Keywords: fuzzy logic, damage indices, seismic parameters, reinforced concrete, accelerograms, fuzzy classification.

It is well known that damage observations on buildings after severe earthquakes exhibit interdependency with the seismic intensity parameters [1]. Numerical elaboration of structural systems quantified the interrelation degree by correlation coefficients [2]. Further, the seismic response of buildings evaluated by a numerical analysis directly depends on the used accelerogram and its intensity parameters. Among the several response quantities, the focus is on the Maximum Inter-Storey Drift Ratio (MISDR). It characterises effectively the damage caused to buildings during earthquakes. Intervals for the values of the damage indices are defined to classify the damage degree as low, medium, large or total.

This paper provides fuzzy logic methodologies to classify the damage degree, based on the seismic accelerograms themselves or their intensity parameters [3]. The first method uses a pattern recognition scheme that is based on the similarity of signal graphs, which belong to the same class. Four classes are determined according to the MISDR (low, medium, large, total). The accelerogram is divided into sub- regions by means of a genetic algorithm. The relative presence of points into each sub region with respect to the region extremes defines fuzzy representations of the accelerogram. Accelerograms with known damage effects are used to define fuzzy models for the desired damage classes.

The second method is based on the intensity parameters of the accelerograms. These are presented as a scaled one-dimensional signal and a genetic algorithm is used to divide the horizontal and vertical axes into intervals and therefore produce sub regions over the signal. A fuzzy model is derived for each intensity parameter set based on the presence of signal points into the region. Intensity parameter sets, with known damage effects, define damage classes and are used for constructing fuzzy model representations of these classes.

In the third method, the seismic intensity parameters are fuzzyfied through properly selected membership functions that represent fuzzy sets of the desired damage classes. Their position is based on a training set of accelerograms with known damage effects. Each parameter is associated to one membership per fuzzy set that indicates its similarity to the specific set and, therefore, to the corresponding class.

The numerical results have shown that the observed classification error of the first approach is large and rates up to 62%, concluding that signal similarity cannot be exploited. On the other hand, the situation is substantially improved in the second and third proposed approaches, where, the correct classification results increase up to 100%.

1

K. Meskouris, "Structural Dynamics", Ernst and Sohn, Berlin, 2000.

2

A. Elenas, K. Meskouris, "Correlation study between seismic acceleration parameters and damage indices of structures", Engineering Structures, 23, 698-704, 2001. doi:10.1016/S0141-0296(00)00074-2

3

L.I. Kuncheva, "Fuzzy Classifier Design", Physica-Verlag, Heidelberg, 2000.

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