Train operation adjustment method based on model predictive control in disturbance scenario

Abstract

The application discloses a train operation adjustment method based on model prediction control under a disturbance scene, and comprises the following steps: S1, adjusting a train operation strategy based on a disturbance scene according to a planned operation diagram, and constructing a train operation dynamic model; S2, taking the punctuality of the train and the regularity of the operation interval as a target function, taking the train operation interval and the control variable as a constraint condition, and constructing an optimal control problem model based on the minimization of the time deviation between the actual train operation and the planned operation diagram according to the train operation dynamic model in step S1; S3, solving the optimal control problem model in step S2 by using a model prediction control method, obtaining an optimal control input vector, and adjusting the train operation state according to the optimal control input vector; the train adjustment method provided by the application adjusts the train operation time and the stop time by obtaining the optimal control input, so that the adjusted operation diagram is as close to the planned operation diagram as possible, thereby improving the speed of the automatic adjustment of the train operation.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit operation management technology, specifically to a train operation adjustment method based on model predictive control under disturbance scenarios. Background Technology

[0002] Urban rail transit is the backbone and core infrastructure of public transportation systems in large cities. With the acceleration of urbanization and the increase in population and economic activity, residents' demand for urban rail transit systems is also increasing significantly. In actual operation, due to unexpected fluctuations in passenger travel demand and other unpredictable factors, trains are inevitably subject to interference, causing them to deviate from their scheduled operating times. Due to the high frequency of train departures, without effective control, interference can easily spread to more and more trains and stations, causing large-scale delays. Frequent interference significantly reduces the operational quality of the urban rail transit system, thus having a negative impact. It is necessary to develop effective adjustment methods to handle interference that reduces system reliability and restore the punctual operation of affected trains as much as possible. Currently, some research on adjustments under disturbance scenarios is based on the remaining time in the operating schedule, which has limited applicability and is prone to resource waste; other existing automatic train adjustment methods do not fully consider comprehensive factors such as passenger satisfaction, operating costs, and service levels, and lack efficient and advanced algorithms to obtain the optimal solution in real time. Summary of the Invention

[0003] To address the aforementioned shortcomings in existing technologies, this invention provides a train operation adjustment method based on model predictive control under disturbance scenarios, proposing an efficient real-time control strategy to achieve automatic adjustment of train operation.

[0004] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0005] A method for adjusting train operation based on model predictive control under disturbance scenarios includes the following steps:

[0006] S1. Based on the planned operation schedule and the disturbance scenario, adjust the train operation strategy and construct a dynamic model of train operation;

[0007] S2. Taking the punctuality of trains and the regularity of train intervals as the objective function, and the train intervals and control variables as constraints, and based on the train operation dynamic model in step S1, construct an optimal control problem model based on minimizing the time deviation between the actual train operation and the planned operation schedule.

[0008] S3. Use the model predictive control method to solve the optimal control problem model in step S2, obtain the optimal control input vector, and adjust the train operation state according to the optimal control input vector.

[0009] The present invention has the following beneficial effects:

[0010] The train operation adjustment method based on model predictive control in disturbance scenarios proposed in this invention can not only obtain control input based on the current state information, but also obtain the optimal control input based on the prediction of its future multi-step state, thereby adjusting the train running time and stopping time, so that the adjusted timetable is as close as possible to the planned timetable, and improving the speed of automatic adjustment of train operation. Attached Figure Description

[0011] Figure 1 This is a flowchart illustrating a train operation adjustment method based on model predictive control under disturbance scenarios proposed in this invention.

[0012] Figure 2 Schematic diagram of adjusting the train-to-ground information transmission structure for train operation;

[0013] Figure 3 This is a schematic diagram of the model predictive control strategy;

[0014] Figure 4 This is a schematic diagram of a single-line urban rail transit system in the embodiment.

[0015] Figure 5 This is a schematic diagram of the time deviation under uncontrolled conditions in the embodiment;

[0016] Figure 6 This is a schematic diagram of time deviation under model predictive control in the embodiment;

[0017] Figure 7 This is a schematic diagram of the control quantities for different stations (sections) in the embodiment;

[0018] Figure 8 This is a schematic diagram of time deviation under state feedback control in the embodiment;

[0019] Figure 9 This is a schematic diagram of the operating interval deviation at different stages under model predictive control in the embodiment.

[0020] Figure 10 This is a schematic diagram of the running interval deviation at station 5 in the embodiment;

[0021] Figure 11 This is a schematic diagram of the running interval deviation at station 6 in the embodiment;

[0022] Figure 12 This is a schematic diagram of the running interval deviation at station 7 in the embodiment;

[0023] Figure 13 This is a schematic diagram comparing time deviations under different prediction ranges in the embodiment;

[0024] Figure 14 This is a schematic diagram comparing control quantities under different prediction ranges in the embodiment. Detailed Implementation

[0025] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0026] like Figure 1 As shown, a train operation adjustment method based on model predictive control under disturbance scenarios includes the following steps S1-S3:

[0027] S1. Based on the planned operation schedule and the disturbance scenario, adjust the train operation strategy and construct a dynamic model of train operation.

[0028] like Figure 2 As shown, in an optional embodiment of the present invention, trains on the line operate according to a given planned timetable, which is formulated in advance by the transportation management department considering passenger travel demand and operating costs. The planned timetable specifies the arrival and departure times of all trains at each station. In actual operation, trains exchange real-time information with the operation control center via LTE-M. Figure 2 The document illustrates the train operation adjustment information transmission structure between the train and the ground. Solid lines represent the upward transmission of real-time status from the train to the operation control center, while dashed lines represent the downward transmission of real-time control commands from the operation control center to the train. The train's real-time status includes its position, actual arrival time, and actual departure time. Based on the received status information, the operation control center sends dispatching commands to the train to adjust its running time and stopping time, ensuring that the train operates as close to the planned timetable as possible. However, in actual train operation, disturbances caused by signal system failures or human factors are unavoidable. Therefore, the planned timetable represents an ideal operating scheme. This embodiment proposes a train operation adjustment strategy to reduce the negative impact of train delays.

[0029] Specifically, step S1 includes S11-S18:

[0030] S11. Calculate the planned train interval based on the train's scheduled departure time at the station.

[0031] The formula for calculating the planned train interval in step S11 is as follows:

[0032]

[0033] Where H represents the planned train interval, This indicates the planned departure time of train i+1 at station j. This indicates the scheduled departure time of train i at station j.

[0034] In this embodiment, it is assumed that there are N trains and S stations on the line, and only one train can run in each section at a time. Overtaking is not allowed in either section or station during operation. Trains and stations are represented by i and j, respectively, where i = 1, 2, ..., N, and j = 1, 2, ..., S. Let D represent the planned departure time of train i at station j, and calculate the planned running interval of the train in step S11. The planned running interval represents the constant time interval between two consecutive trains departing from the same station.

[0035] S12. Based on the planned train intervals in step S11, establish the planned departure time relationship for each train at each station.

[0036] In step S12, the planned departure time relationship for each train at each station is established as follows:

[0037]

[0038] Among them, R j S represents the planned travel time of a train from station j to station j+1. j+1 a represents the minimum stopping time of the train at station j+1. j+1 This represents the ratio of the additional stop time at station j+1 to the planned train interval H.

[0039] In this embodiment, a j+1 The delay rate, which reflects the impact of the operating interval on the dwell time, is a parameter estimate obtained from a large amount of actual observation data of each station, namely departure time and dwell time. Its value may vary for different urban rail transit lines.

[0040] S13. Calculate the actual departure time of the train at the next station based on the actual departure time of the train at the previous station.

[0041] The formula for calculating the actual departure time of the train at the next station in step S13 is as follows:

[0042]

[0043] in, This indicates the actual departure time of train i+1 at station j. This indicates the actual departure time of train i at station j. This represents the actual travel time of train i from station j to station j+1. This represents the actual stopping time of train i at station j+1.

[0044] S14. Calculate the actual travel time of the train from station to station based on the control quantity of the train's travel time from station to station and the disturbance of the train's travel time from station to station.

[0045] The formula for calculating the actual travel time of the train from station to station in step S14 is as follows:

[0046]

[0047] in, This represents the planned travel time for train i from station j to station j+1. This represents the control quantity indicating the travel time of train i from station j to station j+1. This represents the disturbance in the travel time of train i from station j to station j+1;

[0048] S15. Based on the assumption that the number of passengers at a station is proportional to the time interval between two consecutive trains departing from that station, calculate the actual stopping time of the train at the station.

[0049] The formula for calculating the actual stopping time of the train at the station in step S15 is as follows:

[0050]

[0051] in, This indicates the actual departure time of train i-1 at station j+1. This represents the control quantity indicating the dwell time of train i at station j+1. This represents the disturbance in the dwell time of train i at station j.

[0052] In this embodiment, the actual stopping time of the train at the station depends on the number of passengers getting on and off the train. It is also assumed that the number of passengers at a station is proportional to the time interval between the departure of two consecutive trains from that station. Therefore, the actual stopping time of the train at the station in step S15 can be calculated.

[0053] S16. Based on the actual travel time of the train from the station to the station in step S14 and the actual stopping time of the train at the station, as well as the actual departure time of the train at the station in step S13, the dynamic relationship between the departure times of two consecutive stations is obtained.

[0054] The dynamic relationship between the departure times of two consecutive stations obtained in step S16 is as follows:

[0055]

[0056] in, This represents the sum of control quantities for train i and This represents the total disturbance experienced by train i and

[0057] S17. Construct the train departure time deviation at the station compared to the planned timetable, and based on the planned departure time relationship of each train at each station in step S12, the dynamic relationship of the departure times of two consecutive stations in step S16, and the train departure time deviation at the station compared to the planned timetable, construct a dynamic model of the time deviation.

[0058] In step S17, the train's departure time at the station deviates from the planned timetable by:

[0059]

[0060] in, This indicates the deviation of train i's departure time at station j from the planned timetable.

[0061] The dynamic model for time deviation in step S17 is as follows:

[0062]

[0063] in, This indicates the deviation of train i's departure time at station j+1 from the planned timetable.

[0064] S18. Construct the time deviation state vector, control input vector, and disturbance vector, and based on the time deviation dynamic model in step S17, construct the train operation dynamic model.

[0065] In step S18, the time deviation state vector, control input vector, and disturbance vector are respectively:

[0066]

[0067]

[0068]

[0069] Where k represents the sampling points, N represents the total number of stations on the urban rail transit line, and X k This represents the time deviation state vector of the k-th sampling point. This indicates the time deviation of train k-1 at station 1. This indicates the time deviation of train k-2 at station 2. This represents the time deviation of train kN at station N, where T represents transpose, and U... kThis represents the control input vector for the k-th sampling point. This indicates the control input for train k at station 0. This indicates the control input for train k-1 at station 1. W represents the control input for train k-N+1 at station N-1. k This represents the interference vector at the k-th sampling point. This indicates the interference of train k at station 0. This indicates the interference of train k-1 at station 0. This represents the interference of train k-N+1 at station N-1.

[0070] The train operation dynamic model in step S18 is as follows:

[0071] X k+1 =AX k +BU k +BW k

[0072] Among them, X k+1 Let A represent the time deviation state vector of the (k+1)th sampling point, and let A and B represent the N×N coefficient matrices respectively.

[0073] In this embodiment, based on the train's departure time deviation from the planned timetable in step S17, the goal of the control action is to minimize the time deviation to improve the operational efficiency of the urban rail transit line. The disturbance term can only be positive, increasing delays by affecting train travel time or station dwell time. Therefore, this embodiment describes all trains and stations by defining a time deviation state vector, a control input vector, and a disturbance vector. Here, k represents a sampling point or decision step, i.e., a sampling point of a discrete event. The dimension of all vectors is N, which is the total number of stations on the urban rail transit line. Set X k elements in Let x represent the time deviation of train kN at station N, and the sum of the train and station indices of all elements is always equal to the step size k. Based on the time deviation dynamic model in step S17, the train operation dynamic model in step S18 can be obtained. In this embodiment, the train operation dynamic model reflects the time deviation of different trains at the same stage. Writing it in the form of a standard difference equation is more convenient for applying advanced control methods, and changes in the number of trains on the track do not change the values ​​of coefficient matrices A and B, nor do they change the time deviation state vector X. k And the dimension W of the interference vector k Furthermore, due to the interference vector W k It is generated randomly and cannot be known in advance, so the controller needs to make a decision at each stage k.

[0074] S2. Using the punctuality of trains and the regularity of their running intervals as the objective function, and the train running intervals and control variables as constraints, and based on the train operation dynamic model in step S1, construct an optimal control problem model based on minimizing the time deviation between the actual train operation and the planned operation schedule.

[0075] Step S2 specifically includes S21-S22:

[0076] S21. Construct an objective function based on train punctuality and regularity of operating intervals, and construct operating interval constraints and control quantity constraints.

[0077] The objective function in step S21 based on train punctuality and regularity of intervals is:

[0078]

[0079] in, U represents the control input vector U that minimizes the objective function J based on the disturbance value at the k-th sampling point and the actual train departure time. k , X represents the transpose of the time deviation state vector at the (k+1)th sampling point. k+1 X represents the time deviation state vector of the (k+1)th sampling point. k This represents the time deviation state vector of the k-th sampling point. U represents the transpose of the control input vector at the k-th sampling point. k Let P represent the control input vector at the k-th sampling point, P, Q, and R represent N-dimensional positive definite constant matrices, which represent the weight factors of the three optimization objectives, respectively, and T represents the transpose.

[0080] In this embodiment, the objective function based on train punctuality and the regularity of train intervals has the following first term: the sum of the squared deviations between the actual and planned departure times, reflecting the train's punctuality; the second term: the sum of the squared deviations of train intervals related to passenger waiting time, reflecting the train's regularity; and the third term: the sum of the squared control inputs, reflecting control costs. By minimizing the objective function, the quality of operation and service is improved. Therefore, the values ​​of P, Q, and R represent trade-offs among different actual operational needs.

[0081] The running interval constraint in step S21 is:

[0082]

[0083] in, This indicates the deviation of train i's departure time at station j+1 from the planned timetable. h represents the deviation of train i's departure time at station j from the planned timetable. minH represents the minimum safe operating interval of the train, and H represents the planned operating interval of the train.

[0084] The control constraints in step S21 are:

[0085]

[0086]

[0087] Among them, u 1j,min u 1j,max u represents the upper and lower bounds for adjusting the running time of different sections. 2j,min u 2j,max This represents the upper and lower bounds for adjusting the stopping time at different stations j. Therefore, u 1j,min +u 2j,min ≤u 1j,max +u 2j,max And order Then there is This represents the control quantity indicating the travel time of train i from station j to station j+1. This represents the control quantity for the dwell time of train i from station j+1 to station j.

[0088] In this embodiment, due to the practical requirements for the safe operation of urban rail transit lines, adjustments must be made considering both interval constraints and control quantity constraints. For safety reasons, the actual departure time interval between two consecutive trains must not be less than the minimum safe operating interval h. min ,Right now And by using the train's departure time deviation from the planned timetable at the station in step S17, the running interval constraint is transformed into a deviation constraint for the departure time of each train, i.e. Thus, the running interval constraint in step S21 is obtained. Secondly, the control action is used to adjust the running time and stopping time of the interval, so the magnitude of the control quantity must satisfy the control quantity constraint formula in step S21, and the lower and upper bounds of the control action are determined by the actual constraints of the train and the track.

[0089] S22. Based on the train operation dynamic model in step S1 and the objective function, running interval time constraint and control quantity constraint based on train punctuality and running interval regularity in step S21, construct the optimal control problem model.

[0090] The optimal control problem model in step S22 is as follows:

[0091]

[0092] stX k+n =AX k+n-1+BU k+n-1 +BW k+n-1

[0093] X k+n-1 -X k+n ≤(Hh min )I N×1

[0094] U k+n-1 ≤U max

[0095] -U k+n-1 ≤-U min n = 1, 2, ..., L

[0096] in, This represents the control input vector used to find the minimum value of the predictive control problem model at the k-th sampling point. X represents the transpose of the time deviation state vector at the (k+n)th sampling point. k+n X represents the time deviation state vector of the (k+n)th sampling point. k+n-1 This represents the time deviation state vector at the (k+n-1)th sampling point. U represents the transpose of the control input vector at the (k+n-1)th sampling point. k+n-1 W represents the control input vector at the (k+n-1)th sampling point. k+n-1 I represents the interference vector at the (k+n-1)th sampling point. N×1 U represents an N-dimensional vector with all elements being 1. max U min Let U represent the maximum and minimum values ​​of the N-dimensional control input vector U, and L represent the optimization step size.

[0097] In this embodiment, step S1 constructs an optimal control problem model based on the train operation dynamic model, and step S21 constructs an optimal control problem model based on the objective function, operation interval constraints, and control quantity constraints related to train punctuality and regularity of intervals. And U max U min This represents the maximum and minimum values ​​of the N-dimensional control input vector U, and its j-th element is equal to... and Optimal control problem model Various commercial solvers can be used to solve the problem efficiently and obtain the optimal control input vector.

[0098] S3. Use the model predictive control method to solve the optimal control problem model in step S2, obtain the optimal control input vector, and adjust the train operation state according to the optimal control input vector.

[0099] like Figure 3As shown, in this embodiment, model predictive control is a control method that predicts the future evolution of the controlled object based on state-space equations and calculates the optimal control input in rolling optimization. Compared with other state feedback control methods, a major advantage of model predictive control is that it can not only predict and obtain the optimal control input based on the current state information, but also obtain the optimal control input based on its prediction of future multi-step states. Specifically, as follows... Figure 3 As shown, Figure 3 This is a schematic diagram of the model predictive control strategy. Figure 3 In this context, the Automatic Train Adjustment (ATS) subsystem within the ATS system is considered the controlled object. The objective of the Model Predictive Controller (MMC) is to calculate the adjustment amounts of the controlled object's control inputs—running time and stopping time—so that the controlled object's output, the adjusted timetable, follows the desired reference value, i.e., the planned timetable. Therefore, at each decision stage, i.e., sampling point k, the MMC needs to solve the optimization problem by iteratively predicting and solving within a prediction range of L steps, where L∈{1,2,3,…}. When based on the current time deviation state vector X... k and interference vector W k When the optimal solution to the optimization problem is obtained, this solution is used as the actual output of the controller and applied to the controlled object, i.e., the ATR system, to adjust train running time and station dwell time, so that the adjusted timetable is as close as possible to the planned timetable. Therefore, this embodiment transforms the solution to the optimal control problem model into solving a set of quadratic programming problems, and uses the optimization toolbox in MATLAB to solve the quadratic programming problems to obtain the optimal control input vector, minimizing the deviation between departure time and running interval from the planned timetable.

[0100] Specifically, step S3 includes S31-S37:

[0101] S31. Define the time deviation state vector. Control input vector in This represents the transpose of the time deviation state vector at the (k+1)th sampling point. This represents the transpose of the time deviation state vector at the (k+2)th sampling point. This represents the transpose of the time deviation state vector at the (k+L)th sampling point, where T denotes the transpose. This represents the transpose of the control input vector at the k-th sampling point. This represents the transpose of the control input vector at the (k+1)th sampling point. The transpose of the control input vector at the k+L-1 sampling point is represented; and based on the time deviation state vector, the control input vector, and the optimal control problem model in step S22, an objective function based on the optimal control problem model is constructed.

[0102] The objective function based on the optimal control problem model in step S31 is:

[0103]

[0104] Where, min U J L This represents finding the objective function J within a finite range of L steps. L The control input vectors U and X at the minimum value T Let X represent the transpose of the time deviation state vector, and U represent the time deviation state vector. T This represents the transpose of the control input vector, where U represents the control input vector. Represent the extensions of matrices P, Q, and R respectively, and E1 and E2 represent coefficient matrices of order NL×NL and NL×1, respectively. And I N Let denot be an N-order identity matrix, NL denotes a dimension of N×L, where N represents the total number of stations on the urban rail transit line, L represents the optimization step size, and T represents the transpose.

[0105] S32. At each sampling point, obtain the time deviation state vector of the train operation dynamic model in step S1, and predict the time deviation state vector within a finite range of L steps.

[0106] The time deviation state vector within the finite range of step S32 is:

[0107] X = A L X k +B L U

[0108] Where X represents the time deviation state vector within a finite range of L steps, X k Let X and A represent the time deviation state vector of the k-th sampling point. L B L Let A be the coefficient matrix within a finite range of L steps, and A L =[A,A 2 ,…,A L ] T ,

[0109] S33. Substitute the time deviation state vector within the finite range of L steps in step S32 into the objective function based on the optimal control problem model in step S31 to solve for the objective function within the finite range of L steps based on the control input vector.

[0110] In step S33, the objective function equation within the finite range of L steps based on the control input vector is:

[0111]

[0112] in, B represents the coefficient matrix within a finite range of L steps. L transpose, This represents the transpose of the coefficient matrix E1 of order NL×NL. It is a constant.

[0113] S34. Apply the constraint equations X of the optimal control problem model in step S22. k+n-1 -X k+n ≤(Hh min )I N×1 Transform it into a matrix form within a finite range of L steps, where X k+n-1 X represents the time deviation state vector of the (k+n-1)th sampling point. k+n h represents the time deviation state vector of the (k+n)th sampling point. min H represents the minimum safe operating interval of the train, and I represents the planned operating interval of the train. N×1 Let represent an N-dimensional vector with all elements being 1; and substitute the time deviation state vector within the finite range of L steps in step S32 into it to obtain the constraint equation based on the finite range of L steps.

[0114] In step S34, the constraint equation X is... k+n-1 -X k+n ≤(Hh min )I N×1 The matrix form within a finite range of L steps is as follows:

[0115] -(E1X+E2)≤(Hh min )I NL×1

[0116] Among them, I NL×1 This represents an NL-dimensional vector whose elements are all 1.

[0117] The constraint equation in step S34 based on the L-step finite range is:

[0118] -E1B L U≤(Hh min )I NL×1 +E1A L X k +E2

[0119] S35. Based on the constraint equations within the L-step finite range in step S34 and the objective function within the L-step finite range based on the control input vector in step S33, construct a quadratic programming problem.

[0120] The quadratic programming problem in step S35 is:

[0121]

[0122] Among them, I NL This represents the NL-order identity matrix.

[0123] S36. Based on the quadratic programming problem constructed in step S35, obtain the optimal control input vector for the quadratic programming problem. Substitute the optimal control input vector into the train operation dynamic model in step S1 and combine it with the disturbance vector to calculate the time deviation state vector of the sampling point.

[0124] S37. Based on the time deviation state vector of the sampling point calculated in step S36, repeat steps S31-S37 until the calculation of the last sampling point is completed, then the train operation status adjustment is completed.

[0125] This embodiment aims to verify the effectiveness of the proposed model predictive control and adjustment method under disturbance scenarios, and performs model solving and visualization based on the MATLAB platform. The demonstration is presented in four parts: the first part introduces the system parameter values ​​required for the solution; the second part introduces Case 1, comparing the application of control under large disturbances and the performance of different control methods, with the system parameters considered constant during the comparison to illustrate the benefits of the proposed model predictive control adjustment strategy in improving train punctuality and regularity of headway in urban rail transit lines; the third part introduces Case 2, studying the impact of different weights in the objective function on improving train punctuality and regularity of headway; and the fourth part introduces Case 3, studying the impact of different prediction ranges in predictive control on adjustment performance. The operating background of the urban rail transit system is selected from the morning peak period of 7:00 to 9:00. In each step of the simulation verification, this embodiment uses the quadratic programming function in the MATLAB optimization toolbox to solve a quadratic programming problem to obtain the optimal value as the optimal adjustment strategy for train operation adjustment under disturbance scenarios.

[0126] like Figure 4 As shown, the first part of this embodiment involves solving for the required system parameter values, using a single urban rail transit line with 10 stations and 6 trains as a background. The system parameters are given in Table 1, with the delay rate and upper and lower limits of control actions for each station assumed to be different constants. Furthermore, the planned operating interval H = 300s, and the minimum safe headway h... min =120s, prediction range L=3, the parameter values ​​are all given based on the actual operating conditions of each station in the reference line, as shown in Table 1 below:

[0127] Table 1 System parameters for different stations

[0128] Station number j <![CDATA[u j,min ]]> <![CDATA[u j,max ]]> <![CDATA[Delay rate a j > 1 -40 45 0.0281 2 -45 50 0.0361 3 -45 50 0.0172 4 -50 60 0.0467 5 -50 45 0.0403 6 -40 55 0.0331 7 -55 45 0.0341 8 -45 50 0.0219 9 -50 50 0.0465 10 -40 50 0.0486

[0129] This embodiment presents Case 1, which involves adjustments with and without control, and under different control strategies. In Case 1, to verify the effectiveness of the proposed model predictive control strategy, it is first compared with no control (i.e., U... k The model predictive control method (MMC) is compared with the state feedback control method under the same conditions. Different control methods have different effects on the optimization effect of the problem, so the MMC method used in this invention is compared with the state feedback control method in the simulation analysis to highlight the efficiency of the MMC method.

[0130] Specifically, let's first assume the initial conditions: there is an initial disturbance assigned a value... The first train was subjected to a 100-second external disturbance during its journey from the depot to its departure from station 1. This exceeded the maximum adjustment value for a single station, therefore, the affected train needed to run through several stations to compensate for the delay. Furthermore, without loss of generality, the weighted parameters P, Q, and R in the objective function are equal and set as an N-dimensional identity matrix, meaning that the requirements for the three optimization objectives—reducing departure time deviation, running interval deviation, and control variables—are the same. The control variables in the optimization problem are the adjustments to train running time and dwell time. Based on the system parameters and initial conditions, the model predictive control strategy is compared with no control (i.e., U... k The comparison is made with the case where the value is 0. For the initial delay of the train, the proposed model predictive control algorithm is applied to solve the optimization quadratic programming problem based on the proposed train operation dynamic model, and the corresponding optimal adjustment amount can be calculated.

[0131] like Figure 5 As shown, Figure 5 The diagram shows the changes in time deviation from train 1 to train 3 at each different station without any control measures applied. It can be seen that during operation, without train adjustments, the delay of the first train will continue to increase and propagate to subsequent trains.

[0132] like Figure 6 As shown, Figure 6 This demonstrates the variation of time deviations from train 1 to train 3 at each different station under the applied model predictive control method. Through comparison... Figure 5 At Figure 6 It can be observed that the application of model predictive control method can effectively reduce train delays and the impact of train 1 on the delays of the subsequent two trains is minimal. Moreover, after the delay is eliminated, the train will continue to run according to the planned schedule. This shows that the model predictive control method proposed in this invention can ensure the stability of the urban rail transit system.

[0133] like Figure 7 As shown, Figure 7 The model predicts how the magnitude of the optimal control action applied to the train varies at different stations under the control strategy, indicating that all control variables satisfy the control constraints. Furthermore, from... Figure 5 It can be observed that, without the application of control, the delay of train 1 will continue to increase during operation, with the corresponding values ​​of train delay exceeding 100 seconds. However, the control action for adjusting the train timetable only needs to be applied at stations 1 to 7, and the value of the control action is less than 35 seconds, which is much smaller than the train delay value. This indicates that the optimized control strategy proposed in this invention improves the efficiency of urban rail transit line recovery under delay conditions.

[0134] In this embodiment, by comparing the proposed optimization strategy based on model predictive control with another adjustment method using state feedback control under the same system parameters and initial conditions, it is found that the optimal decision of the latter is obtained through single-step optimization, while model predictive control obtains the optimal decision through rolling optimization based on future state evolution, which is a multi-step optimization.

[0135] like Figure 8 As shown, Figure 8 The variation of time deviation from train 1 to train 3 at each different station is demonstrated under the application of the state feedback control method. By comparison, it can be observed that both the state feedback control method and the model predictive control method can effectively reduce delays and ultimately reduce them to zero. However, compared to the state feedback control method, the delay propagated from train 1 to subsequent trains is smaller under the model predictive control method, meaning the initial delay has a smaller impact on subsequent trains, and the time deviation can be reduced to zero more quickly, recovering from the delay. In this embodiment, the computation time is only 1.08 seconds on a personal computer with an eight-core CPU and 16.00GB of memory, demonstrating that the model predictive control adjustment strategy proposed in this invention can guarantee real-time performance.

[0136] This embodiment introduces Case 2, which studies the impact of different weights in the objective function on improving train operation regularity. Setting different weights for each optimization objective in the objective function will produce different adjustment effects. The objective function contains three terms: the first term represents the deviation between the actual departure time and the planned departure time of the train; minimizing the first term means improving train punctuality; the second term represents the deviation in train intervals; minimizing the second term means improving the regularity of train operation on the line; and the last term represents the magnitude of the control action used to adjust train running time and station dwell time. Under ideal operating conditions without disturbance, the objective function is 0. First, assume the initial time deviation is X1 = [0, 100, 80, 75, 0, 0, 0, 0]. T .

[0137] like Figure 9 As shown, the model predicts the following train interval deviations at stations 3 to 6: Figure 9 As shown, this indicates that when disturbances occur, the trend of actual train intervals deviating from planned intervals fluctuates, but then, under control, the interval deviation gradually converges to zero, meaning the actual intervals remain at the nominal level, and the regularity of intervals is improved. The regularity of intervals in urban rail transit lines helps reduce the average waiting time for passengers.

[0138] In this embodiment, the verification is performed by comparing the changes in train interval deviation under five different weights (P, Q, and R) in the objective function. The five different weights are P = I, Q = 10I, P = I, Q = 1I, P = I, Q = I, P = I, Q = 0.5I, and P = I, Q = 0.1I, where I is an N-dimensional identity matrix and R remains unchanged.

[0139] like Figure 10 As shown, Figure 10 The deviation of the running interval of the five stations under different weights is shown.

[0140] like Figure 11 As shown, Figure 11 The deviation of the running intervals of the six stations under different weights is shown.

[0141] like Figure 12 As shown, Figure 12 The deviation of the running interval of the 7 stations under different weights is shown.

[0142] In this embodiment, from Figures 10-12 The train interval deviation can be observed to decrease as the weight Q of the train interval deviation increases, resulting in a smaller overall deviation at different stages and a more stable and rapid reduction to zero. With P = I and Q = 10I, the fluctuation of the train interval deviation is minimal, decreasing most evenly and converging to zero, demonstrating better train regularity and resulting in less variation in average passenger waiting time. Furthermore, an excessively large P at any of the three stations leads to a larger overall interval deviation and greater fluctuations. Therefore, in actual operation, if urban rail transit lines operate according to the published train schedule, the values ​​of the elements in P are generally greater than the values ​​of the elements in Q and R to recover from delays as quickly as possible. On the other hand, if trains are running during peak hours, for high-density urban rail transit lines with huge passenger volumes, the value of P can be zero to maintain a regular train departure interval as much as possible and avoid a large number of passengers being stranded on the platform waiting to board. Therefore, according to... Figures 10-12 The results require selecting a suitable set of objective function weights based on the actual conditions of urban rail transit lines to ensure a balance between train punctuality and regularity of train services.

[0143] This embodiment introduces Case 3, which analyzes the impact of different prediction ranges L on departure time deviation and the speed of recovery from delays under the model predictive control method. In this embodiment, the simulation results consider three prediction range values: L=1, L=2, and L=3. It is assumed that the train is subjected to the following disturbances during operation:

[0144] like Figure 13 As shown, Figure 13 The departure time deviations of trains 1 to 3 under different prediction ranges L.

[0145] like Figure 14 As shown, Figure 14 The values ​​are the control actions for trains 1 to 3.

[0146] In this embodiment, from Figures 13-14 It can be observed that all three prediction ranges can eliminate train departure time deviations and ensure the normal operation of urban rail transit lines. However, these three prediction ranges produce different adjustment effects, and it can be found that increasing L has a better adjustment effect on reducing delays. Compared with L=1 and L=2, the time deviations of trains 2 and 3 at each station are significantly smaller under L=3, indicating that using a model with a larger prediction range for predictive control to adjust for time deviations has less impact on subsequent trains and can recover from delays more quickly.

[0147] Table 2 in this embodiment shows the computation time and total objective function value required to solve the model under different prediction ranges L in the MATLAB runtime environment. Table 2 is shown below:

[0148] Table 2 Comparison of computation time and objective function value under different prediction ranges.

[0149] Prediction range L Calculation time (s) objective function value L＝1 0.1094 5.5345×104 L＝2 1.2500 2.7842×104 L＝3 1.3125 1.1805×104 L＝4 1.4063 1.2971×104 L＝5 1.5313 3.7755×104

[0150] Table 2 shows that the computation time for solving the model increases with increasing L, but remains within 2 seconds, meeting the requirements for real-time adjustment. The overall objective function value decreases rapidly from L=1 to L=3, reaching its lowest value at L=3, and then increases slightly with further increases in L. However, considering the applicability of the problem, a larger prediction range L is not always better. Therefore, an appropriate prediction range should be selected to handle the adjustment problem, taking into account the scale of the adjustment problem (i.e., the number of variables in the model) and the upper and lower limits of the actual control actions that can be taken, to avoid wasting resources.

[0151] Specific embodiments have been used to illustrate the principles and implementation methods of this invention. The descriptions of the embodiments above are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

[0152] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A train operation adjustment method based on model predictive control under a perturbed scenario, characterized in that, The method comprises the following steps: S1, according to the planned operation diagram, adjusting the train operation strategy based on the disturbance scene, and constructing a train operation dynamic model; S2, taking the punctuality of the train and the regularity of the operation interval as the objective function, taking the train operation interval and the control quantity as the constraint condition, and according to the train operation dynamic model in step S1, constructing an optimal control problem model based on minimizing the time deviation of the actual train operation from the planned operation diagram; S3, solving the optimal control problem model in step S2 by using the model predictive control method to obtain an optimal control input vector, and adjusting the train operation state according to the optimal control input vector, specifically: S31. Define the time deviation state vector. Control input vector ,in Indicates the first Transpose of the time deviation state vector of each sampling point Indicates the first Transpose of the time deviation state vector of each sampling point Indicates the first Transpose of the time deviation state vector of each sampling point Indicates transpose. Indicates the first The transpose of the control input vector at each sampling point Indicates the first The transpose of the control input vector at each sampling point Indicates the first Transpose of the control input vector at each sampling point; And based on the time deviation state vector, the control input vector and the optimal control problem model in step S22, a target function based on the optimal control problem model is constructed; S32, at each sampling point, the time deviation state vector of the train operation dynamic model in step S1 is obtained, and step S31, the time deviation state vector within a limited range is predicted; S33, bringing the time deviation state vector in step S32 Step S31, bringing the time deviation state vector in step S32 Step S31, bringing the time deviation state vector in step S32 S34. Apply the constraint equations of the optimal control problem model in step S22. Convert to The matrix form within a finite range, where, Indicates the first The time deviation state vector of each sampling point Indicates the first The time deviation state vector of each sampling point This indicates the minimum safe operating interval for trains. Indicates the planned interval between train services. Indicates that all elements are 1 dimensional vector; and in step S32 Substituting the time deviation state vector within a finite range into it, we obtain the result based on Constrained equations within a finite range; S35. Solving the quadratic programming problem based on the constraints in the limited range and the objective function in the limited range in step S34. S33. Constructing a quadratic programming problem based on the control input vector in step S32. S34. Solving the quadratic programming problem based on the constraints in the limited range and the objective function in the limited range in step S33. S36, according to the quadratic programming problem constructed in step S35, obtaining the optimal control input vector of the quadratic programming problem, and bringing the optimal control input vector into the train operation dynamic model in step S1 and combining the interference vector to calculate the time deviation state vector of the sampling point; S37, according to the time deviation state vector of the sampling point calculated in step S36, repeating steps S31-S37 until the calculation of the last sampling point is completed, and then the train operation state adjustment is completed.

2. The train operation adjustment method based on model predictive control in a perturbation scenario according to claim 1, characterized in that, Step S1 specifically comprises: S11, calculating the planned operation interval of the train according to the planned departure time of the train at the station; S12, establishing the planned departure time relationship of each train at each station according to the planned operation interval of the train in step S11; S13, calculating the actual departure time of the train at the next station according to the actual departure time of the train at the previous station; S14, calculating the actual running time of the train from the station to the station according to the control quantity of the running time of the train from the station to the station and the disturbance of the running time of the train from the station to the station; S15, calculating the actual stopping time of the train at the station according to the assumption that the number of passengers at a station is proportional to the time interval between two consecutive trains departing from the station; S16, obtaining the dynamic relationship of the departure time of two consecutive stations based on the actual running time of the train from the station to the station in step S14, the actual stopping time of the train at the station and the actual departure time of the train at the station in step S13; S17, constructing the departure time deviation of the train at the station compared with the planned operation diagram, and based on the planned departure time relationship of each train at each station in step S12, the dynamic relationship of the departure time of two consecutive stations in step S16 and the departure time deviation of the train at the station compared with the planned operation diagram, constructing a time deviation dynamic model; S18, constructing a time deviation state vector, a control input vector and an interference vector, and based on the time deviation dynamic model in step S17, constructing a train operation dynamic model.

3. The train operation adjustment method based on model predictive control in a perturbation scenario according to claim 2, characterized in that, The calculation formula of the planned operation interval of the train in step S11 is: wherein denotes the planned running interval of the train, denotes the planned departure time of the train at the station, denotes the planned departure time of the train at the station, denotes the planned departure time of the train at the station; The planned departure time relationship of each train at each station in step S12 is: wherein, denotes the planned running time of the train from the station to the station , denotes the minimum stop time of the train at the station , denotes the additional stop time at the station in relation to the planned running interval of the train . The calculation formula of the actual departure time of the train at the next station in step S13 is: wherein, denotes a train at a station the actual departure time, denotes a train at a station the actual departure time, denotes a train from a station to a station the actual running time, denotes a train at a station the actual stop time; The calculation formula of the actual running time of the train from the station to the station in step S14 is: wherein denotes a train leaving a station arriving at a station planned running time, denotes a train running time at a station arriving at a station control quantity for the running time of a train denotes a train running time at a station arriving at a station disturbance of the running time of a train; The calculation formula of the actual stopping time of the train at the station in step S15 is: wherein representing a train at a station , an actual departure time, representing a train at a station , a control quantity for dwell time, representing a train at a station , a disturbance for dwell time; The dynamic relationship of the departure times of two consecutive stations obtained in step S16 is: wherein denotes the sum of control quantities of the train , denotes the total disturbance to which the train is subjected; The departure time deviation of the train at the station compared with the planned operation diagram in step S17 is: wherein, indicates a train at a station deviation from the scheduled departure time; The time deviation dynamic model in step S17 is: wherein, indicates a train at a station deviation from the scheduled departure time; The time deviation state vector in step S18 is: wherein, denotes a sampling point, denotes the total number of stations of the urban rail transit line, denotes a time deviation state vector of the sampling point, denotes a train time deviation at a station, denotes a train time deviation at a station, denotes a train time deviation at a station, denotes a train time deviation at a station, denotes a train time deviation at a station, denotes a transpose; The control input vector in step S18 is: wherein, denotes the control input vector of the th sampling point, denotes the control input of the train at the station , denotes the control input of the train at the station , denotes the control input of the train at the station , The disturbance vector in step S18 is: wherein, denotes the interference vector of the th sampling point, denotes the interference of the train at the station, denotes the interference of the train at the station, denotes the interference of the train at the station, denotes the interference of the train at the station, denotes the interference of the train The train operation dynamic model in step S18 is: wherein, denotes the time offset state vector of the denotes the coefficient matrix of order​​​ 4. The train operation adjustment method based on model predictive control in a perturbation scenario according to claim 1, characterized in that, Step S2 specifically includes: S21, constructing an objective function based on train punctuality and running interval regularity, and constructing running interval constraints and control quantity constraints; S22, constructing an optimal control problem model according to the train operation dynamic model in step S1 and the objective function based on train punctuality and running interval regularity, the running interval time constraint and the control quantity constraint in step S21.

5. The train operation adjustment method based on model predictive control in a perturbation scenario according to claim 4, characterized in that, The objective function based on train punctuality and running interval regularity in step S21 is: wherein, denotes the disturbance value based on the th sampling point and the actual departure time of the train, denotes the control input vector which minimizes the objective function , denotes the transpose of the time deviation state vector of the th sampling point, denotes the time deviation state vector of the th sampling point, denotes the time deviation state vector of the th sampling point, denotes the transpose of the control input vector of the th sampling point, denotes the control input vector of the th sampling point, , , denotes an N-dimensional positive definite constant matrix, representing the weight factors of the three optimization objectives, respectively, denotes the transpose; The running interval constraint in step S21 is: wherein, denotes a train at a station deviation from the scheduled departure time, denotes a train at a station deviation from the scheduled departure time, denotes a minimum safe running interval of a train, denotes a scheduled running interval of a train; The control quantity constraint in step S21 is: in, , This indicates the upper and lower limits for adjusting the operating time of different sections. , Indicates different stations Upper and lower limits for adjusting stop time. Indicates train At the station Arrive at the station The control quantity of runtime, Indicates train At the station The amount of time to control the stop time; The optimal control problem model in step S22 is: wherein denotes the control input vector for the prediction control problem model at the th sampling point, denotes the transpose of the time deviation state vector at the th sampling point, denotes the time deviation state vector at the th sampling point, denotes the time deviation state vector at the th sampling point, denotes the transpose of the control input vector at the th sampling point, denotes the control input vector at the th sampling point, denotes the disturbance vector at the th sampling point, denotes an dimensional vector with all elements being 1, , denotes the maximum and minimum of an dimensional control input vector , denotes the optimization step size.

6. The train operation adjustment method based on model predictive control in a perturbation scenario according to claim 4, characterized in that, The objective function based on the optimal control problem model in step S31 is: wherein denotes the control input vector that minimizes the objective function over a finite range of control input vectors , denotes the transpose of the time-derivative state vector, denotes the time-derivative state vector, denotes the transpose of the control input vector, denotes the control input vector, , , denote the matrices , , the extension of , denote the , coefficient matrices of order denote the matrices of dimension , and denotes the total number of stations of the urban rail transit line, denotes the optimization step size, denotes the transpose; The time deviation state vector within the L-step finite range in step S32 is: wherein denotes a time bias state vector, denotes a time bias state vector for the first sampling point, , denotes a coefficient matrix for the k steps. The step S33 is based on the control input vector The step S33 is based on the control input vector The step S33 is based on the control input vector wherein denotes the transpose of the coefficient matrix of L steps, denotes the transpose of the coefficient matrix of order denotes a constant; In step S34, the constraint equations are... The matrix form within a finite range of L steps is as follows: wherein, represents a 1-by-1 matrix vector; The constraint equation based on the L-step finite range in step S34 is: The quadratic programming problem in step S35 is: wherein denotes the identity matrix of order n.

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