Rail transit train cooperative dispatching method

Abstract

The application discloses a rail transit train cooperative scheduling method and belongs to the technical field of train scheduling. The application firstly constructs a single train local target function and constraint containing net power, punctuality error and other elements, and then establishes a multi-train total target function and constraint in accordance with the single train local target function and constraint. Subsequently, the total target function is decomposed to obtain a global coordination term, which is integrated into the local target function to form a local sub-problem. Finally, the local sub-problem is solved and a predicted trajectory is sent, the trajectory conflict is checked by a signal coordinator, and the global variable and Lagrange multiplier vector are updated until convergence is achieved, so that multi-objective optimization and line global energy consumption optimization are realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of train scheduling, in particular to a rail transit train cooperative scheduling method. BACKGROUND

[0002] In the field of rail transit, with the expansion of the operation scale and the upgrading of green transportation demand, train energy saving has become the core research direction of the industry, and the research focus has gradually shifted from single train energy optimization to multi-train cooperative energy saving in the past 20 years. Currently, the industry has formed a certain technical foundation: on the one hand, single train energy saving is mainly achieved by optimizing the ATO (Automatic Train Operation) system operation curve and adjusting the traction and braking strategy combined with the train dynamics model; on the other hand, in the multi-train cooperative research, some schemes introduce model predictive control (MPC) algorithm to try to optimize the running state, or based on the principle of regenerative braking to recover braking energy and store it in the energy pool, while there are also technical explorations to optimize train control and cooperative driving strategy through reinforcement learning, distributed model predictive control, etc. to balance the energy saving effect and basic operation needs.

[0003] However, the existing technology still has key bottlenecks in the multi-train cooperative energy saving scenario: the existing schemes are difficult to simultaneously meet the multi-train operation safety constraints (including the safety distance constraint of the same direction, the signal blocking time window constraint of the opposite direction or the crossing turnout area), the operation index constraints (on-time rate, accurate parking, comfort), and the efficient allocation and utilization of regenerative braking energy in a unified optimization framework. Specifically, most schemes focus only on single train energy optimization, ignoring the coupling constraints between multiple trains; or although they consider multi-train cooperation, they do not include the capacity limit of the regenerative braking energy pool, energy transmission and storage loss into the global optimization objective, resulting in low utilization rate of regenerative energy; in addition, some schemes involving multi-objective optimization lack an engineering coupling constraint solving path, making it difficult to balance optimization solving efficiency and control accuracy under complex line conditions, and unable to achieve global energy optimization of the line, which is a core obstacle to the application of rail transit multi-train cooperative energy saving technology. SUMMARY

[0004] In view of the above deficiencies in the prior art, the rail transit train cooperative scheduling method provided by the present application solves the problem that the prior art scheme cannot simultaneously consider the multi-train operation safety constraints (safety distance, signal blocking time window), operation index constraints (on-time rate, accurate parking, comfort) and efficient utilization of regenerative braking energy in a unified optimization framework, and lacks an engineering coupling constraint solving path under multi-train coupling constraints, and cannot achieve global energy optimization of the line.

[0005] In order to achieve the above application purposes, the technical scheme adopted by the present application is as follows: a rail transit train cooperative scheduling method, comprising the following steps:

[0006] S1. Based on the net power, punctuality error penalty, acceleration change penalty, and endpoint state deviation of each train, establish a local objective function for each train and set constraints on the local objective function.

[0007] S2. Based on the local objective function of a single train, establish the overall objective function for multiple trains, and set constraints on the overall objective function;

[0008] S3. Decompose the overall objective function to obtain the global coordination term, and add the global coordination term to the local objective function to obtain the local subproblems;

[0009] S4. Solve the local subproblems of a single train under the constraints of the local objective function and send the predicted trajectory. The signal coordinator checks the predicted trajectories of each train based on the constraints of the overall objective function. If there is a conflict, update the global common variables and the Lagrange multiplier vector until convergence.

[0010] Furthermore, the expression for the local objective function in S1 is: ,

[0011] Wherein, J(μ) i,k Let be the local objective function of the i-th train at time k, where α is the weight of the net power and β is the weight of the punctuality error penalty. ρ represents the weight of the penalty term for the change in acceleration, and ρ represents the weight of the deviation from the final state. Let be the net power of the i-th train at time k. Let $\frac{i}{i}$ be the penalty for the punctuality error of the $i$-th train at time $k$. For the penalty term of acceleration change, Let represent the endpoint state deviation of the i-th train, where i is the train number, k is the time number, and N is the prediction time domain length.

[0012] Furthermore, the constraints of the local objective function in S1 include: safety clearance constraints, signal blocking time window constraints, and regenerative braking energy distribution constraints.

[0013] Furthermore, the expression for the safety clearance constraint is: Among them, s i-1 (k) represents the position of the (i-1)th train at time k, s i (k) represents the position of the i-th train at time k, D0 is the basic safety distance between trains, τ is the time interval, and v i (k) represents the speed of the i-th train at time k, where i is the train number and k is the time number;

[0014] The signal blocking time window constraint includes:

[0015] A1, define a set of available times for a section;

[0016] A2, predict the time of train entering a target section;

[0017] A3, restrict the single train entering time in the set of available times;

[0018] A4, restrict the time interval of multiple trains entering the same section;

[0019] The regenerative braking energy distribution constraint includes:

[0020] B1, constrain the energy pool capacity range;

[0021] B2, determine the energy pool absorption power;

[0022] B3, calculate the energy loss according to the regenerative power and the energy of the energy pool;

[0023] B4, calculate the next time energy of the energy pool according to the energy loss, the energy of the energy pool, the regenerative power and the absorption power.

[0024] Further, the total objective function in S2 is the minimum value of the sum of the local objective functions of all trains;

[0025] The constraint conditions of the total objective function include: train spacing coupling constraint, energy pool constraint and section time window constraint.

[0026] Further, the expression of the local sub-problem in S3 is: ,

[0027] Wherein, μ i,m+1 is the acceleration vector of the i-th train in the local m+1 iteration, μ i,m is the acceleration vector of the i-th train in the local m iteration, J(μ i,m ) is the local objective function of the i-th train in the local m iteration, argmin is to find the μ i,m that makes the expression take the minimum value, U i is the set of acceleration values that the i-th train can take at all times, θ is the penalty parameter, A i is the coupling state extraction matrix of the i-th train, z m is the global public variable of the local m iteration, λ i,m is the Lagrange multiplier vector of the i-th train in the local m iteration, || || is the two norm, the global coordination term, m is the number of local iteration times, and i is the number of trains.

[0028] Further, S4 includes the following sub-steps:

[0029] S41, solve the local sub-problems of the single train under the constraint condition of the local objective function, obtain a predicted trajectory, and send the predicted trajectory to the signal coordinator;

[0030] S42, check the predicted trajectories of the trains on the signal coordinator according to the constraint condition of the total objective function, and update the global common variable when there is a conflict;

[0031] S43, update the Lagrange multiplier vector according to the updated global common variable,

[0032] S44, judge whether to converge according to the updated global common variable, send the current acceleration vector to the train when converging, and feed back the updated global common variable and the Lagrange multiplier vector to each train when not converging, and jump to step S41.

[0033] Further, the formula for updating the global common variable in S42 is: Wherein, z l+1 is the global common variable of the signal coordinator in the l+1th iteration, is the projection operator of the common variable, A i is the coupling state extraction matrix of the ith train, μ i,l+1 is the acceleration vector of the ith train on the signal coordinator in the l+1th iteration, λ i,l is the Lagrange multiplier vector of the ith train on the signal coordinator in the lth iteration, l is the number of iteration times on the signal coordinator, i is the number of trains, and M is the number of trains.

[0034] Further, the formula for updating the Lagrange multiplier vector in S43 is:

[0035] Wherein, λ i,l+1 is the Lagrange multiplier vector of the ith train on the signal coordinator in the l+1th iteration.

[0036] Further, the first element in the Lagrange multiplier vector is used to control the train spacing coupling constraint, the second element in the Lagrange multiplier vector is used to control the energy pool constraint, and the third element in the Lagrange multiplier vector is used to control the section time window constraint.

[0037] The beneficial effects of the present application are:

[0038] ​The application is for the problem that it is difficult to consider the multi-train operation safety constraint, operation index constraint and regenerative braking energy efficient utilization in a unified optimization framework. The local objective function of a single train is established, the net power of each train (related to regenerative braking energy utilization and energy consumption), punctual error penalty (corresponding to punctual rate constraint), acceleration variation penalty (corresponding to comfort constraint) and terminal state deviation are considered, and corresponding constraint conditions are set. Then, the total objective function of multi-trains is constructed, and the multi-train operation safety constraint is taken as the constraint condition of the total objective function, so that the multi-train operation safety, operation index and regenerative braking energy efficient utilization are considered in a unified optimization framework from the global perspective.

[0039] The application is for the problem that the optimization solution lacks engineering path and cannot realize the global energy consumption optimization of the line under the coupling constraint of multi-trains. The total objective function is decomposed to obtain a global coordination term, the global coordination term is added to the local objective function to obtain a local sub-problem, and the single train is solved under the local sub-problem and corresponding constraint and sends a predicted trajectory. Then, the predicted trajectory of each train is checked based on the constraint condition of the total objective function by means of a signal coordinator. If there is a conflict, the global public variable and Lagrange multiplier vector are updated, and through such an iterative process until convergence, an engineering optimization solution path is formed, the coupling constraint of multi-trains can be effectively handled, and finally the global energy consumption optimization of the line is realized. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 It is a flowchart of a rail transit train cooperative scheduling method.

[0041] Figure 2 It is a schematic diagram of the overlapping area of different train traction and braking stages in the same power supply area.

[0042] Figure 3 It is a diagram of the relative relationship of each level of train operation control speed. DETAILED DESCRIPTION

[0043] The specific embodiments of the application are described below to facilitate the understanding of the application by those skilled in the art, but it should be clear that the application is not limited to the scope of the specific embodiments. For those skilled in the art, it is obvious that all the changes within the spirit and scope of the application defined and determined by the appended claims are obvious, and all the application and creation utilizing the concept of the application are within the scope of protection.

[0044] As shown in Figure 1 A rail transit train cooperative scheduling method includes the following steps:

[0045] S1, establish a local objective function of each train according to the net power, punctuality error penalty, acceleration variation penalty and terminal state deviation, set constraint conditions for the local objective function;

[0046] S2, establish a total objective function of multiple trains according to the local objective function of each train, set constraint conditions for the total objective function;

[0047] S3, decompose the total objective function to obtain a global coordination term, add the global coordination term to the local objective function to obtain a local sub-problem;

[0048] S4, solve the local sub-problem of each train under the constraint conditions of the local objective function and send the predicted trajectory, the signal coordinator checks the predicted trajectory of each train based on the constraint conditions of the total objective function, and updates the global public variable and Lagrange multiplier vector when there is a conflict until convergence.

[0049] In this embodiment, the expression of the local objective function in S1 is: ,

[0050] Wherein, J(μ i,k ) is the local objective function of the ith train at the kth time, α is the weight of the net power, β is the weight of the punctuality error penalty, is the weight of the acceleration variation penalty, ρ is the weight of the terminal state deviation, is the net power of the ith train at the kth time, is the punctual error penalty of the ith train at the kth time, is the acceleration variation penalty, is the terminal state deviation of the ith train, i is the number of the train, k is the number of the time, and N is the length of the prediction time domain.

[0051] α, β, , ρ can be dynamically adjusted according to the operation strategy, and the punctuality is emphasized in peak period and the energy consumption is emphasized in off-peak period.

[0052] The expression of the net power is:

[0053]

[0054]

[0055] ,

[0056] Wherein, is the traction power of the ith train at the kth time, is the regenerative power of the ith train at the kth time, a i (k) is the acceleration of the ith train at the kth time, Fres,i (v i (k) represents the running resistance of the i-th train at time k, v i (k) represents the speed of the i-th train at time k, m i Let η be the mass of the i-th train, and max be the maximum of the two values. regen For regenerative braking feedback efficiency.

[0057] During the braking phase, the train generates regenerative braking energy, which is collected and stored in an energy pool, such as... Figure 2 As shown.

[0058] The expression for running resistance is: Among them, C 0,i C is the coefficient of static friction and rolling resistance. 1,i C is the drag coefficient for the first-order velocity term, reflecting a portion of mechanical friction and aerodynamic drag. 2,i This is the drag coefficient for the square of the velocity, reflecting the characteristic that air resistance increases with the square of the velocity.

[0059] The expression for running speed is: ,

[0060] Among them, v i (k-1) represents the speed of the i-th train at time k-1, T s For the sampling period, a i (k-1) represents the acceleration of the i-th train at time k-1.

[0061] Set an emergency braking speed limit for the operating speed: v i (k) < V, V = [v] e,1 , …, v e,R ], where V is the emergency braking speed limit vector, v e,1 To limit the speed at orbital position 1, v e,R The speed limit is set at position R on the track, where R is the number of speed limits. Since subways have track conditions (curves, gradients, etc.), the specific emergency braking speed limit needs to be found based on the specific location on the track.

[0062] In situations where the operating speed needs to be lower than the emergency braking speed limit, such as... Figure 3 As shown, Figure 3 The ATP system speed limit is a speed limit set by the Automatic Train Protection (ATP) system to ensure train operation safety and prevent speeding. The ATO operating speed represents the actual operating speed under the control of the Automatic Train Operation (ATO) system. It is the ATP system emergency braking trigger speed. If the actual speed of the train reaches this value, the ATP system will forcibly trigger emergency braking to ensure that the train stops within a safe distance.

[0063] The expression of the punctual error penalty is: wherein max is the maximum of the two, is the predicted arrival time of the ith train, is the planned arrival time of the ith train.

[0064] The predicted arrival time is set as The predicted time point is calculated by the speed and position relationship formula, and the speed and position relationship formula is: ,

[0065] wherein s i (k) is the position of the ith train at the kth moment, s i (k-1) is the position of the ith train at the k-1th moment, T s is the sampling period, a i (k-1) is the acceleration of the ith train at the k-1th moment.

[0066] The expression of the acceleration change penalty is: ,

[0067] wherein a i (k) is the acceleration of the ith train at the kth moment, a i (k-1) is the acceleration of the ith train at the kth moment.

[0068] The acceleration change penalty is related to passenger comfort, and setting the acceleration change penalty can improve passenger comfort.

[0069] The end state deviation, i.e., the arrival position deviation, has the expression:

[0070] ,

[0071] wherein s arr,pre is the arrival distance after the predicted train travels according to the planned time, s is the target position at which the train should accurately stop, s0 is the initial distance, is the planned arrival time of the ith train, a i (k) is the acceleration of the ith train at the kth moment.

[0072] In this embodiment, the constraint conditions of the local objective function in S1 include: safety distance constraint, signal blocking time window constraint and regenerative braking energy distribution constraint.

[0073] In this embodiment, the expression of the safety distance constraint is: ,

[0074] wherein s i-1(k) is the position of the i-1th train at the kth time, s i (k) is the position of the i-1th train at the kth time, s i (k) is the position of the i-1th train at the kth time, s

[0075] τ determines the dynamic safety distance, which is related to the current speed of the train.

[0076] The safety distance constraint can only solve the problem of safe rear-end collision between trains running on the same track in the same direction, while the signal blocking time window constraint essentially solves the resource conflict problem based on the same location at the same time, such as opposite running trains, straight and lateral trains entering the same turnout area, etc.

[0077] The signal blocking time window constraint includes:

[0078] A1, define the available time set of the section: Where W is the available time set, t 1,min is the entry time of the first section, t 1,max is the clear time of the first section, t j,min is the entry time of the jth section, t j,max is the clear time of the jth section, t n,min is the entry time of the nth section, t n,max is the clear time of the nth section, ∪ is the union set, j is the number of sections, and n is the number of sections.

[0079] A2, predict the time of the train entering the target section: ,

[0080] Where, is the predicted entry time of the ith train in the jth section, s j is the entry position of the jth section, s 0 is the current position of the train, t unc is the time factor of error and system transmission delay, t0 is the current time, v avg,i is the average speed before entering the section;

[0081] A3, limit the single train entry time in the available time set: Where, is the predicted entry time of the ith train in the jth section, and j is the number of selected blocking sections in n sections.

[0082] A4, limit the time interval of multiple trains entering the same section: i and r, ,

[0083] wherein T is the estimated entry time of the i-th train into the j-th section, is the estimated entry time of the r-th train into the j-th section, is the minimum time for clearance confirmation, and r is another train.

[0084] The regenerative braking energy of the train needs to be reasonably distributed in the line, that is, in a time period, the total feedback energy cannot exceed the battery capacity and the absorption capacity, and the energy distribution in the pool needs to meet the demand.

[0085] The regenerative braking energy distribution constraints include:

[0086] B1, constraint the energy pool capacity range: ,

[0087] wherein E pool (k) is the energy of the energy pool at the k-th moment, is the maximum capacity of the energy pool;

[0088] B2, determine the absorption power of the energy pool: ,

[0089] wherein, is the absorption power of the energy pool at the k-th moment, d sched is the scheduling allocation weight coefficient, T s is the time step;

[0090] B3, calculate the energy loss according to the regenerative power and the energy of the energy pool: wherein L loss (k) is the energy loss, is the regenerative power of the i-th train at the k-th moment, and λ is the storage loss coefficient;

[0091] B4, calculate the next moment energy of the energy pool according to the energy loss, the energy of the energy pool, the regenerative power and the absorption power: ,

[0092] wherein E pool (k+1) is the energy of the energy pool at the k+1-th moment.

[0093] In this embodiment, the total objective function is the minimum value of the sum of the local objective functions of all trains: ,

[0094] wherein min is the minimum value, μ i,k is the acceleration vector of the i-th train at the k-th moment, J(μ i,k ) is the local objective function of the i-th train at the k-th moment, and M is the number of trains.

[0095] The constraint conditions of the total objective function include train spacing coupling constraint, energy pool constraint and section time window constraint.

[0096] The expression of train spacing coupling constraint is: ,

[0097] wherein g ir (μ i ,μ r ) is the constraint of train i and r spacing coupling, D safe is the safety spacing, s i (k) is the position of the i-th train at the k-th time, s r (k) is the position of the r-th train at the k-th time, and ε is the train set.

[0098] The train spacing coupling constraint is used to represent the train spacing coupling and how to realize the safety spacing.

[0099] The expression of energy pool constraint is: ,

[0100] wherein h(μ 1, μ 2,…, μ M ) is the energy pool constraint, is the absorbed power of the energy pool at the k-th time, T s is the time step, E pool (k) is the energy of the energy pool at the k-th time, is the maximum capacity of the energy pool.

[0101] The expression of section time window constraint is: wherein is the section time window constraint, t i is the time when the i-th train enters a section, t is the time when the section allows the train to enter, W is the available time set, and || is the absolute value.

[0102] μ 1, μ 2,…, μ M is the M acceleration vectors, μ i =[a i (1),…, a i (L)], a i (1) is the first acceleration of the i-th train, a i (L) is the L-th acceleration of the i-th train, and L is the number of accelerations in an acceleration vector.

[0103] In the section time window constraint, if the current speed causes the train to enter a section at a time that does not satisfy the available time set, the speed is forced to be reduced to satisfy it.

[0104] The expression of the local sub-problem in S3 is: ,

[0105] where μ i,m+1 is the acceleration vector of the ith train in the local m+1th iteration, μ i,m is the acceleration vector of the ith train in the local mth iteration, J(μ i,m ) is the local objective function of the ith train in the local mth iteration, argmin is to find the μ i,m that makes the expression take the minimum value, U i is the set of accelerations that the ith train can take at all times, θ is the penalty parameter, A i is the coupling state extraction matrix of the ith train, z m is the global common variable in the local mth iteration, λ i,m is the Lagrange multiplier vector of the ith train in the local mth iteration, || || is the two-norm, is the global coordination item, m is the number of local iterations, and i is the number of the train.

[0106] A i μ i,m represents the "global coupling mapping" of the local control variable (mapping the local control variable μ i,m of train i to the "dimension of the global common variable", such as "time of entering a section", "energy request amount", etc., reflecting the influence of the local decision on the global.

[0107] The expression of the coupling state extraction matrix A i is: ,

[0108] where C s is the position-related state extraction sub-matrix, C t is the time window-related state extraction sub-matrix, C P is the power-related state extraction sub-matrix, R is the real number field, L is the length of the acceleration vector, N s is the dimension of the position-related state quantity, N t is the dimension of the time window-related state quantity, and N P is the dimension of the power-related state quantity.

[0109] The value of N s is usually 1, the value of N t is usually 1, and the value of N P is usually 1.

[0110] Position-related state extraction sub-matrix C s For extracting the safety-critical position, the structure is: row vector (and is a sparse vector, i.e. most elements are 0, only the critical position is 1), when L = 10 (understandable as having 10 time steps or data points, 1 second per step), the vector is [0 0 0 1... 0], which means extracting the position s of the 3rd time step (because the index starts from 0, the 4th element corresponds) from the multi-dimensional position data of the train i (3), this position is a critical position related to safety constraints (such as the train needing to meet the safety distance with the preceding train at this position, etc.), and the 1st row, 4th column (because the subscript starts from 0) of the matrix is 1, so as to identify that the position of the i-th train at the 3rd second has an impact on the safety distance.

[0111] Time window-related state extraction sub-matrix C t For extracting the braking power of the train, the structure is: row vector (sparse), when L = 10, the vector is [0 0 0... 1...0], which extracts , the 1st row, 6th column (because the subscript starts from 0) of the matrix is 1, indicating that the 6th second affects the i-th train to enter a certain section of the time window caused by the train speed not meeting the requirements.

[0112] Power-related state extraction sub-matrix C P For extracting the braking power of the train, the structure is: row vector (sparse), when L = 10, the vector is [0 0 0... 0...1], which extracts , the 2nd row, 11th column (because the subscript starts from 0) of the matrix is 1, indicating that the braking power of the i-th train at the 10th second affects the energy pool constraint.

[0113] Global common variable z m The expression is: , where is a safety projection operator, is a time interval projection operator, is a capacity allocation projection operator, s i (k) is the position of the i-th train at the k-th time, t i (k) is the time when the i-th train enters the section at the k-th time, is the regenerative power of the i-th train at the k-th time, and M is the number of trains.

[0114] z m represents the global common variable at the m-th iteration (such as "uniform safety distance constraint", "uniform section time window", "global energy allocation scheme", which is a "consistent variable" shared by all trains).

[0115] The safety projection operator is used to enforce the headway constraint, and the capacity projection operator is used to prevent overuse of energy.

[0116] The expression of the Lagrange multiplier vector is: ,

[0117] where λ i,m,1 is the first element of the Lagrange multiplier vector used to control the train spacing coupling constraint, λ i,m,2 is the second element of the Lagrange multiplier vector used to control the energy pool constraint, and λ i,m,3 is the third element of the Lagrange multiplier vector used to control the section time window constraint.

[0118] The initial values of the three elements of the Lagrange multiplier vector can be set, for example, the initial value of the first element is set to 30 m, the initial value of the second element is set to 800 kW, and the initial value of the third element is set to 90 s.

[0119] The penalty parameter θ is used to control the consistency of the local decision and the global public variable - the greater θ is, the more emphasis is placed on matching the global variable.

[0120] In this embodiment, S4 includes the following steps:

[0121] S41, solving the local sub-problem of a single train within the constraint condition of the local objective function to obtain a predicted trajectory, and sending the predicted trajectory to the signal coordinator;

[0122] S42, checking the predicted trajectory of each train according to the constraint condition of the total objective function on the signal coordinator, and updating the global public variable when there is a conflict;

[0123] S43, updating the Lagrange multiplier vector according to the updated global public variable,

[0124] S44, judging whether to converge according to the updated global public variable, and sending the current acceleration vector to the train when converging, and feeding back the updated global public variable and the Lagrange multiplier vector to each train when not converging, and jumping to step S41.

[0125] In this embodiment, convergence means whether the difference between the updated global public variable and the target global public variable reaches a preset range.

[0126] The acceleration vector is the decision vector of the train, the train operation is controlled by adjusting the acceleration, and the train operation speed and position can also be calculated by the acceleration, therefore, the prediction trajectory is based on the acceleration vector, combined with the operation speed and position formula, and further deduced to obtain the multi-dimensional operation state sequence of the train at each time step in the prediction time domain, such as position, speed, traction / braking power and arrival time.

[0127] The formula for updating the global common variable is: ,

[0128] Wherein, z l+1 is the global common variable of the l+1th iteration on the signal coordinator, is the projection operator of the common variable, A i is the coupling state extraction matrix of the i-th train, μ i,l+1 is the acceleration vector of the i-th train on the signal coordinator at the l+1th iteration, λ i,l is the Lagrange multiplier vector of the i-th train on the signal coordinator at the lth iteration, l is the number of iteration times on the signal coordinator, i is the number of trains, and M is the number of trains.

[0129] μ i,l+1 is the control variable (such as acceleration command) of the i-th train obtained at the l+1th iteration in the "local update" step. A i μ i,l+1 is the linear relationship between the control variable of the i-th train and the "global coupling part" (reflecting the association between the train and the common variable). λ i,l is the i-th Lagrange multiplier at the lth iteration (used to coordinate the consistency of the train and the common variable).

[0130] The signal coordinator first fuses the "local information (coupling term + Lagrange multiplier)" of all trains and takes the average at the l+1th iteration, then projects this "averaged result" into the constraint set Z of the common variable, and finally obtains the new common variable z l+1 . The constraint set Z is the set of all "multi-train coordination constraints" that the global common variable must satisfy. ,

[0131] Wherein, λ i,l+1 is the Lagrange multiplier vector of the i-th train on the signal coordinator at the l+1th iteration.

[0132] The present application solves the global optimization problem by decomposition-coordination strategy, the core of which is to convert the coupling constraint into a sub-problem that can be independently solved by each train. The process is divided into three steps:

[0133] 1. Train parallel optimization: each train independently calculates a local optimal solution and uploads a prediction trajectory;

[0134] 2. Signal coordination arbitration: integrate trajectories, check safety / energy constraints and update common variables;

[0135] 3. Multiplier correction bias: correct train control quantities according to coordination results.

[0136] The present application decomposes the complex multi-train coupling constraint problem into sub-problems that can be distributedly solved through the "local optimization-global arbitration-multiplier feedback" cycle. The core is to replace the direct constraint with a quadratic penalty term, so that each train can consider global coordination while pursuing its own energy optimization.

[0137] In the present embodiment, the solving algorithm uses ADMM (Alternating Direction Method of Multipliers).

[0138] The present application can consider multi-train operation safety constraints, operation index constraints and regenerative braking energy efficient utilization in a unified optimization framework. The net power of each train (related to regenerative braking energy utilization and energy consumption), punctuality error penalty (corresponding to punctuality rate constraints), acceleration variation penalty (corresponding to comfort constraints) and terminal state deviation are taken into account by establishing a local objective function for each train, and corresponding constraint conditions are set. Based on this, a total objective function for multiple trains is constructed, and multiple train operation safety constraints are taken as constraint conditions of the total objective function, so that multiple aspects of demand are considered from a global perspective, and the consideration of multi-train operation safety, operation index and regenerative braking energy efficient utilization in a unified optimization framework is realized.

[0139] The present application provides an engineering optimization solving path for solving the problem of lack of engineering optimization solving path and inability to achieve line global energy optimization under multi-train coupling constraints. The total objective function is first decomposed to obtain a global coordination term, which is added to the local objective function to obtain a local sub-problem. Each train is solved under its own local sub-problem and corresponding constraints and sends a predicted trajectory. Then, with the help of a signal coordinator, the predicted trajectories of each train are checked based on the constraint conditions of the total objective function. If there is a conflict, the global common variable and the Lagrange multiplier vector are updated. Through such an iterative process until convergence, an engineering optimization solving path is formed, which can effectively handle the coupling constraints of multiple trains and ultimately achieve line global energy optimization.

[0140] The above is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for coordinated scheduling of rail transit trains, characterized in that, Includes the following steps: S1. Based on the net power, punctuality error penalty, acceleration change penalty, and endpoint state deviation of each train, establish a local objective function for each train and set constraints on the local objective function. S2. Based on the local objective function of a single train, establish the overall objective function for multiple trains, and set constraints on the overall objective function; S3. Decompose the overall objective function to obtain the global coordination term, and add the global coordination term to the local objective function to obtain the local subproblems; S4. Solve the local subproblems of a single train under the constraints of the local objective function and send the predicted trajectory. The signal coordinator checks the predicted trajectories of each train based on the constraints of the overall objective function. If there is a conflict, update the global common variables and the Lagrange multiplier vector until convergence. The expression for the local objective function in S1 is: , Wherein, J(μ) i,k Let be the local objective function of the i-th train at time k, where α is the weight of the net power and β is the weight of the punctuality error penalty. ρ represents the weight of the penalty term for the change in acceleration, and ρ represents the weight of the deviation from the final state. Let be the net power of the i-th train at time k. Let $\frac{i}{i}$ be the penalty for the punctuality error of the $i$-th train at time $k$. For the penalty term of acceleration change, Let N be the endpoint state deviation of the i-th train, where i is the train number, k is the time number, and N is the prediction time domain length. The expression for the punctuality error penalty is: , Where max represents the maximum of the two values. Let be the predicted arrival time of the i-th train. Let i be the planned arrival time of the i-th train; The expression for the penalty term for the change in acceleration is: , Among them, a i (k) represents the acceleration of the i-th train at time k, a i (k-1) represents the acceleration of the i-th train at time k; The destination state deviation, also known as the arrival position deviation, is expressed as follows: , Among them, s arr,pre To predict the distance the train will travel after it arrives at the scheduled time, s is the target position where the train should stop precisely; The expression for the local subproblem in S3 is: , Where, μ i,m+1 Let μ be the acceleration vector of the i-th train in the (m+1)-th iteration at local location. i,m Let J(μ) be the acceleration vector of the i-th train in the m-th iteration at the local location. i,m Let be the local objective function of the i-th train in the m-th iteration, and argmin be the value of finding μ that minimizes the expression. i,m U i Let A be the set of possible accelerations for the i-th train at all times, θ be the penalty parameter, and A be the set of possible accelerations for the i-th train at all times. i Extract the coupling state matrix for the i-th train, z m Let λ be the global public variable in the local m-th iteration. i,m Let |i| be the Lagrange multiplier vector of the i-th train in the m-th iteration at local location, and |i| be the L2 norm. For global coordination, m is the number of local iterations, and i is the train number.

2. The rail transit train cooperative scheduling method according to claim 1, characterized in that, The constraints of the local objective function in S1 include: safety distance constraints, signal blocking time window constraints, and regenerative braking energy distribution constraints.

3. The rail transit train cooperative scheduling method according to claim 2, characterized in that, The expression for the safety distance constraint is: , Among them, s i-1 (k) represents the position of the (i-1)th train at time k, s i (k) represents the position of the i-th train at time k, D0 is the basic safety distance between trains, τ is the time interval, and v i (k) represents the speed of the i-th train at time k, where i is the train number and k is the time number; The signal blocking time window constraint includes: A1. Define the set of available time for the defined segment; A2. Predict the time it will take for the train to enter the target section; A3. Limit the entry time of a single train to the set of available times; A4. Limit the time interval between multiple trains entering the same section; The regenerative braking energy distribution constraints include: B1. Limitation of energy pool capacity; B2. Determine the energy pool's absorption power; B3. Calculate the energy loss based on the regeneration power and the energy in the energy pool; B4. Calculate the energy of the energy pool at the next moment based on the energy loss, the energy of the energy pool, the regeneration power, and the absorption power.

4. The rail transit train cooperative scheduling method according to claim 1, characterized in that, The overall objective function in S2 is the minimum of the sum of the local objective functions of all trains; The constraints of the overall objective function include: train spacing coupling constraints, energy pool constraints, and section time window constraints.

5. The rail transit train cooperative scheduling method according to claim 1, characterized in that, S4 includes the following steps: S41. Solve the local subproblems of a single train within the constraints of the local objective function to obtain the predicted trajectory, and send the predicted trajectory to the signal coordinator. S42. On the signal coordinator, the predicted trajectories of each train are checked according to the constraints of the overall objective function, and the global common variables are updated when conflicts exist. S43. Update the Lagrange multiplier vectors based on the updated global public variables. S44. Based on the updated global common variables, determine whether convergence has occurred. If convergence has occurred, send the current acceleration vector to the train. If convergence has not occurred, feed back the updated global common variables and Lagrange multiplier vectors to each train and jump to step S41.

6. The rail transit train cooperative scheduling method according to claim 5, characterized in that, The formula for updating the global public variable in S42 is as follows: , Among them, z l+1 For the (l+1)th iteration of the signal coordinator, For the projection operator of common variables, A i Extract the coupling state matrix for the i-th train, μ i,l+1 Let λ be the acceleration vector of the i-th train on the signal coordinator in the (l+1)th iteration. i,l Let be the Lagrange multiplier vector of the i-th train on the signal coordinator in the l-th iteration, where l is the iteration number on the signal coordinator, i is the train number, and M is the number of trains.

7. The rail transit train cooperative scheduling method according to claim 6, characterized in that, The formula for updating the Lagrange multiplier vector in S43 is as follows: , Where, λ i,l+1 Let be the Lagrange multiplier vector of the i-th train in the (l+1)-th iteration on the signal coordinator.

8. The rail transit train cooperative scheduling method according to claim 5, characterized in that, The first element of the Lagrange multiplier vector is used to control the coupling constraint of train spacing, the second element is used to control the energy pool constraint, and the third element is used to control the time window constraint of the section.

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