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Risk Management of natural disasters: A Fuzzy-Probabilistic PDF

164 Pages·2006·11.46 MB·English
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„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“. ii To My Parents iii iv 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 v 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. vi 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 vii 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 viii 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 ix 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 x

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the physical knowledge required for a purely probabilistic risk analysis are sufficient. This insufficient information will afflict the .. 6.3.2 Main programs .
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