges for Delay Patterns. Table 1 Initial Delay Index Range for Delay Mode

[0030] This embodiment explicitly defines the calculation method for the transition probability characteristics between late-delay modes, and the technical effect is reflected in: Quantitative calculation formulas are given for the transition probabilities of four types of late-delayed patterns: A (mild), B (moderate), C (severe), and D (extreme), enabling a quantitative description of the evolution law of late-delayed patterns and making the transition characteristics of late-delayed patterns calculable and predictable. The probability calculation method based on transfer frequency closely matches the characteristics of delay propagation data in actual train operation, improving the objectivity and accuracy of delay pattern evolution analysis and providing reliable evolutionary characteristics for subsequent prediction models.

[0031] Specifically, based on the evolutionary characteristics analysis of late-arriving modes, the evolutionary characteristics between late-arriving modes are obtained, including: the transition probability characteristics and propagation path characteristics between late-arriving modes; (1) The transition probability features between late-arrival modes in S2 are calculated as follows: ; —The transition probability from pattern i to pattern j; —The frequency of switching from late arrival mode i to late arrival mode j; —The sum of the frequencies of transitions from late-arrival mode i to all possible states; S={A,B,C,D} — Set of late-delay patterns; —Late-delay pattern index; A-A type delay mode, used to represent minor delay scenarios; B-B class delay mode is used to represent medium delay scenarios; C-C class delay mode, used to represent severe delay scenarios; D-D class delay mode is used to represent extreme delay scenarios.

[0032] This formula is actually the result of dividing the frequency of late-time mode i transitioning to late-time mode j by the total frequency of late-time mode i transitioning to all late-time modes. In this way, the evolution of late-time modes can be described by the transition probabilities between modes.

[0033] For example, through statistical analysis of actual operation data of the Wuhan-Guangzhou High-Speed ​​Railway, this application constructed a delay mode transition probability matrix, as shown in Table 2. This matrix reflects the transition patterns between different delay modes and reveals the dynamic characteristics of delay propagation.

[0034] Table 2 Late-delay mode transition probability matrix

[0035] The transition probability matrix reveals strong persistence among similar late-delay patterns, with each pattern exhibiting the highest probability of self-sustaining. Pattern A (mild lateness) demonstrates a high self-sustaining probability of 68.2%, indicating strong self-recovery capabilities and a low likelihood of evolving into more severe late-delay patterns. In contrast, Pattern D (extreme lateness) also shows a high self-sustaining probability of 67.8%, suggesting that extreme lateness, once it occurs, is often difficult to recover from in a short period and easily triggers chain reactions. The transition probability between adjacent late-delay patterns is high, while the probability of transitioning across levels is significantly reduced. Furthermore, severe lateness (types C and D) exhibits a significant self-reinforcing effect (62.9% for type C and 67.8% for type D), indicating that its propagation process easily forms positive feedback.

[0036] (2) The late-delay mode propagation path feature steps between late-delay modes in S2 include: Based on spatial propagation characteristics, the propagation paths of different delay patterns in the network show significant differences. According to the constructed delay pattern classification system (four categories: A / B / C / D) and the pattern conversion probability matrix in Table 2, combined with the statistical analysis of various evaluation indicators in the initial delay impact indicators in the previous chapters and the range table of initial delay indicators for delay patterns in Table 1, the mean values ​​of the initial delay indicators under different delay patterns are calculated and shown in Table 3. Then, the propagation path characteristics of the four types of delay patterns are analyzed respectively.

[0037] Table 3. Average values ​​of initial delay indicators under the delay mode.

[0038] The propagation path of delayed arrivals is an important manifestation of the evolution of delayed arrival patterns. By analyzing the propagation paths under different delayed arrival patterns, the spatial and temporal characteristics of delayed arrival propagation can be revealed.

[0039] Delay Pattern A: Samples of delay pattern A were extracted, representing 58.04% of the total. The average initial delay time was 4.63 minutes, the average number of affected trains was less than 3, and the average total impact time was less than 10 minutes, only 7.49 minutes. Furthermore, according to Table 1, the initial delay time range for pattern A is [4, 11] minutes, indicating that the initial delay time for each station under this pattern will not exceed 11 minutes, the number of affected trains ranges from 1 to 6, and the total impact time is concentrated in the [4, 12] minutes range. According to Table 2, the self-sustaining probability of pattern A is 68.2%, and the total probability of transitioning to a more severe pattern is only 31.8%, indicating that its propagation range is likely limited to a single station or 1-2 adjacent stations. Combined with… Figure 16 The train number of carriages affected by the track layout showed very few outliers in Mode A, indicating a short propagation chain and easy absorption. Minor delays could be recovered through local redundancy time compensation or fine-tuning of scheduling, without triggering a chain reaction, exhibiting "point-like propagation," see [link to relevant documentation]. Figure 5 A schematic diagram of the propagation path of late-delay diffusion in late-delay mode A.

[0040] Analysis shows that delay pattern A is mainly characterized by point-like propagation, which is a minor delay. The delay propagation path is relatively short, the impact is limited to a single or a few adjacent stations, the number of affected trains is often small, the delay propagation effect is weak, and the train timetable has a strong self-recovery capability.

[0041] Delay Pattern B: Delay Pattern B samples accounted for 25.11%, with an initial average delay time increasing to 6.31 minutes, an average of 4.19 affected trains, and an average total impact time of 16.70 minutes. The total impact time range expanded to [11, 25] minutes. The self-maintain probability of Delay Pattern B was 54.6%, and the probability of transitioning to Pattern C was 28.1%. (Combined with...) Figure 15 The initial delay time distribution in the box plot shows that Pattern B exhibits a significant right skew and contains some outliers with a long tail. This phenomenon indicates that delays may spread and easily trigger a chain reaction of subsequent train delays, forming a linear propagation chain along the line. That is, moderate delays are transmitted station by station through a chain reaction effect in the inter-station timetable, extending the impact along the line. Figure 6 .

[0042] Therefore, delay pattern B often exhibits linear propagation characteristics, belonging to moderate delays. The delay propagation path gradually lengthens, and the impact expands to multiple stations. The increase in initial delay time leads to subsequent train delays, forming a local delay propagation chain. At this time, the dispatching system needs to suppress delay propagation by adjusting train intervals and speed curves.

[0043] Delay Pattern C: By extracting samples of delay pattern C (10.26% of the total), the average initial delay time increased to 9.43 minutes, leading to an average increase in the number of affected trains to 5.27 and a significant increase in the average total delay impact time to 32.99 minutes. According to Table 2, the self-maintaining probability of pattern C is 62.9%, and the probability of transitioning to pattern D is 14.9%. This indicates that its higher initial delay time may exacerbate arrival and departure line conflicts at hub stations (such as Hengyang East Station), forming a "one-to-many" diffusion path. (See Table 2 for details.) Figure 7 A schematic diagram of the propagation path of late-delay mode C.

[0044] Delay pattern C begins to exhibit branching propagation, indicating severe delays affecting multiple sections. The significant increase in initial delay time exacerbates the propagation effect, forming a regional delay propagation network. At this point, a "one-to-many" diffusion may occur at hub stations, exhibiting non-linear diffusion. The dispatching system needs to adopt more proactive adjustment strategies, such as temporary stops and adjustments to train routes, to mitigate the impact of delays.

[0045] Delay Pattern D: The sample size for Delay Pattern D was 6.59%. Although the initial delay time range of Pattern D was similar to that of Pattern C, the average initial delay time of Pattern D was as high as 11.21 minutes, significantly increasing the range of the total time index to [39, 98] minutes, causing the system to enter an unstable state. Table 2-10 shows its self-maintaining probability of 67.8%, forming a positive feedback loop. Delays are prone to network diffusion, especially at high-level stations and hub stations, where extreme delays are likely to occur. Figure 8 A schematic diagram of the propagation path of the late-delay mode D.

[0046] Delay pattern D is a typical example of network propagation, representing extreme delays that affect the entire line and even cross-line trains. The extreme increase in initial delay time leads to a maximum delay propagation effect, forming a global delay propagation network that spreads through hub nodes to multiple lines, creating a complex delay propagation network. At this point, the dispatching system needs to activate emergency plans, adjust train schedules, and even suspend some train services to restore system order.

[0047] S3. Combining the multidimensional evaluation index system and the evolutionary characteristics, construct as follows: Figure 2 The initial delay impact index prediction model shown is as follows: It is used to predict the delay impact index corresponding to each delay pattern in the acquired train time map based on real-time train operation data, and obtain the delay impact index prediction result. This embodiment limits the module composition of the initial delay impact index prediction model, and the technical effect is reflected in: A combined network structure of multidimensional CNN + bidirectional LSTM + attention mechanism + fully connected layer is adopted, which takes into account both the spatial and temporal features of late data and solves the problem of insufficient prediction accuracy of traditional machine learning models for multidimensional late data. By assigning weights to time features through an attention mechanism, the system can automatically focus on feature information that plays a key role in the impact of delays, thereby further improving the accuracy of the prediction model. The model's modules have clear division of labor and work in a progressive manner, enabling efficient processing and feature extraction of real-time train operation data. It can quickly predict the impact indicators of various delay patterns based on real-time data, providing real-time and accurate reference for scheduling decisions.

[0048] This embodiment proposes a novel CNN-BiLSTM-AM initial late point index prediction model by integrating CNN, BiLSTM, and AM into a single framework. See Figure 2 The flowchart of CNN-BiLSTM-AM is shown. This framework is built from five basic modules: input module, feature extraction module, sequence learning module, attention module, and prediction module.

[0049] In the feature extraction module, a CNN is used as the spatial feature extractor. Its multi-layered convolutional structure can effectively capture the local spatial correlations of the input data. Through stacked convolutional and pooling layers, the CNN extracts discriminative spatial feature representations from the original input. These high-level features processed by the CNN are then fed into a bidirectional long short-term memory network for temporal modeling. In the sequence learning module, sequence features are first extracted and encoded by a BiLSTM, and then processed by an attention layer. In the attention module, the attention mechanism highlights key features through dynamic weight allocation, improving the model's prediction accuracy. Finally, in the prediction module, fully connected layers are stacked with the output layer to perform the final prediction. The above components include hyperparameters such as kernel size, number of kernels, loss function type, and number of neurons. The following will describe each module of the proposed prediction model in detail: One possible design is that the initial delay impact index prediction model in S3 includes: The input module is used to process the initial late arrival index data through at least one multi-dimensional CNN combination to obtain preprocessed data; This approach uses a data processing method that combines initial late arrival index data with one (or more) multidimensional CNNs as the input module. The input data is organized in a way suitable for deep learning algorithms, which reduces the impact of zero values ​​and differences in the data, improves the training process, and enhances prediction performance.

[0050] A feature extraction module is used to extract spatial features from the preprocessed data by stacking multiple convolutional and pooling layers; as a possible design, the convolutional neural network in the feature extraction module includes: Convolutional layers are used to extract local features from input data; Pooling layers are used to sample the obtained local features and output high-order abstract feature maps; A fully connected layer is used to combine and transform the high-order abstract feature map to output the spatial features.

[0051] By stacking multiple convolutional and pooling layers, more important features are extracted from the input. Through a hierarchical convolutional module design, abstract semantic features of the input data can be extracted progressively. After the convolutional kernel captures spatial features through local connectivity, max pooling reduces the dimensionality of the feature map, significantly decreasing the model parameter size. In the feature extraction block, the ReLU activation function is used; its piecewise linearity alleviates gradient instability and accelerates model convergence. After each pooling layer, batch normalization is used as an effective regularization strategy. Besides regularization, it effectively suppresses inter-layer covariate shift, combining regularization and training acceleration to increase the network's generalization ability. Then, the mean of each batch of training data is calculated. With variance Dynamic calculations are performed, followed by scaling and translation transformations of the features, where learnable parameters... and Enhanced the network's feature adaptation capability, constant term This is used to ensure numerical stability and reduce sample differences between layers. Therefore, this technique helps to accelerate the training process. The specific formula is as follows: ; ; ; ; in The size of the batch gradient descent is defined. and It represents the input and output of the i-th observation in batch gradient descent. This is the average value of the minimum gradient descent. It is the variance of the minimum batch sample. It is a constant close to zero. It's a scaling parameter. It is a bias parameter.

[0052] In terms of dimensionality handling strategy, convolutional layers employ equal-size padding to maintain the spatial resolution of the feature map and avoid loss of edge information. To address the temporal processing requirements of the subsequent bidirectional long short-term memory network, a feature flattening operation reconstructs the multidimensional convolutional output into a one-dimensional vector, achieving dimensional adaptation from spatial features to temporal features. This architecture design reduces computational complexity while ensuring effective transfer of cross-modal features.

[0053] The sequence learning module is used to generate temporal features by combining a bidirectional long short-term memory neural network layer and a regularization layer to serialize the spatial features. Specifically, the sequence learning module learns the temporal patterns of extracted features through feature extraction blocks. It consists of BiLSTM layers and dropout layers. To effectively avoid overfitting, dropout regularization is applied after each BiLSTM layer during the sequence learning module's operation. The core principle of dropout is that instead of training all neurons in the network, a subset is randomly selected for training. In each iteration of the training step, a certain percentage of neurons output zero and are inactive. This allows the network to learn more effective features and improves the model's generalization ability.

[0054] As one possible design, the bidirectional long short-term memory neural network includes: Two parallel LSTM units are used to process the spatial features from both forward and backward directions to obtain the generated temporal features. ; The two parallel LSTM units include a forward LSTM network and a reverse LSTM network. Forward LSTM networks process sequence features sequentially to obtain forward information. ; The inverse LSTM network processes sequence features in reverse chronological order to obtain inverse information. ; Combining the aforementioned positive information and the reverse information Perform element-wise addition of vectors to generate time features. ; ; Among them, ⊕ — vector element-wise addition operation, used for summing the forward and reverse output components.

[0055] The attention module is used to calculate the attention weights of the temporal features through an attention mechanism. Specifically, an attention layer is added at the end of the sequence learning module, which has different levels of importance for the impact of late arrivals. The weights assigned to their hidden states are also different. Therefore, a high-level vector that integrates all useful information about the impact of late arrivals can be obtained. One possible design is that, in the step of calculating the attention weights of the temporal features through an attention mechanism: Attention scores are obtained by using input data features or output data features from the previous layer. , ; in, —Attention score; —The weight of the attention mechanism; —Bias in attention mechanisms; —Input data features or previous layer output data features; pass The function normalizes the attention score, and then normalizes the attention score. Convert to probability distribution form , ; Based on probability distribution form The value vector v is weighted and summed to generate the final attention value SH. .

[0056] The prediction module consists of a fully connected layer and an output layer. The fully connected layer performs non-linear calculations on the feature values ​​obtained by the attention module to obtain the final prediction result.

[0057] For example, the initial delay impact index prediction model training method proposed in this application mainly includes three stages: data preparation, model training, and model evaluation, such as... Figure 9 The training process of the CNN-BiLSTM-AM model is shown in the diagram below. The main steps are as follows: (1) Input data: Input the data required for training CNN-BiLSTM-AM; (2) Data standardization: Given the significant differences in the numerical values ​​of the input data, in order to optimize the training effect of the model, the input data is standardized and normalized. This process aims to eliminate the influence of data units and ensure that each feature has equal influence in model training. (3) Dataset partitioning: The entire dataset is divided into a training set, a validation set, and a test set in an 8:1:1 ratio. The training set is used for learning the model's parameters, the validation set is used to tune the model's hyperparameters, and the test set is used to evaluate the model's final performance. (4) Network initialization: Initialize the parameters of each layer of the CNN-BiLSTM-AM model. Specifically, the parameters of the LSTM units are initialized using a normal distribution, and the weight matrix of the attention mechanism layer is initialized, etc. (5) CNN layer computation: The input data passes through the convolutional and pooling layers in the CNN layer in sequence. The convolutional layer extracts local features by sliding the convolutional kernel across the input data; the pooling layer samples the output of the convolutional layer to obtain local features and output values. In this layer, the spatial features of the input data are obtained through the feature extraction module and passed to each layer of the sequence learning module; (6) BiLSTM layer computation: The input features capture temporal dependencies through forward and backward LSTM layers to obtain the output data of the CNN layer through the BiLSTM layer, and obtain the output value; (7) Attention mechanism layer calculation: The output data of the BiLSTM layer is processed by the attention mechanism layer to calculate the attention weight of each feature, highlighting the more influential features in the prediction results; (8) Fully connected layer computation: Summarize the output data and map it to the output space; (9) Calculation error: Compare the predicted value calculated by the fully connected layer with the actual value of the data set, and calculate the corresponding mean absolute error. Use the backpropagation algorithm to update the parameters in each epoch, use the Adam optimizer to perform gradient descent, and update the network parameters layer by layer until the maximum epoch value is reached. (10) Determine the termination condition: whether the preset number of training rounds has been reached, or whether the validation set loss has not decreased significantly for several consecutive rounds, or whether the model accuracy has reached the target threshold. If at least one termination condition is met, training ends. Otherwise, training will continue; (11) Performance evaluation: Make predictions and calculate evaluation metrics on the test set.

[0058] After data preprocessing, the number of convolutional kernels is set to 128. The model loss function is the mean absolute error (MAE), as shown in the following formula: ; in, —The actual value of the i-th train —Estimated value of the i-th train; The model uses loss function minimization as the optimization objective and updates network parameters from the output layer to the input layer through backpropagation. The training configuration using Python is as follows: batch size is set to 32, the optimizer is Adam, and the initial learning rate is 0.001. To improve training efficiency and prevent overfitting, the following strategy is implemented: if the validation set error does not improve within 10 consecutive iterations, the learning rate is automatically reduced by 10%; if the error decreases by less than 0.01 within 20 iterations, the training process is terminated. See Table 4 for detailed parameter configurations of the CNN-BiLSTM-AM model.

[0059] Table 4. Parameter Settings for Combined Model

[0060] The prediction model was built and trained in Python 3.11, using the TensorFlow 2.11.1 framework to build the neural network, and leveraging the NVIDIA GeForce RTX 3060 Laptop GPU to accelerate the training process. Model hyperparameter optimization was performed using Keras 3.2.1, and the inference phase utilized the CPU (Intel i7-12700H).

[0061] This application provides a detailed analysis of the performance of the CNN-BiLSTM-Attention model using the mean absolute error (MAE) of the loss function as an evaluation metric. The loss function is a core evaluation metric in the optimization process of deep learning models; its function is to quantify the degree of deviation between the model's predicted output and the true label, helping to optimize model parameters and make the prediction results more accurate. Figure 10 The fitting of the loss function is shown.

[0062] from Figure 10 As can be seen, with the increase in training epochs, the loss function curves of the training and validation sets enter a stable convergence phase from the 10th epoch. The two curves show a high degree of synchronization in the convergence interval, with the final loss value of the training set being 0.037 and the validation set loss being approximately 0.045. This indicates that the model did not exhibit overfitting during training. This demonstrates that the model's training effect is good and it also reflects good generalization performance.

[0063] Furthermore, this application addresses arrival delays separately. Number of trains affected And the total time affected The predictive performance of the three key indicators was compared and analyzed. Figure 11 , Figure 12 , Figure 13 The results show the comparison between the predicted and actual values ​​of the CNN-BiLSTM-AM model for various initial delay impact indicators.

[0064] As can be observed from the above charts, the predicted values ​​of the combined model are basically consistent with the actual values, with small differences. This indicates that the CNN-BiLSTM-Attention model demonstrates high accuracy and stability in predicting the three initial late point impact indicators.

[0065] S4. By establishing train motion equations, the train behavior characteristics under different delay modes are quantitatively analyzed, and a multi-objective optimization model is constructed based on the train behavior characteristics. The multi-objective optimization model is used to generate delayed train operation strategies. One possible design is that S4 establishes precise train motion equations to quantitatively analyze train behavior characteristics under different delay modes. Based on a single-mass model, it constructs longitudinal dynamic equations for the train, quantifying the train's motion state from three dimensions: acceleration, velocity, and spatial coordinates. This enables precise and quantitative analysis of train behavior characteristics under different delay modes. The equations introduce a slewing mass coefficient to consider the equivalent mass influence of rotating parts, making the mathematical representation of train motion more closely reflect actual operating conditions and improving the accuracy of behavior characteristic analysis. The quantified train motion equations provide a solid physical foundation for the subsequent construction of multi-objective optimization models, allowing the generation of optimization strategies to better align with the train's actual operating capabilities and dynamic laws, including: A longitudinal dynamics model of the train is constructed based on a single-mass point model. ; ; ; —Overall quality of the train; t—the point in time when the train departs; —Slewing mass coefficient, used to reflect the equivalent mass effect of rotating parts of a train; —The instantaneous speed of the train at time t; —The spatial coordinates of the train at time t; —Output control force, representing the net external force applied to the train; —Characterizes the resultant resistance force acting on the train at time t.

[0066] Specifically, the train's output control force consists of two mutually exclusive components: traction force FA, used for acceleration and constant speed operation, and braking force FB, used for deceleration. Based on the train's operating characteristics, these two forces cannot act on the locomotive system simultaneously; that is, when the train is in traction or cruising mode, only traction force exists; while in braking mode, only braking force is effective.

[0067] Train output traction force: Train output traction force refers to the actual force output by the traction system to overcome resistance and propel the train forward during starting, acceleration, or climbing. The magnitude of the traction force directly affects the train's acceleration, climbing ability, and overall performance. Traction force is the tangential force between the train and the track, propelling the train along the track. The main source of traction force is the train's traction system (such as the torque of the electric motor or the output power of the internal combustion engine), which is transmitted to the track through wheel-rail contact, generating the forward propulsion for the train.

[0068] Taking a certain type of EMU train using the CTCS-4 level train control system as an example, its traction force is divided into three stages: ; in, This represents the maximum traction force that the train can output. This indicates the maximum power output of the traction system; This is the first critical speed, which is the speed point at which the train transitions from the constant torque region to the region of linear torque decrease. The second critical speed marks the transition point from the linear torque decrease region to the constant power region.

[0069] These key parameters constitute the traction characteristics of the EMU, and their specific values ​​are shown in Table 5.

[0070] Table 5 Traction characteristic parameters of a certain type of EMU

[0071] Train output braking force: Train output braking force refers to the force actually output by the braking system to slow down or stop the train during deceleration or stopping. The magnitude of the braking force directly affects the train's deceleration effect, braking distance, and safety. Braking force is the opposing force between the train and the track, which slows down the train or stops it. The main source of braking force is the train's braking system, including mechanical brakes (such as brake shoe brakes and disc brakes) and electric brakes (such as resistor brakes and regenerative brakes). Braking force is transmitted to the track through wheel-rail contact, slowing down the train's forward speed. Based on the braking system characteristics of this type of EMU, the piecewise function of the train's commonly used braking deceleration as a function of speed can be expressed as: ; in, Let t represent the train's service braking deceleration at time t. Substituting this deceleration into the dynamic equations, the train's service braking force can be calculated. .

[0072] ; Train running resistance: Train running resistance refers to the various opposing forces that a train experiences during operation. These forces cause the train to consume energy and slow down. Understanding and controlling train running resistance is crucial for improving train operating efficiency, reducing energy consumption, and ensuring safe operation.

[0073] One possible design is that, in S4, a multi-objective optimization model is constructed based on the train behavior characteristics. This model aims to minimize the initial delay time, the number of affected trains, and the total delay impact time. This achieves multi-dimensional collaborative optimization of operational efficiency in train delay scheduling, overcoming the limitations of single-objective optimization in existing research. The optimization objectives are highly consistent with the previously constructed multi-dimensional evaluation index system, making the optimization model design more targeted and enabling direct control over the core impact indicators of delays, thus improving the actual optimization effect of the scheduling strategy. The model focuses on optimizing the variable parts of the initial delay impact indicators, making the optimization strategy more practical and enabling adjustable and implementable delay control in actual train operation, including: Train operation optimization involves multi-dimensional objective trade-offs. This section constructs an optimization framework from three dimensions: initial delay time, number of affected trains, and total delay impact time. For the train delay problem in high-speed railway systems, a multi-objective optimization model based on a non-dominated genetic algorithm is established. This model achieves overall system performance optimization by adjusting train operating conditions. The multi-problem optimization objective of this model is to minimize the variable part of the initial delay impact indicators of the delayed train sequence: initial delay time, number of affected trains, and total impact time. That is, in S4, a multi-objective optimization model is constructed based on the train behavior characteristics, and the multi-objective optimization model is used to minimize the variable part of the initial delay impact indicators. The multi-objective optimization model is as follows: ; in, —Initial delay time calculation model; —Affects the train number calculation model; —Affects the total time calculation model.

[0074] (1) Initial delay time The initial delay time reflects the direct impact of the disturbance. During train operation, the initial delay often propagates backward through network effects, so its derivative effects need to be considered comprehensively.

[0075] ; ; ; ; In the formula, It is the distance the train travels under traction conditions, which can be uniquely determined based on the speed at the cruising point; It is the distance the train travels under cruising conditions, which can be uniquely determined based on the distance between stations, the speed at the cruising point, and the speed at the braking point. It is the distance the train travels under coasting conditions, which can be uniquely determined based on the cruising point speed and the braking point speed; It is the train's running distance under braking conditions, which can be uniquely determined based on the braking point speed; It is the instantaneous speed of the train at time t; Represents the spatial coordinates of the train at time t; the sum of the travel distances of the train in its four stages. Reaching the distance between stations At that time, the actual train running time was obtained. Record Finding the minimum initial delay time is equivalent to finding the train travel time. Shortest.

[0076] (2) Number of trains affected Minimizing the number of affected trains is a key objective in reducing the range of system disturbances. This is achieved by applying constraints based on the train running times specified in the timetable. Seeking to minimize the number of trains affected The operational plan. This indicator is directly related to the efficiency of restoring the road network's operational order and is also an important parameter for measuring operational quality.

[0077] ; ; —The train running time specified in the timetable is determined by the scheduled departure time of the departure station and the scheduled arrival time of the arrival station; —Actual train travel time; —Indicates whether the train is delayed; a 0-1 variable, meaning whether the actual running time is greater than the planned running time.

[0078] (3) The impact of delays on total time When the system cannot return to normal operation in the short term, the optimization focus shifts to minimizing the total time affected by delays. The model calculates the interval running time using the following formula. This minimizes the impact of delays over time. This strategy helps reduce the long-term impact of delays on subsequent operations and improves the system's resilience.

[0079] ; One possible design is that S4 constructs a multi-objective optimization model based on the train's behavioral characteristics. This requires considering two key constraints: clearly defining the speed limit and the safety constraints of the minimum safe following interval between trains. Safety boundaries are defined from two dimensions: train speed and spatial position, ensuring that the generation of optimization strategies always prioritizes operational safety, thus solving the problem of insufficient balance between efficiency and safety in traditional scheduling. A comfort constraint based on a Gaussian evaluation model of the rate of change of acceleration is designed. A quantified comfort function regulates the smoothness of train operation, avoiding excessive acceleration or deceleration to catch delays, which could lead to a decrease in passenger comfort. This achieves coordinated optimization of the three objectives of operational safety, operational efficiency, and passenger comfort. All constraints are represented by quantitative formulas, making the solution of the optimization model more standardized and computable, improving the efficiency and accuracy of optimization strategy generation. Specifically, this application uses the train's cruising speed and braking speed as core decision variables, achieving multi-objective coordinated optimization by precisely controlling the train's operating condition transition process. This approach is highly feasible, as cruising speed and braking speed are key control parameters during train operation and directly affect operational efficiency. Furthermore, by adjusting these two parameters, a flexible balance can be achieved between running time, the scope of delay impact, and the total duration of delay impact, while ensuring safety and comfort. The system can also dynamically adjust the speed parameter based on actual operating conditions, improving the adaptability of the optimization scheme. When constructing a multi-objective optimization model, to ensure the feasibility and practicality of the optimization scheme, the following two types of key constraints need to be considered: (1) Safety constraints are used to ensure that train operation does not violate the track speed constraints while maintaining a safe inter-vehicle distance. These constraints are rigid requirements of the model and must be strictly followed in any optimization process. Train operation safety is an unshakable red line requirement for train operation, and its constraint conditions are as follows: ; ; ; in, —The maximum permissible operating speed of this line; —The actual position of train i-1 at time t; —The actual position of train i at time t; —The actual tracking interval between adjacent trains is determined by the spatial running distance between adjacent trains; —The minimum safe following interval is determined by the speed vt of the vehicle ahead at time t.

[0080] Comfort constraints are quantified using a Gaussian evaluation model, which calculates comfort indices during train operation. This model considers changes in train acceleration and its impact on passenger comfort, ensuring the acceptability of the optimized solution in practical applications by limiting the range of these parameters. The formula is as follows: ; ; ; —The average comfort function of train i, with a threshold of To meet international comfort evaluation standards, a threshold value is required. The value is 0.8; —The rate of change of acceleration of train i at time t; —The acceleration of train i at time t; and The width coefficient and center position of the Gaussian evaluation model are respectively set to 0.8 and 0.

[0081] These constraints and the optimization objective together constitute a complete multi-objective optimization framework, providing a theoretical basis for solving delayed train operation adjustment schemes. Under this constraint system, the next section will introduce in detail the optimization algorithm design based on NSGA-II.

[0082] S5. Combine the initial delay impact index prediction model and the multi-objective optimization model to calculate the train operation diagram at the current sampling time, obtain the corresponding delayed train operation strategy, and adjust the train operation according to the current delayed train operation strategy.

[0083] One possible design is that, in step S4, which generates the delayed train operation strategy, the NSGA-II algorithm is used to solve the multi-objective optimization model. This can efficiently output the Pareto optimal solution set, solving the problem of conflicting objectives and difficulty in finding the optimal solution in multi-objective optimization problems. Furthermore, it combines the ideal solution / negative ideal solution with the relative proximity index C. iPrioritizing the Pareto solution set enables quantitative screening of the optimal solution, providing dispatchers with a clear basis for strategy selection and resolving the scheduling decision-making difficulties caused by the multiple solutions in the Pareto solution set. The complete steps of model solving, matrix standardization, solution screening, and priority ranking standardize and systematize the solution process of multi-objective optimization models, enabling rapid generation of optimal delayed train operation strategies. This achieves real-time and efficient adjustment of train operations, improving the overall operational efficiency and resilience to delays in the railway network. Step 1: Solve the multi-objective optimization model using the NSGA-II algorithm and output the Pareto optimal solution set; represent the Pareto optimal solution set as a decision matrix, and perform weighted standardization on the decision matrix to obtain the standardized weight matrix; Step 2: Determine the ideal solution Z+ and the negative ideal solution Z- based on the standardized weight matrix; Step 3: Calculate the distances from each solution to the ideal point and the negative ideal point based on the ideal solution Z+ and the negative ideal solution Z-; Step 4: Calculate the relative proximity index C for each solution based on the distances from each solution to the ideal point and the negative ideal point. i Based on proximity index C i Obtain the priority order of the solutions in the Pareto solution set.

[0084] Specifically, in multi-objective optimization problems, NSGA-II typically generates a set of non-dominated optimal solutions during the solution process. To select the optimal solution from these solutions, the weighted average operator COWA is introduced to calculate the weights of the n objective function indices, effectively reducing the influence of the less reliable solutions at both ends of the Pareto optimal solution set on the weighting. Finally, combined with the weights, the TOPSIS method is used to quantitatively evaluate the Pareto optimal solution set. This method is based on the concepts of ideal solutions and negative ideal solutions, and achieves a scientific ranking of Pareto optimal solutions by evaluating the distance relationship between each solution and the ideal and negative ideal points. The steps of the TOPSIS method are as follows: Step 1: Represent the Pareto optimal solution set as a decision matrix. Given m non-dominated solutions, each containing n objective function values, the decision matrix... To eliminate the influence of dimensions, the matrix needs to be standardized to obtain a standardized matrix. The COWA operator is used to calculate the weights of n indicators. According to the following formula: ; ; ; in, This refers to drawing i from m-1 elements. The number of possible combinations of a single element. This leads to the introduction of the weight vector W = ( , ,..., ), each component The weights represent the corresponding objective function, and the sum of the weights is 1. Multiplying the weight vector by the standardization matrix yields the weighted standardization matrix V = W × R.

[0085] Step 2: Determine the ideal solution Z+ and the negative ideal solution Z- based on the weighted standardization results. The ideal solution and the negative ideal solution satisfy the following: ; ; Step 3: Calculate the distances from each solution to the ideal point and the negative ideal point: ; ; , The distances from each solution to the ideal point and the negative ideal point, where m is the total number of elements in the sample, and v i,j For j solutions, For the ideal point value, It is a negative ideal point value.

[0086] Step 4: Then, the relative proximity of each solution can be calculated: ; Relative proximity index This value reflects the overall performance of the solution; a larger value indicates that the solution is closer to the ideal point and farther from the negative ideal point, meaning better overall performance. Sort the solutions in the Pareto solution set in descending order of proximity to obtain their priority ranking.

[0087] The elitist strategy in NSGA-II is the third core feature of this algorithm. This strategy preserves high-quality solutions while ensuring population diversity. NSGA-II maintains population quality by implementing an elitist retention mechanism, retaining high-quality individuals in each generation. Specifically, a parent population of size N is merged with a child population of equal size to form a temporary population of size 2N. When forming a new generation, the algorithm starts from the optimal frontier and sequentially incorporates the entire frontier layer into the new population. When a frontier layer cannot be fully incorporated, individuals in that layer are selected based on their crowding distance, prioritizing those with larger crowding distances, until the new population size reaches the preset value N.

[0088] NSGA-II performs exceptionally well in handling large-scale multi-objective optimization problems. It can handle various types of objective functions, including linear and nonlinear, continuous and discrete ones. Furthermore, by introducing a crowding mechanism to maintain population diversity, this design effectively prevents the algorithm from getting trapped in local optima.

[0089] Optimization process flow of NSGA-II genetic algorithm Figure 14 As shown in the figure: The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0090] This application uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. In summary, the content of this specification should not be construed as a limitation of this application.

Claims

1. A train operation adjustment method based on initial delay classification and pattern deduction, characterized in that, include: S1. Based on the delay propagation mechanism, construct a multi-dimensional evaluation index system for train delays; The multi-dimensional evaluation index system includes: initial delay time, number of affected trains, and total delay impact time; S2. Based on the multidimensional evaluation index system, a clustering algorithm is used to divide the train delay sequence into four types of delay patterns, and the evolution characteristics of the delay patterns are obtained. The evolutionary features include: the transition probability features between late-arrival modes and the propagation path features; S3. Combine the multi-dimensional evaluation index system and the evolution characteristics to construct an initial delay impact index prediction model, which is used to predict the delay impact index corresponding to each type of delay mode in the acquired train operation diagram based on real-time train operation data, and obtain the delay impact index prediction result. S4. By establishing train motion equations, the train behavior characteristics under different delay modes are quantitatively analyzed, and a multi-objective optimization model is constructed based on the train behavior characteristics. The multi-objective optimization model is used to generate delayed train operation strategies. S5. Combine the initial delay impact index prediction model and the multi-objective optimization model to calculate the train operation diagram at the current sampling time, obtain the corresponding delayed train operation strategy, and adjust the train operation according to the current delayed train operation strategy.

2. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 1, characterized in that, The transition probability features between late-delay modes in S2 are calculated as follows: ； —The transition probability from pattern i to pattern j; —The frequency of switching from late arrival mode i to late arrival mode j; —The sum of the frequencies of transitions from late-arrival mode i to all possible states; S={A,B,C,D} — Set of late-delay patterns; —Late-delay pattern index; A-A type delay mode, used to represent minor delay scenarios; B-B class delay mode is used to represent medium delay scenarios; C-C class delay mode, used to represent severe delay scenarios; D-D class delay mode is used to represent extreme delay scenarios.

3. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 1, characterized in that, The initial delay impact index prediction model in S3 includes: The input module is used to process the initial late arrival index data through at least one multi-dimensional CNN combination to obtain preprocessed data; The feature extraction module is used to extract spatial features from the preprocessed data by stacking multiple convolutional and pooling layers; The sequence learning module is used to generate temporal features by combining a bidirectional long short-term memory neural network layer and a regularization layer to serialize the spatial features. An attention module is used to calculate the attention weights of the time features through an attention mechanism; The prediction module is used to perform non-linear calculations on the attention weights obtained by the attention module through the fully connected layer and the output layer to obtain the final prediction result.

4. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 3, characterized in that, The convolutional neural network in the feature extraction module includes: Convolutional layers are used to extract local features from input data; Pooling layers are used to sample the obtained local features and output high-order abstract feature maps; A fully connected layer is used to combine and transform the high-order abstract feature map to output the spatial features.

5. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 4, characterized in that, The bidirectional long short-term memory neural network includes: Two parallel LSTM units are used to process the spatial features from both forward and backward directions to obtain the generated temporal features. ; The two parallel LSTM units include a forward LSTM network and a reverse LSTM network. Forward LSTM networks process sequence features sequentially to obtain forward information. ; The inverse LSTM network processes sequence features in reverse chronological order to obtain inverse information. ; Combining the aforementioned positive information and the reverse information Perform element-wise addition of vectors to generate time features. ; ； Among them, ⊕ — vector element-wise addition operation, used for summing the forward and reverse output components.

6. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 4, characterized in that, In the step of calculating the attention weights of the time features using an attention mechanism: Attention scores are obtained by using input data features or output data features from the previous layer. , ； in, —Attention score; —The weight of the attention mechanism; —Bias in attention mechanisms; —Input data features or previous layer output data features; pass The function normalizes the attention score, and then normalizes the attention score. Convert to probability distribution form , ； Based on probability distribution form The value vector v is weighted and summed to generate the final attention value SH. 。 7. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 1, characterized in that, In S4, by establishing precise train motion equations, the train behavior characteristics under different delay modes are quantitatively analyzed, including: A longitudinal dynamics model of the train is constructed based on a single-mass point model. ； ； ； —Overall train quality; t—the point in time when the train departs; —Slewing mass coefficient, used to reflect the equivalent mass effect of rotating parts of a train; —The instantaneous speed of the train at time t; —The spatial coordinates of the train at time t; —Output control force, representing the net external force applied to the train; —Characterizes the resultant resistance force acting on the train at time t.

8. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 1, characterized in that, In S4, a multi-objective optimization model is constructed based on the train behavior characteristics. The multi-objective optimization model is used to minimize the variable part of the initial delay impact index. The multi-objective optimization model is as follows: ； in, —Initial delay time calculation model; —Affects the train number calculation model; —Affects the total time calculation model.

9. The train operation adjustment method based on initial delay classification and pattern deduction according to claim 1, characterized in that, The constraints of the multi-objective optimization model include: Security constraints; ； ； ； in, —The maximum permissible operating speed of this line; —The actual position of train i-1 at time t; —The actual position of train i at time t; Comfort constraints: ； ； ； —The average comfort function of train i, with a threshold of ; —The rate of change of acceleration of train i at time t; —Gaussian evaluation model width coefficient; —The center position of the width of the Gaussian evaluation model; —The acceleration of train i at time t.

10. A train operation adjustment method based on initial delay classification and pattern deduction according to claim 9, characterized in that, In step S4, which is used to generate the delayed train operation strategy, Step 1: Solve the multi-objective optimization model using the NSGA-II algorithm and output the Pareto optimal solution set; represent the Pareto optimal solution set as a decision matrix, and perform weighted standardization on the decision matrix to obtain the standardized weight matrix; Step 2: Determine the ideal solution Z+ and the negative ideal solution Z- based on the standardized weight matrix; Step 3: Calculate the distances from each solution to the ideal point and the negative ideal point based on the ideal solution Z+ and the negative ideal solution Z-; Step 4: Calculate the relative proximity index C for each solution based on the distances from each solution to the ideal point and the negative ideal point. i Based on proximity index C i Obtain the priority order of the solutions in the Pareto solution set.

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