Fragility curves, also known as damage functions [1] are used to approximate damage from natural hazards. The term fragility means the probability of attaining a limit state, conditioned on a particular value of random demand. More simply, fragility is a measure of vulnerability or estimate of overall risk. Fragility functions can be developed using different methods, heuristic, empirical, analytical or a combination of two methods. Heuristic functions are developed using the consensus opinion of structural engineering experts with years of experience designing various types of structures and observing the behaviour of such structures in past earthquakes. Empirical functions are based on observed data, while analytical damage functions are based on models of idealized structural types.

Since most fragility curves have a characteristic shape, for its description a simpler analytical expression of the functions could be used, where a single parameter can account for the exceeding probabilities of the four types of damage. It is assumed that the use of a single parameter allows more flexibility to the fragility curve model, when one is trying to represent the effects of continuous wearing of the building during the lifecycle, as well as for the repairs that occur from time to time.

We used ten regression models [2]: Quadratic Model, Rational Model, Exponential Association Model, Logistic Model, Multiple Multiplicative Factor (MMF) Model, Reciprocal Quadratic Model, Saturation Growth-Rate Model, Gompertz Model, Geometric Model, and Harris Model.

In our GA model, we used real value encoding for the chromosomes. We used a population of 40 individuals, and the tournament selection method. Starting from the approximate solution found so far, an evolutionary hill climbing was applied, relying only on mutation to get increasingly closer to the actual optimum. This hybrid approach seems to greatly improve the accuracy of the solution, because the hill climbing procedure approaches the local optimum very fast.

By analysing the regression data, it was found that the lowest error rates are given by the MMF and Gompertz models, so we proposed a simplified version of those two models, which need only one parameter in order to define fragility curves.

1

A.M. Reinhorn, R. Barron-Corverra, A.G. Ayala, "Spectral Evaluation of Seismic Fragility of Structures", Proceedings of ICOSSAR 2001, Newport Beach CA, 2001.

2

D.G. Hyams, "Data Modeling Equations", http://www.ebicom.net/dhyams/cmodels.htm, 2005.

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