A rolling optimization method for the operating speed of an autonomous electric bus fleet

Abstract

This invention relates to a rolling optimization method for the operating speed of an autonomous electric bus fleet, comprising the following steps: Step 1, defining model parameters; Step 2, establishing a bus fleet operating speed generation algorithm; Step 3, establishing a collaborative optimization model for bus fleet operating speed; Step 4, solving the collaborative optimization model for bus fleet operating speed; Step 5, deriving the rolling optimization method for fleet operating speed. This invention, based on factors such as intersection signal timing schemes, further considers the safety distance constraints and weaving effects between buses in front and behind. It rolls out the inter-station travel speed scheme when a single bus in the fleet is about to depart from a stop, avoiding situations where the safety distance constraints between buses in the fleet are not met, effectively improving the economy and on-time arrival of buses, thereby increasing the attractiveness of the public transportation system.

Description

Technical Field

[0001] This invention belongs to the field of urban public transportation management technology, and specifically relates to a rolling optimization method for the operating speed of an autonomous electric bus fleet. Background Technology

[0002] Existing autonomous electric buses combine the low emissions and high energy efficiency of electric vehicles with the comfort and efficiency of autonomous driving technology, making them a key research and development direction for the public transportation industry. However, when optimizing the operating speed of autonomous electric buses, only factors such as onboard battery characteristics and intersection signal timing schemes are considered. Factors such as safe distance constraints for the electric bus fleet, interactions between vehicles, the number of passengers boarding and alighting at stops, and random fluctuations in vehicle waiting times at stops are not comprehensively considered. This results in poor punctuality, low economic efficiency, and failure to meet safety constraints, making operation impossible.

[0003] Therefore, in addition to considering factors such as intersection signal timing schemes, it is necessary to further consider the safety distance constraints and weaving effects between buses in front and behind, and to use a rolling optimization strategy to minimize random fluctuations in the number of passengers getting on and off at stations and the vehicle's stopping time at stations, and to establish a rolling optimization method for the operating speed of an autonomous electric bus fleet. Summary of the Invention

[0004] To address the issues of poor on-time arrival and low vehicle economy when bus fleets operate on dedicated lanes, this invention proposes a rolling optimization method for the operating speed of autonomous electric bus fleets.

[0005] This invention relates to a rolling optimization method for the operating speed of an autonomous electric bus fleet, comprising the following steps:

[0006] Step 1: Define model parameters;

[0007] Step 2: Establish an algorithm for generating bus fleet speed;

[0008] Step 3: Establish a collaborative optimization model for bus fleet operating speed;

[0009] Step 4: Solve the collaborative optimization model for bus fleet operating speed;

[0010] Step 5: Determine the rolling optimization method for fleet speed.

[0011] Beneficial effects

[0012] This invention, based on factors such as intersection signal timing schemes, further considers the safety distance constraints and weaving effects between buses in front and behind, and establishes a rolling optimization method for the operating speed of an autonomous electric bus fleet. When a single vehicle in the bus fleet is about to depart from a stop, the inter-stop travel speed scheme is rolled out, avoiding situations where the safety distance constraints between buses in the fleet are not met, effectively improving the economy and punctuality of bus vehicles, and thus increasing the attractiveness of the public transportation system. Attached Figure Description

[0013] Figure 1 This is a flowchart of the rolling optimization method for the operating speed of an autonomous electric bus fleet according to the present invention.

[0014] Figure 2 Recommended running speed for Pareto solution generation in this invention

[0015] Figure 3 Optimization results of the actual operating speed and travel distance curves for buses 1-3 Detailed Implementation

[0016] The following combination Figures 1 to 3 This implementation method will be described in detail.

[0017] This invention relates to a rolling optimization method for the operating speed of an autonomous electric bus fleet, comprising the following steps:

[0018] Step 1: Define model parameters;

[0019] (1) Define road environment parameters

[0020] The stop is abstracted as a point mass, and the starting and ending points of the inter-stop journey are both this point mass. Similarly, the signalized intersection is abstracted as a point mass, and the location of this point mass is equivalent to the location of the stop line at the signalized intersection. The inter-stop journey is divided into F segments using the stop line at the signalized intersection as the dividing line. The endpoint of segment 1 to segment F-1 is the stop line at the intersection, and the endpoint of segment F is the stop. The starting and ending points of segment f (1≤f≤F) are respectively located at distances from the starting point of the target inter-stop journey. and The unit is meters (m).

[0021] (2) Define bus parameters

[0022] The bus about to depart from this stop is defined as the target bus (numbered bus 1), and the nearest bus ahead of it is numbered bus 0. The inter-stop journey that the target bus is about to enter is the target inter-stop journey. Correspondingly, the previous inter-stop journey that it just left is the upstream inter-stop journey. There are a total of I-1 (I≥1) buses currently in the upstream inter-stop journey, numbered sequentially from bus 2 to I-1 (I≥1); bus i (0≤i≤I) at time... Starting from this stop with an initial velocity of 0 m / s, the distance between the starting point and the beginning of section 1 is... The unit is meters (m).

[0023] Let time be represented by discrete variable t, and time interval be Δt, in seconds. For ease of calculation, t will be used in the following sections. i Indicates and The time difference, in seconds, is therefore The speed of bus i is a discrete variable v i (t), in m / s; acceleration is a discrete variable. i (t), in m / s 2 The distance to this stop is a discrete variable s. i (t), in meters;

[0024] (3) Define signalized intersection parameters

[0025] Based on the time obtained from the vehicle-road communication equipment The set of green light time windows for road segment f afterwards The set contains N green light time windows arranged in chronological order. A green light time window is a continuous time interval with the start time of the green light phase granting right-of-way to the bus fleet as the lower limit and the end time of the green light phase as the upper limit. The nth green light time window of road segment f is... The lower limit is The upper limit is

[0026] Step 2: Establish an algorithm for generating bus fleet speed;

[0027] First, given the base speeds of the two buses between stations, determine whether they meet the safe distance constraints. For buses that meet the safe distance constraints, their base speeds between stations can remain unchanged; for buses that do not meet the safe distance constraints, the speed of the following bus needs to be further adjusted. Buses experience a "speed-constant speed-speed-speed-speed" operating condition on each route segment. Therefore, their basic operating process on each route segment is divided into three stages: "speed-constant speed-speed," where the base speed of the bus in each stage is described by different operating parameters.

[0028] Step 2-1: Algorithm for Generating Basic Inter-station Running Speed ​​of a Single Vehicle

[0029] The values ​​of the stage operation parameters are restricted, and an algorithm for generating the basic inter-station operation speed of a single vehicle is established using the stage operation parameters as input.

[0030] (1) Constraints on the value of phase operation parameters

[0031] The operating speed of all buses on each road segment is divided into three stages, represented by variables p = 1, 2, and 3 respectively; the speed curves for stages 1 and 3 are set as cosine function speed curves:

[0032]

[0033] In the formula, T i,f,p The duration of i in stage p of segment f, in seconds; bus t i,f,p (0≤t i,f,p ≤T i,f,p Let t be a continuous time variable, representing the time t when bus i is running on road segment f. i,f,p This represents the time difference between the current moment and the start time of stage p, in seconds. and Let α and β represent the initial velocity and target velocity of bus i in segment f at stage p, respectively, in m / s; π is pi; α i,f,p This represents the control parameter for the shape of the cosine function velocity curve; v i,f,p (t i,f,p ) indicates that the bus is at t i,f,p The speed, expressed in m / s;

[0034] The speed curve for the second stage is a constant function speed curve:

[0035]

[0036] Constrain the relationship between the operating speeds of the bus in two adjacent phases, and assign a value to the initial velocity of each segment:

[0037] v i,f,p (T i,f,p ) = v i,f,p+1 (0), p∈{1,2} (3)

[0038]

[0039] In the formula, This represents the actual final speed of bus i on road segment f-1, in m / s; it needs to be calculated considering the actual following behavior of the vehicle. It also affected the order in which the route operating speed of bus i was generated;

[0040] To avoid abrupt acceleration changes between adjacent phases, the constrained cosine function velocity curve can be obtained from... Shift to

[0041]

[0042] Constrain bus i on the distance it travels in each road segment:

[0043]

[0044]

[0045]

[0046] In the formula, and s represents the distance of bus i from the starting and ending points of road segment f to this stop, respectively, in meters; safe is the safe distance that should be maintained when the buses in front and behind are stationary, in meters; i′ is an intermediate variable used to assist in the calculation.

[0047] (2) Algorithm for generating the basic speed of the target bus between stations

[0048] Determine the signal status when bus 1 arrives at the intersection. If it encounters a red light, impose a speed constraint on the vehicle and calculate the red light waiting time based on the green light time window.

[0049]

[0050]

[0051]

[0052]

[0053] In the formula, Let f be the red light waiting time for bus 1 on segment f′, in seconds; if bus 1 is in the first... If an individual arrives at the intersection within a red light window following a green light window, then the lower limit of that red light window is the [number]th ... The upper limit of the green light time window, and the upper limit of the red light time window is the [number]th [number]. The lower limit of the green light time window, Equation (11) is the lower limit of the green light time window. Calculation;

[0054] The bus speed is restricted to 0 m / s when it arrives at the target stop.

[0055]

[0056] Calculate the total travel time of bus 1 on route segment f (1≤f≤F):

[0057]

[0058] In the formula, T′ 1,f Let T′ be the total travel time of bus 1 on road segment f (1≤f≤F) at its base operating speed, expressed in seconds. For the first F-1 road segments, T′... 1,f Includes bus waiting time at red lights;

[0059] Generate the inter-station operating speed by combining the operating speeds of bus 1 at all stages and intersections:

[0060]

[0061]

[0062]

[0063] In the formula, since Therefore v′ 1,f (t) and Both represent the base speed of bus 1 on road segment f at time t, in m / s; v′1(t) and Both represent the basic operating speed of bus 1 during its journey between all target stations at time t, in m / s;

[0064] (3) Algorithm for generating the running speed of buses between basic stations behind

[0065] The constraints in step (1) apply to buses 2 through 1. The difference is that the stopping time fluctuates randomly, making it difficult to determine the signal status when the bus arrives at the intersection. Therefore, some stage operating parameters are no longer used as decision variables, and fixed calculation rules are designed to adapt to the random fluctuations in stopping time. The target speed of buses 2 through 1 in stage 3 of segment f, and the durations of stages 2 and 3 are no longer optimization variables, but rather adaptively changing quantities whose values ​​are related to T. i dep It is related to the operating speed of the first two stages.

[0066] The calculation rules for the parameters are as follows: If the end of the road segment is an intersection, buses are limited to only three scenarios: "passing through the intersection at a constant speed", "passing through the intersection at a reduced speed", and "stopping at a reduced speed"; if the end of the road segment is a target stop, different basic operating speed algorithm generation rules are formulated based on whether the vehicle stops at the stop.

[0067] An algorithm is established to generate the basic operating speed of bus 2 to I on road segment 1 to F-1 in the scenario of "passing through an intersection at a constant speed". When the vehicle can pass through at a constant speed in the third stage, the target speed of the third stage is set to equal the initial speed of the third stage, the duration of the third stage is set to 0s, and the duration of the second stage is calculated.

[0068]

[0069]

[0070]

[0071] In the formula, For bus i to maintain the same target speed in both phases 2 and 3 The total travel time between stations calculated by the operator, in seconds;

[0072] An algorithm is established to generate the basic operating speed of buses from section 2 to section I on road segment 1 to F-1 under the "deceleration and stopping" scenario: When the vehicle cannot pass through the intersection during the green light period while maintaining a constant speed in the third stage, the deceleration time of the bus in the third stage is defined as a fixed duration. The unit is seconds (s), and its execution speed is as follows:

[0073]

[0074]

[0075]

[0076]

[0077]

[0078] In the formula, As an intermediate variable, it represents the duration of Phase 2, calculated assuming the bus decelerates to 0 m / s in Phase 3, in seconds. Under this assumption, the bus arrives at the intersection within the red light window, and the preceding green light window adjacent to this red light window is numbered as follows:

[0079] An algorithm is established to generate the basic operating speed of bus 2 to I on road segments 1 to F-1 under the scenario of "decelerating through an intersection": When the above two scenarios are not met, the bus will decelerate through the intersection. In this case, the time when the bus departs from the next road segment is defined as the upper limit of the green light time window, and the operating speed in stage 3 is recalculated.

[0080]

[0081] In the formula, It is the green light window number for the bus to start;

[0082] Establish an algorithm for generating the basic operating speed of bus 2 to I on road segment F:

[0083]

[0084]

[0085] By concatenating the operating speeds at all road segments and intersections, we can obtain the operating speeds of bus 2 to I between the base stations on road segment F:

[0086]

[0087]

[0088]

[0089] In the formula, v′ i,f (t) and Both represent the base speed of bus i on road segment f at time t, in m / s; v′ i (t) and Both represent the basic operating speed of bus i during its journey between all target stations at time t, in m / s;

[0090] Step 2-2: Algorithm for Correcting the Actual Inter-Station Running Speed ​​of the Fleet

[0091] Based on the generated basic inter-station operating speed, it is necessary to further determine whether the safe distance constraints are met between all vehicles in the fleet, and establish an algorithm to correct the actual inter-station operating speed of the fleet.

[0092] Based on the actual travel distance s of bus i-1 throughout the entire road segment i-1 (t), using the car-following model proposed by the PATH Lab at the University of California to calculate the expected car-following speed of bus i in road segment f without the influence of the vehicle in front:

[0093]

[0094] In the formula, e′ i,f (t), e′ i,f (t-Δt) both represent the difference between the actual and expected distance between bus i and bus i-1, the difference being e′ i,f (t) represents the difference at time t, while e′ i,f (t-Δt) represents the difference at time t-Δt, in meters; Let be the expected following speed of bus i at time t+Δt when it is not affected by the vehicle in front, in m / s;

[0095] Find the time when bus i follows the car in front on road segment f:

[0096]

[0097] In the formula, These are intermediate variables in the solution process; solve(eq,var,cons) is the solution function, which means solving the equation eq with respect to variable var under constraint const. When a real root exists, the output result is the root with the smallest value in the solution set; otherwise, the output result is null. This indicates the moment when bus i begins to follow the vehicle in front on segment f;

[0098] like This means that even when bus i travels at the base operating speed, it can maintain a safe distance from the vehicle in front. In this case, the corrected actual operating speed of the bus is the same as the base operating speed.

[0099]

[0100] like Indicates from time Initially, bus i, traveling at its base speed, could no longer maintain a safe distance from the vehicle in front; therefore, at time... Previously, the actual operating speed of the corrected bus i was the same as the base operating speed, at time... Afterwards, the actual operating speed of bus i, as corrected, is the same as the following speed:

[0101]

[0102] In the formula, This indicates the moment when bus i finishes following the vehicle in front at point f on the road segment;

[0103] The revised actual operating speed does not allow the following scenario: the vehicle in front passes through at the end of the green light, and the vehicle behind follows the vehicle in front through the intersection during the red light, i.e.:

[0104]

[0105] Assign values ​​to the speeds of bus i at the times it arrives at the end of the route and at the time it starts from the beginning of the route:

[0106]

[0107] Step 3: Establish a collaborative optimization model for bus fleet operating speed;

[0108] Step 3-1: Calculation of the objective function

[0109] (1) Construction of vehicle economic indicators

[0110] Vehicle economy is measured by the weighted sum of total battery energy consumption of all buses between the stations studied. The lower the total energy consumption, the higher the economy of the inter-station operating speed scheme.

[0111] Calculation of the total weighted battery energy consumption of all buses:

[0112]

[0113] In the formula, Z1 is the first term of the objective function, representing the weighted sum of the total battery energy consumption of all buses, in kWh; w 1,i , which is a weighting coefficient used to measure the importance of the economic efficiency of bus i; It is the battery output power of bus i at time t, in W;

[0114] The calculation method is as follows:

[0115]

[0116] In the formula, The net power of the bus's i-battery used to drive the wheels after regenerative braking is taken into account, and the unit is W; The total power supplied by the battery to the auxiliary facilities of the bus, measured in W, is obtained from the sensor.

[0117] The calculation method is as follows:

[0118]

[0119]

[0120] In the formula, δ is the instantaneous power of the wheels of bus i, in W; i To account for the inertia coefficients of all rotating components in the transmission system; These are rolling resistance parameters; θ is the air resistance coefficient; θ is the road gradient, in rad; g is the acceleration due to gravity, in m / s². 2 ;ρ air Air density, in kg / m³ 3 ;m i The vehicle mass, measured in kg, is the total weight of the vehicle including the total weight of passengers. and These represent the power system efficiency, motor efficiency, battery efficiency, and regenerative braking energy efficiency of bus i, respectively.

[0121] (2) Construction of arrival timeliness indicators

[0122] Since passenger satisfaction decreases with greater deviation from the scheduled arrival time, the on-time arrival index is defined as the weighted sum of the absolute values ​​of the differences between the actual arrival time and the scheduled arrival time for all buses, i.e.:

[0123]

[0124] Where: Z2 is the second term of the objective function, describing the punctuality of all buses; s; w 2,i , which is a weighting coefficient used to measure the importance of the on-time performance indicator of bus i; This indicates the scheduled arrival time of bus i.

[0125] Step 3-2: Expression of Constraints

[0126] The operating speed of all buses between stations should meet the restrictions imposed by vehicle and road conditions, namely:

[0127]

[0128] a min ≤a i (t)≤a max (40)

[0129]

[0130] In the formula, and These are the minimum and maximum speed values, in m / s; a min and a max Minimum and maximum acceleration values, in m / s². 2 ; and The shortest and longest durations of bus segment f in phase p are given in seconds.

[0131] Step 3-3: Establishing the Opportunity-Constrained Programming Model

[0132] For random variables and m i The input is processed using a chance-constrained programming model to solve for the optimal decision variables. and T i,f,p According to step 2-1(3), when 1≤f≤F-1 and 2≤i≤I, T i,f,2 and T i,f,3 It is not a decision variable and has its own independent calculation rules;

[0133] Bus departure time i (2≤i≤i) Let be a random variable, and follow the mean of . Standard deviation is The probability density function is:

[0134]

[0135] The number of passengers on bus i (2≤i≤1) is a random variable, which in turn leads to the total mass m of the vehicle. i Follow the mean Standard deviation is The probability density function of the given information follows a normal distribution.

[0136]

[0137] The smaller the two indicators, the better the optimization effect; and since both have randomness, they are transformed into mathematical expectations to establish a chance-constrained programming model, with the optimization objective being:

[0138] min E(Z1) (44)

[0139] min E(Z2) (45)

[0140] In the formula, E(g) represents the expected value;

[0141] The opportunity-constrained programming model allows the given inter-station operating speed scheme to deviate from the given constraints to a certain extent; therefore, the constraints are:

[0142]

[0143]

[0144]

[0145] In the formula, β1 and β2 are the confidence levels given in advance by the decision-maker; Pr{g} represents the probability measure of the event occurring.

[0146] Step 4: Solve the collaborative optimization model for bus fleet operating speed;

[0147] Step 4-1, Stochastic Simulation Technique

[0148] The objective functions E(Z1), E(Z2) and the probability measures in formulas (47) and (48) are calculated using stochastic simulation techniques.

[0149] (1) Input decision variables;

[0150] (2) Basic parameter settings: number of simulations is Num; initial values ​​of counters Ct1 and Ct2 are 0; empty sets S1 and S2;

[0151] (3) Generate random numbers based on probability density distribution. and m i ;

[0152] (4) Based on generation and m i Calculate Z1, Z2, and a i (t) and T i,f,p The possible values ​​of ;

[0153] (5) Z1 and Z2 are recorded in sets S1 and S2; determine a min ≤a i (t)≤a max If true, then Ct1←Ct1+1; Determine if true. Whether it is true or not, if it is true, then Ct2←Ct2+1;

[0154] (6) Repeat steps (3)-(5) a total of Num times;

[0155] (7) Output results: E(Z1) and E(Z2) are the mean values ​​of all elements in sets S1 and S2, respectively; let Pr{a min ≤a i (t)≤a max} equals Ct1 / Num, It equals Ct2 / Num.

[0156] Step 4-2: Multi-objective particle swarm optimization algorithm embedding stochastic simulation techniques

[0157] The multi-objective particle swarm optimization (MPS) algorithm, which incorporates stochastic simulation techniques, is used to solve for the optimal stage operation parameters. The stochastic simulation technique assists in calculating the objective function and determining constraints, while the multi-objective PMS algorithm searches for the Pareto optimal combination of decision variables. In the multi-objective PMS algorithm, each particle represents a set of stage operation parameters, and the particle's position indicates the specific value of each parameter. Each particle has two fitness values, corresponding to two index values ​​in the model, and these two fitness values ​​are set to be equal to the two objective function values.

[0158] (1) Set the iteration count G = 0 and the program running time T. con =0, particle population size is Ω pop External archives U p The size is Ω rep Maximum number of iterations G Max The inertia weight is ω, the acceleration factors are c1 and c2, and the maximum allowable CPU computation time is T. Max ;

[0159] (2) Randomly initialize Ω pop Given the position and velocity of each particle, calculate all fitness values ​​for each particle;

[0160] (3) Compare the fitness values ​​of all particles, filter out the inferior and non-inferior solutions, and add the non-inferior solutions to the external archive set U. p The density information of particles is used to maintain the archive set. When the number of solutions in the archive set exceeds Ω... rep At that time, an adaptive mesh method was used to remove some particles to keep the file set size fixed;

[0161] (4) Determine the individual particle leader P best and Global Guide G best When two particles with simultaneously better fitness values ​​cannot be found, one of the current Pareto optimal particles is randomly selected as the individual guide P. best Based on density information, the particle with the lowest crowding level is selected as the global guide G. best ;

[0162] (5) Update particle position and velocity based on the traditional fixed weight method;

[0163] (6) Record the CPU processing time T from (3) to (5). step Let G = G + 1, T con =T con +T step If termination condition 1 or 2 is met, output the solution in the external archive set as the Pareto optimal solution; otherwise, return to (3); where termination condition 1: G > G Max Termination condition 2: T con >T Max .

[0164] Step 5: Determine the rolling optimization method for fleet speed;

[0165] Based on all Pareto optimal stage operation parameters of buses output in step 4, and combined with the fleet operation speed generation algorithm in step 2, a set of Pareto optimal schemes for inter-station operation speed is generated for decision-makers to select.

[0166] The Pareto optimal solution selection rule is as follows: If the timeliness index of all Pareto optimal solutions is greater than or equal to T... fixed If the timeliness index is less than T, then the Pareto optimal solution with the smallest timeliness index is selected as the recommended Pareto optimal solution; if there exists a timeliness index less than T... fixed If we find the Pareto optimal solution, then we select the one with the smallest economic index among these Pareto optimal solutions as the recommended Pareto optimal solution, where T... fixed Take 10 seconds;

[0167] The selected fleet speed optimization scheme is applied to the target buses; the optimization process is continuously applied to buses that are about to depart from this stop in chronological order to achieve rolling optimization of the bus fleet's speed between target stops; and then rolling optimization of the bus fleet's speed along the entire route / bus lane is achieved.

[0168] Example:

[0169] The research object was an autonomous driving bus fleet operating on Renmin Avenue in Changchun City, Jilin Province on January 6, 2022. A representative section of the route between stops was used as the research environment to verify the effectiveness of the proposed method. The route was 852m long and included two signalized intersections. Three bus routes operated along this route: routes 6, 13, and 108. One bus fleet, numbered 1-3, was about to depart from the stop. All three buses were manufactured by the same company and were identical in model, with the following basic parameters: curb weight, 11350kg; vehicle dimensions, 10.5×2.5×3.2m. 3 Rated passenger capacity: 76 people; windward area: 7.29m² 2 Maximum acceleration, 4 m / s² 2 Minimum acceleration, -4 m / s² 2 The HVAC system power is 6401W. When bus 1 travels between stations, optimizing its speed requires the following information obtained from the V2I communication equipment: the average gradient between stations is 0°; the first green light at intersection 1 after bus 1 starts is 6:43:33, and the green light at intersection 2 is 6:43:04; bus 1 departs from stop 5 at 6:42:30, and the scheduled arrival time is 6:44:30; the number of passengers, obtained from sensors, is 16; the departure times of buses 2 and 3 from stop 5 are random variables, following normal distributions with means of 6:42:38 and 6:42:56, and standard deviations of 2s and 2s, respectively; the exact passenger numbers, obtained through the bus APP, are 24 and 42, respectively; the scheduled arrival times are 6:43:57 and 6:44:13, respectively; buses 1-3 all stop at stop 6.

[0170] In the solution algorithm, the number of random simulations is set to Num = 50. Some basic parameters used in the multi-objective particle swarm optimization algorithm are: Ω pop =300, Ω rep =100, G Max =100, ω=0.8, c1=0.1, c2=0.1, T Max =3s. The algorithm outputs the Pareto optimal solution, and based on the recommended Pareto optimal solution selection rules in step 5, the recommended Pareto solution is obtained.

[0171] Because the departure times of buses 2 and 3 fluctuate randomly, based on the speed generation algorithm in step 2, it is recommended that the speed of bus 1 generated by the Pareto solution be fixed between stops, while the speeds of buses 2 and 3 fluctuate randomly, as shown in the attached diagram. Figure 2 As shown.

[0172] The optimized process was continuously applied to the three buses in the fleet according to their actual departure times. The actual optimized operating speed results are shown in the attached figure. Figure 3 As shown, the energy consumption of buses 1-3 are 0.525kWh, 0.534kWh, and 0.542kWh, respectively, and their on-time performance indicators are 0.462s, 1.834s, and 2.253s, respectively. This demonstrates that the proposed automatic driving electric bus fleet speed rolling optimization method can flexibly support factors such as the number of signalized intersections and different signal timings between stations, and generates effective inter-station operating speed schemes even when bus departure times fluctuate randomly.

[0173] The above description of the present invention is only a preferred embodiment of the present invention and is not intended to limit the implementation of the present invention. Those skilled in the art can easily make corresponding modifications or alterations based on the main concept and spirit of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection claimed in the claims.

Claims

1. A rolling optimization method for the operating speed of an autonomous electric bus fleet, characterized in that, Includes the following steps: Step 1: Define model parameters; Step 2: Establish an algorithm for generating bus fleet speed; Step 3: Establish a collaborative optimization model for bus fleet operating speed; The steps for calculating the objective function are as follows: (1) Construction of vehicle economic indicators Vehicle economy is measured by the weighted sum of total battery energy consumption of all buses between the stations studied. The lower the total energy consumption, the higher the economy of the inter-station operating speed scheme. Calculation of the total weighted battery energy consumption of all buses: In the formula, The first term of the objective function represents the weighted sum of the total battery energy consumption of all buses, in kWh. These are weighting coefficients used to measure the performance of buses. The importance of vehicle economy; It is a moment Get off the bus The battery output power, measured in W; The calculation method is as follows: In the formula, To consider the regenerative braking of buses The net power of the battery used to drive the wheels, measured in watts (W). The total power supplied by the battery to the auxiliary facilities of the bus, measured in W, is obtained from the sensor. The calculation method is as follows: In the formula, For buses The instantaneous power of the wheel, expressed in W; To account for the inertia coefficients of all rotating components in the transmission system; These are rolling resistance parameters; This refers to the air drag coefficient; Road gradient, in rad; This is the acceleration due to gravity, measured in m / s². 2 ; Air density, in kg / m³ 3 ; The vehicle mass, measured in kg, is the total weight of the vehicle including the total weight of passengers. , , and They represent buses The efficiency of the power system, the efficiency of the electric motor, the efficiency of the battery, and the efficiency of regenerative braking energy; (2) Construction of arrival timeliness indicators Since passenger satisfaction decreases with greater deviation from the scheduled arrival time, the on-time arrival index is defined as the weighted sum of the absolute values ​​of the differences between the actual arrival time and the scheduled arrival time for all buses, i.e.: in: Let s be the second term of the objective function, describing the punctuality of all buses; These are weighting coefficients used to measure the performance of buses. The importance of timeliness indicators; Indicates the bus schedule Arrive on time; The time when bus i departs from this stop with an initial velocity of 0 m / s; The total time that bus i spends on road segment f is expressed in seconds. Step 4: Solve the collaborative optimization model for bus fleet operating speed; Step 5: Determine the rolling optimization method for fleet operation speed.

2. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 1, characterized in that, In step 1, the defined model parameters include: road environment parameters, bus vehicle parameters, and signalized intersection parameters.

3. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 1, characterized in that, In step 2, the values ​​of the stage operation parameters are restricted. Using the stage operation parameters as input, an algorithm for generating the basic inter-station running speed of a single vehicle is established. The calculation steps are as follows: (1) Constraints on the value of operation parameters in each stage The operating speed of all buses on each road segment is divided into three stages, and variables are used in each stage in turn. This indicates that the speed curves for stages 1 and 3 are cosine function speed curves: In the formula, for On the road section stage The duration, in seconds; bus For continuous time variables, ;the bus On the road section During runtime, Indicates the current moment and stage The time difference at the start time, in seconds; and They represent buses On the road section stage Initial velocity and target velocity, in m / s; Pi; This represents the control parameter for the shape of the velocity curve of the cosine function; Indicates that the bus is at The speed, expressed in m / s; The speed curve for the second stage is a constant function speed curve: Constrain the relationship between the operating speeds of the bus in two adjacent phases, and assign a value to the initial velocity of each segment: In the formula, Indicates bus On the road section The actual final velocity, in m / s; needs to be calculated considering the actual following behavior of the vehicle. This also affected the buses. The order in which the road segment operating speeds are generated; To avoid abrupt acceleration changes between adjacent phases, the constrained cosine function velocity curve can be obtained from... Shift to Restricting buses Distance traveled on each road segment: In the formula, and They represent buses On the road section The distances from the starting point and the destination to this stop, in meters; This is the safe distance that should be maintained when buses in front and behind are stationary, and the unit is meters (m). These are intermediate variables used to assist in calculations; For road section The distance between the starting point and the starting point of the journey between the destination and the destination, in meters; For bus i at time The distance between the starting point and the starting point of segment 1 when starting from the current stop with an initial velocity of 0 m / s, in meters; (2) Algorithm for generating the running speed of the target bus between basic stations Determine the signal status when bus 1 arrives at the intersection. If it encounters a red light, impose a speed constraint on the vehicle and calculate the red light waiting time based on the green light time window. : In the formula, For bus 1 on the section of road Red light waiting time, measured in seconds; If bus 1 is in If an individual arrives at the intersection within a red light window following a green light window, then the lower limit of that red light window is the [number]th ... The upper limit of the green light time window, and the upper limit of the red light time window is the [number]th [number]. +1 lower limit of green light time window, formula Yes Calculation; The bus is required to travel at a speed of 0 m / s when it arrives at the target stop. Calculate the total travel time of bus 1 on road segment f. In the formula, Let f be the total travel time of bus 1 on road segment f when it travels at the base operating speed. The unit is s, in front Each section of road, Includes bus waiting time at red lights; Generate the inter-station operating speed by combining the operating speeds of bus 1 at all stages and intersections: In the formula, since ,so and All indicate Bus No. 1 is on the route The basic operating speed, in m / s; and All indicate The basic operating speed of bus 1 during its journey between all target stations is given in m / s. (3) Algorithm for generating the running speed of buses between base stations behind the bus The constraints in step (1) apply to bus 2 to Applicable, some stage operating parameters are no longer used as decision variables, and fixed calculation rules are designed to adapt to the random fluctuations in the stop time; define bus 2 to On the road section The target velocity of Phase 3, and the durations of Phases 2 and 3, are adaptively variable quantities, whose values ​​are related to... It is related to the operating speed of the first two stages; The calculation rules for the parameters are as follows: If the end of the road segment is an intersection, the bus is limited to only three scenarios: "passing through the intersection at a constant speed", "passing through the intersection at a reduced speed", and "stopping at a reduced speed"; if the end of the road segment is a target stop, different basic operating speed algorithm generation rules are formulated based on whether the vehicle stops at the stop. Establish a scenario where the bus travels at a constant speed through an intersection. On section 1 to The basic running speed generation algorithm is as follows: When the vehicle can pass through the third stage at a constant speed, the target speed of the third stage is set to equal the initial speed of the third stage, the duration of the third stage is set to 0 s, and the duration of the second stage is calculated: In the formula, For buses Both phases 2 and 3 follow the same target speed. The total travel time between stations calculated by the operator, in seconds; Establish a "slow down and stop" scenario for buses 2 to 3 On section 1 to The basic speed generation algorithm is as follows: When a vehicle cannot pass through the intersection during the green light period while maintaining a constant speed in Phase 3, the time for the bus to decelerate in Phase 3 is defined as a fixed duration. The unit is seconds (s), and its execution speed is as follows: In the formula, As an intermediate variable, it is the duration of stage 2 calculated assuming the bus decelerates to 0 m / s in stage 3, in seconds; Under this assumption, the bus arrives at the intersection within the red light window, and the preceding green light window adjacent to this red light window is numbered as follows: ; Establish a scenario where buses 2 to 300 slow down when passing through an intersection. On section 1 to The basic operating speed generation algorithm: When the above two scenarios are not met, the bus will slow down to pass through the intersection. At this time, the time when the bus departs from the next road segment is defined as the upper limit of the green light time window, and the operating speed in stage 3 is recalculated. In the formula, It is the green light window number for the bus to start; Establish bus 2 to On the road section Basic running speed generation algorithm: By piecing together the operating speeds of all road segments and intersections, we can obtain the speeds of bus 2 to... On the road section Basic inter-station operating speed: In the formula, and All indicate Get off the bus at any time On the road section The basic operating speed, in m / s; and All indicate Get off the bus at any time The base operating speed for the entire journey between target stations, in m / s; 4. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 3, characterized in that, In step 2, based on the generated basic inter-station operating speed, it is necessary to further determine whether the safe distance constraints are met between all vehicles in the fleet, and establish an algorithm to correct the actual inter-station operating speed of the fleet. Based on buses Actual driving distance of the entire road section The car-following model proposed by the PATH Lab at the University of California was used to calculate the bus speed. On the road section Expected following speed without being affected by the vehicle in front: In the formula, , All indicate buses With bus The difference between the actual vehicle spacing and the expected vehicle spacing is that... express The difference at time, and express The difference at time t, in meters; for Get off the bus at any time The expected following speed when unaffected by the vehicle in front, in m / s; Solve the bus problem On the road section When to follow the car in front: In the formula, These are intermediate variables in the solution process; It is the solution function, representing the constraint. Below is a discussion about variables The equation The solution is performed, and if a real root exists, the output is the root with the smallest value in the solution set; otherwise, the output is... ; Indicates bus In the section of the road The moment you start following the car in front; like , indicating bus Maintaining a safe distance from the vehicle in front while operating at the base speed ensures that the corrected actual operating speed of the bus is the same as the base speed. like , indicating from time At the beginning, the bus Driving at the basic operating speed no longer allows for maintaining a safe distance from the vehicle in front; therefore, at any given moment... Previously, the revised bus The actual operating speed is the same as the base operating speed, at time... Afterwards, the revised bus The actual running speed is the same as the car-following speed: In the formula, Indicates bus In the section of the road The moment when following the car in front ends; The revised actual operating speed does not allow the following scenario: the vehicle in front passes through at the end of the green light, and the vehicle behind follows the vehicle in front through the intersection during the red light, i.e.: For buses Speed ​​assignments for arrival at the end of the road segment and departure from the starting point of the road segment:

5. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 1, characterized in that, In step 3, the inter-station operating speed of all buses should meet the restrictions imposed by vehicle and road conditions, namely: In the formula, and These are the minimum and maximum speed values, in m / s; and Minimum and maximum acceleration values, in m / s². 2 ; and For buses Section stage The shortest and longest durations, in seconds.

6. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 5, characterized in that, In step 3, for random variables and The input is processed using a chance-constrained programming model to solve for the optimal decision variables. and , for On the road section stage The duration, in seconds; For buses On the road section stage The target speed is expressed in m / s. According to step (3) of the single-vehicle basic station running speed generation algorithm, when... and hour, , and It is not a decision variable and has its own independent calculation rules; Bus departure times For random variables, ; Follow the mean Standard deviation is The probability density function is: The number of passengers on bus i is a random variable. This leads to a decrease in the total mass of the vehicle. Follow the mean Standard deviation is The normal distribution; Its probability density function is: The smaller the two indicators, the better the optimization effect; and since both have randomness, they are transformed into mathematical expectations to establish a chance-constrained programming model, with the optimization objective being: In the formula, Represents the mathematical expectation; The opportunity-constrained programming model allows the given inter-station operating speed scheme to deviate from the given constraints to a certain extent; therefore, the constraints are: In the formula, and A confidence level pre-defined for decision-makers; It represents a measure of the probability of an event occurring.

7. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 3, characterized in that, In step 4, the objective function is calculated using stochastic simulation techniques. , and formula , The probability measure in, where The mathematical expectation of the weighted sum of the total battery energy consumption of all buses. Find the expected value of the punctuality of all buses. The steps are as follows: (1) Input decision variables; (2) Basic parameter settings: Simulation count is Num; Counter and Initial value is 0; empty set and ; (3) Generate random numbers based on probability density distribution and ; (4) Based on generation and ,calculate , , and The value of ; (5) and Recorded in a collection and Middle; Judgment Is it true? If it is true, then... ;judge Is it true? If it is true, then... ; (6) Repeat steps (3)-(5) a total of Num times; (7) Output results: and Sets and The mean of all elements in the set; let equal , equal .

8. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 7, characterized in that, In step 4, a multi-objective particle swarm optimization (PSO) algorithm with embedded stochastic simulation technology is used to solve for the optimal stage operation parameters. The stochastic simulation technology is used to assist in the calculation of the objective function and the determination of constraints, while the multi-objective PSO algorithm is used to search for the Pareto optimal combination of decision variables. In the multi-objective PSO algorithm, each particle represents a set of stage operation parameters, and the position of the particle represents the specific value of the stage operation parameter. Each particle has two fitness values, corresponding to two index values ​​in the model, and the two fitness values ​​are set to be equal to the two objective function values ​​respectively. (1) Set the number of iterations Program runtime The particle population size is External archives The size is Maximum number of iterations The inertia weight is The acceleration factor is and Maximum allowed CPU computation time ; (2) Random initialization Given the position and velocity of each particle, calculate all fitness values ​​for each particle; (3) Compare the fitness values ​​of all particles, filter out the inferior and non-inferior solutions, and add the non-inferior solutions to the external archive set. The density information of particles is used to maintain the archive set. When the number of solutions in the archive set exceeds... At that time, an adaptive mesh method was used to remove some particles to keep the file set size fixed; (4) Identify individual particle guides and global guide When two particles with simultaneously better fitness values ​​cannot be found, one of the current Pareto-optimal particles is randomly selected as the individual leader. ; The particle with the lowest crowding level is selected as the global guide based on density information. ; (5) Update particle position and velocity based on the traditional fixed weight method; (6) Record the CPU processing time from (3) to (5). ,make , If termination condition 1 or 2 is met, the solution in the external archive set is output as the Pareto optimal solution. Otherwise, return to (3); where termination condition 1: Termination condition 2: .

9. The method for rolling optimization of the operating speed of an autonomous electric bus fleet according to claim 8, characterized in that, In step 5, based on all the Pareto optimal stage operation parameters of buses output in step 4, and combined with the fleet operation speed generation algorithm in step 2, a set of Pareto optimal schemes for inter-station operation speed is generated for decision-makers to select. The Pareto optimal solution selection rule is as follows: If the timeliness index of all Pareto optimal solutions is greater than or equal to... Therefore, the Pareto optimal solution with the lowest timeliness index is selected as the recommended Pareto optimal solution; If the timeliness index is less than If we find the Pareto optimal solution, then we select the Pareto optimal solution with the smallest economic index among these Pareto optimal solutions as the recommended Pareto optimal solution. Take 10 seconds; The selected fleet speed optimization scheme is applied to the target buses; the optimization process is continuously applied to buses that are about to depart from this stop in chronological order to achieve rolling optimization of the bus fleet's speed between target stops; and then rolling optimization of the bus fleet's speed along the entire route is achieved.

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