A train multi-section energy-saving operation curve planning method based on grouping backpack

Abstract

The present invention provides a multi-section energy-saving operation curve planning method for trains based on grouped backpacks, belonging to the technical field of train operation energy-saving optimization. The method comprises the following steps: first, obtaining the optimal operating Pareto frontier between stations, obtaining the "time-energy consumption" relationship from an offline database, further optimizing and adjusting the operation time between stations, and then generating energy-saving operation curves for each section based on a single-section energy-saving driving algorithm. This method minimizes the total energy consumption of the entire train line and achieves the goal of energy-saving driving for the entire line. The present invention solves the problems of high online computing time complexity and inability to guarantee calculation accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of train operation energy-saving optimization, and in particular relates to a train multi-section energy-saving operation curve planning method based on grouping backpacks. Background Art

[0002] The operation process of a train between stations includes four control conditions: traction, cruising, coasting and braking. The ordered set of control conditions and their corresponding distances applied when the train departs from the platform and stops at the next station is called the train driving operation strategy. Each set of operation strategies corresponds to a certain operating time, traction energy consumption and regenerative braking energy consumption. When the utilization rate of regenerative energy is known, for a specified operating time between stations, there is at least one set of operation strategies that minimizes the total energy consumption of the train between stations. This set of operation strategies is the optimal operation strategy under the current operating time conditions, and is also a non-dominated solution in the entire feasible domain, namely the Pareto solution. The set of all optimal operation strategies is the Pareto optimal solution set, and its corresponding "energy consumption-time" Pareto frontier is as follows: Figure 1 The red curve in the middle shows this. Taking any two Pareto solutions on the Pareto frontier, the corresponding optimal train trajectory is shown in the blue curve.

[0003] Due to the different line conditions between stations, the corresponding optimal control Pareto frontiers are different, such as Figure 1 As shown in , the Pareto fronts between the two stations are represented by red and blue respectively. Figure 2 As can be seen, the energy-saving effects of allocating additional running time between two stations, given the same running time, vary significantly. For the same station, the energy-saving effects of adding additional running time based on different running times also vary significantly. The total running time of a train on the entire line is fixed, and the running time allocation strategy between stations determines the total traction energy consumption of the train on the entire line.

[0004] Disadvantages of existing technology:

[0005] 1) Treating the entire line as a large interval for interpolation calculations results in high time complexity and cannot meet the requirements of online replanning;

[0006] 2) The effect of regenerative braking energy was not considered during the Pareto curve fitting process, which may lead to excessive fitting complexity or inaccurate results.

[0007] 3) The current method of using priority queues to process Pareto curves has higher time and space complexity.

[0008] That is, there are technical problems such as the time complexity is too high to be used for online planning; the discrete accuracy is insufficient; and the time complexity is too high. Summary of the Invention

[0009] In response to the above-mentioned deficiencies in the prior art, the present invention provides a train multi-section energy-saving operation curve planning method based on grouped backpacks, which solves the problems of high online computing time complexity and inability to guarantee computing accuracy.

[0010] In order to achieve the above objectives, the technical solution adopted by the present invention is: a train multi-section energy-saving operation curve planning method based on grouping backpacks, comprising the following steps:

[0011] S1. Generate the maximum capacity operation curve based on the most energy-efficient operation strategy of the bicycle, and build an offline database through the discrete Pareto curve;

[0012] S2, initialization and parameter definition;

[0013] S3. Perform an outer loop process, traversing from the first interval to the last interval. Given the total surplus time and the selected curve of the previous interval, calculate the total remaining time of the subsequent interval for the curve number traversal of the interval. Each interval is considered as a group, and the surplus time allocated to each interval is considered as an item.

[0014] S4. Perform a middle-level loop process, initialize the curve index k to 0, and traverse from the first curve to the last curve in the interval to obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent intervals. The energy consumption reduction of each curve relative to the maximum capacity of the interval is considered as its value, and it is required that a curve must be selected in each interval to achieve the maximum filling of the backpack;

[0015] S5. Perform inner loop processing, traverse the surplus time in reverse order, and traverse from the total surplus time W of the entire line in descending order to find the curve combination selected in each interval under different total surplus times. In this case, the problem of finding the surplus time is converted into a grouping knapsack problem;

[0016] S6. Calculate the energy consumption reduction newEnergy brought about by selecting the new curve number in the current interval. In response to the energy consumption reduction newEnergy being greater than the maximum energy consumption reduction dp[i][j], update the maximum energy consumption reduction dp[i][j] to be equal to the energy consumption reduction newEnergy, and record the curve number index obtained by the selected outer loop, middle loop, and inner loop processing, where dp[i][j] represents the maximum energy consumption reduction in the first i intervals under the j surplus time;

[0017] S7, determine whether the traversal of the outer layer, middle layer and inner layer is completed, if so, go to step S8, otherwise update the traversal variable and return to step S3;

[0018] S8. Obtain the running time of each interval based on the maximum capacity running time of the single interval curve recorded by the Pareto curve in step S1 and the selected curve number index recorded in step S6;

[0019] S9. Based on the operating time of each section, the optimal driving strategy for a single section is used to generate the optimal operating conditions for each section, and the planning of the energy-saving operating curve for multiple sections of the train is completed.

[0020] The beneficial effects of the present invention are as follows: the present invention is based on the most energy-saving driving strategy for a single vehicle, stores the Pareto curve of the train in each section as an offline database, and uses the energy consumption of the maximum capacity operation curve of each section as a benchmark. The surplus time exceeding the maximum capacity operation time is reasonably allocated to each section. Each section is regarded as a group, each allocated surplus time is regarded as an item, and the energy consumption reduction of each curve relative to the maximum capacity operation of the section is regarded as its value. It is required to select a curve in each section to achieve the maximum filling of the backpack and ultimately achieve the goal of maximizing energy conservation quantification, that is, while allocating all surplus time, significantly reducing energy consumption, and after calculating the timetable, the optimal energy-saving operating condition sequence of each section is inversely calculated according to the operation strategy calculation method under the given operating time, thereby achieving the goal of minimizing total energy consumption under the time allocation of the entire line. That is, on the basis of the existing Pareto curve of a single vehicle in a single section, the present invention fully considers the influence of regenerative braking energy, thereby achieving the goal of minimizing total energy consumption under the time allocation of the entire line.

[0021] Furthermore, the step S1 includes the following steps:

[0022] S101. Generate maximum capacity operating curves for different ranges and vehicle weights based on the most energy-efficient operating strategy for the single vehicle;

[0023] S102: Obtain the maximum operating time T for interval i based on the maximum capacity operating curves for different intervals and vehicle weights. i,max and maximum energy consumption E i,max ;

[0024] S103, calculate the Pareto curve under a given surplus time, discretize the Pareto curve with a certain step size, and record the running time T of the k-th curve i,k and energy consumption E i,k ;

[0025] S104. Based on the results of step S102 and step S103, an offline database of Pareto curves for each section of the train is constructed.

[0026] The beneficial effect of the above further solution is that the present invention can significantly improve the accuracy and efficiency of online calculations by constructing a "time-energy consumption" offline database based on the most energy-saving driving strategy. By utilizing the existing database and performing a large amount of calculations in the offline stage, more accurate calculation efficiency can be obtained.

[0027] Furthermore, the step S2 is specifically as follows:

[0028] Define dynamic programming array dp;

[0029] Define the meaning and size of dp[i][j] as (m+1)×(W+1); where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time, m represents the number of intervals, and W represents the total surplus time of the entire line, that is, the excess time of the operation plan relative to the maximum capacity operation time;

[0030] Initialize all elements to negative infinity;

[0031] Define CurveChoices[i][j] to store the curve number index combination selected in the first i intervals and at the jth surplus time;

[0032] The initial state dp[0][0]=0 is set, where dp[0][0]=0 means that the maximum energy consumption reduction of the entire line is 0 when the surplus time is 0.

[0033] Furthermore, the step S3 is specifically as follows:

[0034] Perform outer loop processing, initialize the interval number to i=1, and traverse from i=1 to i=m, where m represents the number of intervals;

[0035] According to the traversal results, given the total surplus time and the selected curve in the previous interval, the total remaining time of the subsequent interval is calculated, and the selected curve number that can maximize the reduction in total energy consumption is selected. Each time step S3 is returned, the value of interval number i is set to i+1. In response to interval number i being greater than m, step S8 is entered.

[0036] Furthermore, the step S4 is specifically as follows:

[0037] Perform middle-level loop processing, initialize the curve index k to 0, from k = 0 to k = n i Traverse, where n i represents the total number of curves in the i-th interval;

[0038] According to the traversal result, the selected curve number that maximizes the total energy consumption reduction in the interval is obtained given the total surplus time of the subsequent interval. Each time step S4 is returned, the value of the curve index number k is set to k+1.

[0039] Further, the specific steps of step S5 are as follows:

[0040] Perform inner loop processing. Initialize the surplus time j = W, and traverse from the surplus time j = W to j = Curve[i][k].ΔTime. Each time step S5 is returned, set the value of the surplus time j to j - 1. If the surplus time j < Curve[i][k].ΔTime, return to step S4, where j represents the surplus time, W represents the total surplus time of the entire line, that is, the time that the operation plan time is more than the maximum capacity operation time, Curve[i][k] represents the k-th curve in the i-th section, which is a structure including time and energy consumption, and ΔTime represents the surplus time that this curve is more than the maximum capacity operation curve of this section;

[0041] According to the traversal results, find the curve combinations selected for each section under different total surplus times, where the problem of finding the surplus time is transformed into a grouped knapsack problem.

[0042] Further, the expression of the objective function for transforming the problem of finding the surplus time into a grouped knapsack problem is as follows:

[0043]

[0044] where Z represents the objective function, m represents the number of sections, n i represents the total number of curves in the i-th section, E i_max represents the operation energy consumption under the maximum capacity in the i-th section, E i,k represents the energy consumption when the k-th curve is adopted in the i-th section, x i,k is a decision variable. When the k-th curve is adopted in the i-th section, x i,k = 1, otherwise, x i,k = 0;

[0045] The constraint conditions for transforming the problem of finding the surplus time into a grouped knapsack problem are as follows:

[0046]

[0047]

[0048] where T i,k represents the energy consumption when the k-th curve is adopted in the i-th section, T i_max represents the operation time under the maximum capacity in the i-th section, T total represents the total surplus time of the entire line.

[0049] The beneficial effect of the above further solution is that the present invention performs initialization and discrete processing of the offline database through the above operations.

[0050] Furthermore, the expression of energy consumption reduction newEngergy brought about by selecting a new curve number in the current interval is as follows:

[0051] newEnergy=dp[i-1][j-Curve[i][k].ΔTime]+Curve[i][k].ΔEnergy

[0052] Curve[i][k].ΔTime=T i,k -T i_max

[0053] Curve[i][k].ΔEnergy=E i,k -E i_max

[0054] Where Curve[i][k] represents the information of the kth curve in the i-th interval, ΔTime represents the extra time of the curve relative to the maximum capacity curve in the interval, ΔEnergy represents the energy consumption reduction of the curve relative to the maximum capacity curve in the interval, Curve[i][k].ΔTime represents the time increase of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, Curve[i][k].ΔEnergy represents the energy consumption reduction of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, T i,k represents the energy consumption under the kth curve in the i-th interval, T i_max represents the running time at the maximum capacity in the i-th interval, E i_max represents the operating energy consumption at the maximum capacity in the i-th interval, E i,k Represents the energy consumption under the k-th curve in the i-th interval.

[0055] The beneficial effect of the above further solution is that, during each traversal, the present invention performs a numerical comparison to update the selected curve for the interval that reaches the maximum value of the objective function in the remaining time, given the known curve information of the previous interval. Because only one numerical comparison step is required, the efficiency of online calculation is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the Pareto frontier for optimal train operation in background technology.

[0057] Figure 2 Schematic diagram of energy saving effect under different operating time allocations in the background technology.

[0058] Figure 3 Schematic diagram of the most energy-efficient control strategy for a bicycle.

[0059] Figure 4 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0060] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0061] Example

[0062] Before describing the present invention, the theoretical results involved in the present invention are first described.

[0063] (1) Optimal energy-saving strategy for a single train and a single section:

[0064] The optimal control strategy for a single train is to reasonably insert coasting conditions on the basis of the maximum capacity curve to ensure that the interval operation time is on time and achieve energy saving. The maximum capacity curve of a single train includes maximum traction, cruising, and maximum braking. The operating energy consumption at this time is the highest, and there is also surplus time. By finding the coasting starting point on the maximum capacity outer envelope curve, a four-stage operation strategy of "maximum traction-cruising-coiling-maximum braking" or "maximum traction-coiling-maximum braking" operating condition sequence is formed. By finding a curve that meets the operation time (such as Figure 3 The optimal operating sequence under a given operating time can be found by calculating the optimal curve of a single interval under a given surplus time, and the relationship between “time-energy consumption” can be obtained to form Figure 2 The Pareto curve shown in Figure 3 is used to establish an offline database.

[0065] (2) Convert the problem of finding surplus time into a grouping knapsack problem:

[0066] The remaining time of the entire line is regarded as the backpack capacity, the remaining time allocated to each interval is regarded as the item, and the energy consumption reduction of this curve relative to the maximum capacity curve of the interval is regarded as the value. The problem is transformed into how to reasonably allocate the remaining time to each interval to maximize the reduction in energy consumption. The objective function is modified accordingly:

[0067]

[0068] Where Z represents the objective function, m represents the number of intervals, and n i represents the total number of curves in the i-th interval, E i_maxrepresents the operating energy consumption at the maximum capacity in the i-th interval, E i,k represents the energy consumption (equivalent to the value of the item) under the kth curve in the i-th interval, x i,k is a decision variable. When the kth curve is used in the i-th interval, x i,k =1, otherwise, x i,k =0.

[0069] In this embodiment, the interval is the group, which is called grouping in the grouped knapsack problem. In this problem, the interval is the group.

[0070] At the same time, the following constraints must be met:

[0071] 1. Only one curve can be selected for each interval:

[0072]

[0073] Among them, i represents the interval, m represents a total of m intervals along the entire line, and the maximum index number is m.

[0074] 2. The constraints on the total surplus time of the entire line are:

[0075]

[0076]

[0077] Among them, T i,k represents the energy consumption (equivalent to the weight of the item) under the k-th curve in the i-th group, T i_max represents the running time under the maximum capacity in the i-th group, T total Indicates the total surplus time of the entire line.

[0078] The solution can be obtained quickly by using two-dimensional dynamic programming.

[0079] (3) Define the data structure:

[0080] In this invention, the following data structures are defined to support the implementation of the algorithm:

[0081] Curve structure: ΔTime: represents the extra time of the curve compared to the maximum capacity operating curve in this interval, in seconds; ΔEnergy: represents the energy consumption reduction of the curve compared to the maximum capacity operating curve in this interval, in kilowatt-hours (kWh).

[0082] (4) Create a dynamic programming array:

[0083] Define dp to represent the maximum energy consumption reduction in the first i intervals under j surplus time, which is (m+1)×(W+1).

[0084] Initialize all elements to negative infinity (indicating an impossible state), that is: dp[i][j] = -∞, dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time.

[0085] Define CurveChoices[i][j]: used to store the combination of the curve index selected in the first i intervals and at the jth rich time.

[0086] Set the initial state: dp[0][0]=0, which means that the maximum energy consumption reduction of the entire line is 0 when the surplus time is 0.

[0087] (5) Three-layer loop traversal to obtain the optimal solution:

[0088] Outer loop: The independent variable is the interval number, and it traverses from the first interval to the last interval. The goal is to calculate the total remaining time of the subsequent interval given the total surplus time and the selected curve of the previous interval, so as to traverse the curve number of the interval.

[0089] Second-level loop: The independent variable is the selected curve number, and it traverses from the first curve to the last curve in the interval. The goal is to obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent interval.

[0090] Inner loop: The independent variable is the surplus time, and the traversal is done from the maximum surplus time in descending order, from the back to the front. The goal is to obtain the curve number selected for each interval under different total surplus times, while ensuring that only one curve can be selected for each interval, and no curve will be selected repeatedly.

[0091] The present invention illustrates the above three-layer loop as follows: the outer loop changes to variable i; the middle loop changes to variable k; and the inner loop changes to variable j. Taking variables ikj as an example, in the loop, variable i is first fixed, then variable k is fixed, and variable j is looped through once. After variable j is looped through, variable k is incremented, then variable k is fixed again, and variable j is looped through once again. After variable k is looped through, variable i is incremented, and variables k and j are reset, and the above process is repeated.

[0092] (6) Update the dynamic programming array:

[0093] When traversing the curve value in reverse, calculate the new value:

[0094] newEnergy=dp[i-1][j-Curve[i][k].ΔTime]+Curve[i][k].ΔEnergy(5)

[0095] Among them, newEnergy represents the energy consumption reduction brought about by selecting a new curve number in the current interval, Curve[i][k] represents the information of the kth curve in the i-th interval, ΔTime represents the extra time of this curve relative to the maximum capacity operating curve in this interval, and ΔEnergy represents the energy consumption reduction of this curve relative to the maximum capacity operating curve in this interval.

[0096] That is, traversing the previous interval reserves surplus time for this curve number, and in this interval, this curve is selected to reduce energy consumption.

[0097] If newEnergy>dp[i][j], update: dp[i][j]=newEnergy.

[0098] Because dp[i][j] is initialized to -∞, it is guaranteed that the selected curve will be updated at least once in each interval, ensuring that each interval is allocated a reasonable running time.

[0099] At the same time, the index of the curve number selected in the interval is recorded: CurveChoices[i][j]=k, where CurveChoices[i][j] represents the curve number selected in the i-th interval when the surplus time is j.

[0100] (7) Curve generation:

[0101] According to the maximum capacity running time of a single interval curve recorded by the Pareto curve and the recorded curve index number CurveChoices[i][W], the running time of each interval is obtained, and the working condition sequence of each interval is generated online according to the most energy-saving driving strategy of a single vehicle.

[0102] Based on the above theoretical analysis, in order to achieve the purpose of the present invention, the present invention involves taking the most energy-efficient driving strategy for a single section into consideration, establishing an offline database based on the Pareto curve of "time-energy consumption" under this strategy, and using the grouped knapsack method to allocate the operating time of the entire line, thereby optimizing the schedule. Using the optimal schedule planned online, the most energy-efficient driving strategy is adopted to generate the operating condition sequence for each section, thereby achieving the purpose of energy-efficient driving for the entire line. Figure 4 As shown, the present invention provides a train multi-section energy-saving operation curve planning method based on grouping backpacks, and its implementation method is as follows:

[0103] S1. Build an offline database, store the Pareto curves of each section of the train, perform discretization processing, and calculate the maximum capacity operation curve of a single section. The implementation method is as follows:

[0104] S102: Obtain the maximum operating time T for interval i based on the maximum capacity operating curves for different intervals and vehicle weights. i,max and maximum energy consumption Ei,max ;

[0105] S103, calculate the Pareto curve under a given surplus time, discretize the Pareto curve with a certain step size, and record the running time T of the k-th curve i,k and energy consumption E i,k ;

[0106] S104. Based on the results of step S102 and step S103, an offline database of Pareto curves for each section of the train is constructed.

[0107] In this embodiment, the maximum capacity curve is calculated in step S101, its energy consumption and time are obtained in step S102, and the energy consumption at other times is calculated in step S103 to form a Pareto curve.

[0108] In this embodiment, an offline database is established, and the maximum capacity operation curves under different intervals and vehicle weights are generated according to the most energy-efficient operation strategy of a single vehicle, and the maximum operation time T of interval i is obtained. i,max and energy consumption E i,max , calculate the Pareto curve under a given surplus time, discretize it with a certain step size, and record the running time T of the kth curve i,k and energy consumption E i,k , the accuracy of the calculation results can be improved through a large number of discretizations.

[0109] S2. Initialize and define parameters, specifically:

[0110] Define the dp array;

[0111] The meaning and size of dp[i][j] are defined as (m+1)×(W+1); where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under the j surplus time, m represents the number of intervals, and W represents the total surplus time of the entire line, that is, the excess time of the operation plan time relative to the maximum capacity operation time.

[0112] Initialize all elements to negative infinity;

[0113] Define CurveChoices[i][j] to store the curve number index combination selected in the first i intervals and at the jth surplus time;

[0114] The initial state dp[0][0]=0 is set, where dp[0][0]=0 means that the maximum energy consumption reduction of the entire line is 0 when the surplus time is 0.

[0115] S3. Perform outer loop processing, traversing from the first interval to the last interval. Given the total surplus time and the selected curve of the previous interval, calculate the total remaining time of the subsequent interval for traversing the curve number of the interval. Specifically:

[0116] Perform outer loop processing, initialize the interval number to i=1, and traverse from i=1 to i=m, where m represents the number of intervals;

[0117] According to the traversal results, given the total surplus time and the selected curve in the previous interval, the total remaining time of the subsequent interval is calculated, and the selected curve number that can maximize the reduction in total energy consumption is selected. Each time step S3 is returned, the value of interval number i is set to i+1. In response to interval number i being greater than m, step S8 is entered.

[0118] In this embodiment, the outer loop iterates through the interval numbers. The goal is to calculate the total remaining time for the subsequent interval, given the total remaining time and the selected curve of the previous interval, to use for the curve number traversal of that interval. Iterates from i = 1 to i = m, initializing the interval number to i = 1. Each time it returns to S3, i = i + 1. If i > m, it jumps to step S7.

[0119] S4. Perform middle-level loop processing, initialize the curve index number k to 0, and traverse from the first curve to the last curve in the interval to obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent intervals. Specifically, it is:

[0120] Perform middle-level loop processing, initialize the curve index k to 0, from k = 0 to k = n i Traverse, where n i represents the total number of curves in the i-th interval;

[0121] According to the traversal result, the selected curve number that maximizes the total energy consumption reduction in the interval is obtained given the total surplus time of the subsequent interval. Each time step S4 is returned, the value of the curve index number k is set to k+1.

[0122] In this embodiment, in the middle loop, the index numbers of each interval are traversed, and the goal is to obtain the selected curve number that maximizes the total energy consumption reduction in the given total surplus time of the subsequent interval. i Traverse, initialize the curve index number to k = 0, each time return to S4 k = k + 1, if k>n i , return to step S3.

[0123] S5. Perform inner loop processing to traverse the surplus time in reverse order, starting from the total surplus time W of the whole line and traversing in decreasing order to find the curve combinations selected for each interval under different total surplus times. Here, the problem of finding the surplus time is transformed into a grouped knapsack problem, which is specifically as follows:

[0124] Perform inner loop processing. Initialize the surplus time j = W. Traverse from the surplus time j = W to j = Curve[i][k].ΔTime. Each time when returning to step S5, let the value of the surplus time j be j - 1. If the surplus time j < Curve[i][k].ΔTime, then return to step S4. Here, j represents the surplus time, W represents the total surplus time of the whole line, that is, the time by which the operation plan time exceeds the maximum capacity operation time. Curve[i][k] represents the k-th curve in the i-th interval, which is a structure including time and energy consumption. ΔTime represents the surplus time by which this curve exceeds the maximum capacity operation curve of this interval;

[0125] According to the traversal results, find the curve combinations selected for each interval under different total surplus times. Here, the problem of finding the surplus time is transformed into a grouped knapsack problem.

[0126] In this embodiment, in the inner loop, traverse and process from the surplus time j = W to j = Curve[i][k].ΔTime. The goal is to obtain the curve numbers selected for each interval under different total surplus times, and at the same time ensure that each interval can select at most one curve and there will be no repeated selection of curves. Initialize j = W. Each time when returning to step S5, j = j - 1. If the surplus time j < Curve[i][k].ΔTime, return to step S4.

[0127] In this embodiment, the expression of the objective function of transforming the problem of finding the surplus time into a grouped knapsack problem is the above formula (1).

[0128] In this embodiment, the constraint conditions for transforming the problem of finding the surplus time into a grouped knapsack problem are the above formula (3) and formula (4).

[0129] S6. Calculate the energy consumption reduction amount newEnergy brought by selecting a new curve number for the current interval. In response to the energy consumption reduction amount newEnergy being greater than the maximum energy consumption reduction amount dp[i][j], update the maximum energy consumption reduction amount dp[i][j] to be equal to the energy consumption reduction amount newEnergy, and record the curve number indexes obtained from the processed outer loop, middle loop, and inner loop. Here, dp[i][j] represents the maximum energy consumption reduction amount for the first i intervals under the surplus time j;

[0130] S7. Determine whether the outer, middle, and inner loops have been traversed completely. If so, enter step S8. Otherwise, update the traversal variables and return to step S3;

[0131] In this embodiment, the expression for calculating the energy consumption reduction amount newEnergy brought about by selecting a new curve number in the current interval is the above formula (5).

[0132] In this embodiment, traversing the previous curve reserves the surplus time allocated to this interval, and the energy consumption reduction of this curve is selected in this interval. Only numerical calculations are performed here, and the time complexity is O(i*j*k), which greatly improves the calculation efficiency. Among them, ijk represents the three variables of interval, surplus time, and curve number.

[0133] In this embodiment, dp[i][j] is checked and updated: if dp[i][j]=newEnergy, the index of the selected curve number is recorded: CurveChoices[i][j]=k.

[0134] S8. Obtain the running time of each interval based on the maximum capacity running time of the single interval curve recorded by the Pareto curve in step S1 and the selected curve number index recorded in step S6;

[0135] In this embodiment, the running time of each interval is output: according to the single interval curve maximum capacity running time recorded by the Pareto curve in step S1 and the selected curve number index CurveChoices[i][W] recorded in step S6, the running time T of each interval is output. i =T i,k Output.

[0136] S9. Based on the operating time of each section, the optimal driving strategy for a single section is used to generate the optimal operating conditions for each section, and the planning of the energy-saving operating curve for multiple sections of the train is completed.

[0137] In summary, the present invention, based on the above design, has the following effects:

[0138] (1) Based on the above background technology, the present invention adopts the optimal driving strategy of a single vehicle, combines the offline "time-energy consumption" database, reasonably allocates the running time of the entire line online, and generates the optimal working condition sequence under the energy-saving timetable. For the total energy consumption of a single train in a single section, a "time-energy consumption" offline database based on the most energy-saving driving strategy is established. Under the condition of keeping the total running time of the entire line unchanged, a grouped knapsack algorithm is adopted to solve the time allocation problem of each section, treating the running section as a group, the allocated running time as an item, and the total energy consumption as the evaluation standard. The goal is to reasonably allocate the surplus time with the lowest total energy consumption of the entire line within the specified time, so as to obtain the most energy-saving curve for each section based on the most energy-saving control strategy under the given time. At the same time, the algorithm design ensures low time complexity to cope with the dynamic re-planning requirements caused by the running time deviation. The present invention uses the knapsack algorithm to solve the problem in the online stage, and verifies the potential and feasibility of reducing energy consumption from a quantitative perspective. In addition, the method combines dynamic programming technology and only performs one step of numerical calculation and comparison during traversal, which has low time complexity and can effectively deal with the punctuality problem that occurs during online operation and realize timely re-planning function. This flexible adjustment mechanism not only improves train energy efficiency but also ensures operational reliability, contributing new ideas and methods to energy conservation and emission reduction in modern railway transportation. Specifically, during online calculations, performing only one numerical comparison can increase computation speed.

[0139] (2) The present invention proposes an optimization method based on the grouped knapsack method for the problem of allocating the operating time of a single train across the entire line. Compared with the previous method of using a priority queue based on the Pareto curve of a single train and a full-line idling operation method, the present invention has a significant energy consumption reduction effect and higher operating efficiency. The present invention fully considers the influence of regenerative braking energy and achieves improved accuracy and efficiency of online calculations by constructing an offline data database. The present invention not only optimizes the time allocation for the entire line and reduces energy consumption, but also combines dynamic programming technology with low time complexity, and can effectively deal with punctuality issues that arise during online operation, thereby achieving timely re-planning functions.

Claims

1. A train multi-section energy-saving operation curve planning method based on grouping backpack, characterized in that: The following steps are involved: S1. Generate the maximum capacity operation curve based on the most energy-efficient operation strategy of the bicycle, and build an offline database through the discrete Pareto curve; S2, initialization and parameter definition; S3. Perform an outer loop process, traversing from the first interval to the last interval. Given the total surplus time and the selected curve of the previous interval, calculate the total remaining time of the subsequent interval for the curve number traversal of the interval. Each interval is considered as a group, and the surplus time allocated to each interval is considered as an item. S4. Perform a middle-level loop process, initialize the curve index k to 0, and traverse from the first curve to the last curve in the interval to obtain the selected curve number that maximizes the total energy consumption reduction in the interval given the total surplus time of the subsequent intervals. The energy consumption reduction of each curve relative to the maximum capacity of the interval is considered as its value, and it is required that a curve must be selected in each interval to achieve the maximum filling of the backpack; S5. Perform inner loop processing, traverse the surplus time in reverse order, and traverse from the total surplus time W of the entire line in descending order to find the curve combination selected in each interval under different total surplus times. In this case, the problem of finding the surplus time is converted into a grouping knapsack problem; S6. Calculate the energy consumption reduction newEnergy brought about by selecting the new curve number in the current interval. In response to the energy consumption reduction newEnergy being greater than the maximum energy consumption reduction dp[i][j], update the maximum energy consumption reduction dp[i][j] to be equal to the energy consumption reduction newEnergy, and record the curve number index obtained by the selected outer loop, middle loop, and inner loop processing, where dp[i][j] represents the maximum energy consumption reduction in the first i intervals under the j surplus time; S7, determine whether the traversal of the outer layer, middle layer and inner layer is completed, if so, go to step S8, otherwise update the traversal variable and return to step S3; S8. Obtain the running time of each interval based on the maximum capacity running time of the single interval curve recorded by the Pareto curve in step S1 and the selected curve number index recorded in step S6; S9. Based on the operating time of each section, the optimal driving strategy for a single section is used to generate the optimal operating conditions for each section, and the planning of the energy-saving operating curve for multiple sections of the train is completed.

2. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 1 is characterized in that: The step S1 comprises the following steps: S101. Generate maximum capacity operating curves for different ranges and vehicle weights based on the most energy-efficient operating strategy for the single vehicle; S102: Obtain the maximum operating time T for interval i based on the maximum capacity operating curves for different intervals and vehicle weights. i,max and maximum energy consumption E i,max ; S103, calculate the Pareto curve under a given surplus time, discretize the Pareto curve with a certain step size, and record the running time T of the k-th curve i,k and energy consumption E i,k ; S104. Based on the results of step S102 and step S103, an offline database of Pareto curves for each section of the train is constructed.

3. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 1 is characterized in that: The step S2 is specifically as follows: Define dynamic programming array dp; Define the meaning and size of dp[i][j] as (m+1)×(W+1); where dp[i][j] represents the maximum energy consumption reduction of the first i intervals under j surplus time, m represents the number of intervals, and W represents the total surplus time of the entire line, that is, the excess time of the operation plan relative to the maximum capacity operation time; Initialize all elements to negative infinity; Define the index combination of the curve number selected in the first i intervals and at the jth surplus time CurveChoices[i][j] for storage; Set the initial state dp[0][0] = 0, where dp[0][0] = 0 means that the maximum energy consumption reduction of the whole line is 0 when the surplus time is 0.

4. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 1 is characterized in that: The specific steps of step S3 are as follows: Perform an outer loop process, initialize the interval number as i = 1, and traverse from i = 1 to i = m, where m represents the number of intervals; According to the traversal result, obtain the curve number of the selected curve that maximizes the total energy consumption reduction by calculating the total remaining time of the subsequent interval under the given total surplus time and the curves selected in the previous interval. Each time step S3 is returned, let the value of the interval number i be i + 1. When the interval number i is greater than m, enter step S8.

5. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 1 is characterized in that: The specific steps of step S4 are as follows: Perform middle-level loop processing, initialize the curve index k to 0, from k = 0 to k = n i Traverse, where n i represents the total number of curves in the i-th interval; According to the traversal results, the selected curve number that can maximize the total energy consumption reduction in the given subsequent interval is obtained. Each time step S4 is returned, the value of the curve index k is set to k+1. If k>n i , return to step S3.

6. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 1 is characterized in that: The specific steps of step S5 are as follows: Perform an inner loop process, initialize the surplus time j = W, and traverse from the surplus time j = W to j = Curve[i][k].ΔTime. Each time step S5 is returned, let the value of the surplus time j be j - 1. If the surplus time j < Curve[i][k].ΔTime, return to step S4, where j represents the surplus time, W represents the total surplus time of the whole line, that is, the time that the operation plan time is more than the maximum capacity operation time, Curve[i][k] represents the kth curve in the ith interval, which is a structure body, and this structure body includes time and energy consumption, and ΔTime represents the surplus time of this curve relative to the maximum capacity operation curve of this interval; According to the traversal result, find the curve combinations selected for each interval under different total surplus times, and convert the problem of finding the surplus time into a grouped knapsack problem.

7. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 6 is characterized in that: The expression of the objective function for converting the problem of finding the surplus time into a grouped knapsack problem is as follows: Where Z represents the objective function, m represents the number of intervals, and n i represents the total number of curves in the i-th interval, E i_max represents the operating energy consumption at the maximum capacity in the i-th interval, E i,k represents the energy consumption under the kth curve in the i-th interval, x i,k is a decision variable. When the kth curve is used in the i-th interval, x i,k =1, otherwise, x i,k =0; The constraint conditions for converting the problem of finding the surplus time into a grouped knapsack problem are as follows: Among them, T i,k represents the energy consumption under the kth curve in the i-th interval, T i_max represents the running time at the maximum capacity in the i-th interval, T total Indicates the total surplus time of the entire line.

8. The train multi-section energy-saving operation curve planning method based on group backpack according to claim 1 is characterized in that: The expression of the energy consumption reduction newEnergy brought by selecting a new curve number in the current interval is as follows: newEnergy = dp[i - 1][j - Curve[i][k].ΔTime] + Curve[i][k].ΔEnergy Curve[i][k].ΔTime=T i,k -T i_max Curve[i][k].ΔEnergy=E i,k -E i_max Where Curve[i][k] represents the information of the kth curve in the i-th interval, ΔTime represents the extra time of the curve relative to the maximum capacity curve in the interval, ΔEnergy represents the energy consumption reduction of the curve relative to the maximum capacity curve in the interval, Curve[i][k].ΔTime represents the time increase of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, Curve[i][k].ΔEnergy represents the energy consumption reduction of the kth curve in the i-1th interval relative to the maximum capacity curve in the i-1th interval, T i,k represents the energy consumption under the kth curve in the i-th interval, T i_max represents the running time at the maximum capacity in the i-th interval, E i_max represents the operating energy consumption at the maximum capacity in the i-th interval, E i,k Represents the energy consumption under the k-th curve in the i-th interval.

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