## 5 Conclusions  
In this paper, we studied the ability of multilayered feedforward perceptron (MLP) networks to reliably predict the influence of the critical angle of seismic excitation \(\theta_{\text{cr}}\) on the seismic damage to RC buildings in real time. To this end, the problem was defined and solved as a pattern recognition (PR) problem. Thus, three different seismic damage classes (SDCs) were defined (\"slight\" or \"S\", \"moderate\" or \"M\", and \"heavy\" or \"H\") on the basis of the maximum interstory drift ratio (MIDR), which is a widely used seismic damage index. Two different approaches for the definition of the PR problem were considered. The first (Approach 1, or A1) is a two-class PR problem where the first class corresponds to buildings for which the SDC for \(\theta=0\) is not increased for \(\theta=\theta_{\text{cr}}\) [Class 1: SDC (\(\theta=\theta_{\text{cr}}\)) = SDC (\(\theta=0\))], whereas the second class corresponds to the opposite condition [Class 2: SDC (\(\theta=\theta_{\text{cr}}\)) > SDC (\(\theta=0\))]. The second approach (Approach 2, or A2) is based on the initial separation of buildings into two categories, namely, the buildings that are classified to the \"S\" SDC for \(\theta=0\), and those that are classified to the \"M\" SDC for \(\theta=0\). Then, two different categories of A2 are defined: in the first framework (A2/C3S), three classes are considered for the buildings that are classified to the \"S\" SDC for \(\theta=0\) (Class 1: SDC (\(\theta=0\)) = \"S\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"S\", Class 2: SDC (\(\theta=0\)) = \"S\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"M\", Class 3: SDC (\(\theta=0\)) = \"S\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"H\"), whereas in the second framework (A2/C2S) two classes for these buildings are defined [Class 1: SDC (\(\theta=0\)) = \"S\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"S\", Class 2: SDC (\(\theta=0\)) = \"S\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"M\" or \"H\"). On the other hand, two classes for the buildings that are classified to the \"M\" SDC for \(\theta=0\) (category A2/C2M) are considered in all cases [Class 1: SDC (\(\theta=0\)) = \"M\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"M\", Class 2: SDC (\(\theta=0\)) = \"M\" \(\rightarrow\) SDC (\(\theta=\theta_{\text{cr}}\)) = \"H\"). Thus, two types of analysis are defined in the framework of A2--\"A2/(C3S + C2M)\" and \"A2/(C2S + C2M)\"--whereas one type of analysis was defined in the framework of A1 (the analysis type \"A1\"). For each of the above-mentioned types of analysis, one category (four in total) of MLP networks (NA1 networks for \"A1\", NA2C3S networks for \"A2/C3S\", NA2C2S networks for \"A2/C2S\", and NA2C2M networks for \"A2/C2M\") was configured and trained using training datasets that were generated by the authors in previous published research on the basis of 3 different versions of 30 properly selected RC buildings (Bare Buildings \"BB\", Regularly Infilled Buildings \"RIB\", and Irregularly Infilled Buildings \"IIB\"). As regards the  
Figure 14: CMs extracted by the optimally configured networks of (**a**) A1 and (**b**) A2. input vectors for the MLP networks, 12 widely used seismic parameters and 3 structural parameters were used. Due to the fact that the scope of the present research is the study of the influence of the critical angle of seismic excitation on the seismic damage, we used the min/max ratios of the values of the selected seismic parameters that correspond to the two recorded horizontal components of excitations, as opposed to of the values extracted using a numerical combination of them. As regards the three structural parameters, the selection of them was also based on the nature of the problem, as well as on general (and macroscopic) indices that influence the seismic damage response of buildings.