ELEVATOR TRAFFIC FLOW PREDICTION USING ARTIFICIAL
INTELLIGENCE
LEE CHOO YONG
A project report submitted in partial fulfillment of the
requirements for the award of the degree of
Master of Engineering (Electrical - Electronics and Telecommunications)
Faculty of Electrical Engineering
Universiti Teknologi Malaysia
APRIL 2008
iii
ACKNOWLEDGEMENT
I would like to take this opportunity to express my deepest gratitude to Dr.
Shahrum Shah bin Abdulah for supervising my project. My utmost thanks also go to
Associate Professor Dr. Mohd. Wazir bin Mustafa for allowing me to take project
under Dr. Shahrum Shah because I am MEL student that suppose to take electronics
or communication project instead of control engineering project. The main reason I
proposed a project related to elevator technology to Dr. Shahrum is I am working in
elevator company and I really hope to contribute something to elevator industry in
Malaysia.
I also appreciated co-operation rendered by my fellow colleagues from Fuji
Lift and Escalator Mfg. Sdn. Bhd, for assisting me to do a good job every day. I
would like to thank my good friends Mr. Teh Cheng Hock and Mr. Yin Earn Chee
for his utmost support for preparing this thesis. I am also indebted to Mr. Koay Teng
Cheang, Mr. Ooi Eng Sim and Mr. Alex Koay for supporting my research in elevator
traffic flow. My fellow course mates should be recognized for their support and
advice in preparing this dissertation. They are Lau Buck Hoon, Wong Goon Weng,
Huzein Fahmi Hj. Hawari, Chuah T.C. and class monitor of Kulim center Zulkanay
Z..
Finally, I would like to express my warmest gratitude to my beloved wife
May Pau, mother and brothers for their support and patience.
iv
ABSTRACT
Elevator traffic flow prediction is essential part of the modern elevator group
control system to enable controller apply the best dispatching strategy based on
predicted traffic flow data to achieve optimum operation with the aim to reduce
average waiting time of passenger for arrival of elevator to serve them. Generally,
elevator traffic flow has high complexity and passenger flow possesses nonlinear
feature which is difficult to be expressed by a certain functional style. In this thesis,
artificial intelligent technique radial basis function neural network (RBF NN) is used
to develop elevator traffic flow prediction model. RBF NN is selected because it is
suitable to model nonlinear system and can be trained using fast 2 stages training
algorithm assures fast convergence. The past interval traffic flow data and traffic
flow data at same time on previous days are used to train RBF NN so that it could
predict traffic flow ahead. Neural network toolbox that incorporates newrbe and
newrb functions in matlab software is employed to develop algorithm and program
of RBF NN. Optimum spread constant that will yield minimum mean square error is
obtained and become input to the RBF NN. Ten cases with different k and p are
studied to evaluate performance of RBF NN. Given training data collected from
field, RBF NN is able to predict elevator up peak traffic flow occur at 8:15 a.m. (in 5
minutes interval) which is short term traffic fairly accurate. Mean square errors from
simulation results are small and some of them could be neglected. The maximum
mean square error is 2.82 for case that use past 3 interval data on 4th day and past 3
days (1st,2nd and 3rd day) data to predict traffic flow on 5th day executed by using
newrb function. It is concluded that RBF NN is an effective artificial intelligent
technique to build elevator traffic flow prediction model.
v
ABSTRAK
Ramalan aliran traffik lif adalah bahagian penting dalam sistem kawalan lif
kumpulan moden supaya pengawal melaksanakan strategi pengangkutan terbaik
berasaskan data ramalan aliran traffik untuk mencapai operasi optimum dengan
tujuan mengurangkan masa tunggu min penumpang.
Amnya, aliran traffik lif
mempunyai kekompleksan yang tinngi dan aliran penumpang memiliki cirri taklinear
yang sukar dinyata oleh corak fungsi tertentu.
Dalam tesis ini, teknik kepintaran
buatan radial basis function neural network (RBF NN) digunakan untuk
membangunkan model ramalan aliran traffik lif. RBF NN dipilih sebab ia sesuai
untuk membentuk sistem taklinear dan boleh dilatih dengan algoritma perlatihan 2
peringkat cepat yang menjamin penumpuan cepat. Data aliran traffik selang masa
lepas dan data aliran traffik pada masa yang sama pada hari-hari lepas digunakan
untuk melatihkan RBF NN supaya ia dapat meramalkan aliran traffik akan dating.
Neural network toolbox yang mengandungi fungsi newrbe dan newrb dalam perisian
matlab digunakan untuk membangunkan algoritma dan aturcara RBF NN. Pemalar
menyebar optimum yang menghasilkan ralat kuasa dua min ( minimum diperolehi
dan dijadikan input kepada RBF NN.
Sepuluh kes telah dikaji untuk menilai
percapaian RBF NN. Dengan membekalkan data latihan yang dikumpul dari tempat
kajian, RBF NN mampu meramalkan aliran traffic puncak atas yang berlaku pada
8:15 a.m. (dalam selang masa 5 minit) iaitu traffik jangka masa pendek dengan agak
tepat. Ralat kuasa dua min dari keputusan-keputusan simulasi adalah kecil dan
sebahagiannya boleh diabaikan. Ralat kuasa dua min maksimum ialah 2.82 untuk
kes yang menggunakan 3 data lepas pada hari keempat and data 3 hari lepas (hari
pertama, kedua dan ketiga) untuk meramalkan aliran traffk pada hari kelima
dilaksanakan dengan fungsi newrb. Ianya dirumuskan bahawa RBF NN ialah teknik
kepintaran buatan yang berkesan untuk membina model ramalan aliran traffik lif.
vi
TABLE OF CONTENTS
CHAPTER
1
2
3
TITTLE
PAGE
DECLARATION
ii
ACKNOWLEDGEMANT
iii
ABSTRACT
iv
ABSTRAK
v
TABLE OF CONTENTS
vi
LIST OF TABLES
viii
LIST OF FIGURES
x
INTRODUCTION
1
1.1
Introduction
1
1.2
Objective of Project
3
1.3
Scopes of Work and Research Methodology
4
1.4
Thesis Outline
5
ELEVATOR TRAFFIC FLOW AND CONTROL
7
2.1
Elevator Traffic Flow
7
2.2
Intelligent Elevator Group Control System
13
2.3
Summary
22
LITERATURE REVIEW
23
3.1
Radial Basis Function Neural Network (RBF NN)
23
3.2
Elevator Traffic Flow Prediction
26
3.3
Summary
38
vii
4
METHODLOGY
39
4.1
Introduction
39
4.2
Problem Statement
39
4.3
Elevator Traffic Flow Data Collection at Field
41
4.4
RBF NN Elevator Traffic Prediction Model Design
47
4.5
Software Implementation and Simulation
50
4.5.1
52
Simulation to Obtain Optimum Spread
Constant
4.5.2
Simulation of Network Performance and Goal
84
for Newrb Function
5
SIMULATION RESULTS AND DISCUSSION
91
5.1
Introduction
91
5.2
Discussion of Results for All Cases
102
5.2.1
Discussion of Simulation Result for Case 1
102
5.2.2
Discussion of Simulation Result for Case 2
103
5.2.3
Discussion of Simulation Result for Case 3
105
5.2.4
Discussion of Simulation Results for Case 4, 5
106
and 6
5.3
6
5.2.5
Discussion of Simulation Results for Case 7
110
5.2.6
Discussion of Simulation Results for Case 8
111
5.2.7
Discussion of Simulation Results for Case 9
113
5.2.8
Discussion of Simulation Results for Case 10
114
Summary
116
CONCLUSION AND FUTURE DEVELOPMENTS
117
6.1
Conclusion
117
6.2
Future Development
118
REFERENCES
119
APPENDIX
124
viii
LIST OF TABLES
TABLE NO.
TITTLE
PAGE
2.1
Recommended average waiting time in seconds
12
2.2
Recommended 5 Minutes Capacity Handling Ratio (%)
13
2.3
Rules to determine the traffic type
17
2.4
Fuzzy rules to determine traffic pattern
18
2.5
Comparison of performance during four traffic patterns
22
3.1
Comparison of prediction results of five different prediction
37
models
4.1
Elevator traffic flow data
43
4.2
Input data and traffic flow to be predicted
49
4.3
Mean square for case 1
64
4.4
Mean square for case 2
66
4.5
Mean square for case 3
68
4.6
Mean square for case 4
70
4.7
Mean square for case 5
72
4.8
Mean square for case 6
74
4.9
Mean square for case 7
76
4.10
Mean square for case 8
78
4.11
Mean square for case 9
80
4.12
Mean square for case 10
82
4.13
Summary of mean square error and optimum spread
84
5.1
Comparison of RBF NN output for newrb and newrbe and
102
real data (Case 1)
5.2
Comparison of RBF NN output for newrb and newrbe and
real data (Case 2)
104
ix
5.3
Comparison of RBF NN output for newrb and newrbe and
105
real data (Case 3)
5.4
Comparison of RBF NN output for newrb and newrbe and
107
real data (Case 4)
5.5
Comparison of RBF NN output for newrb and newrbe and
108
real data (Case 5)
5.6
Comparison of RBF NN output for newrb and newrbe and
109
real data (Case 6)
5.7
Comparison of RBF NN output for newrb and newrbe and
110
real data (Case 7)
5.8
Comparison of RBF NN output for newrb and newrbe and
112
real data (Case 8)
5.9
Comparison of RBF NN output for newrb and newrbe and
113
real data (Case 9)
5.10
Comparison of RBF NN output for newrb and newrbe and
real data (Case 10)
115
x
LIST OF FIGURES
FIGURE NO.
TITTLE
PAGE
1.1
Block diagram of AI-2200C elevator group control system
2
1.2
Block
3
diagram
of
multi-agent
coordination
based
elevator group control scheduling
2.1
Typical elevator traffic pattern for a weekday
8
2.2
Example of typical elevator traffic pattern for a weekday
8
2.3
Incoming, outgoing and inter-floor traffic flow in building
9
2.4
Up peak traffic profile
10
2.5
Up peak traffic profile occurs twice
10
2.6
Down peak traffic profile
11
2.7
Block diagram of performance tuning EJ-1000FN control
14
system
2.8
TMS9000 group control system block diagram
15
2.9
Membership function for incoming, outgoing and inter-floor
16
components
2.10
Membership function for incoming traffic intensity
16
2.11
Structure of the fuzzy elevator group control system
19
2.12
Overview of proposed elevator group control system
20
2.13
Block diagram of traffic predictor
21
3.1
Architecture of RBF NN
24
3.2
Number of passengers arriving main terminal on a working
27
3.3
Number of passengers leaving main terminal on a working
28
day
3.4
Total number of passengers on a working day
28
xi
3.5
The maximum proportion of inter-floor traffic flow on a
29
working day
3.6
Second proportion of inter-floor traffic flow on a working
29
real data (Case 1)
3.7
Architecture of WNN
30
3.8
Elevator incoming traffic prediction on a working day by
31
ES
3.9
Elevator outgoing traffic prediction on a working day by
31
ES
3.10
Total number of passengers prediction on a working day by
32
and ES
3.11
Prediction of total number of passengers on a working day
33
3.12
Prediction of incoming traffic flow on a working day
34
3.13
Prediction of outgoing traffic flow on a working day
34
3.14
WSVM prediction model
36
3.15
Comparison of prediction result and real traffic flow data
37
4.1
Right shifting of up peak traffic flow
40
4.2
Up peak traffic flow pattern during holiday and when
40
function is conducted in the building
4.3
Main entrance at BHL Tower, Penang
41
4.4
Side view of Menara BHL
42
4.5
Lift lobby at Menara BHL
42
4.6
Elevator traffic flow on Monday
44
4.7
Elevator traffic flow on Tuesday
44
4.8
Elevator traffic flow on Wednesday
45
4.9
Elevator traffic flow on Thursday
45
4.10
Elevator traffic flow on Friday
46
4.11
Elevator traffic flow from Monday to Friday
46
4.12
Flow chart to develop and fine tune the RBF NN based
47
4.13
RBF NN elevator traffic flow prediction model
48
4.14
Optimum spread constant for newrbe function (for case 1)
53
4.15
Optimum spread constant for newrb function (for case 1)
54
4.16
Optimum spread constant for newrbe function (for case 2)
54
4.17
Optimum spread constant for newrb function (for case 2)
55
4.18
Optimum spread constant for newrbe function (for case 3)
55
xii
4.19
Optimum spread constant for newrb function (for case 3)
56
4.20
Optimum spread constant for newrbe function (for case 4)
56
4.21
Optimum spread constant for newrb function (for case 4)
57
4.22
Optimum spread constant for newrbe function (for case 5)
57
4.23
Optimum spread constant for newrb function (for case 5)
58
4.24
Optimum spread constant for newrbe function (for case 6)
58
4.25
Optimum spread constant for newrb function (for case 6)
59
4.26
Optimum spread constant for newrbe function (for case 7)
59
4.27
Optimum spread constant for newrb function (for case 7)
60
4.28
Optimum spread constant for newrbe function (for case 8)
60
4.29
Optimum spread constant for newrb function (for case 8)
61
4.30
Optimum spread constant for newrbe function (for case 9)
61
4.31
Optimum spread constant for newrb function (for case 9)
62
4.32
Optimum spread constant for newrbe function (for case 10)
62
4.33
Optimum spread constant for newrb function (for case 10)
63
4.34
Training of network for newrb function (for case 1)
85
4.35
Training of network for newrb function (for case 2)
85
4.36
Training of network for newrb function (for case 3)
86
4.37
Training of network for newrb function (for case 4)
86
4.38
Training of network for newrb function (for case 5)
87
4.39
Training of network for newrb function (for case 6)
87
4.40
Training of network for newrb function (for case 7)
88
4.41
Training of network for newrb function (for case 8)
88
4.42
Training of network for newrb function (for case 9)
89
4.43
Training of network for newrb function (for case 10)
89
5.1
Simulation result for newrb function (for case 1)
92
5.2
Simulation result for newrbe function (for case 1)
92
5.3
Simulation result for newrb function (for case 2)
93
5.4
Simulation result for newrbe function (for case 2)
93
5.5
Simulation result for newrb function (for case 3)
94
5.6
Simulation result for newrbe function (for case 3)
94
5.7
Simulation result for newrb function (for case 4)
95
5.8
Simulation result for newrbe function (for case 4)
95
5.9
Simulation result for newrb function (for case 5)
96
5.10
Simulation result for newrbe function (for case 5)
96
xiii
5.11
Simulation result for newrb function (for case 6)
97
5.12
Simulation result for newrbe function (for case 6)
97
5.13
Simulation result for newrb function (for case 7)
98
5.14
Simulation result for newrbe function (for case 7)
98
5.15
Simulation result for newrb function (for case 8)
99
5.16
Simulation result for newrbe function (for case 8)
99
5.17
Simulation result for newrb function (for case 9)
100
5.18
Simulation result for newrbe function (for case 9)
100
5.19
Simulation result for newrb function (for case 10)
101
5.20
Simulation result for newrbe function (for case 10)
101
CHAPTER 1
INTRODUCTION
1.1
Introduction
Elevators are installed in the buildings to satisfy the vertical transportation
needs. It is stipulated in Building Bylaws that elevator(s) shall be installed in the
building that contains four or more floors to facilitate traffic flow. Architect and
building service engineer play the role in designing elevator system for new building.
Elevator traffic flow is fundamental element in elevator group control system.
Accurate elevator traffic flow prediction is crucial to the planning and dispatching
strategy of elevator group control system.
During the peak traffic period,
performance of elevator group control system depends on prediction of traffic flow.
For instance, Mitsubishi Electric Co. has successfully developed an intelligent
elevator group control system AI-2200C which is recently available in market. It
incorporates neural network based traffic flow prediction module as shown in Figure
1.1. The role of traffic prediction module is to precisely recognize current traffic flow
in real time and predict traffic flow in the next several minutes based on both past
and current operating data. The predicted traffic flow data is then feedback to ruleset selection module to simulate rule sets in group controller in order to achieve
optimum dispatching of elevators to serve passengers.
2
Figure 1.1 Block diagram of AI-2200C elevator group control system.
Hitachi Elevator Engineering Co. developed FI series artificial intelligence
elevator group supervisory control systems to improve transportation efficiency in
building. FI series control system incorporates traffic flow recognition module. The
module could learn traffic flow pattern of individual building and stored in database.
Control system will employ this data to forecast traffic flow and assign more lifts to
serve floor with heavy traffic flow.
In recent research to design a elevator group control system based on multiagent coordination approach (Zong et al, 2006a), traffic flow prediction function is
also incorporated into coordination mechanism (core structure) so that the system
could reduce the average waiting time of passengers at most of the traffic flow
pattern. The block diagram of multi-agent coordination based elevator group control
scheduling is illustrated in Figure 1.2.
From the above examples, it could be
concluded that traffic flow prediction module is the very important element in
elevator group control system.
3
Local knowledge
Non-local
module
Local scheduler
information
Coordination
mechanism
Schedule
elevator
Figure 1.2 Block diagram of multi-agent coordination based elevator group
control scheduling.
The elevator traffic flow fluctuates significantly in morning, lunch hour and
evening. Generally, elevator traffic flow possesses non linear feature which is very
difficult to be expressed by a certain functional style. Various methods have been
employed as a fundamental to design elevator traffic flow prediction model. These
methods include Morlet wavelet function, support vector machine, least squares
support vector machine and wavelet support vector machine. Most of the articles
related to elevator technology are published by researchers from China due to strong
growth of elevator market as stated in 2006 annual report of Kone Corporation.
1.2
Objective of Project
Objective of this project is to develop an algorithm to predict short term up
peak elevator traffic flow in building by using radial basis function neural network
(RBF NN).
4
The radial basis function is one of the common architecture of artificial
neural network. The RBF NN is chosen because it has been widely used for nonlinear function approximation. A minimal RBF NN has been developed by Lu Y. et
al. (1997) to identify time-varying non-linear system. Besides that, capability of
RBF NN has also been further enhanced. The two stages training procedure adapted
in numerous RBF NN applications usually yields satisfactory result (Husain, 2002).
Nowadays, there are only limited research and development works related to
elevator technology being carried out in Malaysia. Tan Kok Khiang (Tan, 1997) and
Kumeresan (Kumeresan and Khalid, 2005) from Universiti Teknologi Malaysia have
developed elevator group control system based on ordinal structure fuzzy reasoning
method which performs better than conventional elevator group control system with
hall call assignment approach and it is believed that the system could be further
enhanced if traffic flow prediction module is incorporated to form a complete
intelligent elevator group control system.
1.3
Scopes of Work and Research Methodology
Scopes of work for this project are to study elevator traffic flow and develop
RBF NN based algorithm by using matlab software to predict up peak traffic flow of
elevator. A case study is carried out to evaluate performance of RBF NN elevator
traffic flow prediction model. Traffic flow data is collected in one commercial
building as training data and testing data. Up peak traffic flow pattern at morning
will be studied and analyzed. Data is collected from 7:30 a.m. – 10:00 a.m (150
minutes) because it covers working hour starts at 8:00 a.m. to 9: 30 a.m.
As
sufficient data is needed to train the RBF NN, data is collected for five working days
continuously. The overall scopes of work in sequence are listed as followings:
•
To study fundamental of elevator traffic analysis.
5
•
To acquire knowledge in radial basis function neural network (RBF NN) and
further understand its application especially in traffic flow prediction.
•
To review past researches related to elevator traffic flow prediction.
•
To acquire skill of using matlab software.
•
To develop RBF NN based algorithm by using matlab software to predict up
peak traffic flow of elevator in office building.
•
To collect data at field. The number of passengers that will use elevator in
five minutes interval shall be recorded as it represents traffic flow.
•
To train the developed algorithm by using collected data.
•
To simulate the developed algorithm by using collected data and verify the
simulated results by comparing with experimental result.
1.4
Thesis Outline
This thesis consists of 5 chapters. Chapter 1 gives a brief introduction of the
project. The importance elevator traffic flow prediction module in modern elevator
control system is discussed. Besides that, chapter 1 also covers objective and scope
of project.
Chapter 2 discusses types of elevator traffic flow and intelligent elevator
control system. Characteristics of incoming, inter-floor and outgoing traffic are
reviewed. Various intelligent elevator group control systems (EGCS) are also being
discussed to provide better understanding of application of artificial intelligent
techniques in elevator engineering. From the researches and development quoted,
fuzzy logic and neural network play important role in intelligent elevator group
control system to provide quality service to elevator users.
6
Chapter 3 is the literature review. It explains fundamental of radial basis
function neural network (RBF NN) which is the technique used in this project.
Advantages and architecture of RBF NN are also being discussed in detail.
Researches related to elevator traffic flow prediction using various artificial
intelligent techniques are also being reviewed. Models in the past researches provide
good basis to develop RBF NN elevator traffic flow prediction model in this project.
Chapter 4 covers methodology of data collection, development of prediction
model and simulation of model using matlab software. Results and discussion of
findings are presented in Chapter 5.
Last but not least, Chapter 6 discusses
conclusion of this project. Besides that, future works are also being discussed in
Chapter 6.
7
CHAPTER 2
ELEVATOR TRAFFIC FLOW AND CONTROL SYSTEM
2.1
Elevator Traffic Flow
The elevator traffic flows could be classified into three types namely
incoming, outgoing and inter-floor traffic as presented by G.C. Barney (1985) in the
book Elevator Traffic Analysis Design and Control which is the most important
reference for elevator traffic analysis. Elevator traffic pattern represents demand of
passenger to travel to particular floor at specific time. For example, majority of
passengers travel to upper floors cause up peak traffic to occur. The typical elevator
traffic pattern for a weekday is illustrated in Figure 2.1 while Figure 2.2 shows the
passengers arrival obtained from NESTE building. The differences of incoming,
outgoing and inter-floor traffic in building are illustrated in Figure 2.3.
8
Figure 2.1 Typical elevator traffic pattern for a weekday.
(Adapted from Barney and dos Santo, 1985)
Figure 2.2 Example of typical elevator traffic pattern for a weekday.
(Adapted from Siikonen, 1997a)
9
Figure 2.3 Incoming, outgoing and inter-floor traffic flow in building.
The incoming traffic is referring to condition when traffic flow is in an
upward direction. The up peak traffic flow occurs in morning when prospective
elevator users enter a building intent to travel to upper floors. If elevator system is
designed to cope efficiently with the morning up peak, then it shall cope with other
traffic pattern such as down peak and random inter-floor traffic. The up peak traffic
is actually result of passengers need to arrive at work place by a specific starting time,
for example 8:30 a.m. The arrival rate profile for morning up peak is illustrated in
Figure 2.3. It is obvious that the up peak traffic occurs before the work starting time
and the arrival rate decay rapidly after the starting time. The handling capacity of
elevators system in 5 minutes prior to starting time (hatched area in Figure 2.3) is the
main concern of elevator system design engineer. Common term for up peak profile
is to state the percentage of the building population that arrives over 30 minutes of
peak activity which is the square area in the Figure 2.4. The passenger arrival is a
stochastic process that could be described by a Poisson distribution (Maeda and
10
Koyama, 2000). In some circumstances, up peak traffic could occur twice due to
working hour for offices in building starts at different time as shown in Figure 2.5.
For example, working hour for company A and company B in same building start at
8:00 a.m. and 8:30 a.m. respectively, therefore it is anticipated that up peak will
occur at 7:55 a.m. and 8:25 a.m.
Figure 2.4 Up peak traffic profile.
\
Figure 2.5 Up peak traffic profile occurs twice.
11
Outgoing traffic is referring to condition where traffic flow is in downward
direction with majority passengers leaving the elevators system at the main terminal
of building. The down peak traffic occurs at the end of working day, for 5:30 p.m.
In fact, evening down peak is the reverse of the morning up peak. Evening down
peak is normally more intense than morning up peak with up to 50% higher demands
and duration of up to 10 minutes. Figure 2.6 illustrates typical departure rate profile
of evening down peak.
Figure 2.6 Down peak traffic profile.
Inter-floor traffic occurs when passengers travel randomly within floors. This
traffic is caused by the normal circulation of people around a building during the
course of their business. Sometimes this traffic is called balanced two way traffic as
it involves both up and down trips. It is balanced traffic because passengers usually
return to their original floor after finishing the business.
12
The up peak percentage arrival rate is defined as the number of passengers
who arrive at the main terminal of a building for transportation to upper floors over
the worst 5 minutes period expressed as a percentage of the total building population.
Elevator system is expected to respond to the peak demand in such a manner as to
quickly and efficiently transport passengers to destination within acceptable waiting
time. The 5 minutes handling capacity of elevator system is the total number of
passengers that it can transport in 5 minutes during the up peak condition. From the
5 minutes handling capacity, the 5 minutes handling capacity ratio could be
determined by dividing it over the total population of building. The average waiting
time (or waiting interval) is average time that passenger need to wait if he/she just
miss any elevator to serve him/her upon arrival to main terminal. As a measure of
elevator system’s operational performance, 5 minutes handling capacity ratio and
average waiting time are the two parameters most often quoted by elevator suppliers.
Table 2.1 and Table 2.2 show the recommended average waiting time for up peak
traffic and 5 minutes handling capacity ratio. These guidelines are set by elevator
manufacturers based on common practice in industry. Recently, Markov network
has been proposed to model elevator traffic flow (Zong et al., 2004).
Table 2.1 Recommended average waiting time in seconds
Type of Building
Recommended
Residential Flats
≤ 90
Hotel
≤ 50
Commercial Office
≤ 40
Hospital
≤ 50
School
≤ 50
Average
13
Table 2.2 Recommended 5 Minutes Capacity Handling Ratio (%)
Type of Building
5 Min Capacity Handling Ratio (%) [up-
Residential Flats
5-7
Hotel
10 - 15
Multiple Tenancy Commercial Office
11 - 15
Single Tenancy Commercial Office
17 - 25
Hospital
8 - 12
School
15 - 25
2.2
Intelligent Elevator Group Control System
Artificial intelligent has been introduced to elevator control system in early
1990’s. A numerous applications of artificial intelligence in lift engineering, they are
expert system control, fuzzy control, artificial neural network control and optimum
variance method as stated in CIBSE Guide D published in 2000. Among artificial
intelligence techniques, fuzzy logic is widely applied. Fuzzy logic controller is used
to control a group of elevators to minimize average waiting time. Some of the
earliest publications by Choi et al. (1993), Zhu and Wu (1993) and Kim et al. (1993)
already showed that performance of elevator control system has been improved
comparing to conventional hall call method when artificial intelligent technique
applies. In 1995, an elevator group control system with fuzzy approach to determine
area weight load biases of elevators in has been proposed (Kim et al., 1995). There
is no traffic flow forecasting module incorporated into elevator control system in
previous mentioned researches.
In 1995, fuzzy neural based elevator group control system was proposed by
Toshiba Corporation, Elevator and Escalator Division (Imasaki, N. et al., 1995). A
traffic forecasting module was incorporated into the EJ-1000FN control system so
14
that it could adapt itself quickly to changes of traffic in building. Fuzzy neural
network will learn to recognize traffic flow pattern in short term (hour order) and
store in memory to establish long term re-learning adaption. The block diagram of
performance tuning EJ-1000FN control system is illustrated in Figure 2.7. This
system is more intelligent than pure fuzzy logic elevator control system as it could
distribute elevators to particular floor with heavier traffic based on forecast.
Elevator
group
Optimal
Forecasted waiting
Evaluation
control
time distribution
Forecasting
Control
Elevator
model
parameter
group
Candidate of control
Assignment
Hall call
parameter
Traffic condition
Figure 2.7 Block diagram of performance tuning EJ-1000FN control system.
In 1997, Kone Corporation has successfully developed intelligent elevator
group control system TMS9000 (Siikonen, 1997a). The block diagram of embedded
expert system TMS9000 is shown in Figure 2.8. The measurement, data storage and
utilization of traffic information are handled in four stages as shown in the figure.
These four stages are as below:
15
•
Firstly, passenger traffic flow (arrivals and departures) is measured and
saved in the short term statistic with other traffic events such as
registration and cancellation of calls. Daily statistics are saved in the long
term statistics.
•
At second stage, exponential smoothing process is applied when adapting
new data in the long term statistical forecast.
•
At third stage, statistical forecasts are utilized in traffic pattern recognition.
•
At fourth stage, the measured passenger traffic and the prevailing traffic
pattern information are used in the landing call allocation and optimal
dispatching of elevators to the floors with heavier traffic.
Learning
and
forecasting
passenger
Measuring
passenger
traffic flow
Recognizing of traffic
pattern fuzzy logic
Dispatching of
elevators
Destination
command
Passenger traffic and elevator status
Figure 2.8 TMS9000 group control system block diagram.
Fuzzy logic is used to recognize traffic pattern in TMS9000.
The
membership function of traffic components and incoming traffic intensity are shown
in Figure 2.9 and Figure 2.10. Table 2.3 shows fuzzy rules to determine traffic type
while Table 2.4 shows fuzzy rules to determine traffic pattern. This method has been
applied in high rise building elevator planning (Siikonen, 1997b).
16
Membership Functions for Traffic Components
1.0
Low
Medium
0.0 0.0
High
50.0
100.0
Component Value
(% of Total Traffic Value)
Figure 2.9 Membership function for incoming, outgoing and inter-floor components.
Membership Functions for Incoming Traffic Intensity
1.0
Light
0.0
0.0
Normal
Heavy
50.0
100.0
Intense
Traffic Intensity
(% of Handling Capacity)
Figure 2.10 Membership function for incoming traffic intensity.
17
Table 2.3 Rules to determine the traffic type.
Incoming
Outgoing
Inter-floor
Traffic Type
high
low
low
incoming
medium
low
low
incoming
low
high
low
outgoing
low
medium
low
outgoing
low
low
high
inter-floor
low
low
medium
inter-floor
medium
medium
low
two-way
medium
low
medium
mixed
low
medium
medium
mixed
18
Table 2.4 Fuzzy rules to determine traffic pattern.
Intensity
intense
intense
intense
intense
intense
intense
intense
intense
intense
heavy
heavy
heavy
heavy
heavy
heavy
heavy
heavy
heavy
normal
normal
normal
normal
normal
normal
normal
normal
normal
light
light
light
light
light
light
light
light
light
Incoming
high
low
low
medium
low
low
medium
medium
low
high
low
low
medium
low
low
medium
medium
low
high
low
low
medium
low
low
medium
medium
low
high
low
low
medium
low
low
medium
medium
low
Outgoing
low
high
low
low
medium
low
medium
low
medium
low
high
low
low
medium
low
medium
low
medium
low
high
low
low
medium
low
medium
low
medium
low
high
low
low
medium
low
medium
low
medium
Inter-floor
low
low
high
low
low
medium
low
medium
medium
low
low
high
low
low
medium
low
medium
medium
low
low
high
low
low
medium
low
medium
medium
low
low
high
low
low
medium
low
medium
medium
Traffic Pattern
intense up-peak (1)
Intense down-peak (2)
intense inter-floor(3)
intense incoming (4)
intense outgoing(5)
intenseinter-floor (6)
intense two-way (7)
intense mixed (8)
intense mixed (9)
up-peak (10)
down-peak (11)
heavy inter-floor (12)
heavy incoming (13)
heavy outgoing (14)
heavy inter-floor (15)
two-way peak (16)
heavy mixed (17)
heavy mixed (18)
incoming (19)
outgoing (20)
inter-floor (21)
incoming (22)
outgoing (23)
inter-floor (24)
two-way (25)
mixed (26)
mixed (27)
light incoming (28)
light outgoing (29)
light inter-floor (30)
light incoming (31)
light outgoing (32)
light inter-floor (33)
light two-way (34)
light mixed (35)
light mixed (36)
In 1998, fuzzy elevator group control system has been proposed by a team of
researchers from Korea (Kim et al., 1998). Further to previous research (Kim et al.,
1996), fuzzy logic is used as the core of the control system and traffic data
management is incorporated in the system. The structure of fuzzy elevator group
control system is illustrated in Figure 2.11.
19
Traffic data management
Control strategy generation
Hall call assignment
Data management
Elevator management
Terminal management
Terminal
Elevator
Elevator
Elevator
Figure 2.11 Structure of the fuzzy elevator group control system.
Traffic data management manages traffic data of passenger by collecting,
learning periodically and prediction. Traffic data is predicted for the next unit time
to help the hall call assignment. Control strategy generation classifies the traffic data
using a fuzzy inference and makes a strategy for hall call assignment in order to
achieve optimum group control operation. The proposed system shows better results
than conventional elevator group control system.
In the recent research to propose modern elevator group control system (Chen
et al., 2006), traffic flow prediction is again playing important role in the system.
Traffic prediction is realized by using support vector machine (SVM). The block
diagram of the proposed system is illustrated in Figure 2.12. The system consists of
20
five modules namely traffic data base, traffic prediction, traffic pattern recognition,
strategy generation and hall call assignment.
Traffic data collection
Traffic database
Elevator group
control system
Traffic prediction
Traffic pattern
recognition
Strategy generation
Hall call assignment
Single elevator
control module
Single elevator
control module
Single elevator
control module
Figure 2.12 Overview of proposed elevator group control system.
They proposed traffic data to be categorized into three parts namely number
of passengers in the entire building, number of passengers entering the main terminal
and number of passengers leaving the main terminal. The block diagram of traffic
predictor is shown in Figure 2.13. X[0], X[t], X[2t], …, X[(n-1)t] are traffic data
sampled every five minutes, t is the sampling interval.
21
X[0]
X[t]
X[2t]
Traffic predictor
X[nt]
…
X[(n-1)t]
Figure 2.13 Block diagram of traffic predictor.
Another passenger based elevator group control system with traffic database
module (traffic flow prediction is used to predict future traffic pattern) also showed
satisfactory result comparing with group control system without traffic database
module (Chiang and Fu, 2002). The simulation result of the research is illustrated in
Table 2.5.
22
Table 2.5 Comparison of performance during four traffic patterns.
Up peak
Down
Inter-
Two
Elevator group control
AWT (s)
40.2
35.4
38.5
17.6
system without traffic
Elevator group control
ART (s)
36.6
31.5
30.0
25.7
AWT (s)
31.5
31.1
36.3
17.6
ART (s)
36.7
24.5
29.6
23.3
AWT
21.6
11.0
5.7
0
ART (%)
-0.2
22.2
1.3
9.3
system with traffic
Improvement
Legend:
AWT represents average awaiting time.
ART represents average riding time.
2.3
Summary
From the researches and development works as discussed in chapter 1.1 and
chapter 2.2, it is proven that elevator group control systems with artificial intelligent
perform better than conventional system. It is also proven that the role of traffic flow
prediction module is important in the elevator group control system as it could
enhance the performance.
Therefore, traffic flow prediction model shall be
developed by using suitable artificial intelligent technique to yield accurate values so
that the group control system could assign the best elevator dispatching strategy.
23
CHAPTER 3
LITERATURE REVIEW
3.1
Radial Basis Function Neural Network (RBF NN)
Artificial neural network (ANN) is the term used to describe a computer
model assumption of the biological brain. ANN is an information processing system
that could perform some tasks (as performed by human brain) like pattern
recognition, pattern matching, prediction etc. The application of an ANN involves
two phase, learning phase and recall phase. In the learning phase, ANN is trained
until it has learned its tasks (through the adaption of its weights) while recall phase is
used to solve the task (for example prediction). ANN has to be trained where
weights adjusted iteratively until error function is minimized before it can be used.
The radial basis function neural network RBF NN is one of the architecture of
ANN (Abdullah, 2005). RBF NN offers one major advantage compared to multilayer perceptrons in that they can be trained using fast 2 stages training algorithm
without the need for time consuming non-linear optimization techniques.
Furthermore, RBF possess the property of best approximation. RBF NN may require
more neurons than standard feed-forward back propagation networks but it performs
24
better than back propagation networks when many training vectors are available.
The architecture of RBF NN is illustrated in Figure 3.1.
Figure 3.1 Architecture of RBF NN.
RBF network consists of three layers namely input layer, hidden layer and
output layer. The number of hidden is to be defined by network designer. If the
number of output Q = 1, the output of RBF NN is expressed as η(x, w) = Σ
w1kΦ( x – ck2). x is an input vector, x∈RRx1, Φ is basis function,
•2
denotes Euclidean norm, w1k is weight in output layer, SI is the number of neurons in
the hidden layer
ayer and ck is RBF center in the input vector space. The equation could
be also expressed as
η(x, w) = ΦT(x)w
(3.1)
where ΦT(x) = [Φ
[ 1( x – c1) Φ2(x – c2) … ΦS1(x – cS1)]
wT = [w11 w12 … w1S1]
(3.2)
25
The basis function Φk(•) is the mathematical function. For example, Φk(x) =
x, Φk(x) = x3 or Φk(x) = exp (-x3/ζ2) which is Gaussian basis function. In order to
achieve good approximation results, large number of input vectors shall be provided
as the centers to ensure as adequate input space sampling. In the training phase, the
correct value of second layer weight need to be determined so that the weight sum of
basis function can approximate the given training output data.
The training
procedure is as below:
1. Set the centers ck using all of the input values or clustering algorithm.
2. Set the required parameter using rule of thumb or algorithm.
3. Write equation of RBF output in matrix form.
 η(x1, w

•


•

•

 (
η ,
 xN w
) 
 φ1 (x1 , c1) • • • φS1 (x1 , cS1)  w11 



•
•
•
 
 • 
=
 • 
•
•
•
 


 
•
•
•
 • 
 


  φ1 (x N , c1) • • • φS1 (x N , cS1) w1S1 
)
(3.3)
4. Define quadratic error e(w) = (y - Φw)T(y - Φw)
where y = [y1 … yN]
5. Solve for optimum set of second layer weight ŵ using least squares formula.
Clustering techniques are used to find a set of centers that more accurately
reflects the distribution of the data points. There are various clustering algorithms
like K-means algorithm, input clustering (IC) algorithm and dynamic clustering
algorithm (Qu et al., 2006). K-means clustering is the simple and common algorithm
used in RBF NN. The K-means algorithm is as below:
1. Assign the input data to random K sets.
2. Compute the mean of each set.
3. Reassign each point to a new set according to which is the nearest mean
vector.
4. Re-compute the mean of each set.
5. Repeat steps 2 and 4 until there is no further change in the grouping of data
points.
6. The mean of the sets will be the RBF centers.
26
RBF NN has been used as a basis to develop a method for approximation and
estimation of nonlinear stochastic dynamic systems (Elanayar and Shin, 1994). More
than one data set is used in order to ensure adequate learning by the neural network
over the domain of interest. A modified recursive least squares training algorithm is
employed to obtain the weights of neural networks. Once, the network will be able
to estimate the states of the unknown nonlinear system. RBF NN has been applied in
non-periodic prediction system. For instance, RBF NN is used to predict field
strength of mobile radio propagation based on collected and stored topographical and
morphographical data (Chang and Yang, 1997).
On the other hand, RBFF NN is also used to predict traffic flow which a
complex system (Qin et al., 2006) as RBF NN with local generalization abilities and
fast convergence speed could overcome shortcomings like slow convergence and
local minimum of back propagation neural network. A research has been carried out
to predict freeway traffic flow by using distributed RBF NN based on fuzzy c-means
clustering algorithm and simulation results show that it could capture the traffic flow
dynamic quite closely (Wang and Xiao, 2003). RBF NN is also being used to
develop a model to predict bus arrival time and it shows better results comparing
with historical data based model and regression model (Jeong and Rilett, 2004). As
conclusion, RBF NN is suitable to be used to develop a prediction model for
nonlinear system due to its advantages and examples as discussed above.
Combination of artificial intelligent techniques and forecasting model
3.2
Elevator Traffic Flow Prediction
Various models have been developed to predict elevator traffic flow in
building, some of them are developed on the basis of neural network and support
vector machine. Neural network has many advantages to establish prediction model
that could overcome inherent limitation of conventional time series forecasting
27
model (Zong, 2000). Firstly, three layer feed forward neural networks with sigmoid
activation function could approximate whatever function. Secondly, neural network
has strong learning capability and adaptability. Thirdly, neural network could
overcome noise problem. In many researches, combination of artificial intelligent
techniques and forecasting model is best suited for short term traffic flow (for
example, elevator traffic flow) prediction.
Neural network with advanced back
propagation algorithm has been built to predict elevator traffic flow (Wang and Dong,
2004). The predicted results of neural network (
(
) and real data (
), exponential smoothing
) are illustrated in Figure 3.2, 3.3, 3.4, 3.5 and 3.6.
Figure 3.2 Number of passengers arriving main terminal on a working day.
28
Figure 3.3 Number of passengers leaving main terminal on a working day.
Figure 3.4 Total number of passengers on a working day.
29
Figure 3.5 The maximum proportion of inter-floor traffic flow on a working day.
Figure 3.6 Second proportion of inter-floor traffic flow on a working day.
The Morlet wavelet function has been used to develop wavelet neural
network (WNN) to predict elevator traffic flow (Huang et al, 2003). From the
wavelet theory, arbitrary function f(x) = L2(R2) can be approximated closely as
30
∑
(3.4)
where n is the number of network nodes, h(•) is basis wavelet, bt is translation factor,
at is dilation factor and wt is link weigh of the network. The architecture of WNN is
shown in Figure 3.7. WNN consists of three layers namely input layer, hidden layer
and output layer. The WNN could overcome the lag of statistical traffic data and has
properties like simple network architecture, fast convergence and higher precision.
The simulation results (consists of real traffic data, predicted data by WNN and other
method, Exponential Smoothing (ES)) of the research are shown in Figure 3.8, 3.9
and 3.10. From the results, it is concluded that WNN is able to predict elevator
traffic flow effectively. WNN with structural risk minimization algorithm (based on
statistical learning theory) is also developed to predict elevator traffic flow (Huang et
al., 2006). Wang et al. (2006) proposed to utilize non-parametric regression theory
and wavelet algorithm to decompose traffic flow data into different channels and
reconstructed prior to removal of noise in the traffic flow information. Then, nearest
neighbour method is employed to predict traffic flow. Therefore, it is anticipated
that wavelet theory will play essential role in elevator traffic flow analysis in future.
Figure 3.7 Architecture of WNN.
31
Figure 3.8 Elevator incoming traffic prediction on a working day by WNN and ES.
Figure 3.9 Elevator outgoing traffic prediction on a working day by WNN and ES.
32
Figure 3.10 Total number of passengers prediction on a working day by WNN and
ES.
Li Z. et al. (2003) employed artificial immune clustering algorithm
(promotion and suppression mechanism) to compress the data collected at field in 5
minutes interval in order to obtain memory dataset. The memory dataset was then
classified by using minimal spanning tree and minimal distance methods. The result
of classification clearly reveals the real feature of elevator traffic flow.
Other
research also proposed elevator traffic flow prediction model based on artificial
immune clustering algorithm (AI – CA). Firstly, AI-CA is used to recognize and
classify elevator traffic flow pattern off-line. Subsequently, Gaussian Mixture Model
(GMM) is used to model multi-mode elevator traffic on-line. Finally, EM algorithm
is used to estimate parameters modeled by GMM in order to predict elevator traffic
flow (Zong et al., 2006b).
Support Vector Machine (SVM) has been proposed to build elevator traffic
pattern recognition (Xu and Luo, 2005). Recently, SVM prediction models are also
being developed to predict elevator traffic flow (Luo et al., 2005). SVM theory was
developed by Vapnik of the AT & T Bell Laboratories in 1995. Like neural network,
33
SVM is also adaptive to complex system and robust in dealing with corrupted data.
Least squares support SVM (LS-SVM) which uses equality constraint and a least
squares error term in order to obtain a linear set of equations in the dual space. Same
as other prediction model, data is collected to train the SVM. It has two ordinal
phases namely training phase and prediction phase (Yan et al., 2006).
The
simulation results of LS-SVM elevator traffic flow prediction model is shown in
Figure 3.11, 3.12 and 3.13. From the below figures, a LS-SVM is an effective
prediction model as it predicts the traffic flow quite close to actual traffic flow.
Figure 3.11 Prediction of total number of passengers on a working day.
34
Figure 3.12 Prediction of incoming traffic flow on a working day.
Figure 3.13 Prediction of outgoing traffic flow on a working day.
Hu, Yang and Zhu proposed an elevator traffic flow prediction model by
using wavelet support vector machine (WSVM) that combines the merits of support
35
vector machine and wavelet analysis theory (Hu et al., 2007). The linear prediction
function is defined as , where x R and y R , R
represents input space and Ø is non linear mapping function. The above equation is
based on data set T x! , y! #$! , where x! denotes the input vector, y! denotes the
desired value and n is the number of data points. In order to parameters w and b,
following objective function shall be minimized.
%
|| ' ∑
(|( ) ( , |* where C > 0is a constant and ε is a small positive
number. The prediction function could take the form
∑
(,( ) ,(- .( , (3.5)
The data points corresponding to the nonzero support vectors ,( ) ,(- .
The
.( , is a Kernel function. The Morlet wavelet kernel function is used. It is
expressed as following.
.( , ∏<= 012 3
.56 78,9 9 :
where α denotes scaling factor.
; >? @)
A8,9 9 A
%B
B
C
(3.6)
Figure 3.14 depicts the structure of WSVM
prediction model. The input vector x consists of two parts, the first part {x (t - i), i =
0, 1, …, k-1} denotes the traffic flow of the past k time intervals and the second part
{x ((t + 1) – 144i), i = 0, 1, …, p}denotes the traffic flow of the same time of past p
working days. The coefficient 144 denotes the sampled data points during a working
day (7:00 – 19:00), f denotes the predicted value at time interval t + 1 and N denotes
the number of support vectors.
36
F
1
,- ) , . , F ) G 1
7F 1
k
k+1
∑
.% , ,E- ) ,E ) 144:
7F 1 ) 144?:
,%- ) ,% k+p
.N , Figure 3.14 WSVM prediction model.
An experiment has been carried out to verify and validate the above model in
Shanghai with parameters of C = 1000, ε = 0.75, parameters of morlet wavelet kernel
function a = 7 and parameters k = 6 and p = 5 of input vector x. Figure 3.15
illustrates the comparison of prediction result and real traffic flow data. As viewed
from the figure, two lines tend to overlap each other implies that prediction result is
approximate closely to real data. Besides that, they also compare prediction results
of five different models as tabulated in Table 3.1 and it is concluded that WSVM
provides the best elevator traffic flow prediction.
37
Figure 3.15 Comparison of prediction result and real traffic flow data.
Table 3.1 Comparison of prediction results of five different prediction models.
ARMA
BP
WNN
GSVM
WSVM
MAE
15.7854
7.9693
2.4565
1.9336
1.7768
MAPE (%)
13.13
9.92
9.75
8.51
8.14
ARMA –
Autoregressive moving average model
RP
-
Back propagation model
WNN -
Wavelet neural network
GVSM -
Gaussian vector support machine
WSVM-
Wavelet vector support machine
MAE -
Mean absolute error
MAPE -
Mean absolute percentage error
38
3.3
Summary
From the past researches, it is fair to say that RBF NN is suitable to be used
to develop elevator traffic flow prediction model since elevator traffic flow is short
time nonlinear process. Various elevator traffic prediction models show that training
and recall procedure are playing important role to ensure that error is minimized to
yield good approximation. Therefore, other methods discussed in this chapter shall
be carefully studied to develop good RBF NN elevator traffic flow prediction model.
39
CHAPTER 4
METHODOLOGY
4.1
Introduction
As a case study, Elevator traffic flow data are collected in Menara BHL
(Penang) in mid of December 2007. There are four elevators in four car group
operation provide service in that building. The traffic flow data has been collected
from 7:30 a.m. to 10:00 a.m. for one week. There are 23 stories in Menara BHL. It
is diversified office building.
4.2
Problem Statement
The collected data at field shall be consistent so that it could be used to train
the network. Therefore, under few circumstances as listed below, data collection
shall not be carried out in order to eliminate data variation. The data collection has
been carried out for a week without any holiday and a day which special function is
conducted in building.
40
•
During raining day, passenger tends to reach office late due to traffic jam
on road. This may cause the up peak traffic flow to shift right with respect
to time as shown in Figure 4.1.
•
Number of incoming passengers will decrease and increase significantly
during holiday and special function is conducted in building. These may
cause the traffic flow pattern is difficult to be determined as shown in
Number of incoming passengers
Figure 4.2.
Normal up peak traffic flow
Up peak traffic flow shift to right due
to late arrival of passengers
Time
Number of incoming passengers
Figure 4.1 Right shifting of up peak traffic flow.
Up peak traffic flow during special
function
Normal up peak traffic flow
Up peak traffic flow during holiday
Time
Figure 4.2 Up peak traffic flow pattern during holiday and when special function is
conducted in the building.
41
4.3
Elevator Traffic Flow Data Collection at Field
Data has been collected in mid of December, 2007. Figure 4.3, 4.4 and 4.5
show main entrance and side view and lift lobby of BHL Tower. Numbers of
passengers enter elevator(s) in 5 minutes intervals which represent traffic flow were
reordered. Collected data is tabulated in Table 4.1.
Figure 4.3 Main entrance at BHL Tower, Penang.
42
Figure 4.4 Side view of Menara BHL.
Figure 4.5 Lift lobby at Menara BHL.
43
Table 4.1 Elevator traffic flow data.
Time (a.m.)
No. of Passengers Enter Lifts
Monday
Tuesday
Wednesda
Thursday
Friday
07:30
3
1
3
2
6
07:35
0
3
1
1
1
07:40
6
7
4
5
4
07:45
2
5
4
5
5
07:50
11
10
12
12
12
07:55
10
10
11
12
13
08:00
15
13
16
14
14
08:05
21
22
25
23
24
08:10
24
22
23
22
21
08:15
32
37
33
33
34
08:20
41
42
42
42
42
08:25
34
35
34
35
34
08:30
39
37
36
35
38
08:35
35
33
28
29
36
08:40
31
31
29
28
31
08:45
29
27
28
28
26
08:50
36
34
34
34
32
08:55
18
19
20
20
20
09:00
16
15
18
17
15
09:05
19
20
20
21
20
09:10
19
19
17
19
19
09:15
16
17
19
16
16
09:20
10
11
10
14
11
09:25
24
20
23
23
26
09:30
12
11
10
9
9
09:35
18
19
19
20
20
09:40
12
11
8
12
10
09:45
13
16
15
14
14
09:50
12
11
9
13
14
09:55
12
15
12
10
12
The graphs for traffic flow are plotted for easier interpretation. They are
illustrated in Figure 4.6, 4.7, 4.8, 4.9, 4.10 and 4.11.
44
No. of Passengers Enter Lifts
Elevator Traffic Flow on Monday
45
40
35
30
25
20
15
10
5
0
Time (a.m.)
Figure 4.6 Elevator traffic flow on Monday.
No. of Passengers Enter Lifts
Elevator Traffic Flow on Tuesday
45
40
35
30
25
20
15
10
5
0
Time (a.m.)
Figure 4.7 Elevator traffic flow on Tuesday.
45
No. of Passengers Enter Lifts
Elevator Traffic Flow on Wednesday
45
40
35
30
25
20
15
10
5
0
Time (a.m.)
Figure 4.8 Elevator traffic flow on Wednesday.
No. of Passengers Enter Lifts
Elevator Traffic Flow on Thursday
45
40
35
30
25
20
15
10
5
0
Time (a.m.)
Figure 4.9 Elevator traffic flow on Thursday.
46
No. of Passengers Enter Lifts
Elevator Traffic Flow on Friday
45
40
35
30
25
20
15
10
5
0
Time (a.m.)
Figure 4.10 Elevator traffic flow on Friday.
Elevator Traffic Flow in One Week
45
35
30
25
Mon
20
Tue
15
Wed
Thu
10
Fri
5
09:50
09:40
09:30
09:20
09:10
09:00
08:50
08:40
08:30
08:20
08:10
08:00
07:50
07:40
0
07:30
No. of Passengers Enter Lifts
40
Time (a.m.)
Figure 4.11 Elevator traffic flow from Monday to Friday.
47
4.4
RBF NN Elevator Traffic Flow Prediction Model Design
The algorithm of the RBF NN shall be developed and trained so that it is able
to predict elevator traffic flow fairly accurate. It is anticipated that algorithm may
not perform satisfactory first time and need to be fine tuned in order to obtain good
result. The flow chart in Figure 4.12 shows
ows the development of algorithm.
Figure 4.12 Flow chart to develop and fine tune the RBF NN based algorithm.
algorithm
The prediction model is designed so that it could predict traffic flow by
referring to traffic flow of past k intervals and traffic flow
ow at same time of past p days.
Figure 4.13 depictss structure of traffic flow prediction model.
model. The input vector x
consists of two parts. The first part {x(t-i),
{x(t
0 ≤ i ≤ k – 1}has
has k nodes whilst the
second part {x((t+1) – 30j, 0 ≤ j ≤ p} has p nodes. The coefficient 30 denotes
numbers of 5 minutes intervals of one working day (data is collected from 7:30 a.m.
to 10:55 a.m.).
48
x(t)
1
φ1
x(t- k + 1)
k
x((t + 1) – 30)
k+1
φ2
∑
y
Output layer
φS1
x((t + 1) – 30p)
k+p
Hidden layer
Input layer
Figure 4.13 RBF NN elevator traffic flow prediction model.
The working principle of prediction model is explained as If the model is
used to predict traffic flow on fifth day by using 4 past data and 4 past working days
data, this illustrates k = 4 and p = 4. As refer to table 4.2, the input data is illustrated
in yellow cells whilst traffic flow to be predicted is illustrated in orange cells.
49
Table 4.2 Input data and traffic flow to be predicted.
t(interval)
x(Persons / 5 minutes)
1
2
3
4
5
0
3
1
3
2
6
1
0
3
1
1
1
2
6
7
4
5
4
3
2
5
4
5
5
4
11
10
12
12
12
5
10
10
11
12
13
6
15
13
16
14
14
7
21
22
25
23
24
8
24
22
23
22
21
9
32
37
33
33
34
10
41
42
42
42
42
11
34
35
34
35
34
12
39
37
36
35
38
13
35
33
28
29
36
14
31
31
29
28
31
15
29
27
28
28
26
16
36
34
34
34
32
17
18
19
20
20
20
18
16
15
18
17
15
19
19
20
20
21
20
20
19
19
17
19
19
21
16
17
19
16
16
22
10
11
10
14
11
23
24
20
23
23
26
24
12
11
10
9
9
25
18
19
19
20
20
26
12
11
8
12
10
27
13
16
15
14
14
28
12
11
9
13
14
29
12
15
12
10
12
50
The algorithm of RBF NN prediction model to predict traffic flow of p+1 day
is
for t = k to 29
set training data to x(t+1-k,p+1), x(t+1,p) and x(t+1,p+1)
train the RBF NN
for t = k to 29
set testing data to x(t+1-k,p+1), x(t+1,p)
test the RBF NN
obtain mean square error between RBF NN output and real data
end
As refer to example (k=4, p=4) illustrated in table 4.2, the first set training data
(t=k=4) is arranged in matrix as following
[ x(0,5) x(1,5) x(2,5) x(3,5) x(4,1) x(4,2) x(4,3) x(4,4) x(4,5) ]
which is
[ 6 1 4 5 11 10 12 12 12 ]
then, subsequent set of training data (t=k=5,p=4) is set as in following matrix
[ x(1,5) x(2,5) x(3,5) x(4,5) x(5,1) x(5,2) x(5,3) x(5,4) x(5,5) ]
which is
[ 1 4 5 12 10 10 11 12 13 ]
The same procedure will repeat until t=29. The first seven values in the matrix are
inputs to RBF NN while the last value is the target of the training.
4.5
Software Implementation and Simulation
Neural network toolbox in matlab is used to program the algorithm of
prediction model. Neural network toolbox incorporates built in design tools for
many neural networks such as perceptron, back propagation and radial basis function.
The RBF NN could be designed with two functions namely newrbe (exact radial
basis network) and newrb (radial basis network). Both newrb and newrbe functions
in neural network toolbox are used to create radial basis network in this project. The
51
newrb function iteratively creates neurons of radial basis network at a time. Neurons
are added to the network until sum square error falls beneath an error goal or a
maximum number of neurons have been reached (Demuth and Beale, 2003). The
newrb function has a format in matlab:
net = newrb (P, T, GOAL, SPREAD)
The above function takes matrices of input vector P and target vector T and design
parameters GOAL (error goal) and SPREAD (spread constant for the radial basis
layer) and returns the network with weights and biases in such a way that outputs are
T when the inputs are P. Goal is set to 0.05 in this elevator traffic flow prediction
model.
The newrbe function is used to create exact neural network. It could produce
a network with zero error on training vectors. It takes the format in matlab:
net = newrbe(P, T, SPREAD)
This newrbe function takes matrices of input vectors P and target vectors and a
spread constant SPREAD for radial basis layer. It returns a network with weights
and biases in such a way that output are exactly T for the inputs P.
The spread constant needs to be large enough so that active input regions of
radial basis neurons overlap enough to ensure several radial basis neurons always
have fairly large outputs at any moment. This makes network functions smoother.
However, spread constant should not be so large that all neurons respond in
essentially the same manner. As such, a program to evaluate the most suitable value
of spread constant for RBF NN prediction model that yields the minimum mean
square error shall be set up. Therefore, the most suitable spread constant could be
easily selected for all cases with different k and p. Performance of both newrbe and
newrb functions is compared and verified.
The output of RBF NN prediction model is simulated in matlab and graphs
for output and real data (testing data) are plotted to give an overview of
approximation of output (predicted data) to real data. Mean square error is used to
52
evaluate performance of RBF NN. The error is calculated as the difference between
target output (real data) and network output (predicted data) and it is stated as
following
%
Mean square error, ε = ∑N
LJt L ) nL N
N
where tk
4.5.1
(4.1)
= target output
nk
= network output
N
= number of data
Simulation to Obtain Optimum Spread Constant
The optimum spread constant for both newrbe and newrb functions is
obtained for various cases as followings.
•
Case 1 :
use past 4 interval data on 4th day and past 3 days (1st,2nd and
3rd day) data to predict traffic flow on 5th day.
•
Case 2 :
use past 4 interval data on 5th day and past 4 days (1st,2nd, 3rd
and 4th day) data to predict traffic flow on 5th day.
•
Case 3 :
use past 3 interval data on 4th day and past 3 days (1st,2nd and
3rd day) data to predict traffic flow on 5th day.
•
Case 4 :
use past 3 interval data on 5th day and past 3 days (2nd, 3rd and
4th day) data to predict traffic flow on 5th day.
•
Case 5 :
use past 4 interval data on 5th day and past 4 days (1st, 2nd, 3d
and 4th day) data to predict traffic flow on 5th day.
•
Case 6 :
use past 2 interval data on 5th day and past 4 days (1st, 2nd, 3d
and 4th day) data to predict traffic flow on 5th day.
•
Case 7 :
use past 2 interval data on 4th day and past 3 days (1st, 2nd and
3rd day) data to predict traffic flow on 5th day.
53
•
Case 8 :
use past 2 interval data on 4th day and past 2 days (2nd and 3rd
day) data to predict traffic flow on 5th day.
•
Case 9 :
use past 2 interval data on 4th day and past 2 days (2nd and 3rd
day) data to predict traffic flow on 4th day.
•
Case 10:
use past 1 interval data on 5th day and past 2 days (2nd and 3rd
day) data to predict traffic flow on 5th day.
The simulation results are illustrated in Figure 4.14 to Figure 4.33.
Horizontal axis represents a set of spread constant range from 0.6 to 25.1 while
vertical axis represents mean square error. The programs to obtain optimum spread
constant are enclosed in appendix.
Figure 4.14 Optimum spread constant for newrbe function (for case 1).
54
Figure 4.15 Optimum spread constant for newrb function (for case 1).
Figure 4.16 Optimum spread constant for newrbe function (for case 2).
55
Figure 4.17 Optimum spread constant for newrb function (for case 2).
Figure 4.18 Optimum spread constant for newrbe function (for case 3).
56
Figure 4.19 Optimum spread constant for newrb function (for case 3).
Figure 4.20 Optimum spread constant for newrbe function (for case 4).
57
Figure 4.21 Optimum spread constant for newrb function (for case 4).
Figure 4.22 Optimum spread constant for newrbe function (for case 5).
58
Figure 4.23 Optimum spread constant for newrb function (for case 5).
Figure 4.24 Optimum spread constant for newrbe function (for case 6).
59
Figure 4.25 Optimum spread constant for newrb function (for case 6).
Figure 4.26 Optimum spread constant for newrbe function (for case 7).
60
Figure 4.27 Optimum spread constant for newrb function (for case 7).
Figure 4.28 Optimum spread constant for newrbe function (for case 8).
61
Figure 4.29 Optimum spread constant for newrb function (for case 8).
Figure 4.30 Optimum spread constant for newrbe function (for case 9).
62
Figure 4.31 Optimum spread constant for newrb function (for case 9).
Figure 4.32 Optimum spread constant for newrbe function (for case 10).
63
Figure 4.33 Optimum spread constant for newrb function (for case 10).
As viewed from figure 4.13 to figure 4.32, variation of spread constant will
cause significant fluctuation in mean square error for cases 1, 3, 7 and 8. The mean
square error is almost constant for spread constant in the range for case 2. Mean
square error is very small and could be neglected for cases 4, 5, 6, 9 and 10.
Common feature for all cases with small mean square error is past k interval data on
mth day and past p days data of are used to predicted future traffic flow on the same
day. While for cases 1, 3, 7 and 8, past k interval data on (m-1)th and past p days
data are used to train the network. Obviously, RBF NN prediction model performs
better when same day data is used to train the network. The mean square error for 10
cases is tabulated in Table 4.3. to Table 4.12.
64
Table 4.3 Mean square error for case 1.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
4162.5
1946.9
1.1
4037.5
1472.2
1.6
3621.3
3060.8
2.1
3108.9
1080.8
2.6
2619.3
903.74
3.1
2184.2
755.3
3.6
1807.4
621.41
4.1
1487.4
498.34
4.6
1096.2
548.88
5.1
923.18
191.52
5.6
806.8
823.53
6.1
680.07
1.7811
6.6
581.47
1.1293
7.1
576
0.76131
7.6
590.76
161.31
8.1
688.01
128.14
8.6
996.04
103.25
9.1
240.87
67.799
9.6
204.98
7.4876
10.1
174.58
7.0918
10.6
148.73
6.7908
11.1
126.74
6.5585
11.6
108.09
10.898
12.1
92.327
9.3546
12.6
78.467
8.1521
13.1
18.846
7.2066
13.6
21.169
3.6508
14.1
14.6
15.1
15.6
16.1
16.6
17.1
17.6
18.124
0.21699
0.034812
0.0013934
33.403
26.543
0.25044
25.337
3.8775
4.0252
4.1173
4.1707
4.1972
4.205
4.1996
4.1849
65
Table 4.3 continued.
18.1
3.8409
4.1634
18.6
4.2184
4.1365
19.1
18.828
4.1051
19.6
17.566
4.0698
20.1
16.487
4.0307
20.6
17.92
3.9877
21.1
18.571
3.9408
21.6
17.001
3.8897
22.1
0.01919
3.8342
22.6
16.42
3.7742
23.1
16.227
3.7093
23.6
16.086
3.6396
24.1
2.15
3.5648
24.6
3.2197
3.485
25.1
15.459
3.4003
66
Table 4.4 Mean square error for case 2.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
2.1488
0.26052
1.1
2.1488
0.26052
1.6
2.1488
0.26052
2.1
2.1488
0.26052
2.6
2.1488
0.26052
3.1
2.1488
0.26052
3.6
2.1488
0.26052
4.1
2.1488
0.26052
4.6
2.1488
0.26052
5.1
2.1488
0.26052
5.6
2.1488
0.26052
6.1
2.1488
0.26052
6.6
2.1488
0.26052
7.1
2.1488
0.26052
7.6
2.1488
0.26052
8.1
2.1488
0.26052
8.6
2.1488
0.26052
9.1
2.1488
0.26052
9.6
2.1488
0.26052
10.1
2.1488
0.26052
10.6
2.1488
0.26052
11.1
2.1488
0.26052
11.6
2.1488
0.26052
12.1
2.1488
0.26052
12.6
2.1488
0.26052
13.1
2.1488
0.26052
13.6
2.1488
0.26052
14.1
2.1488
0.26052
14.6
2.1488
0.26052
15.1
2.1488
0.26052
15.6
2.1488
0.26052
16.1
2.1488
0.26052
16.6
2.1488
0.26052
67
Table 4.4 continued.
17.1
2.1488
0.26052
17.6
2.1488
0.26052
18.1
2.1488
0.26052
18.6
2.1488
0.26052
19.1
2.1488
0.26052
19.6
2.1488
0.26052
20.1
2.1488
0.26052
20.6
2.1488
0.26052
21.1
2.1488
0.26052
21.6
2.1488
0.26052
22.1
2.1488
0.26052
22.6
2.1488
0.26052
23.1
2.1488
0.26052
23.6
2.1488
0.26052
24.1
2.1488
0.26052
24.6
2.1488
0.26052
25.1
2.1488
0.26052
68
Table 4.5 Mean square error for case 3.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
6942.7
1308.4
1.1
6706.2
653.76
1.6
5939.7
546.71
2.1
4995.6
438.55
2.6
4082.7
363.02
3.1
3264.4
314.68
3.6
2553.4
482.88
4.1
1954.7
640.06
4.6
1471
0.67466
5.1
759.47
0.0032801
5.6
686.62
125.86
6.1
671.84
12.706
6.6
747.64
11.764
7.1
278.02
94.308
7.6
421.6
63.081
8.1
260.16
42.006
8.6
220.67
9.6758
9.1
183.94
71.466
9.6
150.57
65.293
10.1
121.44
60.829
10.6
97.285
57.619
11.1
84.764
55.347
11.6
75.083
53.785
12.1
67.04
36.105
12.6
39.883
0.11766
13.1
60.57
0.49481
13.6
26.81
1.0327
14.1
22.467
1.6615
14.6
19.105
3.4299
15.1
16.492
3.0631
15.6
14.454
2.7973
16.1
15.773
2.5988
16.6
17.277
2.4461
69
Table 4.5 continued.
17.1
17.618
2.3247
17.6
9.8249
2.2249
18.1
15.014
2.1402
18.6
41.722
2.0657
19.1
6.1934
1.9984
19.6
18.144
1.9358
20.1
6.6829
7.7333
20.6
2.82
7.8526
21.1
6.1505
7.8992
21.6
51.9
7.876
22.1
3.5372
7.7877
22.6
4.4483
7.6404
23.1
6.3782
7.4417
23.6
10.9
7.2
24.1
53.001
6.9242
24.6
6.2703
6.6231
25.1
7.1267
6.3052
70
Table 4.6 Mean square error for case 4.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
0
1308.4
1.1
4.67E-31
653.76
1.6
1.87E-30
546.71
2.1
2.63E-31
438.55
2.6
9.47E-30
363.02
3.1
2.63E-31
314.68
3.6
1.43E-30
482.88
4.1
9.47E-30
640.06
4.6
9.47E-30
0.67466
5.1
1.55E-29
0.0032801
5.6
1.05E-29
125.86
6.1
9.49E-29
12.706
6.6
2.92E-32
11.764
7.1
3.38E-29
94.308
7.6
2.99E-29
63.081
8.1
1.68E-29
42.006
8.6
2.99E-29
9.6758
9.1
1.05E-30
71.466
9.6
3.38E-29
65.293
10.1
3.38E-29
60.829
10.6
1.64E-28
57.619
11.1
1.87E-30
55.347
11.6
1.24E-27
53.785
12.1
2.92E-30
36.105
12.6
1.02E-28
0.11766
13.1
1.16E-28
0.49481
13.6
9.36E-28
1.0327
14.1
1.87E-30
1.6615
14.6
2.26E-28
3.4299
15.1
1.35E-28
3.0631
15.6
8.21E-29
2.7973
16.1
4.22E-29
2.5988
16.6
8.44E-30
2.4461
71
Table 4.6 continued.
17.1
3.86E-28
2.3247
17.6
6.18E-29
2.2249
18.1
8.95E-28
2.1402
18.6
2.02E-27
2.0657
19.1
2.46E-29
1.9984
19.6
1.08E-27
1.9358
20.1
1.05E-28
7.7333
20.6
2.99E-29
7.8526
21.1
9.36E-28
7.8992
21.6
2.66E-27
7.876
22.1
1.24E-27
7.7877
22.6
2.29E-29
7.6404
23.1
5.25E-28
7.4417
23.6
2.69E-28
7.2
24.1
3.34E-27
6.9242
24.6
9.47E-30
6.6231
25.1
3.22E-27
6.3052
72
Table 4.7 Mean square error for case 5.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
0
5.35E-29
1.1
0
5.35E-29
1.6
4.85E-31
3.94E-28
2.1
4.85E-31
2.73E-29
2.6
1.21E-29
4.38E-29
3.1
1.94E-30
3.81E-28
3.6
4.37E-30
2.73E-29
4.1
2.73E-29
2.35E-28
4.6
3.03E-30
2.73E-29
5.1
1.21E-31
8.77E-28
5.6
5.78E-28
5.87E-29
6.1
1.49E-28
7.96E-28
6.6
0.00E+00
3.22E-27
7.1
3.11E-29
2.05E-29
7.6
1.94E-30
1.57E-28
8.1
4.85E-31
4.52E-28
8.6
1.21E-31
1.47E-29
9.1
1.21E-31
1.17E-28
9.6
1.66E-28
1.75E-29
10.1
1.75E-29
2.04E-28
10.6
1.21E-31
4.08E-28
11.1
3.03E-30
3.59E-27
11.6
5.87E-29
3.93E-29
12.1
1.49E-28
1.17E-28
12.6
2.35E-28
1.42E-27
13.1
9.51E-29
6.99E-29
13.6
1.02E-28
4.85E-29
14.1
1.21E-29
4.97E-28
14.6
2.80E-28
1.21E-31
15.1
1.09E-28
7.59E-29
15.6
3.03E-30
3.93E-29
16.1
3.11E-29
1.10E-27
16.6
4.37E-30
3.67E-28
73
Table 4.7 continued.
17.1
4.85E-29
8.56E-28
17.6
1.66E-28
2.05E-29
18.1
6.42E-29
5.35E-29
18.6
1.21E-29
4.67E-28
19.1
1.47E-29
5.95E-30
19.6
2.57E-28
3.41E-28
20.1
1.21E-29
1.75E-29
20.6
1.24E-28
2.91E-28
21.1
1.02E-28
1.85E-28
21.6
3.16E-28
3.54E-28
22.1
6.42E-29
5.78E-28
22.6
5.00E-27
1.05E-27
23.1
1.57E-28
1.75E-29
23.6
2.57E-28
2.95E-27
24.1
1.66E-28
3.93E-29
24.6
1.57E-28
1.94E-28
25.1
1.94E-28
1.21E-31
74
Table 4.8 Mean square error for case 6.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
0
1.22E-27
1.1
4.51E-31
7.76E-28
1.6
4.51E-29
4.91E-28
2.1
2.82E-30
9.48E-29
2.6
6.34E-32
2.93E-28
3.1
6.34E-30
4.69E-28
3.6
4.51E-31
8.37E-29
4.1
1.38E-30
1.79E-27
4.6
1.13E-29
1.79E-27
5.1
1.19E-30
6.49E-29
5.6
2.28E-30
1.87E-28
6.1
3.53E-28
2.89E-27
6.6
2.54E-29
5.21E-28
7.1
1.49E-29
6.17E-28
7.6
1.01E-30
9.03E-28
8.1
1.23E-27
2.08E-27
8.6
1.24E-29
3.65E-29
9.1
1.76E-29
7.21E-30
9.6
4.51E-29
1.13E-31
10.1
1.76E-31
1.80E-30
10.6
6.76E-29
3.65E-29
11.1
7.91E-29
8.84E-29
11.6
1.42E-28
9.96E-28
12.1
1.63E-28
2.60E-27
12.6
1.01E-28
1.89E-28
13.1
1.13E-31
6.51E-28
13.6
3.65E-29
4.06E-30
14.1
2.65E-28
5.36E-27
14.6
4.06E-28
4.42E-27
15.1
1.58E-27
6.82E-27
15.6
3.66E-28
2.89E-27
16.1
7.49E-28
1.08E-27
16.6
1.67E-28
7.58E-28
75
Table 4.8 continued.
17.1
7.61E-26
8.18E-26
17.6
1.71E-28
8.34E-27
18.1
2.07E-26
2.10E-26
18.6
1.15E-28
5.21E-28
19.1
1.04E-27
1.75E-25
19.6
2.95E-26
3.18E-27
20.1
4.88E-25
8.58E-27
20.6
5.65E-27
3.53E-25
21.1
1.80E-24
2.96E-25
21.6
2.89E-29
2.73E-26
22.1
8.05E-26
2.89E-29
22.6
7.00E-26
6.07E-27
23.1
4.54E-26
9.48E-25
23.6
2.60E-27
3.29E-26
24.1
6.79E-26
8.26E-25
24.6
7.85E-27
3.67E-24
25.1
4.06E-26
1.70E-24
76
Table 4.9 Mean square error for case 7.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
6184.10
386.54
1.1
3920.40
399.00
1.6
2482.30
254.04
2.1
1596.20
170.35
2.6
1031.50
124.39
3.1
663.90
580.85
3.6
423.38
124.84
4.1
269.52
3.08
4.6
133.82
0.82
5.1
175.05
0.03
5.6
1290.60
0.21
6.1
58.61
3.22
6.6
44.68
2.07
7.1
35.64
3.95
7.6
49.62
0.40
8.1
136.14
0.47
8.6
15.85
7.98
9.1
4.97
6.32
9.6
8.13
0.53
10.1
3.75
0.53
10.6
2.80
0.54
11.1
2.50
2.50
11.6
1.63
2.01
12.1
1.32
1.64
12.6
77.13
1.36
13.1
1.17
1.17
13.6
0.03
1.02
14.1
0.67
0.93
14.6
0.03
0.87
15.1
0.00
0.83
15.6
0.02
0.82
16.1
0.83
8.55
16.6
0.90
8.90
77
Table 4.9 continued.
17.1
0.99
9.32
17.6
1.08
0.33
18.1
10.31
0.30
18.6
10.85
0.26
19.1
11.42
0.23
19.6
12.01
0.20
20.1
12.61
10.41
20.6
0.14
10.43
21.1
13.80
10.41
21.6
0.11
10.36
22.1
0.15
10.29
22.6
0.70
10.21
23.1
0.03
10.11
23.6
0.15
9.99
24.1
0.01
9.87
24.6
9.74
9.74
25.1
140.73
9.61
78
Table 4.10 Mean square error for case 8.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
6184.10
51.10
1.1
3920.10
33.18
1.6
2466.10
19.51
2.1
1532.80
1351.70
2.6
933.94
162.18
3.1
564.49
279.30
3.6
340.92
88.81
4.1
207.47
19.73
4.6
126.56
14.00
5.1
141.33
75.09
5.6
31.11
51.19
6.1
35.62
37.53
6.6
24.18
9.57
7.1
16.00
1.82
7.6
11.49
1.81
8.1
7.69
2.36
8.6
5.14
25.77
9.1
0.64
23.21
9.6
0.50
23.21
10.1
0.35
25.21
10.6
0.26
29.20
11.1
0.11
0.11
11.6
0.25
1.38
12.1
0.21
6.52
12.6
0.53
5.77
13.1
0.01
5.12
13.6
2.68
4.54
14.1
0.31
4.00
14.6
6.96
3.49
15.1
0.00
3.00
15.6
5.28
2.54
16.1
0.00
2.10
16.6
0.00
1.68
79
Table 4.10 continued.
17.1
129.49
1.31
17.6
3.32
3.32
18.1
0.03
3.00
18.6
0.05
2.63
19.1
43.76
2.24
19.6
2.47
1.86
20.1
0.05
1.50
20.6
91.76
1.17
21.1
2.45
0.88
21.6
2.50
0.63
22.1
0.71
0.42
22.6
9.84
0.20
23.1
0.32
0.32
23.6
0.87
0.46
24.1
41.38
0.62
24.6
11.03
0.79
25.1
3.33
0.98
80
Table 4.11 Mean square error for case 9.
Spread Constant
Mean Square Error
newrb
newrbe
0.6
4.62E-28
1.39E-27
1.1
8.53E-28
2.50E-27
1.6
1.15E-28
2.08E-28
2.1
9.81E-29
1.15E-28
2.6
4.91E-28
1.89E-28
3.1
1.90E-29
4.76E-28
3.6
7.33E-29
1.18E-27
4.1
1.49E-29
4.76E-28
4.6
2.82E-30
1.20E-27
5.1
1.80E-28
1.62E-29
5.6
4.97E-29
5.52E-28
6.1
1.13E-31
5.52E-28
6.6
2.37E-29
1.24E-27
7.1
3.65E-29
3.41E-28
7.6
6.76E-29
2.08E-28
8.1
7.04E-29
3.66E-28
8.6
5.96E-29
6.49E-29
9.1
3.41E-30
2.18E-28
9.6
2.42E-27
8.93E-28
10.1
1.13E-31
9.81E-29
10.6
1.65E-27
1.42E-28
11.1
1.01E-28
1.36E-27
11.6
3.99E-28
8.22E-27
12.1
1.12E-26
3.41E-27
12.6
7.12E-28
8.84E-29
13.1
2.90E-26
1.36E-26
13.6
2.89E-29
5.87E-26
14.1
3.43E-27
4.69E-27
14.6
1.08E-27
3.18E-27
15.1
4.50E-26
3.05E-26
15.6
4.06E-30
9.87E-26
16.1
1.57E-26
1.71E-25
16.6
6.71E-27
4.51E-27
81
Table 4.11 continued.
17.1
5.27E-26
1.04E-26
17.6
7.82E-25
2.60E-26
18.1
9.54E-26
4.01E-24
18.6
2.60E-26
2.31E-25
19.1
3.02E-25
8.10E-26
19.6
1.10E-25
6.79E-26
20.1
2.94E-25
1.30E-24
20.6
3.53E-26
1.61E-24
21.1
2.60E-27
1.17E-23
21.6
1.89E-24
2.60E-26
22.1
2.29E-25
9.94E-24
22.6
4.82E-24
9.66E-25
23.1
2.10E-24
9.56E-25
23.6
1.76E-25
5.49E-25
24.1
9.47E-24
9.81E-24
24.6
2.17E-23
9.79E-23
25.1
7.51E-23
5.43E-23
82
Table 4.12 Mean square error for case 10.
Mean Square Error
Spread Constant
newrb
newrbe
0.6
1.09E-31
3.29E-28
1.1
1.74E-30
9.21E-28
1.6
1.09E-29
5.33E-28
2.1
1.09E-29
6.96E-30
2.6
4.54E-29
5.27E-29
3.1
4.60E-30
1.32E-29
3.6
3.38E-29
1.81E-27
4.1
2.87E-29
4.35E-29
4.6
6.53E-29
5.66E-27
5.1
2.45E-29
7.68E-28
5.6
4.35E-31
4.10E-27
6.1
4.35E-31
3.22E-27
6.6
1.39E-27
2.13E-29
7.1
7.68E-28
1.18E-27
7.6
7.61E-27
1.11E-26
8.1
1.77E-28
1.99E-26
8.6
1.01E-26
4.46E-28
9.1
6.44E-25
4.35E-27
9.6
1.81E-25
5.46E-27
10.1
2.59E-26
4.71E-27
10.6
1.34E-25
1.25E-25
11.1
1.36E-27
4.13E-26
11.6
3.50E-26
2.54E-25
12.1
1.13E-24
1.31E-25
12.6
8.53E-27
9.69E-25
13.1
2.38E-24
1.05E-25
13.6
2.72E-23
2.26E-24
14.1
2.31E-25
2.29E-24
14.6
5.48E-23
4.78E-25
15.1
9.21E-23
1.17E-24
15.6
2.07E-21
2.76E-24
16.1
4.02E-26
1.27E-23
16.6
3.23E-21
5.79E-23
83
Table 4.12 continued.
17.1
5.84E-24
1.78E-23
17.6
8.24E-22
2.46E-25
18.1
2.98E-22
2.28E-23
18.6
3.40E-25
5.37E-22
19.1
6.21E-24
1.26E-22
19.6
2.32E-21
8.38E-22
20.1
3.59E-23
1.06E-20
20.6
5.88E-21
1.84E-20
21.1
8.22E-20
7.85E-20
21.6
2.92E-20
5.72E-21
22.1
9.98E-21
6.00E-22
22.6
3.54E-20
3.98E-20
23.1
1.39E-20
4.84E-19
23.6
2.09E-18
1.30E-19
24.1
5.20E-22
3.53E-20
24.6
2.42E-20
4.82E-19
25.1
8.91E-21
4.01E-19
The mean square error and optimum spread constant for all cases obtained
from simulation are summarized in Table 4.13.
84
Table 4.13 Summary of mean square error and optimum spread constant.
Case
4.5.2
Optimum Spread Constant
Mean Square Error
newrb
newrbe
newrb
newrbe
1
15.6
7.1
0.0014
0.76
2
0.6 - 25.1
0.6 - 25.1
2.15
0.2605
3
20.6
5.1
2.82
0.00328
4
0.6
1.6
0
2.6295E-31
5
0.6
14.6
0
1.2136E-31
6
0.6
9.6
0
1.1269E-31
7
15.1
5.1
0.00044056
0.031554
8
15.1
11.1
1.107E-06
0.10656
9
6.1
5.1
1.1269E+31
1.6228E+29
10
0.6
2.1
1.0881E+31
6.9637E+30
Simulation of Network Performance and Goal for Newrb Function
In newrb function, a goal is set at 0.05. A graph shows training curve, goal
and epochs is generated when newrb function is debugged and executed. Graphs for
10 cases are illustrated in Figure 4.34 to Figure 4.43.
85
Figure 4.34 Training of network for newrb function (for case 1).
Figure 4.35 Training of network for newrb function (for case 2).
86
Figure 4.36 Training of network for newrb function (for case 3).
Figure 4.37 Training of network for newrb function (for case 4).
87
Figure 4.38 Training of network for newrb function (for case 5).
Figure 4.39 Training of network for newrb function (for case 6).
88
Figure 4.40 Training of network for newrb function (for case 7).
Figure 4.41 Training of network for newrb function (for case 8).
89
Figure 4.42 Training of network for newrb function (for case 9).
Figure 4.43 Training of network for newrb function (for case 10).
90
From above graphs, network performance of case 1, 2 and 5 reaches goal
(0.05). Case 1, 2 and 5 use 4 past interval data (k=4) to train the network results
better performance compared with other cases with k = 2 or k = 3. As such, k plays
important role in RBF NN performance.
91
CHAPTER 5
SIMULATION RESULTS AND DISCUSSION
5.1
Introduction
This chapter discusses matlab simulation results of RBF NN traffic flow
prediction model for 10 cases. The real data and predicted traffic flow data (output
of RBF NN) are plotted on the same graph to provide overview of deviation between
them.
In vertical axis, red line represents real data while blue line represents
predicted traffic flow. Horizontal axis represent time interval of 5 minutes as traffic
flow data was collected every 5 minutes at field. They are illustrated in Figure 5.1 to
Figure 5.20.
92
Figure 5.1 Simulation result for newrb function (for case 1).
Figure 5.2 Simulation result for newrbe function (for case 1).
93
Figure 5.3 Simulation result for newrb function (for case 2).
Figure 5.4 Simulation result for newrbe function (for case 2).
94
Figure 5.5 Simulation result for newrb function (for case 3).
Figure 5.6 Simulation result for newrbe function (for case 3).
95
Figure 5.7 Simulation result for newrb function (for case 4).
Figure 5.8 Simulation result for newrbe function (for case 4).
96
Figure 5.9 Simulation result for newrb function (for case 5).
Figure 5.10 Simulation result for newrbe function (for case 5).
97
Figure 5.11 Simulation result for newrb function (for case 6).
Figure 5.12 Simulation result for newrbe function (for case 6).
98
Figure 5.13 Simulation result for newrb function (for case 7).
Figure 5.14 Simulation result for newrbe function (for case 7).
99
Figure 5.15 Simulation result for newrb function (for case 8).
Figure 5.16 Simulation result for newrbe function (for case 8).
100
Figure 5.17 Simulation result for newrb function (for case 9).
Figure 5.18 Simulation result for newrbe function (for case 9).
101
Figure 5.19 Simulation result for newrb function (for case 10).
Figure 5.20 Simulation result for newrbe function (for case 10).
102
5.2
Discussion of Results for All Cases
Simulation results are analyzed and discussed for 10 cases.
Each case
evaluates performance of RBF NN traffic flow prediction model with specified k and
p parameters and the day which comparison would be made between real data and
simulated result. On the other hand, both newrbe and newrb functions in neural
network toolbox are used to predict and simulate traffic flow based on input vector
and target vector. Optimum spread constants are also obtained for all cases with
newrb and newrbe functions.
5.2.1
Discussion of Simulation Result for Case 1
In case 1, past 4 interval data on 4th day and past 3 days (1st,2nd and 3rd day)
data are used to predict traffic flow on 5th day. From simulation results, RBF NN
prediction model with newrb and newrbe functions able to predict up peak traffic
accurately. There are only three continuous RBF NN output (5 minutes the peak) are
found deviated from real data quite significantly. The output of RBF NN prediction
model and real data are summarized in Table 5.1. The mean square error for newrb
function is 0.0014 while mean square error for newrbe function is 0.76131.
Performance of newrbe functionis better than newrb function. Overall performance
of RBF NN prediction model is considered satisfactory.
Table 5.1 Comparison of RBF NN output for newrb, newrbe and real data (Case 1).
Real Data
RBF NN Output
newrb
newrbe
12
12.228
15.017
13
12.184
11.736
14
14.189
15.568
103
Table 5.1 Continued.
5.2.2
24
23.423
23.104
21
21.45
22.053
34
33.323
28.679
42
41.963
40.978
34
34.905
34.086
38
34.596
33.652
36
28.812
26.685
31
27.857
25.287
26
27.056
26.169
32
31.214
28.695
20
21.38
22.108
15
16.622
18.866
20
21.712
21.383
19
18.887
19.652
16
14.628
16.049
11
14.782
15.277
26
23.014
22.762
9
10.772
13.699
20
21.831
21.294
10
16.432
17.589
14
15.818
17.572
14
13.709
15.931
12
10.025
13.56
Discussion of Simulation Result for Case 2
In case 2, past 4 interval data on 5th day and past 4 days (1st,2nd, 3rd and 4th
day) data are used to predict traffic flow on 5th day. From simulation results, RBF
NN prediction model with newrb and newrbe functions able to predict up peak traffic
accurately.
Three continuous RBF NN output (5 minutes the peak) are found
deviated from real data but the deviation is not significant. The output of RBF NN
104
prediction model and real data are summarized in Table 5.2. The mean square error
for newrb function is 2.15 while mean square error for newrbe function is 0.2605.
Again, performance of newrbe function is better than newrb function. Generally,
performance of RBF NN prediction model is satisfactory.
Table 5.2 Comparison of RBF NN output for newrb, newrbe and real data (Case 2).
Real Data
RBF NN Output
newrb
newrbe
12
12.267
12.197
13
13.353
13.209
14
14.486
14.34
24
24.674
24.51
21
20.639
20.677
34
33.705
33.395
42
42
42
34
33.517
33.601
38
37.296
37.54
36
31.706
32.949
31
29.616
29.927
26
26.469
26.395
32
32.067
31.941
20
20.405
20.327
15
15.289
15.289
20
19.854
20.05
19
18.716
19.011
16
16.115
15.66
11
10.192
11.113
26
27.566
27.436
9
8.8025
8.7643
20
20.157
20.267
10
9.373
10.082
14
13.649
13.557
14
14.351
14.615
12
12.088
11.521
105
5.2.3
Discussion of Simulation Result for Case 3
In case 3, past 3 interval data on 4th day and past 3 days (1st,2nd and 3rd day)
data are used to predict traffic flow on 5th day. From simulation results, RBF NN
prediction model with newrb and newrbe functions able to predict up peak traffic
accurately which is same as previous cases. Three continuous RBF NN output (5
minutes the peak) are found deviated from real data quite significant which is very
similar to case 1. The mean square error for newrb function is 2.82 while mean
square error for newrbe function is 0.00328. Again, performance of newrbe function
is better than newrb function.
Performance of RBF NN in case 3 is close to
performance in case 1 but not as good as case 2. This shows that RBF NN use past k
interval data on mth day and past p days data as training data to predict traffic flow on
same day performs better than RBF NN trained by using past k interval data on (m1)th day. The value of p either is 3 days (case 3) or 4 days (case 4) does contribute
significant effect in predicting traffic flow. Generally, performance of RBF NN
prediction model is considered satisfactory. The output of RBF NN prediction model
and real data are summarized in Table 5.3.
Table 5.3 Comparison of RBF NN output for newrb, newrbe and real data (Case 3).
Real Data
RBF NN Output
newrb
newrbe
5
7.2314
13.779
12
11.513
13.411
13
12.512
12.233
14
11.573
15.196
24
23.874
22.68
21
21.574
21.904
34
31.204
25.472
42
41.925
39.967
34
34.924
33.371
38
33.478
32.587
36
28.923
24.402
106
Table 5.3 Continued.
5.2.4
31
28.513
23.285
26
25.809
24.437
32
30.068
24.981
20
22.018
20.78
15
17.657
18.946
20
21.095
21.222
19
18.536
19.773
16
16.104
17.702
11
14.117
16.65
26
22.424
22.371
9
8.0899
14.756
20
21.653
20.934
10
14.019
18.342
14
15.49
16.481
14
13.875
17.46
12
11.077
15.176
Discussion of Simulation Results for Case 4, 5 and 6
In case 4, past 3 interval data on 5th day and past 3 days (2nd, 3rd and 4th day)
data are used to predict traffic flow on 5th day. For case 5 and 6, past 4 and 2 interval
data on 5th day and past 4 days data (1st, 2nd, 3d and 4th day) are used to train RBF
NN prediction model.
From simulation results for case 4, 5 and 6, RBF NN
prediction model with newrb and newrbe functions able to predict traffic flow
accurately which is better than previous cases. The mean square error for both newrb
and newrbe functions are very small and could be neglected. This shows that RBF
NN use past k interval data on mth day and past continuous p days data as training
data to predict traffic flow on same day will yield very good result. RBF NN was
well trained due to data on 1st, 2nd, 3rd and 4th day are close to each other.
Performance of RBF NN prediction model is considered excellence. The output of
107
RBF NN prediction model and real data for case 4, 5 and 6 are summarized in Table
5.4, Table 5.5 and Table 5.6 respectively.
Table 5.4 Comparison of RBF NN output for newrb, newrbe and real data (Case 4).
Real Data
RBF NN Output
newrb
newrbe
5
5
5
12
12
12
13
13
13
14
14
14
24
24
24
21
21
21
34
34
34
42
42
42
34
34
34
38
38
38
36
36
36
31
31
31
26
26
26
32
32
32
20
20
20
15
15
15
20
20
20
19
19
19
16
16
16
11
11
11
26
26
26
9
9
9
20
20
20
10
10
10
14
14
14
14
14
14
12
12
12
108
Table 5.5 Comparison of RBF NN output for newrb, newrbe and real data (Case 5).
Real Data
RBF NN Output
newrb
newrbe
12
12
12
13
13
13
14
14
14
24
24
24
21
21
21
34
34
34
42
42
42
34
34
34
38
38
38
36
36
36
31
31
31
26
26
26
32
32
32
20
20
20
15
15
15
20
20
20
19
19
19
16
16
16
11
11
11
26
26
26
9
9
9
20
20
20
10
10
10
14
14
14
14
14
14
12
12
12
109
Table 5.6 Comparison of RBF NN output for newrb, newrbe and real data (Case 6).
Real Data
RBF NN Output
newrb
newrbe
4
4
4
5
5
5
12
12
12
13
13
13
14
14
14
24
24
24
21
21
21
34
34
34
42
42
42
34
34
34
38
38
38
36
36
36
31
31
31
26
26
26
32
32
32
20
20
20
15
15
15
20
20
20
19
19
19
16
16
16
11
11
11
26
26
26
9
9
9
20
20
20
10
10
10
14
14
14
14
14
14
12
12
12
110
5.2.5
Discussion of Simulation Results for Case 7
In case 7, past 2 interval data on 4th day and past 3 days (1st, 2nd and 3rd day)
data are used to predict traffic flow on 5th day. Like previous cases, the up peak is
predicted accurately.. The mean square error for both newrb and newrbe functions
are 0.00044 and 0.031554 respectively. One common feature of case 1, 3 and 7 is
past data on 4th day and past 3 days data are used to train RBF NN in order to predict
traffic flow on 5th day. The simulation result shows that its performance is better
than performance of case 1 and case 3. This shows that higher k value does not
guarantee better performance in predicting traffic flow. Generally, performance of
RBF NN prediction model is considered satisfactory.
The output of RBF NN
prediction model and real data for case 7 is summarized in Table 5.7.
Table 5.7 Comparison of RBF NN output for newrb, newrbe and real data (Case 7).
Real Data
RBF NN Output
newrb
newrbe
4
5.6832
9.8933
5
4.189
4.381
12
11.779
12.149
13
12.993
13
14
13.759
13.959
24
24.232
24.407
21
20.227
20.739
34
33.177
33.225
42
41.436
40.842
34
34.465
33.879
38
37.528
37.485
36
35.19
33.251
31
34.523
27.971
26
28.581
25.466
32
30.046
28.911
20
20.185
19.977
111
Table 5.7 Continued.
5.2.6
15
15.743
15.399
20
20.39
20.661
19
18.411
19.475
16
15.774
16.095
11
11.014
11
26
26.721
24.671
9
6.3568
13.097
20
19.375
20.067
10
10.02
10
14
14.429
15.243
14
13.945
14.07
12
11.717
11.745
Discussion of Simulation Results for Case 8
In case 8, past 2 interval data on 4th day and past 2 days (2nd and 3rd day) data
are used to predict traffic flow on 5th day.
From simulation result, RBF NN
prediction model with newrb and newrbe functions able to predict up peak accurately
with small mean square error. Case 8 is actually similar to case 1, 3 and 7 but with
the lowest k and p value (k=2 and p=2). This shows that higher k and p values do
not guarantee better performance in predicting traffic flow. Good performance of
RBF NN prediction model in case 8 is caused selection of optimum spread constant.
As such, it is concluded that spread constant plays important role in RBF NN
prediction model. Like case 4, 5 and 6, performance of RBF NN prediction model is
excellence. The output of RBF NN prediction model and real data for case 8 is
summarized in Table 5.8 and they are no difference because mean square error could
be neglected.
112
Table 5.8 Comparison of RBF NN output for newrb, newrbe and real data (Case 8).
Real Data
RBF NN Output
newrb
newrbe
4
4
4
5
5
5
12
12
12
13
13
13
14
14
14
24
24
24
21
21
21
34
34
34
42
42
42
34
34
34
38
38
38
36
36
36
31
31
31
26
26
26
32
32
32
20
20
20
15
15
15
20
20
20
19
19
19
16
16
16
11
11
11
26
26
26
9
9
9
20
20
20
10
10
10
14
14
14
14
14
14
12
12
12
113
5.2.7
Discussion of Simulation Results for Case 9
In case 9, past 2 interval data on 4th day and past 2 days (2nd and 3rd day) data
are used to predict traffic flow on 4th day.
From simulation result, RBF NN
prediction model with newrb and newrbe functions able to predict up peak accurately
with small mean square error. It is expected because past interval data on 4th day is
used to train RBF NN even k and p values are small. Again, this shows that k and p
values are not major factor in RBF NN but optimum spread constant. The output of
RBF NN prediction model and real data for case 9 is summarized in Table 5.9 and
they are no difference because mean square error could be neglected.
Table 5.9 Comparison of RBF NN output for newrb, newrbe and real data (Case 9).
Real Data
RBF NN Output
newrb
newrbe
5
5
5
5
5
5
12
12
12
12
12
12
14
14
14
23
23
23
22
22
22
33
33
33
42
42
42
35
35
35
35
35
35
29
29
29
28
28
28
28
28
28
34
34
34
20
20
20
17
17
17
21
21
21
114
Table 5.9 Continued.
5.2.8
19
19
19
16
16
16
14
14
14
23
23
23
9
9
9
20
20
20
12
12
12
14
14
14
13
13
13
10
10
10
Discussion of Simulation Results for Case 10
In case 10, only past 1 interval data on 5th day and past 2 days (2nd and 3rd day)
data are used to predict traffic flow on 5th day. The 4th day data is not used to ensure
that is not continuity in p. From simulation result, RBF NN prediction model with
newrb and newrbe functions still able to predict up peak accurately with small mean
square error. It could be past interval data on 5th day is used even k=1 to train RBF
NN. Again, this proves that k and p values are not major factor in RBF NN but
optimum spread constant. Besides that, collected traffic flow data is also consistent
and no significant deviation among readings at particular time from Monday to
Friday. This cause discontinuity in previous days data training is not contributing to
significant deviation in prediction. The output of RBF NN prediction model and real
data for case 10 is summarized in Table 5.10.
115
Table 5.10 Comparison of RBF NN output for newrb, newrbe and real data (Case
10).
Real Data
RBF NN Output
newrb
newrbe
1
1
1
5
4
4
5
5
5
12
12
12
12
13
13
14
14
14
23
24
24
22
21
21
33
34
34
42
42
42
35
34
34
35
38
38
29
36
36
28
31
31
28
26
26
34
32
32
20
20
20
17
15
15
21
20
20
19
19
19
16
16
16
14
11
11
23
26
26
9
9
9
20
20
20
12
10
10
14
14
14
13
14
14
10
12
12
116
5.3
Summary
From simulation results for 10 cases, RBF NN prediction model is able to
predict up peak traffic which occur at 8:15 a.m. from Monday to Friday. Training
data is consistent and no fluctuation among traffic flow readings at particular time for
continuous five working days. This causes RBF NN prediction model perform
consistently. Architecture of RBF NN is designed to predict elevator traffic flow by
training with past k interval data and past p data and simulation results for case 1, 3,
7, 8 and 9 show that higher k and p values do not assure that RBF NN would perform
better than RBF NN trained with lower k and p values.
On the other hand,
simulation result of case 10 shows that discontinuity of past days training data does
not downgrade performance of RBF NN because training data is consistent for five
days. It is believed that prediction capability of RBF NN would be downgraded if
there are fluctuations in training data.
From simulation results, satisfactory performance of RBF NN with either
newrbe or newrb function is obtained. The goal of 0.05 set in newrb function is good
enough for RBF NN to yield good results. Besides that, Optimum spread constant is
the parameter plays main role in deciding performance of RBF NN prediction model.
Minimum mean square error is obtained when optimum spread constant is used as
input to the RBF NN for all cases. As conclusion, elevator traffic flow prediction
model developed by using radial neural network able to predict short term traffic
flow fairly accurate in morning.
117
CHAPTER 6
CONCLUSION AND FUTURE DEVELOPMENTS
6.1
Conclusion
In this thesis, radial basis function neural network (RBF NN) which is one of
artificial intelligent technique widely used in pattern recognition is used to develop
elevator traffic flow prediction model. In elevator traffic flow prediction models
developed by employing artificial intelligent techniques (example: square support
machine), past k interval data and past p days data (k and p are positive integer) are
used to train the core network of prediction model. The same principle is adopted to
design and develop elevator traffic flow prediction model in this thesis. RBF NN
prediction model developed in this thesis is an effective model to perform traffic
flow prediction as it needs only one week data to train the core network to predict
short term up peak traffic with good results. Shorter training period is advantage of
prediction model as it would not occupy many memory slots in controller to store
training data. Performance of elevator group control system is determined by its
capability to handle up peak traffic in morning. Therefore, this RBF NN traffic flow
prediction model could be integrated into elevator group control system to enhance
its performance. Main controller could assign more elevators to serve the main floor
or command elevators return to main floor upon completion of service at the time
when up peak occurs during working days with reference to prediction result
118
feedback by RBF NN prediction model. This will benefit elevator users as average
waiting time at the up peak hour is being reduced.
Neural network toolbox with newrb and newrbe built in functions in matlab
software is good tool to develop RBF NN prediction model because it is user friendly
and simulates results in graphical format which leads to easier interpretation.
Optimum spread constant shall be determined so that RBF NN prediction model will
yield good results whether newrbe or newrb function is excuted.
6.2
Future Development
In this thesis, up peak elevator traffic flow in morning prediction is focused,
scope of research could be expanded to predict elevator traffic flow for one whole
day by acquiring more training data. Besides that, case study in this thesis has
evaluated effectiveness of RBF NN prediction model office building in Penang only
and it should be evaluated in other type of buildings such as hospital, hotel or
residential apartment in other major cities in Malaysia like Kuala Lumpur and Johor
Bahru. At the same time, a comprehensive database of elevator traffic flow could be
established in Malaysia which is useful reference for building service engineers or
elevator engineers. It also possible to incorporates other methods in the RBF NN to
form a hybrid model in future in order to develop more sophisticated elevator traffic
flow prediction model.
RBF NN prediction model for elevator up peak traffic flow is also possible to
be modified so that it could be used to predict traffic flow in highway tolls. With the
predicted data, highway authority could introduce plan to reduce traffic congestion at
peak hour effectively.
119
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APPENDIX
Program in matlab to determine optimum spread constant for case 1 (newrb)
[x] = initelevdata;
spread=15.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 4 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,5) x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:7)',Data(:,8)',0.05, spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
125
MSEresult(jj,1)=(sum(rbfoutput'-x(5:30,6)).^2)./26;
end
figure; plot(MSEresult);
126
Program in matlab to determine optimum spread constant for case 1 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 4 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,5) x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:7)',Data(:,8)',spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(5:30,6)).^2)./26;
end
127
Program in matlab to determine optimum spread constant for case 2 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;spread=26;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:8)',Data(:,9)',0.05,spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,6) x(t+1,5) x(t+1,4) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(5:30,6)).^2)./26;
end
figure; plot(MSEresult);
128
Program in matlab to determine optimum spread constant for case 2 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;spread=26;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:8)',Data(:,9)',spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,6) x(t+1,5) x(t+1,4) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(5:30,6)).^2)./26;
end
figure; plot(MSEresult);
129
Program in matlab to determine optimum spread constant for case 3 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:6)',Data(:,7)',0.05,spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(4:30,6)).^2)./27;
end
figure; plot(MSEresult);
130
Program in matlab to determine optimum spread constant for case 3 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)',spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(4:30,6)).^2)./27;
end
figure; plot(MSEresult);
131
Program in matlab to determine optimum spread constant for case 4 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:6)',Data(:,7)',0.05,spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(4:30,6)).^2)./27;
end
figure; plot(MSEresult);
132
Program in matlab to determine optimum spread constant for case 4 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)',spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(4:30,6)).^2)./27;
end
figure; plot(MSEresult);
133
Program in matlab to determine optimum spread constant for case 5 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:8)',Data(:,9)',0.05, spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(5:30,6)).^2)./26;
end
figure; plot(MSEresult);
134
Program in matlab to determine optimum spread constant for case 5 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:8)',Data(:,9)',spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(5:30,6)).^2)./26;
end
figure; plot(MSEresult);
135
Program in matlab to determine optimum spread constant for case 6 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,6)).^2)./28;
end
figure; plot(MSEresult);
136
Program in matlab to determine optimum spread constant for case 6 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,6)).^2)./28;
end
figure; plot(MSEresult);
137
Program in matlab to determine optimum spread constant for case 7 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:5)',Data(:,6)', 0.05,spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,6)).^2)./28;
end
figure; plot(MSEresult);
138
Program in matlab to determine optimum spread constant for case 7 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:5)',Data(:,6)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,6)).^2)./28;
end
figure; plot(MSEresult);
139
Program in matlab to determine optimum spread constant for case 8 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:4)',Data(:,5)', 0.05,spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,6)).^2)./28;
end
figure; plot(MSEresult);
140
Program in matlab to determine optimum spread constant for case 8 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:4)',Data(:,5)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,6)).^2)./28;
end
figure; plot(MSEresult);
141
Program in matlab to determine optimum spread constant for case 9 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:4)',Data(:,5)', 0.05,spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,5)).^2)./28;
end
figure; plot(MSEresult);
142
Program in matlab to determine optimum spread constant for case 9 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 2 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:4)',Data(:,5)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(3:30,5)).^2)./28;
end
figure; plot(MSEresult);
143
Program in matlab to determine optimum spread constant for case 10 (newrb)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 1 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=1:29,
Data(t,:)=[x(t,6) x(t+1,5) x(t+1,4) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:3)',Data(:,4)', 0.05,spread);
% Test data
% Preparing data for test
for t=1:29,
chkData(t,:)=[x(t,6) x(t+1,5) x(t+1,4)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(2:30,5)).^2)./29;
end
figure; plot(MSEresult);
144
Program in matlab to determine optimum spread constant for case 10 (newrbe)
[x] = initelevdata;
spread=0.1;
recordspread=spread;
for jj=1:1:50
spread=spread+0.5;
recordspread(jj,1)=spread;
% Use past 1 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=1:29,
Data(t,:)=[x(t,6) x(t+1,5) x(t+1,4) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:3)',Data(:,4)', spread);
% Test data
% Preparing data for test
for t=1:29,
chkData(t,:)=[x(t,6) x(t+1,5) x(t+1,4)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult(jj,1)=(sum(rbfoutput'-x(2:30,5)).^2)./29;
end
figure; plot(MSEresult);
145
Program in matlab for case 1 (newrb)
[x] = initelevdata;
spread=15.6;
% Use past 4 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,5) x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:7)',Data(:,8)',0.05,spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(5:30,1),x(5:30,6),'r*-');
hold on; plot(x(5:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(5:30,6)).^2)./26;
146
Program in matlab for case 1 (newrbe)
[x] = initelevdata;
spread=7.1;
% Use past 4 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,5) x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:7)',Data(:,8)',spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(5:30,1),x(5:30,6),'r*-');
hold on; plot(x(5:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(5:30,6)).^2)./26;
147
Program in matlab for case 2 (newrb)
[x] = initelevdata;
spread=25.1;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:8)',Data(:,9)',0.05,spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,6) x(t+1,5) x(t+1,4) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(5:30,1),x(5:30,6),'r*-');
hold on; plot(x(5:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(5:30,6)).^2)./26;
148
Program in matlab for case 2 (newrbe)
[x] = initelevdata;
spread=5.1;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:8)',Data(:,9)',spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,6) x(t+1,5) x(t+1,4) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(5:30,1),x(5:30,6),'r*-');
hold on; plot(x(5:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(5:30,6)).^2)./26;
149
Program in matlab for case 3 (newrb)
[x] = initelevdata;
spread=20.6;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:6)',Data(:,7)',0.05,spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(4:30,1),x(4:30,6),'r*-');
hold on; plot(x(4:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(4:30,6)).^2)./27;
150
Program in matlab for case 3 (newrbe)
[x] = initelevdata;
spread=10;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,5) x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)',spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(4:30,1),x(4:30,6),'r*-');
hold on; plot(x(4:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(4:30,6)).^2)./27;
151
Program in matlab for case 4 (newrb)
[x] = initelevdata;
spread=0.6;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:6)',Data(:,7)',0.05,spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
figure;
plot(x(4:30,1),x(4:30,6),'r*-');
hold on; plot(x(4:30,1),rbfoutput','co-');
MSEresult=(sum(rbfoutput'-x(4:30,6)).^2)./27;
end
152
Program in matlab for case 4 (newrbe)
[x] = initelevdata;
spread=1.6;
% Use past 3 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=3:29,
Data(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)',spread);
% Test data
% Preparing data for test
for t=3:29,
chkData(t-2,:)=[x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
figure;
plot(x(4:30,1),x(4:30,6),'r*-');
hold on; plot(x(4:30,1),rbfoutput','co-');
MSEresult=(sum(rbfoutput'-x(4:30,6)).^2)./27;
end
153
Program in matlab for case 5 (newrb)
[x] = initelevdata;
spread=0.6;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:8)',Data(:,9)',0.05,spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(5:30,1),x(5:30,6),'r*-');
hold on; plot(x(5:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(5:30,6)).^2)./26;
154
Program in matlab for case 5 (newrbe)
[x] = initelevdata;
spread=14.6;
% Use past 4 interval data and past 4 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=4:29,
Data(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)
x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:8)',Data(:,9)',spread);
% Test data
% Preparing data for test
for t=4:29,
chkData(t-3,:)=[x(t-3,6) x(t-2,6) x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(5:30,1),x(5:30,6),'r*-');
hold on; plot(x(5:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(5:30,6)).^2)./26;
155
Program in matlab for case 6 (newrb)
[x] = initelevdata;
spread=0.6;
% Use past 2 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:6)',Data(:,7)',0.05,spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,6),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,6)).^2)./28;
156
Program in matlab for case 6 (newrbe)
[x] = initelevdata;
spread=9.6;
% Use past 2 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:6)',Data(:,7)',spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,5) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,6),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,6)).^2)./28;
157
Program in matlab for case 7 (newrb)
[x] = initelevdata;
spread=15.1;
% Use past 2 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:5)',Data(:,6)',0.05, spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,6),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,6)).^2)./28;
158
Program in matlab for case 7 (newrbe)
[x] = initelevdata;
spread=5.1;
% Use past 2 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,2) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:5)',Data(:,6)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,6) x(t,6) x(t+1,4) x(t+1,3) x(t+1,2)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,6),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,6)).^2)./28;
159
Program in matlab for case 8 (newrb)
[x] = initelevdata;
spread=15.1;
% Use past 2 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:4)',Data(:,5)',0.05, spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,6),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,6)).^2)./28;
160
Program in matlab for case 8 (newrbe)
[x] = initelevdata;
spread=11.1;
% Use past 2 interval data and past 3 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:4)',Data(:,5)',spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,6),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,6)).^2)./28;
161
Program in matlab for case 9 (newrb)
[x] = initelevdata;
spread=6.1;
% Use past 2 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:4)',Data(:,5)',0.05, spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,5),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,5)).^2)./28;
162
Program in matlab for case 9 (newrbe)
[x] = initelevdata;
spread=5.1;
% Use past 2 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=2:29,
Data(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3) x(t+1,5)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:4)',Data(:,5)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t-1,:)=[x(t-1,5) x(t,5) x(t+1,4) x(t+1,3)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(3:30,1),x(3:30,5),'r*-');
hold on; plot(x(3:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(3:30,5)).^2)./28;
163
Program in matlab for case 10 (newrb)
[x] = initelevdata;
spread=5;
% Use past 1 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=1:29,
Data(t,:)=[x(t,6) x(t+1,5) x(t+1,4) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrb(Data(:,1:3)',Data(:,4)',0.05, spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t,:)=[x(t,6) x(t+1,5) x(t+1,4)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(2:30,1),x(2:30,6),'r*-');
hold on; plot(x(2:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(2:30,6)).^2)./29;
164
Program in matlab for case 10 (newrbe)
[x] = initelevdata;
spread=2.1;
% Use past 1 interval data and past 2 days data to predict the future 1
% interval ahead
% Preparing data for training
for t=1:29,
Data(t,:)=[x(t,6) x(t+1,5) x(t+1,4) x(t+1,6)];
end
% Training our rbf NN
[elevatortrafficnet] = newrbe(Data(:,1:3)',Data(:,4)', spread);
% Test data
% Preparing data for test
for t=2:29,
chkData(t,:)=[x(t,6) x(t+1,5) x(t+1,4)];
end
% Testing our RBF NN
rbfoutput = sim(elevatortrafficnet,chkData');
figure;
plot(x(2:30,1),x(2:30,6),'r*-');
hold on; plot(x(2:30,1),rbfoutput','co-');
% Evaluating error (i.e. good of estimates)
% How good is our prediction?
% Use MSE
MSEresult=(sum(rbfoutput'-x(2:30,6)).^2)./29;