Tackling Non-linearity in Seismic Risk Estimation using Fuzzy Methods J. Ruben´ G. Cardenas´ 1, Angela` Nebot2, Francisco Mugica2 and Helen Crowley1 1IUSS UME School Via Ferrata 45, Pavia, Italy 2Soft Computing Group, Technical University of Catalonia, Jordi Girona Salgado 1-3, Barcelona, Spain Keywords: Fuzzy Sets, Risk Management, Natural Hazards, Vulnerability Index, Social Vulnerability, Seismic Vulnera- bility, Inference System. Abstract: Traditional approaches to measure risk to natural hazards considers the use of composite indices. However, most of the times such indices are built assuming linear interrelations (interdependencies) between the ag- gregated components in such a way that the final index value is based only on an accumulative or scalable structure. In this paper we propose the use of Fuzzy Inference Systems type Mamdami in order to aggregate physical seismic risk and social vulnerability indicators. The aggregation is made by establishing rules (if- then type) over the indicators in order to get an index. Finally a quantitative seismic risk estimation is made though the convolution of these two main factors by means of fuzzy inferences, in such a way that no linear assumptions are used along the estimation. We applied the fuzzy model over the city of Bogota Colombia. We consider that this approach is a useful way to estimate a measure of an intangible reality such as seis- mic risk, by assuming the urban settlement’s complexity where the interrelations between the associated risk components are inherently non-linear. The proposed model possess a practical use over the risk management field, since the design of the logic rules uses a smooth application of risk management knowledge following a multidisciplinary approach, thus making the model easily adapted to a particular circumstance or context regardless the background of the final user. 1 INTRODUCTION aged because an earthquake occurrence (including lost lives) have a solid framework of analysis and ex- Holism (from greek: all, whole, entire) is an episte- perimentation. Even if that the large majority of seis- mology position which postulate that complex sys- mic hazard, vulnerability and exposure models con- tems cannot be completely understood by taking un- siders a probabilistic approach, the engineering field der scope each of their components in a separate has the possibility to compare their results with ex- way. The holism defines then, the basis for a non- perimental data, that can be obtained either from sim- reductionism methodology for the study of systems. ulations or practical experiments. Although physical The idea behind holism is ”the integration of the parts, risk models uses approximations, there is a mark of through its synergies, to understand the whole” (Car- reference to compare. At the other hand, how can we dona, 2001). According to a holistic approach, the estimate an intangible reality such as social vulnera- ”whole” is more complex than the sum of its con- bility? stituent elements, therefore the total behavior of the Social vulnerability is a crucial aspect of risk man- system cannot be derived from its fundamental com- agement. There can be no analysis or management ponents without considering the trade off of informa- without a social vulnerability understanding however, tion (energy) between them. If we intent to frame risk vulnerability have embedded confuse concepts that to natural hazards into a holistic or integral scheme, may leads towards many (and some times different) we need to take into account the complexities over an conclusions. Nevertheless, most of the approaches urban environment. In this terms, an important part of used to define social vulnerability, focuses over the the urban complexities can be considered as a result susceptibility and capacities of urban elements to act of the non linear interrelationships between the mul- against external influences, thus understanding vul- titude of components conforming the urban system. nerability as a sort of detector capable to determine The physical risk, defined as the seismic risk com- the state of the system. Therefore, social vulnerabil- ponent that reflects the type of assets that can be dam- ity becomes an essential source of information in or- González Cárdenas J., Nebot À., Mugica F. and Crowley H.. 532 Tackling Non-linearity in Seismic Risk Estimation using Fuzzy Methods. DOI: 10.5220/0005577905320541 In Proceedings of the 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (MSCCES-2015), pages 532-541 ISBN: 978-989-758-120-5 Copyright c 2015 SCITEPRESS (Science and Technology Publications, Lda.) TacklingNon-linearityinSeismicRiskEstimationusingFuzzyMethods der to implement suitable hazard and mitigation as- sessments, reduction and disaster preparedness that requires first of all, the identification of the vari- ous dimensions of vulnerability over a society, either economic, institutional structure or environmental re- sources. Carreno˜ et al. (2012) proposed a seismic risk model from a holistic perspective, by considering that seismic risk is the result of physical risk (those el- ements susceptible to be damage or destroyed) and an aggravation coefficient that includes both, the re- silience and the fragility of an urban environment. By describing physical risk and social aggravation by means of indices the final estimation of seismic risk is made by means of the so called Moncho’s equation. In this paper, we built a holistic seismic risk fuzzy model considering Cardona-Carreno˜ risk descriptors. By establishing fuzzy logic rules between such de- scriptors we were able to aggregate them all into a single seismic risk index without assuming a linear behavior between the descriptors. We found seismic risk tendencies and spatial distributions patterns over Bogota (Colombia) by performing a classical Mam- Figure 1: Carreno˜ et al. (2012) Holistic Seismic Risk dani fuzzy approach, supported by well established Model. fuzzy theory, which is characterized by a high expres- sive power and an intuitive human-like manner. Thus, considering seismic risk as produced for physical and an aggravation coefficient; the risk in- dex provides an approximate vision of the state of the 2 CARRENO’S˜ MODEL social capital infrastructure. The physical risk is evaluated by using the Equa- Taking as a base Cardona’s original model (2001), tion 2, ˜ et al. Carreno (2012) proposed a seismic risk model p considering an integral (holistic) approach, regarding RPh = ∑ wRPhiFRPhi (2) seismic risk as a function of the potential damage on i=1 assets (considering hazard intensities) plus the socioe- where F are the physical risk descriptors, w are conomic fragilities and lack of resilience of the con- RPhi RPhi their weights assessed by an analytic hierarchy pro- text. In this view, seismic risk would be the result cess (Carreno˜ et al., 2007; Saaty and Vargas, 1991), of physical risk, aggravated by social conditions and and p the total number of considered descriptors in lack of resilience capacities. Carreno˜ et al. model re- the estimation. The physical risk descriptors values lies in the use of descriptors for both: physical risk can be obtained from previous physical risk evalua- (see the 8 physical risk descriptors of Figure 1) and tions (damage scenarios) already made at the studied social aggravation (see the 11 aggravation descriptors location. of Figure 1). The aggravation coefficient, F, depends on a A conceptualization of Carreno’s˜ seismic risk weighted sum of an aggravation descriptors set as- model can be seen in Figure 1. sociated to socioeconomic fragility of the commu- Carreno˜ et al. (2012) obtained a seismic risk eval- nity (F ) and lack of resilience of exposed context uation for Bogota city by means of indicators that SFi (F ), according to Equation 3, leads to the calculation of a total risk index. This is LR j obtained by direct application of Moncho’s equation m n described in 1: F = ∑ wSFiFSFi + ∑ wLR jFLR j (3) i=1 j=1 RT = RPh (1 + F) (1) where wSFi and wLR j are the assessed weights on where RT is the total risk, RPh is the physical risk and each factors and m and n the total number of descrip- F is a aggravation coefficient. tors for fragility and lack of resilience, respectively. 533 SIMULTECH2015-5thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand Applications The descriptors values were obtained from existent 3 FUZZY SEISMIC RISK MODEL databases and statistical data of the studied area. The use of descriptors conforms an indirect tech- The integral frame that we followed was built in the nique to estimate a quantitative measure of change. believe that seismic risk can be viewed as the convo- The final aim is to describe intangible realities, hidden lution of two principal components: the social aggra- trends or different classes of information in a com- vation and physical risk, which in turn forms the total posite manner in order to present them all as quantifi- seismic risk of an urban center. The Fuzzy Seismic able entities that can be compared across space and Risk Model (FSRM) is divided in three main mod- time scales. Basically, descriptors are an encapsu- ules or sections: Social Aggravation, Physical Risk, lation of a more complex reality using a single con- and Total Risk. Each one of them is conformed by dif- struct, and they can be used solely as independent en- ferent submodules. The main objective is to be able tities of measure, or they can be aggregated to form to estimate seismic risk for an urban center consid- indices. Since an index is intended to describe a par- ering social and physical aspects trough fuzzy infer- ticular attribute, the attribute will determine a sort of ence modeling, therefore, not assuming a linear inter- causality structure between it and the descriptors that dependency between seismic risk components. can be either reflective (the attribute influences the de- scriptors) or formative (the descriptors influence the 3.1 Aggravation Coefficient attribute). The main difference is based in the internal correlation of the descriptors.