Multilayer Perceptron Models for Surface Ozone Study in ...lbms03.cityu.edu.hk/theses/abt/phd-bc-b22182275a.pdf · Abstract i Abssttrraacctt Multilayer perceptron (MLP) models have

Multilayer Perceptron Models for

Surface Ozone Study in Hong Kong

under the Trans-boundary

Air Pollution Impact

WANG DONG

DOCTOR OF PHILOSOPHY

CITY UNIVERSITY OF HONG KONG

SEPTEMBER 2007

CITY UNIVERSITY OF HONG KONG

香港城市大學

Multilayer Perceptron Models

for Surface Ozone Study in Hong Kong

under the Trans-boundary

Air Pollution Impact

在跨界空氣汚染影響下用感知器

模型對香港臭氧之研究

Submitted to

Department of Building and Construction

建築系 In Partial Fulfillment of the Requirements

For the Degree of Doctor of Philosophy

哲學博士學位

by

Wang Dong

王東

September 2007

二零零七年九月

Abstract

i

AAbbssttrraacctt

Multilayer perceptron (MLP) models have been experiencing a popularity resurgence

for predicting surface ozone level, based on the data of its influential variables colleted

locally from air quality monitoring and meteorology stations around the interested area.

In this dissertation, MLP, not only used traditionally as a predictive model but also an

assessment tool, will be employed to study ozone variation in three typical air

monitoring stations in Hong Kong, the ozone variation of where are believed to be

under different scale of trans-boundary air pollution impact. The optimal topology of

each MLP model used for assessment or prediction was identified by 3-fold cross

validation for two prediction horizons respectively. For assessment work, result from

both prediction horizons shows no remarkable difference. While for prediction work,

performance of all MLP models for 1-day ahead prediction was generally worse than

that for the current-day prediction due to the prolonged prediction horizon.

The preliminary statistical analysis showed the trans-boundary air pollution did exert

different scale of influence on local ozone level in each target air monitoring station,

according to the data for all local and regional ozone influential variables collected

from the whole study area that are defined as Hong Kong territory, Guangdong

Province and part of South China Sea.

MLP trained by automatic relevance determination (named by MLP-ARD), a Bayesian

MLP, was embedded into a two-staged variables selection scheme to assess what were

Abstract

ii

the ozone key influential variables for each air monitoring station respectively. The

variables selection/assessment result from MLP-ARD was comparable with that from

the best method in the literature. The ozone key influential variables from such

selection scheme will further be used as input variables for MLP models developed

later for ozone prediction.

By comparing the predictive performance of MLP-ARD between with and without

regional ozone influential variables as inputs, it was found that trans-boundary air

pollution exerted the largest impact on Tap Mun (TM), the modest on Tung Chung

(TC), and the least on Tsuen Wan (TW) air monitoring station in Hong Kong. The

result also showed the advantage of MLP-ARD, which provided an interval estimation

for the possible ozone variation, in the prediction for ozone episode days, over the

MLP trained by Levenberg-Marquardt (LM) algorithm (named by MLP-LM), which

only provided a point estimation.

MLP-ARD, MLP-LM as well as most MLP models in the literature were trained by

the gradient-based algorithm, which potentially suffered from local minimum problem.

Two hybrid MLP models, based on the standard particle swarm optimization (PSO)

algorithm, will be developed for avoiding this problem in ozone prediction. The reason

for using hybrid model instead of using MLP trained by standard PSO (named by

MLP-PSO) directly is that standard PSO for MLP training will probably not obtain

good convergence reliability in the high dimension weight space, which could

influence the models‘ performance on the ozone-polluted days.

Abstract

iii

Therefore, the aim of two hybrid models was to improve such convergence reliability

by using additional techniques before and after the standard PSO training for MLP

respectively. The first hybrid model was HMC–MLP–PSO. It employed hybrid Monte

Carlo (HMC) method to sample the weight matrix from the posterior probability

distribution of the estimated optimal weight matrix first, and then these sampled

weight matrices were used to initialize ―weight matrix swarm‖ of PSO, before MLP

trained by standard PSO starts. Aiming at exploiting the advantage of both PSO and

LM for MLP training, the other hybrid model was MLP–PSO–LM, which timely

inserted LM to help MLP-PSO avoid stagnation problem.

The performance of two hybrid models was better than MLP-ARD, MLP-LM and

MLP-PSO in terms of several statistics and exceedance indicators. The predictive

performance of all MLP models in this dissertation was finally evaluated. From the

operational point of view, MLP–PSO–LM was recommended for government

authority usage due to its smallest false negative rate for ozone-polluted day

prediction.

Table of Contents

v

TTaabbllee ooff CCoonntteennttss

ABSTRACT ......................................................................................................................................... I

ACKNOWLEDGEMENTS .................................................................................................................... IV

TABLE OF CONTENTS ........................................................................................................................ V

LIST OF FIGURES .............................................................................................................................. IX

LIST OF TABLES ................................................................................................................................ XI

NOMENCLATURE ........................................................................................................................... XIV

CHAPTER 1 GENERAL INTRODUCTION ........................................................................................... 1

1.1 A REGIONAL VIEW OF AIR POLLUTION IN HONG KONG .............................................................................. 1

1.2 BASICS ABOUT TROPOSPHERIC OZONE VARIATION .................................................................................... 5

1.2.1 Ozone Chemistry ................................................................................................................ 5

1.2.2 Meteorology–pollutant interactions .................................................................................. 7

1.3 AIR POLLUTION MODELING ................................................................................................................. 8

1.3.1 A brief review of two categories modeling approach ........................................................ 8

1.3.2 Model comparison works in the literature ....................................................................... 10

1.4 BASICS ABOUT MLP ........................................................................................................................ 12

1.5 TWO CONCEPTS FOR DEVELOPING MLP TRAINING ALGORITHMS ............................................................... 13

1.5.1 Training algorithms in maximum likelihood concept ....................................................... 14

1.5.2 Training algorithms in Bayesian concept ......................................................................... 16

1.6 REVIEW OF OZONE PREDICTION WITH ANN ......................................................................................... 18

1.7 RESEARCH OBJECTIVES ..................................................................................................................... 21

1.8 DISSERTATION OUTLINE .................................................................................................................... 23

Table of Contents

vi

CHAPTER 2 STUDY AREA AND PRELIMINARY ANALYSIS OF FIELD DATA ....................................... 28

2.1 STUDY AREA................................................................................................................................... 29

2.1.1 Hong Kong territory .......................................................................................................... 29

2.1.2 Pearl River Delta region in Guangdong Province ............................................................. 33

2.1.3 North part of South China Sea .......................................................................................... 37

2.2 FIELD DATA ANALYSIS ....................................................................................................................... 38

2.2.1 Missing data ..................................................................................................................... 38

2.2.2 Statistical analysis for the imputed data set .................................................................... 40

2.3 CONCLUSION REMARKS .................................................................................................................... 54

CHAPTER 3 SELECTION AND ASSESSMENT FOR OZONE KEY INFLUENTIAL VARIABLES

SITE-SPECIFICALLY .......................................................................................................................... 57

3.1 SPATIAL INPUT VARIABLES SELECTION, STAGE ONE ................................................................................. 58

3.1.1 Connection weight analysis and sensitivity analysis ........................................................ 58

3.1.2 Performance indicators .................................................................................................... 62

3.1.3 MLP in ARD framework .................................................................................................... 65

3.1.4 Ranking RI for spatial input variables by MLP-ARD for current-day prediction ................ 68

3.1.5 Ranking RI for spatial input variables by NCW method for current-day prediction ......... 85

3.1.6 The key spatial input variables selection for current-day prediction ................................ 88

3.1.7 Ranking RI for spatial input variables by MLP-ARD for 1-day ahead prediction .............. 89

3.1.8 Ranking RI for spatial input variables by NCW method for 1-day ahead prediction ...... 100

3.1.9 The key spatial input variables selection for 1-day ahead prediction ............................ 102

3.2 TEMPORAL INPUT VARIABLES SELECTION, STAGE TWO ........................................................................... 103

3.3 CONCLUSION REMARKS .................................................................................................................. 108

CHAPTER 4 INTERVAL PREDICTION AND THE TRANS- BOUNDARY AIR POLLUTION IMPACT

ASSESSMENT, FOR OZONE VARIATION WITH MLP-ARD MODEL ..................................................... 110

4.1 INTRODUCTION ............................................................................................................................ 110

4.2 METHODOLOGY ........................................................................................................................... 112

Table of Contents

vii

4.2.1 Prediction by MLP-ARD................................................................................................... 112

4.2.2 Experiment setting ......................................................................................................... 114

4.3 RESULTS AND DISCUSSION .............................................................................................................. 115

4.3.1 Topic 1: prediction performance comparison between MLP-ARD and MLP-LM ............ 115

4.3.2 Topic 2: impact assessment for the trans-boundary air pollution on ozone variation

site-specifically.............................................................................................................................. 123


CHAPTER 5 IMPROVE POINT PREDICTION FOR OZONE POLLUTED DAYS BY USING HMC-MLP-PSO

MODEL 140

5.1 INTRODUCTION ............................................................................................................................ 140

5.2 METHODOLOGY ........................................................................................................................... 144

5.2.1 Hybrid Monte Carlo and MLP weight matrix sampling .................................................. 145

5.2.2 Particle swarm optimization .......................................................................................... 147

5.2.3 HMC-MLP-PSO ................................................................................................................ 150

5.2.4 Experiment setup ............................................................................................................ 150


5.3.1 Initializing strategy comparison ..................................................................................... 152

5.3.2 Models performance comparison with different initializing strategy ............................ 156

5.3.3 Performance comparison between MLP trained by PSO-based algorithms and MLP

trained by the individual-based algorithms .................................................................................. 163

5.3.4 Performance comparison between air monitoring stations during ozone polluted days for

the PSO-trained MLP .................................................................................................................... 164


CHAPTER 6 IMPROVE POINT PREDICTION FOR OZONE POLLUTED DAYS BY USING MLP-PSO-LM

MODEL 175

6.1 INTRODUCTION ............................................................................................................................ 175

6.2 METHODOLOGY ........................................................................................................................... 177

Table of Contents

viii

6.2.1 MLP model trained with LM algorithm .......................................................................... 177

6.2.2 MLP trained with standard particle swarm optimization (MLP-PSO) ............................ 178

6.2.3 MLP-PSO-LM, MLP alternatively trained by PSO and LM ............................................... 178

6.2.4 Experiment preparation and models setup .................................................................... 179


6.3.1 Comparison of convergence history ............................................................................... 180

6.3.2 Prediction comparison between MLP-PSO-LM, HMC-MLP-PSO and MLP-PSO .............. 185


CHAPTER 7 CONCLUSIONS AND DISCUSSIONS ........................................................................... 203

7.1 CONCLUSIONS FOR THE SPECIFIC CHAPTERS ........................................................................................ 203

7.2 GENERAL CONCLUSIONS ................................................................................................................. 207

7.3 DISCUSSIONS ............................................................................................................................... 209

7.3.1 Comparative review for prediction result in the literature study ................................... 209

7.3.2 Original Contributions .................................................................................................... 212

7.3.3 Limitations and future study recommendations ............................................................ 213

LIST OF PUBLICATIONS .................................................................................................................. 216

REFERENCE ................................................................................................................................... 217

APPENDIX ..................................................................................................................................... 228

List of Figures

ix

LLiisstt ooff FFiigguurreess

Figure 1-1 Annual average of major air pollutants in Hong Kong in four types of monitoring station

................................................................................................................................................ 3

Figure 1-2 A simplified tropospheric ozone dynamic equilibrium without anthropogenic emissions

................................................................................................................................................ 6

Figure 1-3 Ozone accumulation with VOCs or hydrocarbons presented ......................................... 6

Figure 2-1 Study area ................................................................................................................. 29

Figure 2-2 Hong Kong environment and the studied monitoring sites ......................................... 30

Figure 2-3 Distribution of average concentrations of nitrogen dioxide in PRDR-AQMN ................ 35

Figure 2-4 Annual averaged diurnal variation of major pollutants at TW, TM and TC ................... 45

Figure 2-5 Annual averaged diurnal trend of temperature in Hong Kong ..................................... 46

Figure 2-6 Annual averaged weekly variation of major pollutants at TW, TM and TC ................... 48

Figure 3-1 Average performance of MLP-ARD with different topology for ozone prediction ........ 74

Figure 3-2 Convergence process for three hyperparameters in three air monitoring stations ...... 75

Figure 3-3 Contour plot of the ranking matrices for the current day prediction ........................... 78

Figure 3-4 Average performance of MLP-ARD with different topology for ozone prediction ........ 92

Figure 3-5 Convergence for three hyperparameters .................................................................... 93

Figure 3-6 Contour plot of the ranking matrices for the 1 day ahead prediciton .......................... 95

Figure 4-1 Performance comparison between MLP-ARD and MLP-LM in current-day prediction 121

Figure 4-2 Performance comparison between MLP-ARD and MLP-LM in 1-day ahead prediction

............................................................................................................................................ 123

Figure 4-3 Performance comparison between MLP-ARD-OKIV and MLP-ARD-LOIV in current-day

prediction ............................................................................................................................ 133

Figure 4-4 Performance comparison between MLP-ARD-OKIV and MLP-ARD-LOIV in 1-day ahead

prediction ............................................................................................................................ 136

List of Figures

x

Figure 5-1 Random versus HMC initialization (on validation data set, current day prediction) ... 154

Figure 5-2 Random versus HMC initialization (on validation data set, 1 day ahead prediction) .. 155

Figure 6-1 General flowchart of MLP-PSO-LM ........................................................................... 179

Figure 6-2 Comparison of convergence history ......................................................................... 184

Figure 6-3 Models comparison for current and 1 day ahead prediction on test dataset ............. 194

Figure 6-4 Models comparison for current and 1 day ahead prediction on test dataset ............. 197

List of Tables

xi

LLiisstt ooff TTaabblleess

Table 1-1 MLP models in this dissertation .................................................................................. 27

Table 2-1 Major sources and pollutants generated in Hong Kong in 2005 .................................... 30

Table 2-2 Contribution of major sectors to regional year pollutant emission inventory ............... 34

Table 2-3 Information of SYNOP stations .................................................................................... 38

Table 2-4 Percentage of missing in original data from year 2001 to 2004 .................................... 40

Table 2-5 Statistics for the collected data (imputed) ................................................................... 41

Table 2-6 Bivariate granger causality test results including the sample 2 , P- value and degree of

freedom ................................................................................................................................ 51

Table 2-7 Number and direction of MSLPG when daily maximum ozone level over 240 3/ mg

.............................................................................................................................................. 53

Table 3-1 List of performance indicators ..................................................................................... 63

Table 3-2 Aggregation for inputs and output for all air monitoring stations for current day

prediction .............................................................................................................................. 69

Table 3-3 Distribution of number of data points in dataset ......................................................... 71

Table 3-4 Ranking result from MLP-ARD with topology scoring the highest 2d in ozone

prediction .............................................................................................................................. 83

Table 3-5 Ranking result from MLP-LM with topology scoring the highest 2d by using NCW

method in ozone prediction ................................................................................................... 87

Table 3-6 The key spatial input variables for each air-monitoring station .................................... 89

Table 3-7 Aggregation for inputs and output for all air monitoring stations for 1 day ahead

prediction .............................................................................................................................. 90

Table 3-8 Distribution of number of data points in dataset ......................................................... 91

List of Figures

xii

Table 3-9 Ranking result from MLP-ARD with topology scoring the highest 2d in ozone

prediction .............................................................................................................................. 98

Table 3-10 Ranking result from MLP-LM with topology scoring the highest 2d by using NCW

method in ozone prediction ................................................................................................. 101

Table 3-11 The key spatial input variables for each air-monitoring station ................................ 103

Table 3-12 The ozone key influential variables (including key spatial and temporal input variables)

for current-day prediction .................................................................................................... 106

Table 3-13 The ozone key influential variables (key spatial and temporal input variables) for 1-day

ahead prediction ................................................................................................................. 107

Table 4-1 Statistics for models comparison for current and 1 day ahead prediction on test dataset

(MLP-ARD v.s. MLP-LM) ....................................................................................................... 118

Table 4-2 Local key ozone influential variables for current-day prediction ................................ 127

Table 4-3 Local key ozone influential variables for 1-day ahead prediction ................................ 128

Table 4-4 Statistics for models comparison for current-day prediction on test dataset

(MLP-ARD-OKIV v.s. MLP-ARD-LOIV) .................................................................................... 129

Table 4-5 Statistics for models comparison for 1-day ahead prediction on test dataset

(MLP-ARD-OKIV v.s. MLP-ARD-LOIV) .................................................................................... 130

Table 4-6 Difference of 2R between MLP-ARD-OKIV and MLP-ARD-LOIV ............................... 130

Table 5-1 Parameters in HMC and PSO for both HMC-MLP-PSO and MLP-PSO .......................... 152

Table 5-2 Statistics for models comparison for current day prediction (HMC-MLP-PSO v.s.

MLP-PSO, low v.s. high dimension weight space) ................................................................. 158

Table 5-3 Statistics for models comparison for 1 day ahead prediction (HMC-MLP-PSO v.s. MLP-PSO,

low v.s. high dimension weight space) ................................................................................. 160


(HMC-MLP-PSO v.s. MLP-PSO) ............................................................................................. 165

Table 5-5 Exceedance prediction with respect to ozone level threshold 120 3/ mg .............. 169

List of Tables

xiii


(MLP-PSO v.s. MLP-PSO-LM) ................................................................................................ 188


(HMC-MLP-PSO v.s. MLP-PSO-LM) ....................................................................................... 190

Table 6-3 Exceedance prediction with respect to ozone level threshold 120 3/ mg .............. 198

Table 7-1 Summary of some selected literature models ............................................................ 211

Nomenclature

xiv

NNoommeennccllaattuurree

Symbols

A Hessian matrix of wS evaluated at MPw

1b input-layer bias group in model MLP-ARD

2b hidden-layer bias group in model MLP-ARD

h

ib bias of neuron i in the hidden layer

o

kb bias of neuron k in the output layer

1C and 2C cognition and social components in PSO algorithm

D dataset

2d Index of agreement

we sum of squares error

DE error function generated by training data in model MLP-ARD

kWE error function generated by weight matrix in model MLP-ARD

f general function representing the MLP‘s mapping from input to output

h

if transfer function of neuron i in the hidden layer

o

kf transfer function of neuron k in the output layer

wxf n ; MLP output with respect to the thn input data

k

iFV fitness value of k

iPo

kGbest the particle with the best fitness value among all the particle population at the

thk generation in

PSO algorithm

h element in the hidden layer

I identity unit matrix

Nomenclature

xv

ki Number of weight in the thk weight group in model MLP-ARD

kwJ Jocobian matrix evaluated at weight matrix w in thk iteration

l number of the total data points in D

L number of neurons in the output layer

0L number of leapfrog steps (trajectory length) algorithm in HMC

N number of neurons in the input layer

o element in the output layer

iO the thi measured data corresponding to the thi input data

1k

iPbest the

thi particle‘s position, which gives the best fitness value within 1k generations in PSO

algorithm

wDp ; likelihood function with respect to w

wxOp ;, joint pdf of x and O

k

iPo position of the thi particle at the thk generation

wxOp ;| conditional pdf of O given input x

DwP | posterior probability distribution

xp unconditional pdf of input x

zq normal distribution function

1Q number of the first inner iteration in model MLP-ARD

2Q number of the second inner iteration in model MLP-ARD

1rand and

2rand

two random numbers in PSO algorithm

jRI RI of thj input variable in percentage

2R coefficient of determination

S number of neurons in the hidden layer

0S number of outer iteration in model MLP-ARD

wS total error function in model MLP-ARD

Nomenclature

xvi

nt the thn target data

v number of weight component

k

iV the velocity of the thi particle at the thk generation in PSO algorithm

maxV velocity limit in PSO algorithm

kwV cumulative error vector

w weight matrix

1w input-layer weight group in model MLP-ARD

2w hidden-layer weight group in model MLP-ARD

MPw most probable values of weight matrix in model MLP-ARD

h

jiw weight that connects the neuron j in the input layer with the neuron i in the hidden layer

o

ikw weight that connects the neuron i in the hidden layer with the neuron k in the output layer

optw optimal weight matrix

x one of MLP input data

ix the thi input data

o

ky output of neuron k in the output layer

sZ normalization factor in model MLP-ARD

Nomenclature

xvii

Greek Alphabet Symbols

hyperparameter in model MLP-ARD

1b hyperparameter with respect to 1b in model MLP-ARD

2b hyperparameter with respect to 2b in model MLP-ARD

1w hyperparameter with respect to 1w in model MLP-ARD

2w hyperparameter with respect to 2w in model MLP-ARD

jw1 hyperparameter associated with thj input neuron in model MLP-ARD

MP

k most probable values of in the in the thk weight group in model MLP-ARD

GYMSLPG hyperparameter associated with input variables GYMSLPG in model MLP-ARD

xNO hyperparameter associated with input variables NOx in model MLP-ARD

SZAPI hyperparameter associated with input variables SZAPI in model MLP-ARD

MP most probable values of in model MLP-ARD

hyperparameter in model MLP-ARD

k number of well-determined parameters for weight group k in model MLP-ARD

time lag between ozone and key spatial input variables

t standard deviation in the output of model MLP-ARD

time step-size in leapfrog algorithm in HMC

intrinsic data noise with a pdf zq

k useful feature in LM algorithm

0 parameter determining when LM should be inserted into PSO training in model

MLP-PSO-LM

MPw most probable values of weight matrix in model MLP-ARD

Nomenclature

xviii

Abbreviations

i]-Ave[D previous thi daily average data

10]-[04Ave 1-D average of hourly data from 04:00-10:00 in previous day

ACC auto-correlation coefficient

ACF auto-correlation function

AIC Akaike's information criterion

ANN artificial neural network

AOE number of all observed exceedances.

APE number of all predicted exceedances.

API air pollution index

AQMN Air Quality Monitoring Network

ARD automatic relevance determination

ARIMA regressive integrated moving average

Ave[04-10] average of hourly data from 04:00-10:00

Ave[D-1] previous daily average data

BP back-propagation algorithm

CA cloud amount

CCC cross correlation coefficient

CCF cross correlation function

CO carbon monoxide

CPE number of the correctly predicted exceedances.

CV cross-validation

DF degree of freedom.

DSMSLPG mean sea level pressure gradient at Dongsha with respect to HKIA

exce. Exceedance of defined ozone level

FNR False negative rate

FPR False positive rate

GA genetic algorithm

GDEMC Guangdong Provincial Environmental Protection Monitoring Centre

GYMSLPG mean sea level pressure gradient at Gaoyao with respect to HKIA

GZ Guangzhou

Nomenclature

xix

H(w, MV) the total energy in HDS

HDS Hamiltonian dynamical system

HKEPD Hong Kong Environmental Protection Department

HKIA Hong Kong international airport

HKO Hong Kong Observatory

HMC hybrid monte carlo method

K(MV) kinetic energy in HMC

LM Levenberg-Marquardt algorithm

LXMSLPG mean sea level pressure gradient at Lianxian with respect to HKIA

MAE Mean absolute error

Max[0-24] daily maximum of hourly data

MBE Mean bias error

ML maximum likelihood

MLP Multilayer perceptron

MLP-ARD-LOIV MLP-ARD only with local ozone influential variables as input variables

MLP-ARD-OKIV MLP-ARD with ozone key influential variables as input variables

MSE Mean square error

MSLP mean sea level pressure

MSLPG mean sea level pressure gradient

MV momentum vector in HMC

NCW new connection weight method

NO nitric oxide

NO2 nitrogen dioxide

NOx nitrogen oxide

O3 ozone

obs. observations

NFr normalized Spearman‘s footrule

PCA principal component analysis

pdf probability density function

PRDR Pearl River Delta region

PSO particle swarm optimization

purelin linear transfer function

Nomenclature

xx

QYMSLPG mean sea level pressure gradient at Qingyuan with respect to HKIA

iRank j rank number for the thi variable in the thj variables ranking realization

RH relative humidity

RI relative importance

RK

rank with respect to RI, from the most important variable or high rank to the least

one or low rank

RMSE Root mean square error

RSP respirable suspended particulates

SCG scaled conjugate gradient algorithm

SI success index

SO2 sulphur Dioxide

SR solar radiation

STMSLPG mean sea level pressure gradient at Shantou with respect to HKIA

SYNOP surface synoptic observation stations

SZ Shenzhen

SZMSLPG: mean sea level pressure gradient at Shenzhen with respect to HKIA.

T temperature

tansig hyperbolic tangent function

TC Tung Chung air-monitoring station

TM Tap Mun air-monitoring station

TNR True negative rate

TPR True positive rate

TS

number of times for corresponding variable ranked at some rank such position within

30 MLP-ARD runs.

TSP total suspended particulate

TW Tsuen Wan air-monitoring station

USEPA United States Environmental Protection Agency

VAR vector autoregressive

VC Vapnik-Chervonenkis

VOCs volatile organic compounds

WD wind direction

WS wind speed

Nomenclature

xxi

ZH Zhuhai

ZJMSLPG: mean sea level pressure gradient at Zhanjiang with respect to HKIA

Documents

Multilayer Perceptron Models for Surface Ozone Study in ...lbms03.cityu.edu.hk/theses/abt/phd-bc-b22182275a.pdf · Abstract i Abssttrraacctt Multilayer perceptron (MLP) models have