# [IEEE 2010 Third International Workshop on Advanced Computational Intelligence (IWACI) - Suzhou, China (2010.08.25-2010.08.27)] Third International Workshop on Advanced Computational Intelligence - A hybrid control for elevator group system

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Third International Workshop on Advanced Computational Intelligence August 25-27,2010 - Suzhou, Jiangsu, China

A Hybrid Control for Elevator Group System

Jian Liu,Chengdong WU,Xin Wang,Weize Wang, and Ting Zhang

Abstract-In order to increase the elevators running

efficiency and quality of service, the optimizing control strategy

of elevators is studied. In this paper a new hybrid control method which optimizes passenger service in an elevator group

is described. It is capable of optimizing the neural-controller

based on Particle Swarm Optimization (PSO) of an elevator group controller. Starting from the operation characteristics of

elevator group control system, the architecture and the traffic

pattern of an elevator group control system are described, and

the optimization cost criterion function is proposed. The PSO

algorithm is used to optimize the weights and biases of the neural network. Some weighted parameters of the Radial Basis

Function (RBF) neural network can be modified based on the

PSO, so that different weight settings and their influence on the elevator supervisory group control (ESGC) performance can be

tested. It can reduce the passenger's average waiting time by

allocating an appropriate number of elevator cars to the lobby floor. The results prove that the hybrid method is effective.

I. INTRODUCTION

The elevator group control problem has received extensive attention because of its theoretical importance and practical significance. It plays an important role in

today's urban life. Elevator systems operate in high-dimensional continuous state spaces and in continuous time as discrete event dynamic systems.Their states are not fully observable and they are non-stationary due to changing passenger arrival rates[I-3]. The elevator group control problem is of inherently stochastic nature. The stream of arriving passengers is a stochastic process. Each passenger introduces three random variables: arrival time, arrival floor and desired destination floor. In addition, the number of passengers is also unknown behind each hall call in real elevator systems.The elevator supervisory group control problem is related to many other stochastic traffic control problems, especially with respect to the complex behavior and too many difficulties in analysis, design, simulation, and control [ 4,5].lt is one of close attention problems that how to control the elevator group in order to improve the service performance.

All the car calls must be served before an elevator can change its direction. The collective principle can also be used for the landing calls, but in a modem group control the landing call service is optimized by more sophisticated algorithms. A typical optimization target is to minimize the average and maximum call times. A landing call comes on

lian Liu is a teacher at the Faculty ofinfonnation and Control Engineering, Shenyang lianzhu University, Shenyang Liaoning China ,and a Ph.D at the Faculty ofinfonnation Science and Engineering,Northeastern University, Shenyang, Liaoning (email: jeanliuIO@163.com).

This work was supported by the Ministry of Housing and Urban-Rural Development, China (201O-K9-22).

978-1-4244-6337-4/10/$26.00 @2010 IEEE 491

when a passenger pushes the call button and is canceled when a car starts to decelerate to the call floor. Behind a landing call there is one or more passengers. Passenger waiting times differ from the landing call times especially during a high passenger arrival rate. Then all the passengers may not fit into a car and they have to wait for another car. Conventionally, the traffic peak periods are recognized on the basis of the car load data and the numbers of car and landing calls. As a result the control operations to serve the traffic peak begin after the peak traffic period has already continued for some time[ 6-7].

In the following the ESGC system control method based on a neural network has been discussed. The PSO algorithm might be useful to determine the parameters of self-adaptive ESGC systems that can handle high maximum traffic situations.

II. THE ELEVATOR GROUP CONTROL SYSTEM

A. Problem Description The elevator group control can be viewed as a combination

of on-line scheduling, resource allocation and stochastic optimal control problem. In a typical elevator system, there are two types of calls. The hall call is given through buttons on the hall of the building, and the car call is given by the passengers inside the elevator. An elevator system has a pair of hall call buttons on each floor, one for up hall call and the other for down hall cull. As soon as a hall call button is pressed, the elevator system must register the hall call, and selects and assigns an elevator to serve the hall call. After serving the hall call, the passenger should press the car call button to register his destination floor and the elevator must move up/down to stop at the destination floor. When all calls are served, the elevator gets look to an idle state.

The elevator group control system consists of three modules: call management module, control strategy module and movement module.

The call management module is mainly used to manage the car calls and the hall calls. The movement status module describes the event where passengers get into or get out of the elevator car, and the movement activities of each elevator between floors, the operation status and so on. The control strategies module is used to record some specific information about the current elevator system. The data signals would be collected from the outside the elevator system. It can learn the current traffic data and predict the future traffic states. The traffic data would be classified and the control model is built, the answer call control signals are sent depending on the traffic data and the status.

B. Traffic Pattern The main streams of traffic flows can be divided roughly

into three traffic components[8]. They are incoming, outgoing and inter-floor passenger traffic components. During the incoming traffic, passengers arrive at the building, and during the outgoing traffic they exit the building. In the inter-floor traffic the passengers travel from one populated floor to another inside the building.

Real traffic patterns during a day are combinations of these three traffic components. For general office building, the traffic intensity is highest in the morning at 8:30 a.m. and during the lunch hour at 12:00 a.m. During the morning up-peak, people arrive at work and it is the most demanding time for the elevator handling capacity. A lot of inter-floor traffic in the morning has also been measured. During the lunch hour there is typically about 40 per cent incoming, 40 percent outgoing, and 20 per cent inter-floor traffic. The lunch hour traffic is the most demanding for the group control capability since there are a lot of car and landing calls to be served. In the evening, people exit the building, and mostly outgoing traffic is forecast.

C. Optimization Cost Criterion Functions An optimal control strategy is a precondition to minimize

service times and to maximize the elevator group capacity. To provide satisfactory performance, we embed the sense of satisfaction of passengers into elevator system, it may be taken as evaluate index for the optimal control strategies. We take waiting time, riding time, and power consumption as parameters of our optimization criterion estimation. The cost of waiting is piecewise linearly increasing with time, and the cost of riding is considered with both the riding time and the moving distance. The cost of power consumption is dependent on the elevator running start /stop number in a certain time . An synthesized weight cost can be defined as follows:

(1)

z = min(,L4 J12 ...... J1;) (2)

Where , i denotes the distributed numbers of elevators i= 1,2, ...... n, J1 denotes the cost criterion functions of the elevators , TAWT(i) is the average passenger waiting time, T RM(i) is passenger riding time, TpCU) is elevator power consumption,W], W2, W3 are weight factors.

III. A HYBRID METHOD APPLIED IN ELEVATOR GROUP CONTROL SYSTEM

The waiting time of the elevators system is one of the most important criterion indexes . Besides speeding up the elevator, learning is a better choice to minimize the waiting time. If the scheduler could know the traffic pattern by analyzing the current statistic data, it would park the elevator at the proper floor to minimize the next passenger's waiting time [9] . This is why elevators system should learning. Here, the RBF neural

492

network learning and PSO optimal algorithm are connected .And a hybrid control method has been presented.

A. RBF Network The radial basis function (RBF) networks provide an

alternative method to accomplish the same work as ANN. However, in contrast to ANN, the RBF network has a more compact topology and less training time for learning. A common learning strategy for an RBF network is to randomly select some input data sets as the RBF centers in the hidden layer.

bo WE R'"

y,

x,

Xn 1----- y.

b.

Fig.I.RBF network structural diagram

Fig.1 shows a schematic diagram of the RBF network.

Where , X = (xi' x2' , XJT E Rn is the network input vector, WE Rhxm is the output matrix, bo , . , bm are the output thresholds, Y = [Yl' ... ' Y m t is the output, (*) is the activation function of the i -the hidden node, Cj is the hidden -layer node center parameter.

The network is comprised of three layers: input layer, hidden layer, and output layer. The input and output layers are presented with training pairs, each consisting of a vector from an input space and a desired network response. Through a defined learning algorithm, the error between the actual and desired response is minimized relative to some optimization criterion. The output nodes of the RBF network can be expressed as follows:

h Yk = L w;; (11x - c; II) i=1

(3)

The output layer variables indicate the prediction values of elevator consumption. They are a linear combination with the hidden nodes, and the power values are adjustable. Equation (3) reveals that the output of the network is computed as a weighted sum of the hidden layer outputs. Fig. 2 presents the RBF centers with different width and position.

The nonlinear output of the hidden layer is radically symmetrical. In this paper, the most widely used Gaussian function is chosen as follows:

J;(x) = exp[ (x -Ci)T \X -Ci) ] , (i = I,2A q) 2CFi

(4)

Where f(x) and Cj are the parameters that control the "width" and "position" of the RBF centers, respectively.

l.2

-8 -6 -4 -2 -0.2 2 4 6 8 Fig.2. RBF centers with different width and position

We construct a network structure RBF (6X IOX3). There are six input variables in input layer: MWT: The floor with max. waiting time. MHC: The floor with max. hall call. MCC: The floor with max. car call. MCCN: The number of car calls at the floor MCC. MSF: The floor with max. stops. MSN: The number of stops at the floor MSF.

There are three output variables in the output layer: Up Peak Pattern: IfYl = U, the traffic pattern is Up Peak

from floor 'V'. Down Peak Pattern: If Y2 = d, the traffic pattern is Down

Peak to floor 'd'. Inter Floor Pattern: If Y3 = I, the traffic pattern is Inter

Floor. For example, if the output vector of the neural network is [I,

0, 0], we can identify the running traffic pattern is Up Peak from floor '1 '. Of course, the scheduler should park the idle elevator at floor 'I'.

It follows from (3) and (4) that there are four sets of parameters governing the mapping properties of the network: the number of centers in the hidden layer, the position ofRBF centers, the width of RBFs, and the weights. In general, a sufficient number of centers are randomly chosen as a subset of the input space according to the probability density function of the training data. Then the stochastic gradient approach is used to tune the other three sets of parameters (that is, the position ofRBF centers, the width ofRBFs, and the weights). The main disadvantage of this method is that it is very difficult to quantify how many numbers of center should be adequate to cover the input vector space. Furthermore, the training algorithm is prone to getting stuck in local minimum. To overcome these limitations, this paper employs the PSO algorithm to determine the parameters .The PSO algorithms are described as below.

B. Particle Swarm Optimization Kennedy and Eberhart proposed the PSO algorithm

conceptually based on social behavior of organisms such as

493

herbs of animals, schools of fish and flocks of birds [10]. PSO is a pseudo- optimization method (heuristic) inspired by the collective intelligence of swarms of biological populations. PSO is a zero- order, non- calculus- based method (no gradients are needed), can solve discontinuous, multimodal, non- convex problems [11].

In PSO, It includes some probabilistic features in the motion of particles. The system initially has a population of random solutions. Each potential solution, called particle, is given a random velocity and is flown through the problem space. The particles have memory and each particle keeps track of previous best position and corresponding fitness. That is, each particle represents an alternative solution in the multidimensional search space. Thus these particles are multidimensional vectors whose trajectories are updated based on the velocity defined by its previous best success,

Phesf ,and the best success achieved by the best particle in the swarm, gbesf ,some useful modifications, use of inertia weight and constriction factors has made the original implementation of the technique very efficient.

The velocity and position of the particles are updated based on the following equations:

V;;+l = WV;; + Clrl (P;esfid -Xi ) + C2r2 (g;esfid -Xi ) (5) Xk+l = Xk + Vk+l id id id (6)

Where X;d and Vid are the current location and velocity vector of the i-th particle in its d-th dimension. OJ is called the inertia weight controls global exploration and local exploitation of the particles, and is usually varied linearly from 0.9 to 0.4 in a decreasing order throughout the simulation. c 1 and c2 are the acceleration constants that act as weights to provide the relative pull for each particle toward

Phesf and gbesf positions. rl and r2 are two uniformly distributed random variables in the range[O, 1] to provide a

stochastic variation in the relative pull toward Phesf andgbest

C. Hybrid Method The PSO algorithm is used to optimize the initial weights

and biases of the neural network. A threshold selection technique is presented as a method to cope with noisy fitness function values during the optimization run. The neural network algorithm of elevator is studied and then the data have collected to emulate the system and got the evaluation parameters of every elevator.

The basic concept of PSO technique lies in accelerating the particle towards its pbest and the gbest locations at each time step. Acceleration has random weights for both pbest and gbest locations.

The flowchart illustrates the steps and update equations of a particle swarm optimizer as shows in Fig.3.

Elevator traffic Data

N Fitness( X> Fimess( G'

N Fimess( X> Fimess( r:

N f(x;) < t:

Elevator Distributing

Fig.3. The PSO flowchart illustrating

The step-by-step algorithm of PSO optimal neural network is given as below.

Step 1: Setup the neural network construction; Initialize a population of particles with random positions and velocities of d dimensions in the problem space:

Step 2: For each particle, evaluate the desired optimization fitness function in d variables.

Step 3: Compare particle's fitness evaluation with particles

Pbesf' If current value is better than Pbesf ' then set Pbesf

494

value equal to the current value and the Pbesf location equal to the current location in d dimensional space.

Step 3: Compare fitness evaluation with the population's

overall previous best. If the current value is better than gbesf' then reset gbesf to the current particles array index and value.

Step 4: Change the velocity and position of the particle according to (5) and (6) respectively. Vid and Xid represent the velocity and position of ith particle with d dimensions respectively and rl and r2 are two uniform random functions.

Step5: Repeat step 2 until a criterion is met, usually a sufficiently good fitness or a maximum number of iterations function evaluations.

IV. SIMULATION IMPLEMENTATION

The proposed PSO based RBF algorithms is applied to elevator system. In order to verify the control algorithmic feasibility, the simulation analysis has been done under different method. The simulation data as show in table 1.

Floor

16

Open time (s)

TABLE I ELEVATOR TRAFFIC DATA

Num.

4

Closing time (s)

3

Capacity Speed (kg) (m/s)

1500

Single-time (s)

1.5

2.5

Turnover time(s)

0.75

Distance (m)

3.3

Cycle(s)

124.5

lO ..---__ _ P '_"o_ 'm_ a_nc_, ' _' 9_B_ 3 3_ 39_' '-..:.7 ' -Go-a' -' _,-' -6-_----.

'" 10 .f i". 1O. f--------------=___J

10 7 0!:----;';1O,---""2""0 --""30,---""4""0 --7.50,----' Stop Tr I 57 Epochs

FigA,RBF training steps

10' ,---P' -"o -'ma_n-c'- " _9 -.99-BO" -,0 -07- , Goa _" _, ,_,-0-0-6 -,

1O' ----------':========-l m

Stop Tr I 970 Epochs FigS PSO training steps

1O ..-__ P._"o_'m _an_"_ i'_ 99_"_36_ . O_07.:.... G_ Oal _i, _, ._.OO _6 __ --,

lO f----------========---J

10., O);----C----;';;1O:----'CCS----;;20;-O --' Stop Tr!IIirIinSiJ 23 Epochs

Fig.6. Hybird method training steps

Figo4-Fig.6 shows the simulation results of waiting time training process. Here, the objective error is 0.000001, (7i = 1 , cl =c2=2, OJrnin = 004, OJmax = 0.95 , rl and r2 is selected as 0.01, 0.05 respectively. It is obvious that the training number of iteration speed of the hybrid method is less than PSO and RBF, and the training time of the PSO and

RBF are longer than the hybrid, the training time are slowly.

OJ 0.1 0.2 0.5

10'

10'

Stop Training I

TABLE 2 NUMBER OF ITERA nON COMPARISON

UNDER DIFFERENT METHODS RBF PSO 55 901

201 305 297 543

ConventbnaJ R8F net'M)rk methOd

100 "" Iterations

Hybird 22 23 15

Fig.7. Different methods comparation

In the paper, the simulation research have been done under the same condition based on different method ,such as RBF neural network , basic PSO and hybrid method, and the simulation results have been compared. For each trial vector, a fitness value should be assigned and evaluated. The least-squared fitting error results for the three cases are given in Fig.7. It is obvious that the hybrid method is faster than PSO and RBF under the same allowable error, and the PSO and RBF are longer than the hybrid. The RBF neural network based on PSO has cut short the elevator run time, and has better convergence.

V. CONCLUSIONS In this paper, the intelligent optimal control method of the

RBF neural network based on PSO algorithm is applied in the

495

elevator group control system to assess the evaluation indicator . The optimization cost criterion function has been presented. According to defects of neural network, PSO algorithm is used to optimize the initial weights and biases of the neural network. On the basis of these results we conclude that the method is effective to determine the elevator waiting time. The results of simulation prove that the neural network based on improved PSO algorithm can avoid local minimum of neural network, reduce numbers and times of training. And it can provide foundation for dispatching and decision of the EGCS. The EGCS could reduce the waiting times of the elevators, and finish the optimal dispatch of elevators to realize the goal of minimum costs.

REFERENCES

[I] Ashok B. Kulkarni, Hien Nguyen and E. W Gaudet, "A comparative evaluation of fine regenerative and nonregenerative vector controlled drives for AC gearless elevators," IEEE Trans Ind. Application., vol. 3, pp: 1431-1437, August 2000. [2] Eun Mi Kim Kusumoto, S. Tsuchiya, T. Kikuno, T., "An approach to safety verification of object-oriented design specification for an elevator control system," IEEE Dept. olIn! & Math. Science, Osaka Univ. vo1.12, pp: 256-263, Feb. 1997. [3] Takahashi, N. Yamada, T. Miyagi, D. Markon, S , "Basic study of optimal design of linear motor for rope-less elevator," IEEE Dept. 0/ Electron. Eng., vol. 7-10, pp: 202-203, April 2008 [4] Parry, I. Houpis, C., "A parameter identification self-adaptive control system," IEEE Trans A utomatic Control, vol. 15, pp: 462-468, January 1970. [5] Tobita, T. Fujino, A Segawa, K Yoneda, K Ichikawa, Y, "A parameter tuning method for an elevator group control system," IEEE IECON, vol. 2, pp:823-828, August 1996. [6] Yuan-Wei Ho Li-Chen Fu, "Dynamic scheduling approach to group control of elevator systems with learning ability," IEEE Dept. 0/ Comput.voU, pp: 2410-2415, Apr 2000. [7] M.AS. Kamal, Junichi Murata, Kotaro Hirasawa, "Elevator Group Control Using Multiagent Task-Oriented," IEEJ Trans. EIS, vol. 125, No. 7, pp: 1140-1146,2005. [8] Robert H. Crites, Andrew G Barto, "Elevator Group Control Using Multiple Reinforcement Learning Agents," Machine Learning, voU3, pp: 235-262, 1998. [9] Manhew Brand and Daniel Nikovski, "Optimal parking of elevator cars in supervisery group control " in preparation/or IEEE Transacions on systems, Man, and Cybernetics ,part B. pp: 212-219,2003. [10] Brandstatter, B. Baumgartner, u., "Particle swarm optimization -mass-spring system analogon," Magnetic, IEEE Transaction on, vol. 38, pp: 997-1000,2000. [II] Baumgartner, U. Magele, C. Preis, K Renhart, W, "Particle swarm

optimisation for Pareto optimal solutions in electromagnetic shape design," Science, Measurement and Technology, lEE Proceedings. Vol. 151, pp: 499-502, 2004.

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