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

Abstract

The invention relates to the field of train operation curve monitoring and calculation, in particular to a rail transit formation train operation curve real-time calculation method based on man-machine interaction, the model comprises a train dynamics model, and state information of formation trains at the next moment is obtained according to operation behaviors of the formation trains at the current moment; the running state of the formation train can be judged according to the information; according to a model predictive control algorithm, real-time problem calculation is carried out on the running curves, under the corresponding running states, of all the trains; the running curve real-time calculation model is based on a distributed interior point method, the running curve real-time calculation problem including all the trains is solved, the control force of each train in the train formation is obtained, and the control force acts on a train running control system; and 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] The present invention relates to the field of train running curve optimization calculation, and in particular to a real-time calculation method for a rail transit train formation running curve based on human-computer interaction. Background Art

[0002] With the acceleration of urbanization, rail transit systems in large cities are gradually reaching capacity. This is particularly true during peak hours, when the concentrated travel demands of commuters create significant peaks in passenger flow. This uneven distribution of passenger flow across time and space poses significant challenges to rail transit system operations.

[0003] To address this issue, flexible platooning technology provides a solution for efficiently improving the flexibility of transport organization and the quality of operational services. It also provides a new technical basis for the design of real-time calculation methods for rail transit platooning train operating curves.

[0004] Through dynamic coupling and decoupling, trains can flexibly adjust their platooning structure based on real-time passenger demand and operating conditions, thereby optimizing line resource utilization. During peak hours, multiple trains can be coupled into a platoon by adjusting their speeds and inter-vehicle spacing, creating a high-density operating mode and improving line capacity. During off-peak hours, trains can operate decoupled to reduce resource waste. There are two types of trains within a platoon: the first train in the platoon is the lead train, and all subsequent trains in the platoon are followers. The coupling and decoupling process involves multiple train operating states and transitions between them. Each state has different objectives and constraints. Switching between models efficiently implements the coupling and decoupling tasks. Real-time calculation of operating curves that considers the entire coupling and decoupling process ensures smoother train operation and improves the operating efficiency of platoons. Flexible platooning technology enables coordinated train control through wireless information interconnection, enabling rapid response and dynamic adjustment of operating strategies in complex operating environments. This further improves the flexibility and efficiency of trains during coupling and decoupling, providing important technical support for the intelligent upgrade and sustainable development of urban rail transit systems.

[0005] In recent years, the rapid development of information technology has significantly improved the speed and efficiency of data processing in rail transit systems. Computers and other equipment are providing increasingly diverse information to train operators, leading to a significant increase in the frequency of human-computer interaction within train operation systems. In complex operating environments, trains undergo coupling and decoupling during operation. These two processes require control over train operation by determining the train's current operating status. Furthermore, the increasing flexibility of train formations and the decreasing distances between trains place higher demands on operational safety. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the present invention aims to provide a real-time calculation method for the operation curve of rail transit platoons based on human-computer interaction, combining the driving characteristics of human drivers in the operation process of rail transit platoons including coupling and decoupling.

[0007] In order to achieve the above purpose, the technical solution adopted by the present invention is:

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

[0009] A train dynamics model is established based on predetermined safety parameter information and is configured to obtain state information of the train in the formation at a next moment based on the operating behavior of the train in the formation at a current moment, and to determine the operating state of the train in the formation based on the information;

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

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

[0012] a train operation control system 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 operation behavior enters corresponding operation 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, and the formation structure is (p1, p2, ..., p m );

[0015] Among them, m means there are m formations in total, p i ,i=1,...,m represents the number of trains in the i-th formation;

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

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

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

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

[0020] For the real-time calculation of the running curve of the platoon, feedback information sampling is usually performed within the sampling period and optimization calculation is performed. 0.5s is selected as the sampling period Δt of the optimization problem. i is the mass of train i, at time point t, the train dynamics model is as follows:

[0021]

[0022] Among them, v i,t is the speed of train i at time t, s i,t is the position of train i at time t. i,t , Fb i,t is the traction and braking force of train i at time t, s i,t+1 and v i,t+1 It represents the position and speed of train i at the next time point t+1 obtained by dynamically updating the variable values ​​at time point t. 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] Among them, α1, α2, α3 represent the basic resistance coefficients of train operation, g is the acceleration of gravity, ω(s i,t ) represents the slope angle.

[0026] During operation, rail transit train formations are subject to limitations imposed by line conditions, equipment, and communication systems. Consequently, these limitations impose constraints on train speed and controllability. Furthermore, the objectives required of the lead and follower trains vary under different operating conditions, resulting in different constraints. Therefore, the design of a real-time calculation model for the train formation's operating curve requires consideration of the constraints imposed on both the lead and follower trains.

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

[0028] The operating speed limit constraint of the first leading train is:

[0029]

[0030] in, is the operating limit speed of the leading train i=1 at the time point t.

[0031] The traction and braking force constraints of the first leading train are:

[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 represents the traction and braking force of the leading train i=1 at time t, F 1,max is the maximum traction force of the leading train i=1, F 1,min is the minimum braking force of the leading train i=1.

[0035] The smooth running constraint of the first leading train is:

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

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

[0038] The control constraint system of the other leading trains includes: the running speed limit constraint of the other leading trains, the traction and braking force constraints of the other leading trains, the running stability constraint of the other leading trains, and the safety distance constraint of the other leading trains;

[0039] The operating speed limit constraints of the other leading trains are:

[0040]

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

[0042] The traction and braking force constraints of the other leading trains are:

[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 represents the traction and braking force of the leading train i∈L / {1} at time point t, F i,max and F i,min represents the maximum traction and braking force of the leading train i∈L / {1};

[0046] The smooth running constraints of the other leading trains are:

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

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

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

[0050]

[0051] Among them, s i-1,t represents the position of the train preceding the leading train i∈L / {1}, that is, the last train in the preceding formation. κ ≥ 1 is a parameter determined by the train's operating environment and status. During operation, train operators can adjust the spacing between adjacent trains based on varying operating conditions. Therefore, under normal circumstances, κ is set to 1. When an unexpected situation deteriorates the environment, train operators can adjust κ to greater than 1 based on experience to increase the spacing between adjacent trains to ensure safe operation. Indicates the minimum safe distance between trains in absolute braking mode. Indicates the minimum safe distance between trains in relative braking mode. The specific calculation method is as follows:

[0052]

[0053] Among them, l i-1 represents the train length of the i-1th car, s m It is a margin value indicating the safety distance, used to ensure the safety of the train. r Indicates the signal transmission time or reaction time of emergency braking, a i,min =F i,min / M i ,i∈L / {1} represents the emergency braking acceleration of the leading train i∈L / {1}.

[0054] For the coupling and decoupling process involving multiple states, the leading train i∈L / {1} adopts relative braking mode in “multi-formation operation” and absolute braking mode in other states. The safety constraints in both braking modes can ensure that the current train can stop before colliding with the preceding train. The preceding train brakes at an acceleration of a. i-1 Braking is performed, and the following vehicle brakes at an acceleration a i During braking, the distance between adjacent trains at any time during the braking process can meet the safety distance constraint, further ensuring the safety of the train operation process.

[0055] According to an embodiment of the present invention, the operation curve real-time meter model includes the objective function of the first leading train and the objective functions of other leading trains, wherein:

[0056] For the real-time calculation of train operation curves in rail transit formations, the goal of the leading train is to maximize its operating speed while satisfying train constraints, thereby increasing departure frequency and improving system operating efficiency. At the same time, the objective function of the first leading train is to minimize train operation energy consumption.

[0057] At time point t and given prediction time domain t p The objective function of the first leading train in all operating states is as follows:

[0058]

[0059] Where T={t,t+1,...,t+t p} represents the set of sampling time points, and the sampling interval is 0.5s; β represents the regenerative braking energy coefficient; ζ i,v ,ζ i,vIndicates the weight coefficient between running speed and running energy consumption;

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

[0061] In a multi-formation operation state, other leading trains adopt the same goal as the leading train, that is, only focusing on the train's operating speed and operating energy consumption:

[0062]

[0063] When the trains are in a coupled or coupled running state, in addition to allowing the trains to run quickly while reducing energy consumption, the distance between adjacent trains should be minimized as much as possible, and the running speed of the rear train should be kept consistent with that of the front train. Based on this, at time point t and given prediction time domain t p , the objective functions of other leading trains are as follows:

[0064]

[0065] Among them, i,tr Represents the weight coefficient related to the tracking target, Tr i Represents the tracking target and can be constructed as:

[0066]

[0067] in, Represents the weight coefficient related to tracking speed and tracking position, Tr 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 approach the train spacing in the relative braking mode. The two objective functions work together to achieve coupling between formations and enable trains in the same formation to maintain a formation structure.

[0068] When the other leading trains are in the decoupling state, the trains between different formations need to be separated and decoupled into different formations. The objective function of the other leading trains is as follows:

[0069]

[0070] Among them, i,de Denotes the weight coefficient related to the train decoupling target, De i Represents a separation target and can be constructed as:

[0071]

[0072] Here, d represents a distance parameter. In order to enable trains in different formations to separate quickly, the leading train in relative braking mode increases the distance from the preceding train until the safe train spacing required in absolute braking mode is met.

[0073] According to an embodiment of the present invention, the real-time operation curve meter model includes a control constraint system for the following train, and the control system constraints of the following train include: an operation speed limit constraint of the following train, a traction and braking force constraint of the following train, an operation smoothness constraint of the following train, and a safety distance constraint of the following train;

[0074] The following train's operating speed limit constraint is:

[0075]

[0076] in, represents the operating limit speed of 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 represents the traction and braking force of the following train i∈F at time point t, F i,max and F i,min represents the maximum traction and braking force of the following train i∈F;

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

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

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

[0084] The following trains in each train formation only use the relative braking mode. Therefore, the safety distance constraint of the following trains is:

[0085]

[0086] in, Indicates the minimum safe distance between trains in the formation in 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 the emergency braking acceleration;

[0089] For all the following trains, the objective of the train is the same as that of other leading trains in the coupled or coupled running state, which is to track the leading train so that the formation structure can be maintained. 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 calculated for each time point in the prediction time domain i,t and braking force Fb i,t Optimization. Incorporating the driver's experience, each train can dynamically adjust its control strategy based on the relative positions and speeds of adjacent trains, enabling real-time adjustments to the train formation structure and maintaining it under different operating conditions. Furthermore, by simulating the human decision-making process, considering the objectives and constraints of the leading and following trains under different states, and the state transition process between different train operating states, a real-time calculation model for the train formation operation curve can be constructed as follows.

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

[0093] Under the model predictive control framework, the real-time calculation model of the operating curve under the multi-formation operation state is shown in the formula:

[0094]

[0095] In the framework of model predictive control, the real-time calculation model of the operation curve under the coupled and coupled operation states is shown as follows:

[0096]

[0097] Under the model predictive control framework, the real-time calculation model of the operating curve of the platoon vehicle in the decoupled state is shown as follows:

[0098]

[0099] The above-mentioned real-time calculation models for train formation operating curves are all solved using distributed computing on each train. Trains can receive information such as the preceding train's position, speed, and braking requirements through train-to-train communication to determine the optimal control strategy and obtain the optimal operating curve for each train. Furthermore, since this problem is a nonlinear optimization problem, an interior point method can be used within each prediction time domain to optimize and solve the control strategy for each train. This strategy can then be applied to the train operation control system to complete the real-time calculation of each train's operating curve throughout the entire time domain.

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

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

[0102] The train operator adjusts the safety level and parameter values ​​according to the current train operation status;

[0103] Among them, when the safety level is normal, the parameter value κ=1;

[0104] When the safety level is non-emergency, the parameter value κ>1, and Ft is reduced. i,t +b i,t ,∈N;

[0105] When the safety level is emergency, 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 sub-problems according to each train. Combined with the interior point method, each sub-problem is converted into the optimization problem expression:

[0107]

[0108] Among them, f i represents the objective function of train i in the corresponding state, μ i X represents the barrier parameter of the model for train i, and its value converges to zero as the distributed interior point method is iterated. i,t Represents the vector of decision variables in the model, h i (·) and g i (·) represent the equality constraints and inequality constraints in the model respectively. i and γ i is the Lagrange multiplier for the equality and inequality constraints in the model. i Indicated by l i,j The vector, l i,j≥0 represents the slack variable introduced for 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 number of iterations k = 0, and enter other parameter values;

[0111] Step 2: Construct the Lagrangian function of the real-time calculation model of each train operation curve, as shown in Equation (32). Given the initial Lagrangian multiplier and The Lagrangian 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 from each iteration can be divided according to global variables and local variables. After formula calculation, the quadratic optimization problem is constructed with the search direction of the global variable as the decision variable and the search direction of the local variable and Lagrange multiplier as parameters:

[0114]

[0115] in, and Denote the coefficient matrix, coefficient vector and coefficient related to the quadratic term, linear term and constant term respectively. Solve (33) to obtain the optimal value of the global variable search direction

[0116] Step 4: Based on the obtained The optimal value can be obtained through its relationship with local variables and the Lagrange multiplier search direction (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 optimal search direction obtained previously:

[0117]

[0118] Wherein, τ = 0.95.

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

[0120]

[0121] in,

[0122] Step 6: Determine the termination condition: Set the convergence tolerance ò, when When , the iteration is terminated; if the condition is not met, 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 calculating a running curve of a rail transit train formation is provided. The method uses the above-mentioned real-time calculation model for calculating a running curve of a rail transit train formation to calculate a running curve of a rail transit train formation in real time, comprising the following steps:

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

[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-machine interaction strategy, and the real-time speed and position information of each train to obtain the real-time calculation problem of the operation curve under the corresponding operation state constructed by each train;

[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 calculated control time domain t c Internal traction force Ft i,t and braking force Fb i,t Act on each train;

[0129] For each train i, according to the next sampling time point t+t c The actual state is repeated until the control process ends.

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

[0131] Compared with traditional multi-objective decision-making methods, this computer program product provides a user-friendly communication interface. The decision-making method starts 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 cost and improves decision-making efficiency.

[0132] The beneficial effects of the present invention are:

[0133] This invention designs a real-time calculation method for the running curve of a rail transit formation train based on human-computer interaction. Taking into account the different objectives and constraints corresponding to different states during the coupling and decoupling process, a real-time calculation model for the running curve of a rail transit formation train is designed. This achieves efficient switching of train running states and quickly and smoothly completes the coupling and decoupling tasks. The application of relative braking in the formation enables protective control of trains with a smaller tracking distance, effectively reducing the safety protection tracking distance between trains, thereby improving the operating efficiency of trains on existing lines. The present invention adopts a distributed solution method, which reduces the amount of calculation and improves computational efficiency compared to centralized methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0134] The present invention has the following accompanying drawings:

[0135] Figure 1 A schematic flow chart of a distributed interior point method for solving the real-time calculation problem of an operating curve in each time domain according to an embodiment of the present invention;

[0136] Figure 2 This is a speed curve of eight trains in the entire operation process including coupling and decoupling under normal circumstances according to an embodiment of the present invention;

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

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

[0139] Figure 5 This is a speed curve of eight trains in operation under emergency conditions according to an embodiment of the present invention. DETAILED DESCRIPTION

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

[0141] As a typical complex system of human-machine integration, rail transit systems effectively improve the safety and efficiency of train operations through the close collaboration between train operators and computers. Taking into account driver behavior characteristics not only enables smooth train state transitions but also enhances passenger comfort, playing a crucial role in ensuring safe and stable train operation. Real-time calculation of train operating curves, incorporating driver behavior characteristics while ensuring train safety, efficiently completes coupling and decoupling tasks, while improving rail transit system efficiency, safety, and passenger experience.

[0142] For optimization problems involving nonlinear objective functions and nonlinear constraints, penalty function methods, interior point methods, gradient projection methods, and sequential quadratic programming methods can be used to solve them. The interior point method, by introducing a barrier function, 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, it is possible to generate real-time operating curves for rail transit train formations during multi-state transitions, while taking into account train operation efficiency, safety, and passenger comfort. Furthermore, by further introducing human-computer interaction strategies into the model predictive control framework, the decision-making process of rail transit train formations in complex operating environments can be refined, generating safer train operating curves to cope with emergencies.

[0143] Example 1:

[0144] like Figure 1-5 As shown, a total of eight trains are involved. The entire operation process is coupled first and then decoupled. The train formation structure changes from (4,4) to (8) after coupling, and returns to (4,4) after decoupling. The present invention takes the intersection of Beijing Fangshan Subway Line and Line 9 as an example, considers three situations: normal, non-emergency, and emergency, and calculates the operation curves of the entire operation process of eight subway trains in real time under the model predictive control framework. Figure 2 The figure shows the speed curves of all trains during the entire operation process under normal circumstances. Figure 3 The figure shows the change in the train spacing between the eight trains during the coupling and decoupling process. The subway train running resistance parameters are shown in Table 1.

[0145] Table 1. Running resistance parameters of subway trains

[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] Set the train length l in the constraint condition i 19m, F i,min -264N,F i,max The maximum operating speed is 220N. is 80km / h, the discrete time interval Δt is 0.5s, the regenerative braking energy coefficient β is 0.1, and J min and J max -0.7m / s respectively 2 , 0.7m / s 2 , s in the safety constraint m is 5m, and the train operation prediction time domain t p is 10s, and the control time domain t c 1s.

[0148] During the entire operation process, the constructed model can minimize the discomfort of passengers. In the Daotian Station-Dabaotai Station section, the front formation slows down and forms an effective formation with the rear formation. In the Fengtai Science and Technology Park Station-Keyi Road Station section, the rear formation slows down, separating an eight-train formation into two formations with a (4,4) structure. The coupling and decoupling process is carried out when all trains are running, reflecting the flexibility of the train formation mode. Since trains in the same formation adopt relative braking mode, and adjacent trains in different formations adopt absolute braking mode, Figure 3 It can be seen that the distance between adjacent trains in the same formation is significantly smaller than the distance between adjacent trains in different formations. During the coupling process, the distance between trains 4 and 5 decreases smoothly from 230 meters to 24 meters, while during the decoupling process it increases from 24 meters to 230 meters. Figure 2 and Figure 3 It can be seen that all trains cooperate with each other to achieve an efficient and flexible coupling and decoupling process, which shows that the present invention effectively promotes the flexible formation of trains during operation, and at the same time realizes short-interval operation while ensuring operational safety, thereby improving the transportation capacity of existing lines.

[0149] When an emergency occurs during the operation of a platoon, the train operator will take appropriate measures according to the urgency of the accident. In the relative braking mode, the distance between platoons is short, which increases the safety risk. Therefore, a human-computer interaction strategy is added to the method of the present invention. If the situation is not urgent, for example, the danger level of some track sections increases slightly due to sudden rain or snow, the safety of the platoon can be ensured by increasing the distance and reducing the speed limit, such as Figure 4 As shown in Figure 1, to ensure the safety of trains in non-emergency situations, all trains slow down to varying degrees, thereby increasing the distance between trains. When the distance between adjacent trains meets the constraints established after changing the parameter κ, all trains adjust their positions and speeds to effectively form a formation 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 by the optimization model to an emergency braking force. All trains can be stopped before the danger point, ensuring safe operation. Therefore, the real-time operation curve calculation model and the distributed approach combined with model predictive control meet the requirements for train operation performance and safety at different emergency levels, demonstrating the practical application potential of the proposed method.

[0150] To better illustrate the advantages of the present invention, we compare the computational performance of the distributed real-time operation curve calculation method proposed in this invention with that of a centralized method. Table 2 shows the computational time of the distributed and centralized methods within the prediction time domain for different train formation structures. According to the proposed distributed computation method, each train must perform parallel information processing, while solving the coordinated quadratic programming problem requires integrating information from all trains. Under the same problem size and termination conditions, the distributed method achieves significantly shorter computation time and higher computational efficiency compared to the centralized method, demonstrating superior performance. As the problem size increases, the computational time of the centralized method significantly accelerates due to its centralized structure. In contrast, even with increased problem size, the distributed method maintains stability and an acceptable computational time. For a (4,4) train formation structure, the computation time of the distributed method is 0.4597 seconds, a 71.55% reduction compared to the centralized method. This demonstrates that the distributed computation method can generate operation curves for train formations in real time, demonstrating practical application value in real life.

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

[0152]

[0153] In addition, in practice, different weight values ​​can be selected according to specific situations and needs to achieve a balance between fast coupling and decoupling, energy consumption and running time.

[0154] The above embodiments are only used to illustrate the present invention, and are not intended to limit the present invention. Ordinary technicians in the relevant technical field 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 scope of protection of the present invention.

[0155] The contents not described in detail in this specification belong to the prior art known to those skilled in the art.

Claims

1. A real-time calculation method for rail transit train formation operation curve based on human-computer interaction, its main features are include: A train dynamics model is established based on predetermined safety parameter information and is configured to obtain information about the next state of the train in the formation based on the current operating behavior of the train in the formation, and to determine the operating state of the train in the formation based on the information; A model predictive control algorithm is configured to calculate, in real time within the prediction time domain, an operating curve for each train under the corresponding operating state, based on the train dynamics model and the control system constraint optimization objective, with the position and operating speed of each train as state variables and the control force of each train as a control variable; A real-time operation curve calculation method is configured to solve the real-time operation curve calculation problem including all the trains based on a distributed interior point method, obtain the control force of each train in the train formation, and apply the control force to the train operation control system; a train operation control system 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 operation behavior enters corresponding operation states in sequence during the virtual formation operation: multi-formation operation, coupling, coupled operation, decoupling and multi-formation operation; The train formation involved in coupling and decoupling consists of n trains, and the formation structure is (p1, p2, ..., p m ); Among them, m means there are m formations in total, p i ,i=1,...,m represents the number of trains in the i-th formation; The train index set that needs to participate in coupling and decoupling is N={1, 2, ..., n}; The set of leading train indexes is L = {1, p1+1, ..., p m +1}; The index set of the following train is F=N / L.

2. The real-time calculation model for rail transit train formation operation curve according to claim 1 is characterized by: The train dynamics model is a discrete model of running dynamics that samples feedback information within a sampling period Δt and performs optimization calculations; Among them, set M i is the mass of train i, at time point t, the train dynamics model is as follows: Among them, v i,t is the speed of train i at time t, s i,t is the position of train i at time t. i,t , Fb i,t is the traction and braking force of train i at time t, s i,t+1 and v i,t+1 It represents the position and speed of train i at the next time point t+1 obtained by dynamically updating the variable values ​​at time point t. represents the basic resistance and additional resistance of train i during operation; The calculation formulas for the additional resistance and the basic resistance are as follows: Among them, α1, α2, α3 represent the basic resistance coefficients of train operation, g is the acceleration of gravity, ω(s i,t ) represents the slope angle.

3. The real-time calculation model for the rail transit train formation operation curve according to claim 1 is characterized in that: The real-time operation curve calculation model includes the control constraint system of the first leading train and the control constraint systems of other leading trains, wherein the control constraint system of the first leading train includes the operation speed limit constraint of the first leading train, the traction force and braking force constraints of the first leading train, and the operation smoothness constraint of the first leading train is: The operating speed limit constraint of the first leading train is: in, is the operating limit speed of the leading train i=1 at the time point t. The traction and braking force constraints of the first leading train are: 0≤Ft 1,t ≤F 1,max (4) F 1,min ≤Fb 1,t ≤0 (5) Among them, Ft 1,t , Fb 1,t represents the traction and braking force of the leading train i=1 at time t, F 1,max is the maximum traction force of the leading train i=1, F 1,min is the minimum braking force of the leading train i=1. The smooth running constraint of the first leading train is: I min ≤(a 1,t+1 -has 1,t )≤J max (6) Among them, J min is the maximum reduction value of the leading train control force per unit time, J max It is the maximum increase in control force per unit time. represents the acceleration of the leading train i=1; The control constraint system of the other leading trains includes: the running speed limit constraint of the other leading trains, the traction and braking force constraints of the other leading trains, the running stability constraint of the other leading trains, and the safety distance constraint of the other leading trains; The operating speed limit constraints of the other leading trains are: in, It represents the operating speed limit of the leading train i∈L / {1} at the time point t. The traction and braking force constraints of the other leading trains are: 0≤Ft i,t ≤F i,max ,i∈L / {1} (8) F i,min ≤Fb i,t ≤0,i∈L / {1} (9) Among them, Ft i,t , Fb i,t represents the traction and braking force of the leading train i∈L / {1} at time point t, F i,max and F i,min represents the maximum traction and braking force of the leading train i∈L / {1}; The smooth running constraints of the other leading trains are: I min ≤(a i,t+1 -has i,t )≤J max ,i∈L / {1} (10) in, represents the acceleration of the leading train i∈L / {1}. The safety distance constraints of other leading trains are: Among them, s i-1,t represents the previous train of the leading train i∈L / {1}, that is, the position of the last train in the previous formation. κ≥1 is a parameter determined according to the train operation environment and status. Indicates the minimum safe distance between trains in absolute braking mode. Indicates the minimum safe distance between trains in relative braking mode. The specific calculation method is as follows: Among them, l i-1 represents the train length of the i-1th car, s m It is a margin value indicating the safety distance, used to ensure the safety of the train. r Indicates the signal transmission time or reaction time of emergency braking, a i,min =F i,min / M i ,i∈L / {1} represents the emergency braking acceleration of the leading train i∈L / {1}.

4. The multi-objective coordinated train operation curve real-time calculation method according to claim 1 is characterized in that: The operation curve real-time calculation model includes the objective function of the first leading train and the objective functions of other leading trains, wherein: The objective function of the first leader train includes: At time point t and given prediction time domain t p The objective function of the first leading train in all operating states is as follows: Where T={t,t+1,...,t+t p } represents the set of sampling time points, and the sampling interval is 0.5s; β represents the regenerative braking energy coefficient; ζ i,v ,ζ i,v Indicates the weight coefficient between running speed and running energy consumption; The objective functions of the other leadership trains include: In a multi-formation operation state, other leading trains adopt the same goal as the leading train, that is, only focusing on the train's running speed and running energy consumption: When the train is in a coupled or coupled running state, under the constraints of the other leading trains, at time point t and given prediction time domain t p , the objective functions of other leading trains are as follows: Among them, i,tr Represents the weight coefficient related to the tracking target, Tr i Represents the tracking target and can be constructed as: in, Represents the weight coefficient related to tracking speed and tracking position, Tr 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 approach the train spacing in the relative braking mode. The two objective functions work together to achieve coupling between formations. When the other leading trains are in the decoupled state, the objective function of the other leading trains is as follows: Among them, i,de Denotes the weight coefficient related to the train decoupling target, De i Represents a separation target and can be constructed as: Here, d represents a distance parameter. In order to enable trains in different formations to separate quickly, the leading train in relative braking mode increases the distance from the preceding train until the safe train spacing required in absolute braking mode is met.

5. The real-time calculation model for rail transit train formation operation curve according to claim 1 is characterized by: The real-time calculation model of the running curve includes a control constraint system of the following train, wherein the control system constraints of the following train include: a running speed limit constraint of the following train, a traction and braking force constraint of the following train, a running smoothness constraint of the following train, and a safety distance constraint of the following train; The following train's operating speed limit constraint is: in, represents the operating speed limit of the following train i∈F at time point t; The traction and braking force constraints of the following train are: 0≤Ft i,t ≤F i,max ,i∈F (16) F i,min ≤Fb i,t ≤0,i∈F (17) Among them, Ft i,t , Fb i,t represents the traction and braking force of the following train i∈F at time point t, F i,max and F i,min represents the maximum traction and braking force of the following train i∈F; The smooth running constraint of the following train is: I min ≤(a i,t+1 -has i,t )≤J max ,i∈F (18) in, represents the acceleration of the following train i∈F. The following trains in each train formation only use the relative braking mode. Therefore, the safety distance constraint of the following trains is: in, Indicates the minimum safe distance between trains in the formation in relative braking mode. The specific calculation method is as follows: Among them, a i,min =F i,min / M i ,i∈F represents the emergency braking acceleration; For all the following trains, the goal of the train is the same as that of other leading trains in the coupled or coupled operation state, which is to track the leading train so that the formation structure can be kept intact. The objective function of the following train is:

6. The real-time calculation model for rail transit train formation operation curve according to claim 1 is characterized by: Under the model predictive control framework, the real-time calculation model of the operating curve under the multi-formation operation state is shown in the formula: In the framework of model predictive control, the real-time calculation model of the operation curve under the coupled and coupled operation states is shown as follows: Under the model predictive control framework, the real-time calculation model of the operating curve of the platoon vehicle in the decoupled state is shown as follows:

7. The real-time calculation model for rail transit train formation operation curve according to claim 1 is characterized by: 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 t, the actual status of each train is measured The train operator adjusts the safety level and parameter values ​​according to the current train operation status; Among them, when the safety level is normal, the parameter value κ=1; When the safety level is non-emergency, set the parameter value κ>1 to reduce Ft i,t +b i,t ,∈N; When the safety level is emergency, the parameter value is Ft i,t +Fb i,t =F i,min ,i∈N; In the prediction time domain t p The original centralized problem is divided into n sub-problems according to each train. Combined with the interior point method, each sub-problem is converted into the optimization problem expression: Among them, f i represents the objective function of train i in the corresponding state, μ i X represents the barrier parameter of the model for train i, and its value converges to zero as the distributed interior point method is iterated. i,t Represents the vector of decision variables in the model, h i (·) and g i (·) represent the equality constraints and inequality constraints in the model respectively. i and γ i is the Lagrange multiplier for the equality and inequality constraints in the model. i Indicated by l i,j The vector, l i,j ≥0 represents the slack variable introduced for the inequality constraint.

8. The real-time calculation model for rail transit train formation operation curve according to claim 1 is characterized by: The iterative optimization process of the distributed interior point method is as follows: Step 1: Set the security level to normal, κ = 1, set the number of iterations k = 0, and enter other parameter values; Step 2: Construct the Lagrangian function of the real-time calculation model of each train operation curve, as shown in Equation (32). Given the initial Lagrangian multiplier and The Lagrangian function is constructed as follows: Step 3: Divide the decision variables related to each train into global variables and local variables The search direction and Hessian matrix obtained from each iteration can be divided according to global variables and local variables. After formula calculation, the quadratic optimization problem is constructed with the search direction of the global variable as the decision variable and the search direction of the local variable and Lagrange multiplier as parameters: in, and Denote the coefficient matrix, coefficient vector and coefficient related to the quadratic term, linear term and constant term respectively. Solve (33) to obtain the optimal value of the global variable search direction Step 4: Based on the obtained The optimal value can be obtained through its relationship with local variables and the Lagrange multiplier search direction (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 optimal search direction obtained previously: Wherein, τ = 0.

95. Step 5: Update the barrier parameters according to the following formula: in, Step 6: Determine the termination condition: set the convergence tolerance when When , the iteration is terminated; if the condition is not met, based on the updated variables, let k = k + 1 and go to step 2.

9. A real-time calculation method for the running curve of a rail transit train formation, characterized in that: The real-time calculation model for the running curve of a rail transit formation train according to any one of claims 1 to 8 is used to perform real-time calculation of the running curve of a rail transit formation train, comprising the following steps: S1: Preset safety parameter information, and use train speed limit information and train friction resistance coefficient as control system input; 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-machine interaction strategy, and the real-time speed and position information of each train to obtain the real-time calculation problem of the operation curve under the corresponding operation state constructed by each train; 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.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to claim 9 are implemented.

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