46862603 Traffic Flow Forecasting Using Grey Neural Network Model

8/12/2019 46862603 Traffic Flow Forecasting Using Grey Neural Network Model

1/48

Traffic flow forecasting

ASEMINAR REPORT

ON

Traffic Flow Forecasting Using Grey NeuralNetwork Model

Transportation division


2/48


ABSTRACT

In this Report, a kind of Grey Neural Network (abbreviates GNN) is

proposed which combines grey system theory with neural network, that is,

the GNN model has been built by adding a grey layer before neural input

layer anda white layer after neural output layer Gray neural network can

elaborate advantages of both grey model and neural network, and enhance

further precision of forecasting The GNN model is employed to forecast areal vehicle traffic flow of !ING"#I highway with favor precision and result,

which is firstly applied GNN to traffic flow forecasting $valuation method has

been used for comparing the performance of forecasting techni%ues The

e&periments show that the GNN model is outperformed G' model and neural

network model, and traffic flow forecasting based on GNN is of validity and

easibility In this study, we consider an application of grey system theory to

the time series data forecasting problem, called grey forecasting, where grey

implies incomplete or uncertain, and grey system describes a system lacking

information about structure messages, operation mechanism and or

behavior documents In case of bad data lacking information, grey

forecasting method is known to be effective in time series data analysis e

present the design of grey forecasting model, and compare it with other

methods



3/48


CONTENTS

*g no

CA!TER "# $NTRO%UCT$ON

++ General-

+- Importance of Traffic orecasting in #ighway

"ector-

+. Need and "trategy of orecasting-

+/ $&periences in Traffic orecasting.

+0 Traffic low orecasting 'odels/

CA!TER ART$F$C$A' NEURA' NET(OR)S *ANN+

-+ hat is

NN1

0

-- #istory of 2NN0

-. hy use NN3

-/ 4iological Inspiration 3

-0 2pplication of 2NN5



4/48


-6 2NN 'odel and 2rchitecture

-6+ Neuron 'odel++

-6- Network architecture+6

CA!TER ,# GRE- S-STEM TEOR- AN% T$ME SER$ES ANA'-S$S

.+ 4ack Ground of Grey "ystem Theory-7

.- undamental concepts of G"T and its main

contents-+

.. Grey Time "eries 2nalysis-.

./ Grey orecasting 'odel-.

CA!TER.# GRE- NEURA' NET(OR)S

/+ 8onstruction of Grey Neural network

'odel-9

/- $&periment Result and 8omparison of GNN, G' (+, +) :NN

.7

CA!TER/; 8onclusions./

References.0



5/48


'ist of figures

0g1no

+ "chematic diagram of biological neurons3

- "ingle Input Neuron+-

. #ard


6/48


3 Neuron with R inputs with 2bbrivated notations+3

9


7/48


CA!TER "

$NTRO%UCT$ON

Traffic flow forecasting is significant to traffic programming, traffic guide,

traffic controlling, traffic management, traffic security, etc It has become an

emphasis %uestion for discussion in traffic engineering domain and one

kernel study in Intelligent Transportation "ystem Grey system theory and

neural networks have been successfully used to predict traffic Grey system

theory utili=es accumulated generating data instead of original data to build

forecasting model, which makes raw data stochastic weak, or reduces noiseinfluence in a certain e&tent, therefore, intrinsic regularity of data can be

searched easily, and model can be built with relatively little data Neural

network has been a primary nonlinear forecasting method because of its

ability of self>learning, nonlinear map and parallel distributed manipulation

Traffic system is a complicated system with rather great stochastic,

traffic flow possess characteristic of great time>dependent and nonlinear If

combine grey system theory with neural networks to build GNN (Grey Neural

Network), we can e&ploit sufficiently the characteristic of grey system model

re%uiring less data and feature of nonlinear map of neural network, and

develop both advantages, thus raise predicting precision much more In this

paper, a kind of forecasting model combining grey system theory with neural

networks is proposed, which adds a grey layer before neural input layer and

a white layer after neural output layer The GNN model is firstly applied to

forecast a real vehicle traffic flow of !ING"#I highway with favorable

precision and prediction result $valuation methods are used for comparing

the performance of forecasting techni%ues, which show that the GNN model

is outperformed G' model and neural network The e&periment shows that

this kind information manipulation and forecasting method based on GNN is

of validity and feasibility



8/48


"1" GENERA'

TRAFF$C FORECAST$NG

Traffic flow forecasting is significant in traffic programming, traffic guide,

traffic controlling, traffic management, traffic security etc It has become an

emphasis %uestion for discussion in traffic engineering domain and in

intelligent transportation system orecasting of data is a key element of

management decision making It becomes all the more important when

decision involves huge investments

"1& $M!ORTANCE OF TRAFF$C F'O( FORECAST$NG $N $G(A-SECTOR#

Transportation is a basic infrastructural facility for the economical, social,

cultural and administrative development country It has been recogni=ed that

the sustainable development of an area is dependent on the type and

%uantum of the transportation infrastructure linking the various centers of

human population, employment, economic growth and market centers

ast depleting financial and other resources and over increasing travel needs

call for careful planning and optimum resource utili=ation in the road sector

as all the decisions regarding planning, construction and maintenance of

road sector are based on estimates of the traffic for the design period, it is

necessary to cut down the dependence on the chance while forecasting the

traffic over estimation of traffic will result in more than necessary capital



9/48


being tied up in a fewer pro?ects, thus preventing other potential pro?ects

being taken up where as under estimation of the traffic will result in

premature failure of the pavement structure, causing heavy financial losses

increased maintenance costs

"1, NEE% AN% STRATEG- OF FORECAST$NG

$&istence in an environment governed by time re%uires allocation of

available time among competing resources in some optimal manner This is

accomplished by making forecasts of future activities and taking the proper

actions as suggested by these forecasts The time series underlying the

process to be forecasts is bound to be influenced by many casual factors

"ome forcing the time series up while conflicting factors act to force the

series down nevertheless it is essential to make forecasts in order to

effectively ad?ust budget and resources

orecasts by e&tending the patterns revealed by smoothing techni%ues, is a

very speculative procedure It must be assumed to start with that past is a

mirror of the future the past trends and cycles will continue in the future this

is seldom the case ,in the end ,mathematical forecasting procedures and

?udgments must work hand in hand thus one must not only smooth the data

and try to e&tend the signal components in to the future but also predict the

impact of unknown factors such as political events, research and inventions,

new land use development ,changes in the present land use ,vehicle use

,change of behavior of vehicle user etc in connections with traffic volumes

The sub?ective evaluations must, in turn, be used to conditions the forecast

obtained from the mathematical forecasting model

"1. E3!ER$ENCES $N TRAFF$C FORECST$NG#

Numbers of methods are available for forecasting ranging from the simplest

methods such as the one using the most recent observations as to forecast

to highly comple& approaches like econometric system of simultaneous

e%uations #owever, the methods for generating forecasts can be broadly



10/48


classified as %ualitative, depending upon the e&tent to which mathematical

and statistical methods are used

@uantitative methods, market research methods, panel consensus, historical

analogy, visionary forecasts etc, involve sub?ective estimation through the

e&perts opinion from a panel of forecasts

#ence such forecast may differ from panel to panel or e&pert to e&pert

"ometimes the divergence in opinion among the e&pert is so e&tensive that

it becomes hard to imagine any substantial could be placed in the results

An the other hand substantial forecasting procedures e&plicitly define how

the forecast is determined the logic is clearly stated and the operations are

mathematical The methods involve e&amination of historical data to

determine the underlying process generating the variable and assuming that

the process is stableB use this knowledge to e&trapolate the process into the

future The two basic types of these models are time series models and

casual models

8asual models e&ploit the relationship between the time series of interest

and one or more other time series data of casual variables Cnowing the

future values o the casual variables, one can use the model to forecast the

dependent variable 4ut the future value of casual variable may itself be

obtained by forecasting it either by casual models or time series models

#ence this method is comple& to operate "ome of the casual models are

regression analysis, econometric models, input>output modelsB anticipation

surveys etcTime series models use only the time history of the variable

being forecasted in order to develop a model for predicting future values

The selection of appropriate forecasting methods is influenced by the

following factors such as ,

+ orm of forecasts re%uired

- orecasts hori=on, period and interval

. Data availability

/ 2ccuracy re%uired

0 4ehavior of process being forecast



11/48


6 8ost of development

3 $ase of pattern

9 'anagement comprehension and cooperation

"1/ TRAFF$C F'O( FORECAST$NG MO%E'S#

"everal types of mathematical models currently e&ist and are used to

forecast the traffic flow

These models range from simple regression to complicated transition

probability method An the other hand grey forecasting model and neural

networks, fu==y logic have been applied in traffic flow forecasting to certain

e&tent

Development of traffic forecasting models has been an active area in the last

couple of decades, which constitute a key component of management

decision making The traffic forecasting model, when considered as a system

with inputs of historical and current data and outputs of future data, behaves

in a nonlinear fashion and varies with time of day Traffic data are found to

change abruptly during the transition times of entering or leaving rush hours

2ccurate and real time models are needed to appro&imate the nonlinear

time variant functions between system inputs and outputs from a continuous

stream of training data

There has been a steady increase in both rural and urban freeway traffic in

recent years resulting in congestion in many freeway systems 2ccurate and

timely forecasting of traffic flow is of paramount importance for effective

management of traffic congestion and decision making The basic types of

forecasting models are given below

+ Time series models

-


12/48


CA!TER &

ART$F$C$A' NEURA' NET(OR)S

&1" (AT $S NEURA' NET(OR)4

2n 2rtificial Neural Network (2NN) is an information processing paradigm

that is inspired by the way biological nervous systems, such as the brain,

process information The key element of this paradigm is the novel structure

of the information processing system It is composed of a large number of

highly interconnected processing elements (neurons) working in unison to

solve specific problems 2NNs, like people, learn by e&ample 2n 2NN is

configured for a specific application, such as pattern recognition or data

classification, through a learning process


13/48


"ome of the background work for the field of neural networks occurred in the

late +5th and early -7th centuries This consisted primarily of

interdisciplinary work in physics, psychology and neurophysiology by such

scientists as #ermann von #elmholt=, $rnst 'ach and Ivan *avlov This early

work emphasi=ed general theories of learning, vision, conditioning, etc,and

did not include specific mathematical models of neuron operation

The modern view of neural networks began in the +5/7s with the work of

arren 'c8ulloch and alter *itts E'c*i/.F, who showed that networks of

artificial neurons could, in principle, compute

any arithmetic or logical function Their work is often acknowledged as the

origin of the neural network field

'c8ulloch and *itts were followed by Donald #ebb , who proposed that

classical conditioning (as discovered by *avlov) is present because of the

properties of individual neurons #e proposed a mechanism for learning in

biological neurons

The first practical application of artificial neural networks came in the late

+507s, with the invention of the perception network and associated learning

rule by rank Rosenblatt Rosenblatt and his colleagues built a perception

network and demonstrated its ability to perform pattern recognition This

early success generated a great deal of interest in neural network research

nfortunately, it was later shown that the basic perception network could

solve only a limited class of problems unfortunately, both RosenblattHs and

indrows networks suffered from the same inherent limitations, #owever,

they were not able to successfully modify their learning algorithms to train

the more comple& networks During the +597s both of these impediments

were overcome, and research in neural networks increased dramatically

New personal computers and workstations, which rapidly grew in capability,

became widely available

In addition, important new concepts were introduced The second key

development of the +597s was the back propagation algorithm for training

multilayer perception networks, which was discovered independently by



14/48


several different researchers The most influential publication of the back

propagation algorithm was by David Rumelhart and !ames 'c8lelland

ERu'c96F

These new developments reinvigorated the field of neural networks In the

last ten years, thousands of papers have been written, and neural networks

have found many applications The field is bu==ing with new theoretical and

practical work 'any of the advances in neural networks have had to do with

new concepts, such as innovative architectures and training rules !ust as

important has been the availability of powerful new computers on which to

test these new concepts

Neural networks will not only have their day but will have a permanent place,

not as a solution to every problem, but as a tool to be used in appropriate

situations In addition, remember that we still know very little about how the

brain works The most important advances in neural networks almost

certainly lie in the future

&1, (- USE NEURA' NET(OR)S4

Neural networks, with their remarkable ability to derive meaning from

complicated or imprecise data, can be used to e&tract patterns and detect

trends that are too comple& to be noticed by either humans or other

computer techni%ues 2 trained neural network can be thought of as an

e&pert in the category of information it has been given to analyse This

e&pert can then be used to provide pro?ections given new situations of

interest and answer what if %uestions

Ather advantages include; 2daptive learning; 2n ability to learn how to do

tasks based on the data given for training or initial e&perience



15/48


+ "elf>Argani=ation; 2n 2NN can create its own organi=ation or

representation of the information it receives during learning time

- Real Time Aperation; 2NN computations may be carried out in parallel,

and special hardware devices are being designed and manufactured

which take advantage of this capability

ault Tolerance via Redundant Information 8oding; *artial destruction of a

network leads to the corresponding degradation of performance #owever,

some network capabilities may be retained even with ma?or network damage

&1.Biological $ns0iration#

2n 2rtificial Neural Network (2NN) is an information processing paradigm

that is inspired by the way biological nervous systems, such as the brain,

process information

The brain consists of a large number (appro&imately +7++) of highly

connected elements (appro&imately +7/connections per element) called

neurons or our purposes these neurons have three principal components;

the dendrites, the cell body and the a&on The dendrites are tree>like

receptive networks of nerve fibers that carry electrical signals into the cell

body The cell body effectively sums and thresholds these incoming signals

The a&on is a single long fiber that carries the signal from the cell body out

to other neurons The point of contact between an a&on of one cell and a

dendrite of another cell is called a synapse It is the arrangement of neurons

and the strengths of the individual synapses, determined by a comple&

chemical process that establishes the function of the neural network igure

+ is a simplified schematic diagram of two biological neurons



16/48


ig;+ "chematic diagram of biological neurons

2rtificial neural networks do not approach the comple&ity of the brain There

are, however, two key similarities between biological and artificial neural

networks irst, the building blocks of both networks are simple

computational devices (although artificial neurons are much simpler than

biological neurons) that are highly interconnected "econd, the connections

between neurons determine the function of the network

It is worth noting that even though biological neurons are very slow when

compared to electrical circuits (+7>.s compared to +7>5s), the brain is able to

perform many tasks much faster than any conventional computer This is in

part because of the massively parallel structure of biological neural

networksB all of the neurons are operating at the same time 2rtificial neural

networks share this parallel structure



17/48


&1/ A!!'$CAT$ONS

The applications are e&panding because neural networks are good at solving

problems, not ?ust in engineering, science and mathematics, but in medicine,

business, finance and literature as well

Their application to a wide variety of problems in many fields makes them

very attractive 2lso, faster computers and faster algorithms have made it

possible to use neural networks to solve comple& industrial problems that

formerly re%uired too much computation

Neural networks have been applied in many fields 2 list of some applications

mentioned in the literature follows

Aeros0ace

#igh performance aircraft autopilots, flight path simulations, aircraft control

systems, autopilot enhancements, aircraft component simulations, aircraft

component fault detectors

Auto5oti6e

2utomobile automatic guidance systems, warranty activity analy=ers

Banking

8heck and other document readers, credit application evaluators

%efense

eapon steering, target tracking, ob?ect discrimination, facial recognition,

new kinds of sensors, sonar, radar and image signal processing including

data compression, feature e&traction and noise suppression, signalJimage

identification

Electronics

8ode se%uence prediction, integrated circuit chip layout, process control,

chip failure analysis, machine vision, voice synthesis, nonlinear modeling

Entertain5ent

2nimation, special effects, market forecasting



18/48


Financial

Real estate appraisal, loan advisor, mortgage screening, corporate bond

rating, credit line use analysis, portfolio trading program, corporate financial

analysis, currency price prediction

$nsurance

*olicy application evaluation, product optimi=ation

Manufacturing

'anufacturing process control, product design and analysis, process and

machine diagnosis, real>time particle identification, visual %uality inspection

systems, beer testing, welding %uality analysis, paper %uality prediction,

computer chip %uality analysis, analysis of grinding operations, chemical

product design analysis, machine maintenance analysis, pro?ect bidding,

planning and management, dynamic modeling of chemical process systems

Medical

4reast cancer cell analysis, $$G and $8G analysis, prosthesis design,

optimi=ation of transplant times, hospital e&pense reduction, hospital %uality

improvement, and emergency room test advisement

Ro2oticsTra?ectory control, forklift robot, manipulator controllers, vision systems

S0eec7

"peech recognition, speech compression, vowel classification, te&t to speech

synthesis

Securities

'arket analysis, automatic bond rating, and stock trading advisory systems

Teleco55unications

Image and data compression, automated information services, real>time

translation of spoken language, customer payment processing systems

Trans0ortation

Truck brake diagnosis systems, vehicle scheduling, routing systems



19/48


&18 ANN MO%E' AN% ARC$TECTURE

&181" NEURON MO%E'

"ingle>Input Neuron#

2 single>input neuron is shown in igure - The scalar input is multiplied by

the scalar weight to form , one of the terms that is sent to the summer The

other input,, is multiplied by a bias and then passed to the summer The

summer output, often referred to as the net input , goes into a transfer

function , which produces the scalar neuron output ("ome authors use the

term activation function rather than transfer function and offset rather than

bias)

The weight corresponds to the strength of a synapse, the cell body is

represented by the summation and the transfer function, and the neuron

output represents the signal on the a&on



20/48


Fig#& "ING+0 then aK f(.(-)L +0)K f(/0)

The actual output depends on the particular transfer function that is chosen

The bias is much like a weight, e&cept that it has a constant input of

+#owever, if you do not want to have a bias in a particular neuron, it can be

omitted

Note that w and b are both adustab!e scalar parameters of the neuron

Typically the transfer function is chosen by the designer and then the

parameters w and b will be ad?usted by some learning rule so that the

neuron inputJoutput relationship meets some specific goal

Transfer Functions#

The transfer function in igure - may be a linear or a nonlinear function of 2

particular transfer function is chosen to satisfy some specification of the

problem that the neuron is attempting to solve

2 variety of transfer functions have been included and Three of the most

commonly used functions are discussed below

ard 'i5it Transfer Function#

The hard !imit transfer function"shown on the left side of igure . , sets the

output of the neuron to 7 if the function argument is less than 7, or + if its



21/48


22/48


ig;/


23/48


T24


24/48


Multi0le;$n0ut Neuron#

eight matri&;

Typically, a neuron has more than one input 2 neuron with R inputs is shown

in igure 6 The individual inputs p+,p-,p. are each weighted by

corresponding elements w+,w-,w.of the weight matri# $

IG;6 '


25/48


represents the connection to the first (and only) neuron from the second

source

e would like to draw networks with several neurons, each having several

inputs urther, we would like to have more than one layer of neurons Mou

can imagine how comple& such a network might appear if all the lines were

drawn It would take a lot of ink, could hardly be read, and the mass of detail

might obscure the main features Thus, we will use an abbre%iated notation

2 multiple>input neuron using this notation is shown in igure3

IG;3 Neuron with R inputs with 2bbrivated notations

&181& NET(OR) ARC$TECTURES

8ommonly one neuron, even with many inputs, may not be sufficient e

might need five or ten, operating in parallel, in what we will call a layer

A 'ayer of Neurons

2 single>!a&er network of " neurons is shown in igure9 Note that each of

the R inputs is connected to each of the neurons and that the weight matri&

now has " rows



26/48


IG;9


27/48


that this weight represents the connection to the third neuron from the

second source

2 layer whose output is the network output is called an output !a&er The

other layers are called hidden

'a&ers( It is shown in fig ):

FI*:)Topology of eed orward Neural Network

Multiple layers:

Now consider a network with several layers $ach layer has its own weight

matri& , its own bias vector b, a net input vector n and an output vector a

e need to introduce some additional notation to distinguish between these

layers e will use superscripts to identify the layers "pecifically, we append



28/48


the number of the layer as a superscript to the names for each of these

variables Thus, the weight matri& for the first layer is written as +, and the

weight matri& for the second layer is written as -as shown in fig +7

IG;+7 Three layer network

2s shown, there are Rinputs, S+neurons in the first layer, S-neurons in the

second layer, etc 2s noted, different layers can have different numbers of

neurons

The outputs of layers one and two are the inputs for layers two and three

Thus layer - can be viewed as a one>layer network with R K "+inputs, "K"-

neurons, and an "+&"- weight matri& The input to layer - is a+, and the

output is a-

ow to !ick Arc7itecture

*roblem specifications help define the network in the following ways;

+ Number of network inputs K number of problem inputs

- Number of neurons in output layer K number of problem outputs



29/48


. Autput layer transfer function choice at least partly determined by

*roblem specification of the output

CA!TER ,

,1" TE BAC)GROUN% OF GST

4ased on widespread divisions in activities of scientific research, the highly

synthetic tendency has brought forward many cross>disciplinary research

activities possessing significant methodological meanings The systemsscience has revealed more profoundly and essentially some important

internal relations among the sub?ects, who have deeply promoted the

integrative progress of modem science and technology ith the help of

these newly emerging fields of study, many complicated problems,

unsolvable before, can be resolved successfully and much deeper

understandings about the nature have been brought forward These cross

disciplinary theories include, to say a few, the systems theory, information

theory and cybernetics, which were formulated during the end of the +5/7s,

the theory of dissipative structures, synergetic and fractals, which started to

be known during the end of the +567s and the beginning of +53As, the ultra

circular theory and general systems theory, which have been more maturing

after late +537s

In a systems research, due to noises from both inside and outside of the

system of our concern and the limitation of our cognitive level, the

information people obtain is always uncertain and limited in scope ith the

development of science and technology and the progress of the social

society, peopleHs understanding about the uncertainties of %arious systems is

much more profound than ever before, and the study on uncertainties is also

more in>depth During the later half of -7 century, in the field of systems



30/48


science and engineering, a variety of systems theories and methodologies on

uncertainty had been emerging constantly or instance, *rofessor long from 8hina It was a new theory and method applicable to the

study of unascertained problems with few data and or poor information Grey

systems theory works on unascertained systems with partially known and

partially unknown information by drawing out valuable information by

generating and developing the partially known information It can describe

correctly and monitor effectively the systemic operational behavior

'any systems, such as social, economic, agricultural, industrial, ecological

biological systems, are named based on the fields and ranges where theresearch sub?ects belong to . In contrary, the name of grey systems is

chosen based on the colors of the sub?ects under investigation or e&ample,

in control theory, the darkness of colors has been commonly used to indicate

the degree of clarity of information Ane of the most well accepted

representations is the so>called Pblack bo&Q, which stands for an ob?ect with



31/48


its internal relations or structure totally unknown to the investigator #ere,

we will use 'ackQ to represent unknown information, PwhiteQ for completely

known information ,and PgreyQ for those information which are partially

known and partially unknown 2ccordingly, we will name the systems with

completely unknown information as black systems, and the systems with

partially known and partially unknown information as grey systems,

respectively

In our daily social economic and scientific research activities, we often face

situations of incomplete information or e&ample, in some studies of

agriculture, even though all the information, related to the area which is

planted, the %uality of seeds, fertili=ers, irrigation, et al, is completely

known, it is still difficult to estimate the production %uantity and the

conse%uent annual income due to various unknowns or vague information

related to labor %uality, the level of technology employed, natural

environment, weather conditions, et al 2s for the case of insects control, we

might have known very well the relationship between the special kind of

insect and its Natural enemies 4ut it might still be difficult for us to achieve

the desirable certainty due to the reason that we do not have enough

information regarding the relationship between the insects of our concern

and the baits, its natural enemies and the baits, one natural enemy and

other natural enemies, one kind of insect and other kinds of insects, et al

or each ad?ustment of a price system in our economy, the decision makers

often face the difficulty of not knowing the definite information on the effect

of the price change on consumers, on the prices of goods, et al 2ll li%uid

pressure systems are difficult to control due to some immeasurable

%uantities $lectricity systems are hard to observe because of the stochastic

parameters of the voltage and currents, which is caused by not having

enough knowledge on motion and parameters In a general social or

economic system, it is difficult to analy=e the effect of the input on the

output for the reasons that there do not e&ist clear differences between the

PinteriorQ and the Pe&teriorQ, the system self and its environment, and that



32/48


the boundary of the system may be sometime easy to tell or on other

occasions difficult to clarify In stochastic works, a same economic variable

could be seen as endogenous by some scholars and e&ternal by some other

scholars The appearance of such a phenomenon is due to the lack of

'odeling information, or the reason that an appropriate systems model has

not been found, or the fact that the right observation and control variables

have not been employed

#aving been developed for more than -7 years, grey "ystems theory has

already built up the framework of a new discipline Its main contents include;

a theory system based on ha=y integration, an analysis system depending on

space of grey incidence, a modeling system with G' as its vital part, a

methodological system on the foundation of grey se%uence generation, and

a technological system 8onstructed mainly by systems analysis, modeling,

forecasting, decision, controlling and optimi=ation #a=y Integration, grey

algebraic system, grey e%uations and grey matri& are the foundation of grey

systems theory, and there are still many problems worth further studying in

order to perfect itself Grey systems analysis consists of mainly grey

incidence analysis, grey clustering and grey statistical evaluation, et al The

generation of grey se%uence relies on functions of se%uence operators

including buffer operator (weakening operator, strengthening operator),

average generation operator, stepwise ratio generation operator, inverse

accumulating generation operator and accumulating generation operator, et

al Grey systems modeling is famished based on the thought of five>step>

modeling 2nd hidden laws are found through the generation of grey

numbers or functions of se%uence operators The new promise of using

discrete data se%uence to construct continuous dynamical differential

e%uations is achieved by interchanging grey difference e%uations with grey

differential e%uations Grey prediction is a %uantitative prediction based on

GM *"


33/48


34/48


35/48


36/48


That is the forecasting model G' (+, I) by e%(.>a)is based on a

difference e%uation concerning

"ince U(+)

(&(+)(

k))K &(7)

(k),kK+,-,.n from e%n (.>b)the difference can berewritten as

here a is called the development of G', and b is called the grey input

The fifth e%n will be satisfied when, if and only if

hen kK-, .n

here =(+)(k) is the mean of &(+)(k) defined as

here kK-, .n

nder the demand for parallel shooting, e% (0) can therefore be transformed

to

here kK-, .n

here a, b are determined to minimi=e the least s%uare error on

& (+)(k)>(b>a O(+)(k)) where

kK-,.n

ie 'in; $T $

here



37/48


4ased on identification algorithm E-F, optimal a and b are given by

or the given discrete n th>dimensional se%uence &(7),the forecasting model

is then determined,with a and b shown by e%n(3)and the se%uence &W (+)(k)

is given by

here kK+, -

(9)

Is said to be the response of the G' (+, +)

2ccordingly the following se%uence

Is said to be the G' (+,+) se%uence of the 2GA and



38/48


Is called the G'(+,+) se%uence while the se%uence

Is called the forecasting se%uence of G' (+, +)

There by, the grey forecasting for a given time series data se%uence &KS&

(7), & (+)& (n) is to determined the correspondent forecasting se%uence

of G' (+, +) by e% (++)



39/48


CA!TER .

.1" TE CONSTRUCT$ON OF GRE- NEURA' NET(OR)

The grey system theory has been initially presented by Deng 1 The grey

system puts each stochastic variable as a grey %uantity or a grey procedure

that changes within a given range or a certain time period It does not rely

on statistical method to deal with the grey %uantityB instead, it uses grey

generating method to deal with these disorderly and unsystematic raw data

and then changes them into a time series data with regularity In this way,

the stochastic degree of the grey %uantity is reduced, and it is easy for some

functions to characteri=e the grey %uantity Grey Neural Network model has

been built according to above ideology GNN model has three basic parts; a

grey layer, a general neural network (such as back propagation), and a white

layer The grey layer before neural input nodes has accumulated generating

operation (2GA)to initial input data, then these new data generated by the

accumulated generating operation are feed into the network, at last, the

white layer after neural output nodes inverses accumulated generation to

the output data of the network Therefore, the prediction value we need is

obtained The construction of GNN model is shown in fig+

Fig""# t7e construction of grey neural network

5odel

Neural network design includes determining network structure, the number

of layers and the number of neurons in every layer Generally, the neural

network adopts neural network back propagation with three layers, and the

NN learning algorithm is error back propagation


40/48


by the grey relational analysis, that is, taking into account the relationships

e&isted between several known traffic flow and the prediction value The

value of m can be determined by thorough tests The GNN model mechanism

is described in the following "uppose the neural network in the GNN model

has n input nodes, the original data & (7)with nVl entries taken as training

sample is

where &(7)(i) is the time series data at time i 4ased on the initial se%uence

&(7), a new se%uence &(+)with nVl entries is generated by the, accumulated

generating operation,

where &((k! is derived as follows;

n train samples to train NN

hen the GNN is successfully trained, it can be used to predict traffic flow

The forecast is estimated through one operation of the inverse of the

accumulated generating operation The prediction value of & (7) (n V "+ can

be written as follows



41/48


where &W(++(nVI) is output value of the Neural Network in GNN model, &W(7)(n

V ++ is output value of the white layer in GNN model, it is prediction value of

&(7) (nV+) at time nVl 4esides the most common method accumulated

generating operation, the grey generating operation done to raw data also

includes multipoint>moving>average, opening the n power or takes the

logarithmic transformation to raw data The original data has been

preprocessed by grey generating operation before feeding into a neural

network the unknown system can be easily characteri=ed by then on linear

function of neural network Thus, the training time of the network can be

shortening, so, while the prediction precision advanced, the convergent

process also can be speeded up

.1& E3!ER$MENT RESU'TS

The time series data of traffic volume in the period of a day from 9: OO to

+3;77at X"#I west in !lNG"#I highway have been used as test data sets,

there are 3-traffic flow data regarding a small car as a unit, and the

sampling interval between two ad?acent data is +7 minutes Three

forecasting model, ie, the Grey Neural Network model, the G' (+,l) grey

model, the Neural Network model are used to forecast this same traffic flow

The time series data from no+ to no6- are used as known data (ie, in>

sample data) to forecast the last +7 data from no6. to no3- (ie, out>of>

sample data) The difference between the actual and the forecast are used

to evaluate the accuracy of the forecasting models our criteria, ie, the

mean root of s%uares error ('R"$), the mean absolute percentage error

('2*$), the ma&imum absolute percentage error('2X2*$), the minimum

absolute percentage error('IN2Y$) are used to compare the performance of



42/48


the GNN model against other two models, ie, the grey forecasting model

G' *+,l+ and the neural network model

T7e Forecasting Results of GM *"


43/48


se this neural network model to forecast the last l7 traffic flow data, theforecasting results are showed in tab!e

T7e Forecasting Results of GNN Model#

2pply GNN model to forecasting traffic flow The raw data goes through one

operation of the accumulated generating operation done by the grey layer,

the forecast is estimated through one operation of the inverse of

accumulated generating operation done by the white layer The neural

network in GNN model has .,layers, from the result of the grey relation, the

number of input nodes is /+,+F

The neurons connection weighs and bias of a success trained neural networkin the GNN model are as follows:



44/48


45/48


Table-; the results obtained from three forecasting models and

compares



46/48


47/48


REFERENCES;

+"#>M2N 8#$NY, G2A>$NG @Y, XING>#$ 2NGY, #'>O#ANG

HTR2I8 Introduction of

Time "eries Data 2nalysis using Grey "ystem TheoryQ +559 "econd

International 8onference on Cnowledge>4ased Intelligent $lectronic "ystem,

-+>-. 2pril +559, 2delaide, 2ustralia $ditors, cheng P2 new grey forecasting model based on 4*

neural network and 'arkov chain P"*RING$R


48/48


3 "tamatios ZCartalopoulosPND$R"T2NDING A N$R2< N$TARC"

2ND OOM

Documents

46862603 Traffic Flow Forecasting Using Grey Neural Network Model