立体车库车位分配模型与仿真分析

立体车库车位分配模型与仿真分析
王小农; 李建国; 贺云鹏
【期刊名称】《《测试科学与仪器》》
【年(卷),期】2019(010)004
【总页数】10页(P369-378)
【关键词】立体车库; 车位分配; 粒子群算法; 灰色神经网络算法; 就近分配原则【作者】王小农; 李建国; 贺云鹏
【作者单位】兰州交通大学自动化与电气工程学院甘肃兰州 730070
【正文语种】中文
【中图分类】U491.7; TP274
0 Introduction
Automated stereo garage is a comprehensive product of automation technology and industry development. As an important tool to reduce traffic pressure, it is a comprehensive automation system which integrates storage with retrieval of the vehicle. The operational efficiency of an automated stereo garage is directly related to the economic cost of the operator and the customer satisfaction. Therefore, it is urgent to improve the operational efficiency of automated stereo garages. The research on automated stereo garage efficiency mainly includes the following two
aspects: 1) allocation of parking spaces, 2) work scheduling.
At present, many scholars have done a lot of research on the improvement of automated stereo garage efficiency. Xia et al. used the improved genetic algorithm to study the access vehicle scheduling in the stereo garage and then used the mixed coding and improved sequential crossover to optimize the access sequence of the vehicle[1]. Lv et al. designed an intelligent access vehicle control algorithm[2] by using mutual exclusion principle to ensure the parallel working of multiple transport vehicles. In addtition, the benefit prioritization algorithm was used to achieve optimal economic efficiency, improve the efficiency of access vehicles and shorten vehicle access time. Sun et al. improved crossover operator genetic algorithm and optimaized the access vehicle schedulings of three different storage capacities in roadway stacking stereo garage, respectively[3]. Pan proposed a mathematical optimization model of the layout and cost of automated stereo garage, which provided a scientific basis for quantitative analysis of stereo garage arrangement[4]. Yang et al. establised a solid and mathematical model of automated stereo garage[5]. Zuo et al. proposed three automated stereo garage access strategies: retrieval vehicle priority strategy, stand strategy in situ and cross-access strategy and analyzed vehicle length in different access strategies. Based on the traditional scheduling method and the number of stacking machines, a new scheduling strategy is proposed by combining the corresponding access strategy with the running speed of the stackers according to the change in vehicle arrival rate to improve stereo garage efficiency[6]. Wei proposed a
vehicle access strategy of automated stereo garage based on the improved genetic algorithm, hybrid coding and adaptive crossover mutation probability[7]. Kuo et al. proposed a two-objective weight method to optimize the vehicle access strategy. Considering transaction waiting time and vehicle utilization, a cycle time model was established[8]. Fukunari et al. proposed an approximate cycle time model for conceptualized automatic storage & retrieval system (AS/RSs) by using random storage and opportunistic pairing of storage & retrieval (S/R) transactions[9]. According to queuing theory, after analyzing stereo garage queuing process, liang proposed a parking and service window queuing model[10]. Based on relevant parameters, the optimal parking space scale and service windows number of parking garage are estimated. Taking automated warehouse as a research object, according to key location allocation principle, li et al. proposed a dynamic location optimization model[11]. By comparing the existing optimization algorithms and multi-objective genetic algorithms, lu proposed a multi-objective genetic algorithm based on weight coefficient transformation method to solve the model.
It can be found that the above research on stereo garage efficiency is mainly from a unilateral consideration: 1) optimization of vehicle access sequence, 2) optimization of vehicle scheduling using algorithm, 3) combination and optimization of different access strategies, and 4) optimization of automated stereo garage layout and cost. But the improvement of stereo garage efficiency not only needs to consider the
above unilateral optimization, but also need to consider vehicle stay time in the garage and the global search ability of the algorithm when the parking spaces are optimized.
In order to solve the above shortcomings, this paper presents a decision model of parking space allocation and simulates the efficiency of automated stereo garage based on grey neural network and particle swarm optimization algorithm. Firstly, the movement status of the automated stereo garage in a real environment is described, and the principle and evaluation indexes of automated stereo garage allocation are introduced. Secondly, the vehicle stay time in the stereo garage is predicted by grey theory and neural network algorithm. Finally, particle swarm optimization algorithm is used to realize the parking space allocation in stereo garage owing to its global optimization ability. By comparing the efficiency indexes of the existing model based on near-distribution principle, it can be found that the propose model has better feasibility and higher operation efficiency.
1 Description of stereo garage movement state
The automated stereo garage in real environment is shown in Fig.1.
Fig.1 Stereo garage model
The stereo garage capacity is 9 layers×21 columns and has a total of 376 parking spaces. There are two I/O ports in the stereo garage, located at layer 9 column 10 and layer 9 column 11, respectively. There are two automated vehicles (AVs) in the stereo garage, which are AV1 and AV2, respectively. The AV movement direction is in the horizontal direction and
the movement is between columns. In the AS/RS system, there are two services types: storage of the vehicle and retrieval of the vehicle. For storage of the vehicle, the AV first loads the vehicle from the I/O port and then stores it the parking space of pre-system allocation. Similarly, for retrieve of the vehicle, the vehicle is fetched by AV from the parking space to the I/O port. AV is the core equipment in automated stereo garage operation and it has a direct impact on normal and efficient operation of automated stereo garage. In the AS/RS system, the steps of storage tasks are first starting the I/O position and then storing the vehicle to the designated parking space,while the steps of retrieval tasks are starting the storage vehicle location and then transporting the vehicle to the I/O position. The AV motion can realize the movement between the columns in the same layer. The movement between layers can be realized by lift. The automated stereo garage is equipped with two lifts: Lift1 and Lift2, whose movement direction is only vertically up and down.
The vehicle arrival time is the duration in which the vehicles arrive outside the garage from the external environment and then the arrival vehicles enters into the AV and Lift queues in chronological order. If AV is idle, AV will enter into the process of vehicle service; if AV is busy, customers have to wait for the AV. For storage of the vehicle, the service time of AV is the duration in which the AV moves from the current location to the I/O port and then the AV carries the vehicle to the specified parking space. For retrieve of the vehicle, service time of AV is the duration in which the Av moves from the current location to the parking port of the vehicle and
then transports it to the I/O por. Thus, the AV complete storage/retrieve task is that the AV carries the vehicle from the I/O port to the pre-system allocated storage parking space or from the parking space of the vehicle to the I/O port. The complete execution task of Lift is that the Lift delivers the AV from the AV layer to the destination layer.
The automated stereo garage model can be described as follows: When the customer is ready to storage the vehicle, the stereo garage control system first determines whether there are idle parking spaces in the garage. If there are idle parking spaces, the stereo garage control system assigns a storage parking space (row, column, side) to the current vehicle. If there is no parking space, the customer leaves. If the assigned parking space is Floor 9, Side 2 and the AV is idle, the current vehicle will be stored in the pre-assigned parking space. If the AV is busy, the current vehicle waits for the AV. If the assigned parking space is on the other layer, column, side and the AV is idle, the control system first judges whether there is Lift idle. If Lift is idle, the current AV carries the vehicle and the current idle Lift conveys the AV to the specified layer. If the AV is busy, the vehicle waits for the AV to be idle. The flow chart of storing the vehicle is shown in Fig.2. When the customer is ready to retrieve the vehicle, the stereo garage control system determines the vehicle parking space including the row, column and side. If the vehicle parking space is Floor 9, Side2 and if AV is idle, the current AVwill transport the vehicle to the I/O port. If the AV is busy, the current vehicle waits for the AV. If the vehicle is on the other layer, column, side and the AV is idle, the control system
determines whether there is Lift idle. If Lift is idle, the current idle Lift conveys the AV to the assigned layer. If Lift is busy, the vehicle waits for the AV. If the AV is busy, the current vehicle waits for the AV to be idle. The flow chart of retrieving the vehicle is shown in Fig.3.
Fig.2 Flow chart of storaging the vehicle
Fig.3 Flow chart of retrieving the vehicle
2 Establishment of model
2.1 Principles of parking allocation
Stereo garage parking allocation mainly follows the following principles: 1) Principle of uniformity and stability
For excessive weight vehicle, centralized parking should be avoided because it may cause force uneven in the stereo garage. In addition, if the center of gravity of stereo garage is too high, the stability and safety of the stereo garage will become bad.
2) Principle of high efficiency
The vehicle should be allocated to the parking spaces closer or far from the garage entrance. Moreover, the parking time should be short.
3) Principle of first come first service
According to the control system order, the first arrival vehicle should be served first to avoid congestion and the prolonged waiting time of the customer.
4) Principle of departure priority
When customer sends out retrieval order, it is important to ensure that the outbound vehicle receives the service with the shortest queue length and
waiting time.
5) Principle of the lowest energy consumption
The AV and lift movement paths affect energy consumption. The vehicle service should ensure that the AV and lift have the lowest energy consumption from the entrance/exit to the parking space to save resources and reduce operation costs.
6) Principle of minimum running time. The running time of AV or lift is determined by the running path of AV or lift. The vehicle service should ensure that the AV or Lift runs from the entrance to the parking space in the minimum period, to improve operational efficiency.
2.2 Mathematical model and evaluation indexes
Taking the stereo garage model in Fig.1 as a research object, Fig.4 is the simplified model of the stereo garage in Fig.1(side2).
The vehicle arrival time is the negative exponential with the parameter of λ, where λ is the mathematical expectation of the vehicle arrival interval. The smaller the λ, the higher the vehicle retri eval/storage frequency. The retrieval/storage vehicle process of automated stereo garage is stereo motion. The AV movement in the horizontal direction is defined as X and the vertical movement direction of lift is defined as Y. The automated stereo garage has m columns and n rows, a total of m×n locations. Vm is the average speed at which the AV moves in the X direction and Vn is the average speed at which the Lift moves in the Y direction. TL is Lift walking time in the Y direction and TA is AV walking time in the X direction. N and W are the width and height of the parking space, respectively. The
coordinates of layer i, column j are (j×N,i×W). TL and TA can be obtained by
(1)
and the storage or retrieve time of the vehicle in layer i, column j is
Tij=max(TL,TA).
(2)
Fig.4 Simplified model of stereo garage in Fig.1
The horizontal movement direction of AV and the vertical movement direction of Lift are approximately horizontal values and ordinate values, respectively. According to the principle of mechanics, vertical direction energy and horizontal direction energy of retrieving/storing the vehicle can be calculated by
(3)
where m is the vehicle mass, g is the gravitational acceleration, and P is the horizontal traction power of stereo garage motor.
And the whole energy of retrieving/storing the vehicle can be calculated by
Wtotal=min(WL+WA).
(4)
Thus the optimization problem of parking space allocation in the automated stereo garage can be transformed into the optimal solutions of Eqs.(3) and (4).
The customer average waiting time T is the ratio of the sum of the waiting time of the customers to be served to the total number N of the customers to be served, and it can be expressed as
(5)
where ti is ith customer’s waiting time and N is the total number of customers.
The customer average waiting queue Q is the ratio of the sum of waiting queues of the customers to be served to the total number of the customers to be served, and it is expresssed as
(6)
where L(j) is jth customer waiting queue length.
The average energy consumption of AV and Lift W is the ratio of the sum of AV and Lift energy consumptions to the total number of customers, and it is expresssed as
(7)
where W(i) is the energy consumption of the ith customer.
The customer average service time S is the ratio of the sum of the customer service hours to the total number of customers, which is used to characterize the acceptance service time of each customer and calculated by
where S(j) is the waiting time of the jth customer.
3 Vehicle stay time prediction based on gray neural network
3.1 Grey forecasting model
Because a gray model can be established based on small amount of incomplete information and mathematical models, therefore it has advatages of less modeling information required, easy operation and high precision modeling[12]. The original data are given by
x(0)={x(0)(1),x(0)(2),…,x(0)(n)}.
(9)
The data have the characteristic of randomness.
The original data for 1-AGO processing are given by
x(1)={x(1)(1),x(1)(2),…,x(1)(n)},
(10)
where x(1) satisfies the first-order ordinary differential equation as
(11)
where a is called the development gray number and u is called the control gray number.
If t=t0, Eq.(11) satisfies the initial condition x(1)=x(1)(t0) and it is given by
(12)
According to the relevant hypothesis, the time response equation is given by
k=1,2,…,n
(13)
The gray prediction modelling approach is obtained according to accumulative sequence in Eq.(10). The constants a and u are estimated by the least squares method. The fitting value is calculated by the time response equation. The prediction value is given by
(14)
According to the original data sequence set of customer stay time in the automated stereo garage in the real life, the prediction value of customer stay time based on gray model is shown in Fig.5.
Fig.5 Prediction value of customer stay time based on gray model
The abscissa is the customer number and the ordinate is the customer stay time corresponding to the different customer numbers.
3.2 Neural network algorithm model
The basic components of the neural network are artificial neurons and the model of the ith neuron is shown in Fig.6[13-14].
Fig.6 Model of ith neuron
In Fig.(6), f(·) is called the activation function; Yi is the output of neuron i; X1-Xn are the input signals from the other neurons; Wij represents the connection weight from neuron j to neuron i; θ represents the offset; and input of neuron i is Xj(1≤j≤n). There are
Yi=f(Nnet(i)),
(15)
(16)
where Nnet(i) means the total inputis, called net activation. It can be seen that the neurons are in a activated state when the net activation is positive and the neurons are in a inhibited state when the net activation is negative. In this simulation, we use the back propagation (BP) neural network learning algorithm. The core idea of instructor learning algorithm is to send the training set into the network. According to the difference between the actual output and the expected output of the network, the weight between the neurons makes the difference between the actual output and the expected output the minimum. The steps are as follows:
1) Taking a sample (Oi,Ii) from the sample set;
2) Calculating the actual output of neural network O;
3) Calculating the output error C;
4) According to C, neural network adjusts the weight vector matrix W;
5) Repeating the above process for each sample set, the entire sample set error does not exceed the specified range of training. The weight vector matrix meets the required requirements.
In this simulation, the customer stay time data set is used as the training sample of the BP neural network. BP neural network parameter settings are as follows:
1) Nodes number set: input layer, hidden layer and the output layer nodes number are 1,3 and 1, respectively;
2) Transfer functions: hidden layer (logsig function), output layer (purelin function);
3) Training mode: traingdx.
The BP neural network model as shown in Fig.7.
Fig.7 BP neural network model
In Fig.7, X is the customer serial number generated according to the customer arrival time and Y is the stay time corresponding to the customer in the stereo garage. The BP neural network predicts the customer stay time, as shown in Fig.8. The abscissa is the customer serial number assigned by the stereo garage control system, and the ordinate is the stay time corresponding to the different customer numbers.
Fig.8 Customer stay time
3.3 Realization of customer stay time predicted based on gray neural network
Neural network can approximate any nonlinear function on the premise that sample data can represent various situations; otherwise, the neural network will be distorted by training. The grey model makes the randomness of the original data weakened. The required samples and the regularity of the data are easy to find out. Gray neural network is combination of gray model and artificial neural network, which can improve the accuracy of prediction and solve the problem of complex uncertainties. Taking the actual customer stay time in an automated stereo garage as the original data set used for gray neural network. The combined data processing process of grey model and neural network is
shown in Fig.9. The linear weight is calculated from outputs 2 and 3 by using the least squares method, and the weights of the grey model and the BP neural network model are 0.496 4 and 0.503 6, respectively.
Fig.9 Combination model of grey model and neural network
Based on the grey neural network, the customer stay time prediction value is shown in Fig.10. By comparing Figs.5, 8 and 10, it can be seen that the prediction accuracy of customer stay time based on gray neural network is significantly higher than those based on the neural network and grey model, respectively.
Fig.10 Grey neural network predicts customer stay time
4 Realization of vehicle location based on particle swarm optimization
4.1 Mathematical model of particle swarm algorithm
Particle swarm optimization is to find the optimal solution in the search space[15-17]. The mathematical model of particle swarm algorithm is described as follows:
The total number of particles is Num_count in the search space. The spatial dimension is D (interger). The vector position coordinates of the ith particle are Xi=(xi1,xi2,…,xiD)T，i=1,2,…,Num_count, Xi is a random solution of the optimization problem. The best position of the ith particle is called the best position of individual history. The vector position coordinates are Pi(pi1,pi2,…,PiD)T, i=1,2,…,Num_count. The positional transformation rate of each particle is Vi(vi1,vi2,…,viD)T,
i=1,2,…,Num_count. The particle g is the best point among all the particles. The particle Pg=(Pg1,Pg2,…,PgD)T is the global optimal position in current
particle search space. Each particle position can be updated by
(17)
where w is the inertia weight; C1 and C2 are called the acceleration factors; R1 and R2 meet the evenly distributed random number. For dimension
d(1≤d≤D), the range of the position change is [Xmin,Xmax] and the range of the position transformation rate is [Vmin,Vmax]. If the position change and position transformation rate exceed the boundary range in the iterative process, the ranges of the position change and position transformation rate are their respective boundary values.
Realization of particle swarm algorithm includes the steps as forllows:
1) In the initialization process, the random location and speed of the particle swarm are set;
2) Fitness value of each particle is calculated;
3) For each particle, its fitness value is compared with the fitness value pi of the best position. If pi is better, pi is considered as the current best position;
4) For each particle, the fitness value is compared with the global position value of best experience. If global value is better, it is considered as the current best position;
5) According to Eq.(17), the particle has evolved velocity and position;
6) If end condition is not satisfied, the algorithm returns to step 2); otherwise, the algorithm perform step 7);
7) Output global optimal value.
4.2 Realization of vehicle location based on particle swarm algorithm After the prediction of the vehicle stay time, the simulation randomly generates 200 customers with negative exponential distribution and λ =
5. The allocation efficiency indexes of parking spaces based on the nearest distribution principle are shown in Fig.11.
It can be seen from Fig.11 that the average waiting time of the customer is 4.393 7 min, the average waiting queue is 4.515 0 ea, the average energy consumption of the AV and Lift is 33.995 8 kJ, and the average service time is 8.576 0 s.
Fig.11 Efficiency index under the principle of the nearest distribution
The efficiency indexes of parking spaces based on particle swarm algorithm are shown in Fig.12.
Fig.12 Efficiency index in particle swarm optimization mode
It can be seen from Fig.12 that the average waiting time of the customer is 0.609 5 min, the average waiting queue is 0.145 0 ea, the average energy consumption of the AV and Lift is 11.232 6 kJ, and the average service time is 6.774 0 s.
Compared with the results based on the nearest distribution principle, when particle swarm optimization is utilized, the average waiting time of customers is reduced by 3.784 2 min, the average service time of customers is reduced by 1.802 0 s, the average energy consumption of the AV and Lift is reduced by 22.763 2 kJ, and the average waiting queue of
customers is reduced by 4.37 ea. Therefore, the particle swarm algorithm is suitable for parking space allocation and can greatly improve the efficiency of the garage.
5 Conclusion
Taking a stereo garage in real life as research object, a stereo garage operation model with first come and first service is established. The evaluation of automated stereo garage operation efficiency is given. It is proved that the particle swarm algorithm for parking space allocation is effective and can reduce the energy consumption. The combination model of gray theory and neural network has the advantages of two models. The overall prediction effect is obviously stronger than that of a single model. The prediction accuracy is improved and the customer stay time. In the future, we will take into account the scheduling problem between AV and Lift to allocate the parking spaces of the stereo garage and serve the modern social life.
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