Risk Management of natural disasters: A Fuzzy-Probabilistic

164 Pages·2006·11.46 MB·English

by  Iman Karimi

„Risk Management of
Natural Disasters:
A Fuzzy-Probabilistic Methodology
and its Application to Seismic Hazard“

Von der Fakultät für Bauingenieurwesen
der Rheinisch-Westfälischen Technischen Hochschule Aachen zur Erlangung des
akademischen Grades eines Doktors der Ingenieurwissenschaften
genehmigte Dissertation

vorgelegt von
Iman Karimi
aus Teheran

Berichter: Universitätsprofessor Dr.-Ing. Konstantin Meskouris
Universitätsprofessor Dr.-Ing. Heribert Nacken
Professor Dr. rer. nat. Eyke Hüllermeier

Tag der mündlichen Prüfung: 27.01.2006

„Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online verfügbar“.
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To My Parents
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Abstract
This study presents a system for assessing and managing the risk of natural disasters,
particularly under highly uncertain conditions, i.e. where neither the statistical data nor
the physical knowledge required for a purely probabilistic risk analysis are sufficient. This
insufficient information will afflict the calculated risk probabilities with imprecision which
ignoring it might lead to an underestimation of the risk. In this study is employed to
complement the Probability Theory with an additional dimension of uncertainty. This
would allow for expressing the likelihood of natural hazards by fuzzy probability. The
fuzzy probability is characterized in terms of possibility-probability distributions (PPD),
for which a new approach has been developed. It is demonstrated that the approach
developed in this thesis can address the deficiencies in both conventional probabilistic
approach and an alternative PPD method.
The new methodology is described by breaking down the risk assessment procedure
to its components, namely hazard assessment and vulnerability analysis. Essentials of
each of these components are identified for the case of seismic hazard. Applying the con-
cept of PPD to seismic hazard analysis generalizes the conventional probabilistic seismic
hazard analysis (PSHA) to fuzzy-probabilistic seismic hazard analysis (FPSHA). It has
been proven that whenever statistical data are adequate or the background knowledge is
credible, the FPSHA results converge to those of PSHA.
Furthermore, uncertainties about the correlation between the parameters of hazard in-
tensity and damage (or loss), i.e. vulnerability relations, have been considered by means
of fuzzy relations. It is shown that fuzzy relations are a more viable form of representing
uncertainties of the structures, especially when material uncertainties are to be consid-
ered. It is also argued that at least in the context of vulnerability of structures, the Fuzzy
Set Theory is a better means of representing uncertainty of seismic vulnerability from a
subjective point of view. Besides, the flexible structure of the developed system allows for
an easy incorporation of other alternative representations of vulnerability. Thus, apply-
ing the developed system for risk assessment does not require starting the vulnerability
analysis of structures from scratch.
Theriskofdamageand/orlossisthenevaluatedbycombiningthehazardPPDandthe
fuzzy vulnerability relation. The result is a fuzzy probabilistic risk (of damage or loss),
which represented in a more realistic and comprehensive way by means of confidence
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levels and intervals. This representation is more reliable because of the consideration of
uncertainties which are ignored in conventional approaches. Moreover, it provides the
decision-maker with a better perception of risk. In order to extend the risk assessment to
risk management, a corresponding benefit-cost model has been developed.
In order to provide evidence for the applicability and practicability of the developed
methodology, two ”real-world” case studies have been analyzed and presented. In the first
case study, it is shown that this approach avoids some obvious defects and drawbacks of
alternative methodswhich ledtoimplausible results, contrarytotheresults obtainedfrom
the proposed method. It is also demonstrated how the damage PPD can be interpreted
in order to gain a more realistic and informative perception of risk. The second case
study demonstrates the other advantage of this system, i.e. its flexibility and ability of
incorporating other solutions.
The developed methodology is particularly appropriate for implementation onto a
web-based risk assessment/management system. The reason is that major computational
tasks can be performed off-line and on-line computations are restricted to selection and
composition of appropriate fuzzy relations. Moreover, the system can be easily updated
and expanded whenever new information is available.
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Acknowledgements
Throughout my academic career many individuals have helped, guided or supported me
that I sincerely thank them all. I acknowledge here some of them who came to my mind
as I was writing this. The names are listed in the chronological order of my first contact
with the individuals, beginning from the present time.
I would like to express my sincere gratitude to my supervisor, Prof. Konstantin Mesk-
ouris, who stood by me and supported me in many ways. I am also extremely grateful
to Prof. Eyke Hu¨llermeier for his cooperation which was a sine qua non of success in this
task. I would like to thank Prof. Hans Ju¨rgen Zimmermann for his advice and for the
time and attention he dedicated to my work. I am so grateful to all my colleagues in the
Department of Structural Statics and Dynamics (LBB), particularly Dr.-Ing. Wolfram
Kuhlmann and Dipl.-Ing. Michael Mistler who were also such true friends to me. I like to
show my appreciation to the all other colleagues in RWTH Aachen University, especially
Dr. Hani Sewilam whom I can never explain how he had helped me to pursue my fate.
A special thank you goes to the founder and father of fuzzy theory, Prof. Lotfi Zadeh,
whose inspiration and encouragements given to me in Istanbul (July 2003), motivated me
to start the work on this subject and his praise and compliments in Beijing (July 2005)
assured me that it had become mature enough to conclude it.
I am also so thankful to all my friends in Europe for giving me their love and support,
especially Ali who has been of such great assistance in all steps of this research work and
my dear friend Nina for making my sweetest moments in Aachen and also for listening to
me patiently with her natural dignity and decency. I cannot forget the wise guidance of
Albrecht (Aldi) either, which came in a critical moment and helped me to summon myself
and get back on track.
Words cannot express my gratefulness for my mentor and M.S. thesis consultant
Prof.Caro LucasfromtheEletrotechnic insituteof University ofTehran, who haschanged
my life in such a good way that I owe him almost everything good that I have achieved
since I met him for the first time in the Fuzzy Systems course. I should also thank
Dr. Shahram Vahdani, my M.S. supervisor, as well as Dr. Asodollah Noorzad, my other
M.S. consultant, who revived my interest and confidence in mathematics. Also, I should
thank all my friends in Tehran University, esp. my dear cousin Kavesh and my dear
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friends Kamal and Soheil.
IappreciatemyteachersinAllameHellischoolwhomIoweagreatdeal,esp. Dr.Yazdi
(Literature),Mr.Araste(Chemistry), Mr.Saa’ati(English), Mr.Helli(Algebra),Mr.Siami
(Algebra), Mr. Azimi (English), Mr. Kazemi (Geometry and New Math) and my deceased
Geometry teacher Mr. Rabbani Azad. Also I would like to thank my friends at school
with whom I had a great time then and with some of them even till now, esp. my dear
comrade Hamidreza who has been a great part of my life since the first school day, not
forgetting Tajalli, Baktash and Arash.
I am sincerely grateful to my eldest brother, Kooshesh, who was like a second father
to me, my brother and mentor Kayvan who has always been there to listen and advise
me, my brother Erfan who has been a good friend and my sister in laws Vida, Nooshin
and Sepide.
NaturallyIshouldthankmyparentswhosincerely gavealltheycouldfortheirchildren
and particularly their last son and I know nobody is happier than them to see that I have
made it till here.
And last but definitely not the least, comes my love of life and the only exception to
the chronological order. Although during the time I was conducting this research work
we had been apart, I never passed a single day without thinking of the precious moments
we had together. Those moment have made my life worth living and were the reason for
me to carry on.
Aachen, Germany Iman Karimi
November 10, 2005
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Contents
Abstract v
Acknowledgements vii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Problem definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Application of fuzzy set theory in risk assessment . . . . . . . . . . . . . . 5
1.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Organization of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Earthquake and Earthquake Risk Analysis 9
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Earthquake Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Size of Earthquakes and ground motion . . . . . . . . . . . . . . . . . . . . 11
2.3.1 Macroseismic Intensity . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.2 Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3.3 Ground motion measures . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.4 Attenuation (predictive) relationships . . . . . . . . . . . . . . . . 15
2.4 Earthquake risk assessment . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Seismic Hazard Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5.1 Deterministic Seismic Hazard Analysis (DSHA) . . . . . . . . . . . 17
2.5.2 Probabilistic Seismic Hazard Analysis (PSHA) . . . . . . . . . . . . 18
2.5.3 Recurrence laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.4 Probability Computations . . . . . . . . . . . . . . . . . . . . . . . 21
2.6 Seismic Vulnerability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.6.1 Representations of seismic vulnerability . . . . . . . . . . . . . . . . 23
2.6.2 Vulnerability Analysis methods . . . . . . . . . . . . . . . . . . . . 26
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3 Formulating Fuzzy Probability in terms of Possibility-Probability dis-
tribution 31
3.1 Why imprecise probability? . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Interval-valued probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.3 Fuzzy Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.4 A new concept of Fuzzy Probability expressed by PPD . . . . . . . . . . . 37
3.4.1 Formalization of background knowledge . . . . . . . . . . . . . . . . 37
3.4.2 Combining prior knowledge with empirical data . . . . . . . . . . . 39
3.4.3 Transforming probability to possibility . . . . . . . . . . . . . . . . 40
3.5 Extension for the probability of exceedance . . . . . . . . . . . . . . . . . . 43
3.6 Discussion and Comparison with the Huang approach . . . . . . . . . . . . 44
4 Fuzzy-Probabilistic Seismic Hazard Analysis (FPSHA) 47
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Why FPSHA? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 Magnitude Possibility-Probability Distribution . . . . . . . . . . . . . . . . 52
4.4 Fuzzy attenuation relation . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.5 Intensity possibility-probability distribution . . . . . . . . . . . . . . . . . 58
4.6 Extension for the probability of exceedance . . . . . . . . . . . . . . . . . . 58
4.7 Extension for multi-source seismic hazard case . . . . . . . . . . . . . . . . 58
5 Fuzzy Vulnerability Analysis 61
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Requirements of Dynamic Vulnerability Analysis . . . . . . . . . . . . . . . 61
5.2.1 Providing time-histories . . . . . . . . . . . . . . . . . . . . . . . . 62
5.2.2 Damage indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3 Fuzzy Vulnerability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.1 Extracting damage index from time-history analyses . . . . . . . . . 68
5.3.2 Considering uncertainties in material properties . . . . . . . . . . . 69
5.3.3 Fuzzy damage states and Fuzzy Vulnerability Relation . . . . . . . 71
5.4 Extracting Fuzzy Vulnerability Relations ... . . . . . . . . . . . . . . . . . 75
5.4.1 Extracting Fuzzy Vulnerability Relation from other numerical pro-
cedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4.2 Transforming Alternate Vulnerability Representations into Fuzzy
Vulnerability Relation . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.5 Overview of the FVA Procedure . . . . . . . . . . . . . . . . . . . . . . . . 77
6 Fuzzy-Probabilistic Risk Management System 79
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
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