problem introduction
According to the data listed in Tables 1, 2, and 3, the train speed-distance curves are designed with the goals of energy consumption, running time, and comfort; complete the comparison of train operation under single-objective and multi-objective optimization; choose one of the schemes, Design the train speed tracking control algorithm and conduct performance analysis.
1 列车参数设置表
Optimization Algorithm Selection:
The PSO algorithm uses particle swarms to search for the best solution to a problem. Each particle represents a candidate solution to the problem, and the position of the particle in the search space represents the solution. The PSO algorithm uses the concept of "goodness of fit" to evaluate the quality of candidate solutions. The fitness of particles is calculated according to the objective function that needs to be optimized.
The MOPSO algorithm is a kind of multi-objective particle swarm optimization algorithm, and its main idea is to achieve multi-objective optimization by maintaining a set of non-dominated solutions (Pareto optimal solution set).
Problem Modeling and Coding and Results
road conditions
The road conditions include the speed limit value of the line, the slope of the line, and other parameters. This article only considers the speed limit and slope.
The general speed limit curve is right-angled, as shown in the red line in the figure. This curve is generated according to the speed limit value (160km/h, 250km/h, 120km/h), and the unit of km/h change is m/s. The unit of abscissa in the figure is m, and the unit of ordinate is m/s.
However, if the red line is directly used as the speed limit curve, when deceleration is required, the deceleration may be delayed, resulting in insufficient braking force of the train to decelerate the train to the specified speed limit value, and it will cross the curve and cause danger.
So we found a braking-based speed limit curve, as shown in the figure. Where the speed limit curve drops, fully consider the braking situation of the train to ensure that when the train is running close to the braking curve, emergency braking can brake the train safely without exceeding the actual speed limit value of the line.
Meanwhile, the curve at the bottom is the slope of the line (-5,-2,2,3,4,4). Therefore, the figure below is the road condition with the speed limit and slope included.
Working condition indication
The control of the rail transit system is almost set in advance, and how to reduce energy consumption in this control process is the most critical purpose. When the train runs between stations, it will calculate a speed limit according to the line conditions, its own train characteristics, and the condition of the line ahead. It is not allowed to exceed this speed limit during train operation. The speed limit is updated periodically. Under the constraint of speed limit, a train usually includes four operating conditions: traction, cruising, coasting and braking.
Traction stage: the train accelerates and the engine is in a state of energy consumption.
Cruising stage: the train is at a constant speed, and the resultant force on the train is 0. Whether the train needs traction or braking depends on the total resistance of the train at that time.
Coasting stage: The train neither pulls nor brakes, the running state of the train depends on the total resistance of the train, and the engine consumes no energy.
Braking stage: the train decelerates, and the engine consumes no energy. If the train adopts regenerative braking technology, the kinetic energy can be converted into electrical energy and fed back to the power supply system for use by other electrical equipment, such as other trains being towed or the air conditioner of this train (the air conditioner of this train consumes less energy, usually can be ignored).
Therefore, it is necessary to design the control strategy in advance, as shown in the code, first perform traction (2), then cruise (1), then coast (0), and then reach the section from the speed limit of 160km/h to 250km/h, and then proceed A new round of traction (2), then cruise (1), then coast (0), then brake (-2) to reach the section where the speed limit is 120km/h, then coast for a certain distance (0), and finally slow down Station (-2), complete control. So stateTable=[2,1,0,2,1,0,-2,0,-2] in the code. The upper limit of the solution and the lower limit of the solution need to complete the conversion of the working conditions within the range of the upper limit and the lower limit, and the specific conversion point is randomly generated in this range.
train traction
resistance
Braking force
objective function
Particle Swarm Algorithm Settings
On the basis of ensuring the accuracy, the speed is guaranteed to the greatest extent, the population size is set to 10, and the maximum number of iterations is 10.
Single objective optimization (energy consumption/time/comfort)
Run chart example
Single Objective Optimization Results
When energy consumption is the optimization goal, the energy consumption is the least. When time is the optimization goal, the time consumption is the least. When the comfort is the optimization goal, the comfort reaches a better level (the comfort value is the smallest)
Multi-objective optimization
The figure below shows the running status of the train in the 30km section. The abscissa is the distance, the unit is m, and the ordinate is the speed, the unit is m/s. It can be seen that the top curve is the improved speed limit curve, and the blue curve is the speed-distance curve optimized by the particle swarm algorithm based on energy, time, and comfort. Driving on this curve, energy consumption, time, and comfort will reach a better and balanced state. The thin purple line below is the line slope, and the red line is the working condition.
Summarize
Design the train speed-distance curve with energy consumption, running time, and comfort as the goals; complete the train operation comparison under single-objective and multi-objective optimization; first, establish the train model (force, control
condition) and road Model (speed limit, slope), and express the model in code. Then, aiming at energy consumption, running time, and comfort, the speed-distance curve of the train is designed through the basic particle swarm optimization algorithm. By optimizing the speed curve, the goal of reducing energy consumption, shortening running time or ensuring the comfort experience of passengers can be achieved, and the final data also verified this point.
Second, we carried out a MOPSO algorithm based on single-objective optimization, and compared them in terms of energy consumption, running time, and comfort. Through comparative experiments, we can evaluate the impact of different optimization objectives on the train operation scheme, and further optimize the train operation strategy to achieve a more ideal effect.
Specific documents, codes, and ideas are welcome to private message me