Rail transit train operation curve real-time calculation model, method and program

Abstract

The present application relates to the field of train operation curve monitoring calculation, and particularly relates to a track traffic formation train operation curve real-time calculation method based on human-computer interaction, the model comprising a train dynamics model, according to the operation behavior of the formation train at the current time to obtain the state information of the formation train at the next time, the operation state of the formation train can be judged according to the information; according to the model predictive control algorithm, the operation curve real-time calculation problem of each train under the corresponding operation state is constructed; the operation curve real-time calculation model is based on the distributed interior point method, the operation curve real-time calculation problem of all trains is solved, the control force of each train in the train formation is obtained, and the control force is applied to the train operation control system; the train operation control system controls the operation behavior of each train in the train formation based on the control force of each train in the train formation obtained by the operation curve real-time calculation method.

Description

Technical Field

[0001] This invention relates to the field of train operation curve optimization calculation, and in particular to a real-time calculation method for train operation curves in rail transit queuing based on human-computer interaction. Background Technology

[0002] With the acceleration of urbanization, the rail transit systems of large cities are gradually reaching capacity saturation. Especially during morning and evening rush hours, the concentrated travel demand of commuters creates significant passenger flow peaks. This uneven distribution of passenger flow in time and space poses a huge challenge to the operation of rail transit systems.

[0003] To address this issue, flexible formation technology offers a solution for efficiently improving the flexibility of transportation organization and the quality of operational services. It also provides a new technological foundation for the design of real-time calculation methods for train operation curves in rail transit formations.

[0004] Through dynamic coupling and decoupling, trains can flexibly adjust their formation structure according to real-time passenger flow demand and operating environment, thereby optimizing the utilization rate of line resources. During peak hours, multiple trains can be coupled into a formation by adjusting their operating speed and spacing, forming a high-density operation mode and improving line capacity. During off-peak hours, trains can operate decoupled, reducing resource waste. There are two types of trains within a formation: the first train in the formation is the leader train, and all subsequent trains are follower trains. The coupling and decoupling process involves multiple train operating states and the switching between states. Each state has different objectives and constraints, and the switching between models can efficiently achieve the coupling and decoupling tasks. Considering the real-time calculation of the operating curves throughout the coupling and decoupling process can make train operation smoother and improve the operating efficiency of train formations. Flexible formation technology enables coordinated control of trains through wireless information interconnection, allowing for rapid response and dynamic adjustment of operating strategies in complex operating environments. This further improves the flexibility and efficiency of trains in the coupling and decoupling process, providing important technical support for the intelligent upgrading and sustainable development of urban rail transit systems.

[0005] In recent years, the rapid development of information technology has significantly improved the data processing speed and efficiency of rail transit systems. The increasingly diverse information provided to train operators by computers and other equipment has led to a substantial increase in the frequency of human-machine interaction in train operation systems. In complex operating environments, trains undergo coupling and decoupling during operation, both processes requiring control of train operation by judging the train's current operating status. Furthermore, the increasingly flexible operation of train platoons and the shortening of train spacing place higher demands on operational safety. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention aims to provide a real-time calculation method for the train operation curve of rail transit platooning based on human-computer interaction, which incorporates the driving characteristics of human drivers in the rail transit platooning operation process, which includes coupling and decoupling.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] According to a first aspect of the present invention, a real-time calculation model for the train operation curve of rail transit queuing is provided, comprising:

[0009] The train dynamics model, established based on predetermined safety parameter information, is configured to obtain the state information of the trains in the queue at the next moment based on the current running behavior of the trains in the queue, and the running state of the trains in the queue can be determined based on this information.

[0010] The model predictive control algorithm is configured to, within the prediction time domain, calculate in real time the running curve of each train under the corresponding running state, based on the train dynamics model and the control system constraint optimization objective, with the position and running speed of each train as state variables and the control force of each train as control variables.

[0011] The real-time running curve calculation model is configured to solve the real-time calculation problem of the running curves of all the trains based on the distributed interior point method, obtain the control force of each train in the train formation, and apply it to the train operation control system.

[0012] The train operation control system is configured to control the operation behavior of each train in the train formation based on the control force of each train in the train formation obtained by the real-time calculation method of the operation curve.

[0013] The train's operation behavior enters the corresponding operating states in sequence during the virtual formation operation: multi-formation operation, coupling, coupled operation, decoupling, and multi-formation operation;

[0014] The train formation involved in coupling and decoupling consists of n trains, with a formation structure of (p1, p2, ..., p...). m );

[0015] Where m represents the total number of formations, p i ,i=1,...,m represents the number of trains in the i-th formation;

[0016] The set of train indices that need to participate in coupling and decoupling is N = {1, 2, ..., n};

[0017] The set of train indexes is L = {1, p1+1, ..., p} m+1};

[0018] The set of indices for following the train is F = N / L.

[0019] According to an embodiment of the present invention, the train dynamics model is a discrete dynamics model that samples feedback information and performs optimization calculations within a sampling period Δt.

[0020] For the real-time calculation of the train queuing operation curve, feedback information is typically sampled within a sampling period, followed by optimization calculations. A sampling period Δt of 0.5s is selected as the optimization problem's sampling period. Here, M is set... i Let i be the mass of train i. At time point t, the train dynamics model is as follows:

[0021]

[0022] Among them, v i,t Let s be the speed of train i at time t. i,t Let Ft be the position of train i at time t. i,t , Fb i,t Let s be the traction and braking forces of train i at time t. i,t+1 and v i,t+1 This represents the position and speed of train i at the next time point t+1, obtained by dynamically updating the variable value at time point t. This represents the basic resistance and additional resistance of train i during operation;

[0023] The calculation formulas for the additional resistance and the basic resistance are as follows:

[0024]

[0025] Where α1, α2, and α3 represent the basic resistance coefficients of train operation, g is the acceleration due to gravity, and ω(s) i,t () indicates the ramp angle.

[0026] Rail transit train platooning is subject to limitations imposed by track conditions, equipment, and communication systems during operation, which consequently imposes constraints on train speed and control capabilities. Furthermore, the objectives that the lead train and following trains need to achieve differ under different operating conditions, leading to varying constraints. Therefore, the design of a real-time calculation model for the platooning train's operating curve must separately consider the constraints imposed on the lead and following trains.

[0027] According to an embodiment of the present invention, the real-time calculation model of the running curve includes a control constraint system for a first leader train (control system constraints for leader train i=1) and control constraint systems for other leader trains (control system constraints for leader train i∈L / {1}). The control constraint system for the first leader train includes a speed limit constraint for the first leader train, traction and braking force constraints for the first leader train, and a smooth running constraint for the first leader train.

[0028] The operating speed limit constraint for the first lead train is as follows:

[0029]

[0030] in, To control the speed of train i=1 at the location of time t.

[0031] The traction and braking force constraints of the first lead train are as follows:

[0032] 0≤Ft 1,t ≤F 1,max (4)

[0033] F 1,min ≤Fb 1,t ≤0 (5)

[0034] Among them, Ft 1,t , Fb 1,t F represents the traction and braking forces of the leading train i=1 at time t. 1,max To generate the maximum traction force for train i=1, F 1,min The minimum braking force for the leading train i=1.

[0035] The operational stability constraints for the first lead train are:

[0036] J min ≤(a 1,t+1 -a 1,t )≤J max (6)

[0037] Among them, J min J represents the maximum decrease in the train control force per unit time. max This represents the maximum increase in control force per unit time. This represents the acceleration of the leading train i=1;

[0038] The control constraint system for other leading trains includes: operating speed limit constraints for other leading trains, traction and braking force constraints for other leading trains, running stability constraints for other leading trains, and safe distance constraints for other leading trains.

[0039] The operating speed constraints for the other lead trains are as follows:

[0040]

[0041] in, This represents the speed limit of the leading train i∈L / {1} at the location of time point t.

[0042] The traction and braking constraints of the other lead trains are as follows:

[0043] 0≤Ft i,t ≤F i,max ,i∈L / {1} (8)

[0044] F i,min ≤Fb i,t ≤0, i∈L / {1} (9)

[0045] Among them, Ft i,t , Fb i,t Let F represent the traction and braking forces of the leading train i∈L / {1} at time t. i,max and F i,min This represents the maximum traction and braking force of the leading train i∈L / {1};

[0046] The operational stability constraints for the other leading trains are as follows:

[0047] J min ≤(a i,t+1 -a i,t )≤J max ,i∈L / {1} (10)

[0048] in, Let i represent the acceleration of the leading train i∈L / {1}.

[0049] Since there is a train running ahead of the leader train i∈L / {1}, in order to ensure the safety of all train operations, the leader train i∈L / {1} needs to satisfy the safety distance constraint of the other leader trains as follows:

[0050]

[0051] Among them, s i-1,t This represents the position of the train preceding the leader train i∈L / {1}, i.e., the last train in the previous formation. κ≥1 is a parameter determined based on the train's operating environment and status. During operation, the train operator can adjust the spacing between adjacent trains according to different operating conditions. Therefore, under normal circumstances, κ=1 is set. When an emergency occurs that causes environmental deterioration, the train operator can adjust κ>1 based on experience to increase the spacing between adjacent trains to ensure safe operation. This indicates the minimum safe distance between trains under absolute braking mode. This represents the minimum safe distance between trains under relative braking mode, and the specific calculation method is as follows:

[0052]

[0053] Among them, l i-1 Let s represent the length of the train with the (i-1)th car. m It is a margin value representing a safe distance, used to ensure train safety. t r This indicates the signal transmission time or reaction time during emergency braking, a i,min =F i,min / M i ,i∈L / {1} represents the emergency braking acceleration of the lead train i∈L / {1}.

[0054] For coupling and decoupling processes involving multiple states, the lead train i∈L / {1} employs relative braking mode during "multi-formation operation" and absolute braking mode in all other states. Safety constraints in both braking modes ensure that the current train can stop before colliding with the preceding train, which has a braking acceleration a. i-1 Braking is applied, and the following vehicle accelerates at a braking speed of a. i During braking, the distance between adjacent trains at any point in the braking process meets the safety distance constraint, further ensuring the safety of train operation.

[0055] According to an embodiment of the present invention, the real-time calculation model of the running curve includes the objective function of a first leader train and objective functions of other leader trains, wherein,

[0056] For the real-time calculation of train operation curves in rail transit queuing, the objective of the lead train is to maximize its operating speed while satisfying train constraints, thereby increasing departure frequency and improving system operating efficiency, while minimizing train operating energy consumption. Based on this, the objective function of the first lead train includes:

[0057] At time point t and given prediction time domain t p Within this context, the objective function of the first leading train under all operating conditions is as follows:

[0058]

[0059] Where T = {t, t+1, ..., t+t} p} represents the set of sampling time points with a sampling interval of 0.5s; β represents the regenerative braking energy coefficient; ζ i,v , ζ i,vThis represents the weighting coefficient that balances operating speed and operating energy consumption.

[0060] The coupling and decoupling process of multi-state transitions means that the leading train i∈L / {1} will take different objectives in different states. First, the objective functions of the other leading trains include:

[0061] In multi-formation operation, other lead trains adopt the same objectives as the lead train, namely, focusing only on the train's operating speed and energy consumption:

[0062]

[0063] When a train is in a coupled or coupled operation state, under the constraints of other leading trains, in addition to ensuring the train runs quickly while minimizing energy consumption, the distance between adjacent trains should be minimized as much as possible, and the speed of the following train should be kept consistent with that of the train in front. Based on this, at time point t and given prediction time domain t p The objective functions for the other leading trains are as follows:

[0064]

[0065] Where, ζ i,tr Tr represents the weighting coefficients associated with the tracking target. i To represent the target being tracked, it can be constructed as follows:

[0066]

[0067] in, Tr represents the weighting coefficients related to tracking speed and tracking position. i The first term aims to reduce the speed difference between two adjacent train formations, and the second term aims to reduce the spacing between adjacent train formations to approximate the train spacing in relative braking mode. The two objective functions work together to achieve coupling between formations, while enabling trains within the same formation to maintain a formation structure.

[0068] When the other lead trains are in a decoupled state, the trains in different formations need to be separated, and the objective function of the other lead trains in the decoupled formations is as follows:

[0069]

[0070] Where, ζ i,de De represents the weighting coefficients related to the train decoupling objective. i The separation target can be constructed as follows:

[0071]

[0072] Where d represents a distance parameter. In order to enable trains in different formations to separate quickly, the lead train in relative braking mode increases the distance between itself and the train in front until the safe train spacing required in absolute braking mode is met.

[0073] According to an embodiment of the present invention, the real-time running curve model includes a control constraint system for following trains. The control system constraints for following trains include: running speed limit constraints for following trains, traction and braking force constraints for following trains, running smoothness constraints for following trains, and safe distance constraints for following trains.

[0074] The speed limit constraint for the following train is:

[0075]

[0076] in, This represents the speed limit for the following train i∈F at time point t;

[0077] The traction and braking force constraints of the following train are:

[0078] 0≤Ft i,t ≤F i,max ,i∈F (16)

[0079] F i,min ≤Fb i,t ≤0, i∈F (17)

[0080] Among them, Ft i,t , Fb i,t Let F represent the traction and braking forces of train i∈F at time t. i,max and F i,min This represents the maximum traction and braking force of the train i∈F;

[0081] The smooth operation constraint of the following train is:

[0082] J min ≤(a i,t+1 -a i,t )≤J max ,i∈F (18)

[0083] in, Let F represent the acceleration of the leading train i∈F.

[0084] Within each train formation, the following trains only use relative braking mode; therefore, the safety distance constraint for the following trains is:

[0085]

[0086] in, This represents the minimum safe distance between trains in a platoon under relative braking mode. The specific calculation method is as follows:

[0087]

[0088] Among them, a i,min =F i,min / M i , i∈F represents emergency braking acceleration;

[0089] For all following trains, the objective of the train is the same as that of other leading trains in coupled or coupled operation states: to track the preceding train to maintain the formation structure. The objective function of the following train is:

[0090]

[0091] According to an embodiment of the present invention, based on the model predictive control algorithm framework, at the current time point t, given the prediction time domain t p The traction force Ft is applied to each time point within the prediction time domain. i,t and braking force Fb i,t The optimization involves combining the driver's experience with the dynamic adjustment of control strategies for each train based on the relative position and speed of adjacent trains. This allows the trains to adjust their formation structure in real time and maintain it under different operating conditions. Furthermore, by simulating human decision-making processes and considering the objectives and constraints of leading and following trains under different conditions, as well as the state transition processes between different train operating states, a real-time calculation model for the train formation operation curve of rail transit can be constructed as follows.

[0092] According to an embodiment of the present invention, the real-time calculation model for the running curve includes:

[0093] Under the model predictive control framework, the real-time calculation model of the operating curves in multi-formation operation is shown in the following equation:

[0094]

[0095] Under the model predictive control framework, the real-time calculation model of the running curves in the coupled and coupled operating states is shown in the equation:

[0096]

[0097] Under the model predictive control framework, the real-time calculation model of the running curve of the queued vehicles in the decoupled state is shown in the following equation:

[0098]

[0099] The aforementioned real-time calculation models for train operation curves all employ distributed computing for each train. Trains can receive information such as the position, speed, and braking requirements of the preceding train through vehicle-to-vehicle communication technology to solve for the optimal control strategy, thus obtaining the optimal operation curve for each train. Furthermore, since the problem is a nonlinear optimization problem, the interior-point method can be used to optimize and solve for the control strategy of each train within each prediction time domain. This strategy is then applied to the train operation control system to complete the real-time calculation of the operation curves of each train throughout the entire time domain.

[0100] According to an embodiment of the present invention, the real-time calculation algorithm flow for the running curve of each train in the real-time calculation model is as follows:

[0101] At sampling time point t, the actual status of each train was measured.

[0102] Train operators adjust safety levels and parameter values ​​based on the current train operating status;

[0103] When the safety level is normal, the parameter value κ = 1;

[0104] In non-emergency situations, when the safety level is κ > 1, decrease Ft. i,t +b i,t ,∈N;

[0105] In an emergency situation, the parameter value is Ft. i,t +Fb i,t =F i,min ,i∈N;

[0106] In the prediction time domain t p The original, centralized problem is divided into n subproblems for each train. Using the interior-point method, each subproblem is transformed into an optimization problem expression:

[0107]

[0108] Among them, f i Let μ represent the objective function of train i under the corresponding state. i X represents the obstacle parameter of the model for train i, whose value converges to zero with the iteration of the distributed interior-point method. i,t h represents the vector consisting of the decision variables in the model. i (·) and g i (·) represent equality constraints and inequality constraints in the model, respectively. λ i and γ i It refers to the Lagrange multipliers for equality and inequality constraints in the model. i Indicated by l i,j The vector formed, l i,j≥0 indicates a slack variable introduced by the inequality constraint. m represents the number of inequality constraints.

[0109] According to an embodiment of the present invention, the iterative optimization process of the distributed interior-point method is as follows:

[0110] Step 1: Set the security level to normal, κ=1, set the iteration count k=0, and input other parameter values;

[0111] Step 2: Construct the Lagrangian function for the real-time calculation model of the running curve of each train, as shown in equation (32). Given the initial Lagrangian multipliers... and The Lagrange function is constructed as follows:

[0112]

[0113] Step 3: Divide the decision variables related to each train into global variables. and local variables The search direction and Hessian matrix obtained in each iteration can be divided according to global and local variables. After formula calculation, a quadratic optimization problem is constructed with the search direction of the global variable as the decision variable and the search directions of the local variables and Lagrange multipliers as parameters:

[0114]

[0115] in, and Let (33) represent the coefficient matrix, coefficient vector, and coefficients associated with the quadratic, linear, and constant terms, respectively. Solving (33) yields the optimal value for the global variable search direction.

[0116] Step 4: Based on the obtained The optimal value can be obtained by considering its relationship with local variables and the search direction of Lagrange multipliers. (Δλ i ) * and (Δγ) i ) * The search step size is calculated according to formula (34), and all decision variables and Lagrange multipliers are updated based on the previously obtained optimal search direction:

[0117]

[0118] Where τ = 0.95.

[0119] Step 5: Update the obstacle parameters according to the following formula:

[0120]

[0121] in,

[0122] Step 6: Determine the termination condition: Set a convergence tolerance of ò, when If the condition is not met, terminate the iteration; if not, based on the updated variables, let k = k + 1 and go to step 2.

[0123] According to a second aspect of the present invention, a method for real-time calculation of the train operation curve of rail transit formation is provided. The method employs the aforementioned real-time calculation model for the train operation curve of rail transit formation to perform real-time calculation of the train operation curve, and includes the following steps:

[0124] S1: Preset safety parameter information, using train speed limit information and train friction resistance coefficient as input to the control system;

[0125] S2: Based on the train dynamics model, the real-time speed and position information of each train is monitored and obtained in each sampling control cycle;

[0126] S3: Based on the model predictive control algorithm, modify the risk level and safety parameter information according to the human-computer interaction strategy, and obtain the real-time speed and position information of each train to solve the problem of real-time calculation of the running curve of each train under the corresponding running state.

[0127] S4: Design a real-time calculation model based on the running curve to solve the real-time calculation problem of the running curve of all the trains, obtain the control force of each train in the train formation, and apply it to the train operation control system.

[0128] According to an embodiment of the present invention, the method further includes calculating the control time domain t. c Internal traction force Ft i,t and braking force Fb i,t It applies to all trains;

[0129] For each train i, based on the next sampling time point t+t c The actual state is determined, and the steps are repeated until the control process ends.

[0130] According to a third aspect of the present invention, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the steps of the method.

[0131] Compared to traditional multi-objective decision-making methods, this invention provides a user-friendly interface through a computer program. The decision-making process can be initiated with a single click, and the output of the decision results is concise and clear, making it easier for users to understand. This effectively reduces the user's learning curve and improves decision-making efficiency.

[0132] The beneficial effects of this invention are as follows:

[0133] This invention designs a real-time calculation method for train operation curves in rail transit platooning based on human-computer interaction. Considering the different objectives and constraints corresponding to different states during coupling and decoupling processes, a real-time calculation model for train operation curves in rail transit platooning is designed, achieving efficient switching of train operation states and quickly and smoothly completing coupling and decoupling tasks. The application of relative braking in platooning enables protective control with a smaller train tracking distance, effectively reducing the safe tracking distance between trains, thereby improving the operational efficiency of trains on existing lines. This invention adopts a distributed solution method, which reduces the computational load and improves computational efficiency compared to centralized methods. Attached Figure Description

[0134] The present invention includes the following figures:

[0135] Figure 1 This is a schematic diagram of the distributed interior-point method for solving the real-time calculation problem of the running curve in each time domain, according to an embodiment of the present invention.

[0136] Figure 2 The speed curves of eight trains under normal conditions during the entire operation process, including coupling and decoupling, are shown in this embodiment of the invention.

[0137] Figure 3 This refers to the change in train spacing between adjacent trains during the coupling and decoupling process in an embodiment of the present invention.

[0138] Figure 4 This is a speed curve of eight trains during operation under non-emergency conditions, according to an embodiment of the present invention.

[0139] Figure 5 This is a speed curve of eight trains during operation in an emergency, according to an embodiment of the present invention. Detailed Implementation

[0140] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[0141] As a typical complex human-machine integrated system, rail transit systems can effectively improve the safety and efficiency of train operation through close collaboration between train operators and computers. By comprehensively considering driving behavior characteristics, not only can smooth transitions between train operating states be achieved, but passenger comfort can also be improved, which is of great significance for ensuring the safe and stable operation of trains. Real-time calculation of the train's operating curve based on driver behavior characteristics, while ensuring train operation safety, can efficiently complete coupling and decoupling tasks, thereby improving the operational efficiency, safety, and passenger experience of the rail transit system.

[0142] For a class of optimization problems constituting nonlinear objective functions and nonlinear constraints, methods such as the penalty function method, interior point method, gradient projection method, and sequential quadratic programming can be used for solving them. The interior point method, by introducing obstacle functions, transforms the constraints into part of the objective function, effectively handling complex nonlinear constraint problems. Combining the interior point method with a distributed computing framework can significantly improve solution efficiency and meet real-time requirements. By combining the distributed interior point method with model predictive control, real-time generation of train operation curves during multi-state transitions in rail transit platooning can be achieved, while simultaneously considering train operation efficiency, safety, and passenger comfort. Furthermore, introducing human-computer interaction strategies into the model predictive control framework can refine the decision-making process of rail transit platooning in complex operating environments, generating safer train operation curves to cope with emergencies.

[0143] Example 1:

[0144] like Figure 1-5 As shown, considering a total of eight trains, the entire operation process involves initial coupling followed by decoupling. The train formation changes from (4,4) to (8) after coupling, and then returns to (4,4) after decoupling. This invention takes the intersection of Beijing Fangshan Metro Line and Line 9 as an example, considering normal, non-emergency, and emergency situations. Under the model predictive control framework, the operating curves of the entire operation process of the eight metro trains are calculated in real time. Figure 2 The image shows the speed curves of all trains during the entire operation under normal conditions. Figure 3 The diagram shows the change in train spacing between the eight trains during coupling and decoupling. The subway train running resistance parameters are shown in Table 1.

[0145] Table 1. Metro Train Running Resistance Parameters

[0146] parameter value unit <![CDATA[M i ]]> 220 kg <![CDATA[α1]]> 1.558e-3 kN / t <![CDATA[α2]]> 8.339e-6 (kNs) / (tm) <![CDATA[α3]]> 4.585e-7 <![CDATA[(kNs 2 ) / (tm 2 )]]>

[0147] The train length l is set as a constraint. i It is 19m, F i,min -264N, F i,max 220N, maximum operating speed limit The speed is 80 km / h, the discrete time interval Δt is 0.5 s, the regenerative braking energy coefficient β is 0.1, and J min and J max They are -0.7 m / s 2 0.7m / s 2 s in safety constraints m The time domain for train operation prediction is t, which is 5m. p The time domain is t = 10s. c It takes 1 second.

[0148] Throughout the operation, the constructed model minimizes passenger discomfort. In the Daotian Station-Dabaotai Station section, the preceding train decelerates to form an effective formation with the following train. In the Fengtai Science Park Station-Keyi Road Station section, the following train decelerates, splitting an eight-train formation into two formations with a structure of (4,4). The coupling and decoupling processes occur during all train operations, demonstrating the flexibility of the train formation mode. Because trains within the same formation use relative braking, while adjacent trains in different formations use absolute braking, therefore... Figure 3 It can be seen that the spacing between adjacent trains within the same formation is significantly smaller than the spacing between adjacent trains in different formations. During coupling, the spacing between trains 4 and 5 smoothly decreases from 230 meters to 24 meters, while during decoupling, it increases from 24 meters to 230 meters. Figure 2 and Figure 3 As can be seen, all trains cooperate with each other to achieve an efficient and flexible coupling and decoupling process. This shows that the present invention effectively promotes the flexible formation of trains during operation, and at the same time, under the premise of ensuring operational safety, it realizes short-interval operation and improves the transport capacity of existing lines.

[0149] When an emergency occurs during train operation, the train operator will take appropriate measures based on the urgency of the incident. In relative braking mode, the shorter spacing between trains in the platoon increases safety risks; therefore, a human-machine interaction strategy is incorporated into the method of this invention. If the situation is not urgent, for example, if the danger level slightly increases in certain track sections due to sudden rain or snow, the safety of the train platoon can be ensured by increasing the spacing and reducing the speed limit. Figure 4 As shown, to ensure train safety in non-emergency situations, all trains decelerate at varying degrees, thus increasing the distance between trains. When the distance between adjacent trains meets the constraints set after changing parameter κ, all trains adjust their positions and speeds to effectively form convoy and continue subsequent operations. If a train encounters a very urgent situation, the system or operator can quickly identify the danger and make an emergency braking decision. Figure 5 As shown, when a train or operator detects an emergency, the train's control force is converted from the optimal control force obtained from the optimization model into an emergency braking force. It can be seen that all trains can stop before the danger point, ensuring safe operation. Therefore, the real-time calculation model of the running curve and the distributed method combining model predictive control meet the requirements for train operation performance and safety under different levels of urgency, demonstrating the practical application potential of the proposed method.

[0150] To better illustrate the advantages of this invention, we compare the computational performance of the distributed real-time calculation method for train operation curves proposed in this invention with that of the centralized method. Table 2 shows the computation time of the distributed and centralized methods in the prediction time domain for different train formation structures. According to the proposed distributed calculation method, each train undergoes parallel information processing, while solving the coordinated quadratic programming problem requires integrating the information of all trains. Under the same problem size and termination conditions, the distributed method exhibits significantly shorter computation time and higher computational efficiency compared to the centralized method, demonstrating superior performance. As the problem size increases, the computation time of the centralized method is significantly accelerated due to its centralized structure. In contrast, even with an increased problem size, the distributed method remains stable and has an acceptable computation time. For the (4,4) train formation structure, the computation time of the distributed method is 0.4597s, which is 71.55% less than that of the centralized method. This demonstrates that the distributed calculation method can achieve real-time generation of train operation curves in a train formation, possessing practical application value in real life.

[0151] Table 2 Comparison of computational performance between centralized and distributed methods

[0152]

[0153] Furthermore, in practice, different weight values ​​can be selected according to specific circumstances and needs to achieve a balance between rapid coupling and decoupling, energy consumption, and runtime.

[0154] The above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Those skilled in the art can make various changes and modifications without departing from the essence and scope of the present invention. Therefore, all equivalent technical solutions also fall within the protection scope of the present invention.

[0155] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A real-time calculation model for the train operation curve of rail transit queuing based on human-computer interaction, characterized by mainly... include: The train dynamics model, established based on predetermined safety parameter information, is configured to obtain information about the next state of the train in the queue based on the current operating behavior of the train in the queue, and the operating state of the train in the queue can be determined based on this information. The model predictive control algorithm is configured to, in the prediction time domain, calculate in real time the running curve of each train under the corresponding running state, based on the train dynamics model and the control system constraint optimization objective, with the position and running speed of each train as state variables and the control force of each train as control variables. The real-time calculation method for the running curve is configured to be based on the distributed interior point method to solve the real-time calculation problem of the running curve of all the trains, obtain the control force of each train in the train formation, and apply it to the train operation control system. The train operation control system is configured to control the operation behavior of each train in the train formation based on the control force of each train in the train formation obtained by the real-time calculation method of the operation curve. The train's operation behavior enters the corresponding operating states in sequence during the virtual formation operation: multi-formation operation, coupling, coupled operation, decoupling, and multi-formation operation; The train formations involved in coupling and decoupling are composed of Composed of 100 trains, the formation is as follows: ; in, Indicates a total of One formation, Indicates the first The number of trains in each formation, of which ; The set of train indices that need to participate in coupling and decoupling is: ; The set of leader train indexes is ; The set of indices for following trains is ; The real-time calculation model for the operating curve includes the objective function of the first leader train and the objective functions of other leader trains, wherein... The objective function of the first leading train includes: At the point of time and given prediction time domain Within this context, the objective function of the first leading train under all operating conditions is as follows: ; in, This represents the set of sampling time points, with a sampling interval of 0.5 s; β Indicates the regenerative braking energy coefficient; This represents the weighting coefficient used by the primary train to balance operating speed and energy consumption. For the first leader train at the time point speed; For the first leader train at the time point traction and braking force; Indicates the time point of the first leader's train Speed ​​limits for operation at the current location; The objective functions of the other leading trains include: In multi-formation operation, other lead trains adopt the same objectives as the lead train, namely, focusing only on the train's operating speed and energy consumption: ; in, To lead the train At the point of time Speed ​​limits for operation at the location; , The leader train At the point of time traction and braking force; , Indicates the leadership train Weighting coefficients for balancing operating speed and operating energy consumption; To lead the train At the point of time Speed ​​limits for operation at the location; To lead the train At the point of time speed; When the train is in a coupled or coupled operation state, under the constraint of the other leading trains, at the time point... and given prediction time domain The objective functions for the other leading trains are as follows: ; in, This represents the weighting coefficients related to the tracking target. To represent the tracking target, construct as follows: ; in The first term aims to reduce the speed difference between two adjacent train formations, while the second term aims to reduce the spacing between adjacent train formations to approximate the train spacing under relative braking mode. The combined effect of these two objective functions enables coupling between train formations. This represents the weighting coefficients related to tracking speed and tracking position; For train At the point of time Location; Indicates the minimum safe distance between trains under relative braking mode; When the other leading trains are in a decoupled state, the objective function of the other leading trains is as follows: ; in, This represents the weighting coefficients related to the train decoupling objective. The separation target is represented as follows: ; in, This represents a distance parameter. In order to enable trains in different formations to separate quickly, the lead train in relative braking mode increases the distance between itself and the train in front until the safe train spacing required in absolute braking mode is met. This indicates the minimum safe distance between trains under absolute braking mode. In the real-time calculation model of the operating curve, the algorithm flow for the real-time calculation of the operating curve of each train is as follows: At the sampling time point The actual status of each train was obtained by measurement. ; Train operators adjust safety levels and parameter values ​​based on the current train operating status; Among them, under the condition of normal security level, the parameter value ; Set parameter values ​​when the safety level is non-emergency. , reduce ; In the event of an emergency, ; In the prediction time domain Internally, the centralized original problem is divided into... Each subproblem, combined with the interior-point method, is transformed into an optimization problem expression: ; ; ; in, Indicates the train in the corresponding state The objective function, Indicates regarding the leadership train The obstacle parameters of the model converge to zero as the distributed interior point method iterates. This represents a vector consisting of decision variables in the model. and These represent equality constraints and inequality constraints in the model, respectively. and It is a Lagrange multiplier for equality and inequality constraints in the model; Indicates by The vector formed This is represented as a slack variable introduced by the inequality constraint.

2. The real-time calculation model for the train operation curve of rail transit queuing according to claim 1, characterized in that: The train dynamics model is based on the sampling period. A discrete model of operational dynamics that samples feedback information and performs optimization calculations within the system; Among them, setting For train The quality at a given time point The train dynamics model is as follows: ; （8） in, For train At the point of time speed, For train At the point of time Location; , Trains At the point of time The traction and braking force, and Indicates at a point in time The train obtained by dynamically updating the variable values At the next point in time Position and velocity; , Indicates train Basic and additional resistance during operation; The calculation formulas for the additional resistance and the basic resistance are as follows: ; ; in, These represent the basic resistance coefficients of the train. It is the acceleration due to gravity. Indicates the slope angle.

3. The real-time calculation model for the train operation curve of rail transit queuing according to claim 2, characterized in that, The real-time calculation model of the operating curve includes a control constraint system for the first leader train and control constraint systems for other leader trains. The control constraint system for the first leader train includes operating speed limits, traction and braking force constraints, and a smooth operation constraint for the first leader train. The operating speed limit constraint for the first lead train is as follows: ; in, To lead the train At the point of time Speed ​​limits for operation at the location; The traction and braking force constraints of the first lead train are as follows: ; ; in, , Indicates the leader train At the point of time The traction and braking force, To lead the train Maximum traction force To lead the train The minimum braking force; The operational stability constraints for the first lead train are: ; in, This represents the maximum decrease in the train control force per unit time. This represents the maximum increase in control force per unit time. Indicates the leader train The acceleration; The control constraint system for other leading trains includes: operating speed limit constraints for other leading trains, traction and braking force constraints for other leading trains, running stability constraints for other leading trains, and safe distance constraints for other leading trains. The operating speed constraints for the other lead trains are as follows: ; in, Indicates the leader train At the point of time Speed ​​limits for operation at the current location; The traction and braking constraints of the other lead trains are as follows: ; ; in, , Indicates the leader train At a given point in time, the traction and braking forces and Indicates the leader train Maximum traction and braking force; The operational stability constraints for the other leading trains are as follows: ; in, Indicates the leadership train The acceleration; The safety distance constraints for the other lead trains are as follows: ; ; in, Indicates the leader train The position of the preceding train, that is, the position of the last train in the preceding formation; These are parameters determined based on the train's operating environment and conditions. This indicates the minimum safe distance between trains under absolute braking mode. This represents the minimum safe distance between trains under relative braking mode, and the specific calculation method is as follows: ; ; in, Indicates the first The length of the train (cars) It is a margin value representing a safe distance, used to ensure train safety; This indicates the signal transmission time or reaction time during emergency braking. Indicates the leader train Emergency braking acceleration.

4. The real-time calculation model for the train operation curve of rail transit queuing according to claim 3, characterized in that: The real-time calculation model of the running curve includes a control constraint system for following trains. The control system constraints for following trains include: running speed limit constraints for following trains, traction and braking force constraints for following trains, running smoothness constraints for following trains, and safe distance constraints for following trains. The speed limit constraint for the following train is: ; in, Indicates following the train At the point of time The operating speed limit at the current location; The traction and braking force constraints of the following train are: ; ; in, , Indicates following the train At the point of time The traction and braking force, and Indicates following the train Maximum traction and braking force; The smooth operation constraint of the following train is: ; in, Indicates following the train The acceleration; Within each train formation, the following trains only use relative braking mode; therefore, the safety distance constraint for the following trains is: ; in, This represents the minimum safe distance between trains in a platoon under relative braking mode. The specific calculation method is as follows: ; in, Indicates emergency braking acceleration; For all following trains, the objective of the train is the same as that of other leading trains in coupled or coupled operation states: to track the preceding train to maintain the integrity of the formation. The objective function of the following train is: 。 5. The real-time calculation model for the train operation curve of rail transit queuing according to claim 4, characterized in that: Under the model predictive control framework, the real-time calculation model of the operating curves in multi-formation operation is shown in the following equation: ; ; ; ; ; ; Under the model predictive control framework, the real-time calculation model of the running curve under coupled and coupled operating states is shown in the following equation: ; ; ; ; ; Under the model predictive control framework, the real-time calculation model of the running curve of the queued vehicles in the decoupled state is shown in the following equation: ; ; ; ; 。 6. The real-time calculation model for the train operation curve of rail transit queuing according to claim 5, characterized in that: The iterative optimization process of the distributed interior-point method is as follows: Step 1: Set the security level to normal. Set the number of iterations Enter other parameter values ​​at the same time; Step 2: Construct the Lagrangian function of the real-time calculation model of the running curve of each train, as shown in Equation (32); Given initial Lagrange multipliers and The Lagrange function is constructed as follows: ； Step 3: Divide the decision variables related to each train into global variables. and local variables The search direction obtained in each iteration can be divided into global and local variables using the Hessian matrix. After formula calculation, a quadratic optimization problem is constructed with the search direction of the global variable as the decision variable and the search directions of the local variables and Lagrange multipliers as parameters: ； in, and Let represent the coefficient matrix, coefficient vector, and coefficients related to the quadratic, linear, and constant terms, respectively; solve equation (33) to obtain the optimal value of the global variable search direction. ; Step 4: Based on the obtained The optimal value can be obtained by examining its relationship with local variables and the search direction of the Lagrange multipliers. and ; Calculate the search step size according to formula (34), and update all decision variables and Lagrange multipliers based on the previously obtained optimal search direction: ； ； in, ; Step 5: Update the obstacle parameters according to the following formula: ； in, ; Step 6: Determine termination conditions: Set convergence tolerance ,when If the condition is not met, terminate the iteration; if not, based on the updated variables, let Proceed to step 2.

7. A method for real-time calculation of the train operation curve of rail transit queuing, characterized in that, The real-time calculation of the train operation curve of rail transit formation using the real-time calculation model of any one of claims 1-6 includes the following steps: S1: Preset safety parameter information, using train speed limit information and train friction resistance coefficient as input to the control system; S2: Based on the train dynamics model, the real-time speed and position information of each train is monitored and obtained in each sampling control cycle; S3: Based on the model predictive control algorithm, modify the risk level and safety parameter information according to the human-computer interaction strategy, and obtain the real-time speed and position information of each train to solve the problem of real-time calculation of the running curve of each train under the corresponding running state. S4: Design a real-time calculation model based on the running curve to solve the real-time calculation problem of the running curve of all the trains, obtain the control force of each train in the train formation, and apply it to the train operation control system.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method of claim 7.

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