## 3 The Proposed Method for the Rapid Seismic Damage Assessment of RC Buildings
The general configuration of an MFPNN, which can be used to solve a PR problem with \(n\) pre-defined classes implementing the supervised learning approach, is depicted in Figure 1. The population of the input parameters, i.e., the parameters that describe the objects (elements of the input vectors \(\mathbf{x}\)) is \(m\). Thus, in this case, the target is the classification of objects described using the \(\mathbf{x}\) vectors (having \(m\) parameters) into \(n\) predefined classes. In order to use PR techniques and ML algorithms for rapid seismic damage assessment, the following should be applied:  
1. The type and number of the characteristics of the objects (i.e., the input \(\mathbf{x}\) vectors) should be selected and classified into pre-defined classes. Furthermore, the corresponding classes' number and type should also be defined (i.e., the output \(\mathbf{o}\) vectors). An important issue, which is also briefly described in Figure 1, is the mapping of output vectors (\(\mathrm{o}_{\mathrm{j}}\) elements) to the classes of the problem. More specifically, the configuration of \(\mathbf{o}\) vectors for each one of the pre-defined classes must be defined. By definition, when the MFPNN extracts an output vector \(\mathbf{o}\) with \(\mathrm{o}_{\mathrm{j}}=1\) and all the other elements of \(\mathbf{o}\) are equal to 0, then the corresponding object (\(\mathbf{x}\) vector) is classified to  
Figure 1: General description of the configuration of an MFPNN used for the solution of PR problems. the class \(j\). For the seismic damage assessment, the input vectors \(\mathbf{x}\) should contain parameters that are crucial for the seismic performance of the RC buildings (structural parameters), as well as parameters that describe the seismic excitation (seismic parameters) [38]. To this end, the input vector \(\mathbf{x}\) consists of two sub-vectors, namely the sub-vector \(\mathbf{x}_{\text{struct}}\) and the sub-vector \(\mathbf{x}_{\text{seism}}\) (Equation (1)): \[\mathbf{x}=\left[\mathbf{x}_{\text{seis}}\,|\,\mathbf{x}_{\text{struct}}\right] ^{\text{T}}\] (1) (2) The structural and seismic parameters should be selected. Since the target of the current paper is the development of the software application based on the PR approach for the rapid seismic damage assessment of RC buildings, no further investigation regarding the optimum selection of the structural and the seismic parameters was performed. Moreover, as explained in the next section, the structure of the software code allows for modifications in the case of MFPNNs with different input parameters (structural and seismic). At this stage of development, already trained and successfully tested MFPNNs were used, while the description of the parametric investigation for the optimum configuration of these MFPNNs is given in [32]. A brief description of the selected input and output parameters of the introduced MFPNNs as well as their configuration parameters are presented herein. Regarding the selection of the _structural parameters_, four parameters were selected to consider parameters that are critical for the seismic performance, and these are also considered in the framework of taxonomy and classification systems proposed for fragility assessment. The parameters selected are the total height of the building (\(\text{H}_{\text{tot}}\)), the ratio of the base shear that is received by RC walls along two perpendicular directions between them: directions 1 and 2 (ratio \(\text{n}_{\text{v1}}\) and ratio \(\text{n}_{\text{v2}}\)), and the structural eccentricity \(\text{e}_{0}\) (i.e., the distance between the mass center and the stiffness center of stories). However, it must be noted that the estimation of the parameter's values could be difficult in the case of the RVI. For this reason, as it will be presented in Section 4.4, the developed software allows the input of user-defined parameters, provided that the values are known from previous studies or measurements.