development of a matlab-based toolbox for tide gauge records using hilbert-huang transform a ...

91 Pages·2013·5.62 MB·English

DEVELOPMENT OF A MATLAB-BASED TOOLBOX FOR TIDE GAUGE
RECORDS USING HILBERT-HUANG TRANSFORM

A THESIS SUBMITTED TO
THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES
OF
MIDDLE EAST TECHNICAL UNIVERSITY

BY

AYDIN JAMALI

IN PARTIAL FULFILMENT OF THE REQUIREMENTS
FOR
THE DEGREE OF MASTER OF SCIENCE
IN
GEODETIC AND GEOGRAPHIC INFORMATION TECHNOLOGIES

SEPTEMBER 2013

Approval of the thesis:

DEVELOPMENT OF A MATLAB-BASED TOOLBOX FOR TIDE GAUGE
RECORDS USING HILBERT-HUANG TRANSFORM
submitted by AYDIN JAMALI in partial fulfillment of the requirements for the
degree of Master of Science in Geodetic and Geographic Information
Technologies Department, Middle East Technical University by,

Prof. Dr. Canan Özgen _____________________
Dean, Graduate School of Natural and Applied Sciences

Assoc . Prof. Dr. Ahmet Coşar _____________________
Head of Department, Geodetic and Geographic Information Technologies

Prof. Dr Mahmut Onur Karslıoğlu
Supervisor, Civil Engineering Dept., METU _____________________

Examining Committee Members:

Assoc. Prof. Dr. Ali Kılıçoğlu _____________________
General Command of Mapping- Retired

Prof. Dr Mahmut Onur Karslıoğlu _____________________
Civil Engineering Dept., METU

Prof. Dr. Zuhal Akyürek _____________________
Civil Engineering Dept., METU

Assist. Prof. Dr. Uğur Murat Leloğlu _____________________
Geodetic and Geographic Information Technologies Dept., METU

Assoc. Prof. Dr. Utku Kanoğlu _____________________
Engineering Sciences Dept., METU

Date: 16.09.2013
I hereby declare that all information in this document has been obtained and
presented in accordance with academic rules and ethical conduct. I also declare
that, as required by these rules and conduct, I have fully cited and referenced all
material and results that are not original to this work.

Name, Last Name: AYDIN JAMALI

Signature:

iv
ABSTRACT

DEVELOPMENT OF A MATLAB-BASED TOOLBOX FOR TIDE GAUGE
RECORDS USING HILBERT-HUANG TRANSFORM

Jamali, Aydin
M.Sc., Department of Geodetic and Geographic Information Technologies
Supervisor: Prof. Dr. Mahmut Onur Karslıoğlu

September 2013, 77 pages
Tidal records are usually processed on the basis of Harmonic Analysis which in fact
works well for linear and stationary data. It is a mathematical procedure which divides
the data in a finite number of harmonic constituents. But the tidal data is in reality
non-linear and non-stationary because of atmospheric and meteorological parameters.
Therefore in this work a MATLAB –based Toolbox has been developed for hourly
tidal data collected from four tide gauge stations at the Turkish costs using Hilbert
Huang Empirical Mode Decomposition (HHEMD) which is an efficient and powerful
method for non-linear and non-stationary time series. Hilbert Huang Empirical Mode
Decomposition (HHEMD) is carried out in two steps. Firstly data are processed by
Empirical Mode decomposition (EMD) which decomposes the signal in a number of
intrinsic mode components (IMFs). The second step is to apply the Hilbert transform
to each IMF in order to find Phase, Amplitude and Instantaneous Frequency of the
signal.
In this study the hourly tidal data are decomposed in tidal and sub-tidal components
using HHEMD and the results of the tidal components are compared with the results
of harmonic analysis. Very long and non-stationary period components are filtered as
sub tidal. Finally the frequency and amplitude of the diurnal and semi-diurnal
component are used to extract the minimum and maximum velocities of the diurnal
and semidiurnal tidal constituents in order to analyze the capability of producing tidal
energies from possible tidal turbines to be located at tidal stations. Also an
exemplarity completeness test has been performed to validate the decomposition of
the time series obtained by the Antalya station utilizing EMD. The result showed that
the signal has been recovered properly.
Keyword: Empirical Mode Decomposition, Hilbert Huang Transform, Intrinsic Mode
Functions, Tidal and sub-tidal phenomena.

v
ÖZ

MAREOGRAF İSTASYONU KAYITLARI İÇİN HILBERT-HUANG DÖNÜŞÜMÜ
KULLANILARAK MATALAB TABANLI YAZILIM PAKETİ GELİŞTİRİLMESİ

Jamali, Aydin
Yüksek Lisans, Jeodezi ve Coğrafi Bilgi Teknolojileri Bölümü
Tez Yöneticisi: Prof. Dr. Mahmut Onur Karslıoğlu

Eylül 2013, 77 sayfa
Genellikle gelgit kayıtları, doğrusal ve durağan veriler için iyi çalışan harmonik
analize dayalı olarak değerlendirilirler. Harmonik analiz, veriyi sonlu sayıda harmonik
bileşene bölen matematik bir prosedürdür. Fakat gerçekte gelgit verisi atmosferik ve
meteorolojik parametreler nedeni ile doğrusal-olmayan ve durağan-olmayan
karakterdedir. Bu nedenle, bu çalışmada Türkiye sahillerindeki dört adet mareograf
istasyonundan toplanan saatlik gel-git dataları ile doğrusal-olmayan ve durağan-
olmayan zaman serileri için etkili ve güçlü bir metod olan Hilbert Huang Deneysel
Mod Ayrıştırma (HHDMA) (Hilbert Huang Empirical Mode Decomposition) yöntemi
kullanılarak, MATLAB tabanlı yazılım paketi geliştirilmiştir. Hilbert Huang Deneysel
Mod Ayrıştırma yöntemi iki adımda gerçekleştirilir. İlk olarak veri, sinyali bir dizi
yapısal mod bileşenine ( intrinsic mode components) ayıran Deneysel Mod Ayrıştırma
(DMA) (Empirical Mode decomposition) yöntemi ile işlenir. İkinci adım, sinyalin faz,
genlik ve anlık frekanslarının bulunması için ikinci adımda her bir yapısal mod
bileşenine Hilbert Dönüşümü uygulanır.
Bu çalışma kapsamında gelgit verisi, HHDMA kullanılarak gelgitsel (tidal) ve gelgit
dışı (sub-tidal) bileşenlere ayrıştırılmıştır ve gelgit bileşenlerinin sonuçları harmonik
analizle karşılaştırılmıştır. Çok uzun ve durağan-olmayan devir bileşenleri, gelgits dışı
bileşen olarak filtrelenmiştir. Son olarak, gelgit istasyonlarına yerleştirilecek olası
gelgit tribünlerden, gelgit enerjisi üretme yeteneğinin analizinde kullanılabilecek
günlük ve yarı günlük gelgit bileşenlerinin minimum ve maksimum hızlarını elde
etmek için günlük ve yarı günlük bileşenlerin frekans ve genlikleri kullanılmıştır.
Ayrıca DMA kullanan Antalya istasyonundan elde edilen zaman serisi ayrışımlarını
doğrulamak için örnek bir tamlık testi gerçekleştirilmiştir. Sonuç sinyalin uygun
biçimde yeniden elde edildiğini göstermektedir.
Anahtar Kelimeler: Deneysel Mod Ayrıştırma, Hilbert Huang Dönüşümü, Yapısal Mod
Fonksiyonları, Gelgitsel ve gelgitsel dışı etkenler.

vi
To my Shima

vii
ACKNOWLEDGEMENT

I wish to thank my supervisor Prof. Dr Mahmut Onur Karslıoğlu for his guidance,
support and advices during my graduate study.

I also thank to examining committee members Assoc. Prof. Dr. Ali Kılıçoğlu, Prof.
Dr. Zuhal Akyürek, Assist. Prof. Dr. Uğur Murat Leloğlu, Assoc. Prof. Dr. Utku
Kanoğlu for their valuable comments and contributions.
I would like to thank my wife Shima for her encouragement, quiet patience and
unwavering love. I would like to thank my family especially my mother and father for
being such a huge supporter through my study and thank them for everything. I have
to say that I couldn't have completed the thesis without my parent. Also, I thank
Shima’s parents for their unending encouragement.
I would like to convey my deepest thank to my friend Eren Erdoğan who has not left
me lonely in my graduate study.
Last but not least, I would like to express my deepest thank to my friend Matt Piroglu
who has been a source of love and energy.

viii
TABLE OF CONTENTS

ABSTRACT…………..………………………………………………………………. v
ÖZ……………………………………………………………………………………. vi
ACKNOWLEDGEMENT…………………………………………………….......... viii
TABALE OF CONTENTS………………………….................................................. ix
LIST OF FIGURES………………………………………………………………….. xi
LIST OF TABLE………………………………………………………………….... xiv
CHAPTERS
1. INTRODUCTION………………………………………..………………………. 1
1.1 History and Background……………………………………..…………….. 1
1.2 Motivation and purpose of study……………………………………..…..... 2
1.3 Thesis outline………………………………………………………….…... 2

2. TIDES …………………………..……………..………………………………..... 3
2.1 Definition of tide…………………………..…………………………………. 3
2.2 Earth and Sun Geometry………………………………….……..…………… 5
2.3 Mathematical theory of ocean tides ………………………………………..… 5
2.3.1 Tidal acceleration and Tidal potential……………………………………. 6
2.3.1.1 Zonal tidal potential…………………………………………………... 8
2.3.1.2 Tesseral tidal potential………………………………………………... 9
2.3.1.3 Sectorial tidal potential…………………………………..…………… 9
2.4 Doodson expansion…………………………………………………………... 9
2.5 Tidal frequencies……………………………………………………………. 10
2.5.1 Instantaneous frequencies…………………………………..…………… 11

3. HARMONIC ANALYSIS AND TIDAL CONSTITUENT…………..………... 13
3.1 Harmonic analysis ………………………………………………..………… 13
3.2 Harmonic constituent………………………………………………..………. 14
3.3 Doodson number…………………………………………………….……… 14
3.4 Shallow water effects on tidal constituents………………………………..... 15

4. NON-STATIONARY DATA PROCESSING METHODS…………………….. 17
4.1 Methods for processing of non-stationary data and linear system……….…. 17
4.1.1 Spectrogram………..…………………………………………………..... 17
4.1.2 Wavelet analysis ………………………………………………………... 18
4.1.3 Empirical orthogonal function expansion………………………………. 18
4.1.4 Other methods…………………………………………………............... 19
ix
4.2 Methods for processing of non-stationary data and non-linear system …...... 19
4.2.1 Empirical mode decomposition………………………………………..... 19
4.2.2 Intrinsic mode functions ………………………………………………... 19
4.2.3 Definition of sifting process……………………………………….…..... 20
4.2.4 Hilbert spectrum………………………………………………………… 25

5. TIDAL STREAM AND TIDAL POWER……………………………………… 27
5.1 Tidal energy………………………………………………………………..... 27
5.2 Tidal power and tidal velocity …………………………………………….... 28

6. MATLAB BASED HHT/HA TOOLBOX……………………………………… 31
6.1 Programing environment…………………………………………………..... 31
6.2 Toolbox definition…………………………………………………………... 31

7. DATA SET, EVALUATION AND RESULTS…………………….………….. 37
7.1 Data set……………………………………………………………………... 37
7.2 Application of Hilbert Huang Transform to tide gauge data records ……… 39
7.2.1 Analysis of tidal data based on the Hilbert Huang Empirical Mode
Decomposition (HHEMD)……………………………………………………… 39
7.2.2 Completeness test………………...…………………………………….. 49
7.2.3 Comparison of the HHT analysis with HA ………...………………….. 51
7.2.4 Analysis of sub-tidal phenomena using HHEMD……………………… 67
7.2.5 Tidal velocity…………………………………………………………… 71

8. CONCLUSION AND FUTURE WORK……………………………………….. 73
8.1 Conclusion……………………………………………………….………….. 73
8.2 Future work…………………………………………………………………. 74
REFERENCES……………………………………………………………………..... 77

x