## 2 Structural Models Used for Generating the Calibration Data  
In this study, the objective is to develop a neural network-based model capable of predicting the response, specifically the acceleration time history, of the top floor translational degree of freedom of a multi-degree-of-freedom (MDOF) building system when subjected to an earthquake event, without relying on any finite element analysis. The underlying motivation behind this endeavor is to eventually contribute, with a refined neural network model, to a rapid estimation of a structure's response, accounting for its nonlinear behavior and the characteristics of the ground, at least in bilinear terms, by utilizing field measurements. More specifically, the proposed model will combine ambient response timeframes of 60 s with earthquake timeframes. For each set of inputs, consisting of the ambient top floor response and the earthquake data, the model will produce the response of the specific MDOF system to the specific seismic event. The data and measurements employed in this study were obtained through a rigorous process involving numerical generation and computational derivation, utilizing the Newmark numerical integration method. This approach was selected to encompass a wide range of MDOF models, ensuring the inclusion of all possible parameter combinations. A comprehensive set of 1197 models was specifically utilized for the purpose of this investigation, ensuring a robust and extensive analysis. The assumptions used to construct these models were based on a building model that can be seen in Figure 1. This reference building model was mainly used for the estimation of the mass baseline per floor. The stiffness matrix is also seen in Table 1. However, the stiffness value was derived after setting the target frequency and target mass. This model was developed using the ADINA v. 9.1.1 analysis software [24]. The number of assumptions and parameters used are shown in Table 1.  
Figure 1: The assumptions table is referring to the typical building model, (the grey arrows denote the three DOFs per storey of the fully fixed frame structure). To capture some level of the nonlinearity of material or/and level of damage, a bilinear capacity curve was constructed, which applied to all structural members of each MDOF model (Figure 2). The general layout of the curve is illustrated in Figure 3 (bilinear capacity curve of all structural members). Each numerically produced ambient acceleration response signal is the sum of the ambient excitation itself with the response of the corresponding MDOF model at the last degree of freedom (top of the building). The case study did not incorporate the soil-structure interaction (SSI). Nevertheless, it can be readily incorporated by utilizing a system of horizontal and vertical springs within fictitious elements, which simulate the diverse bedrock layers and their influence on the structure [25]. The signals in this study have a sampling rate of 100 Hz, and their duration is consistently 60 s. It is important to note that these signals are intentionally generated without any electronic noise. This is because it is assumed that the measurements will either be obtained using low noise accelerographs or processed using some form of neural network for denoising the signal. Each building model in the dataset comprises 1 to 7 floors, with a mass ranging from 80% to 120% of the typical values mentioned in Table 1 and with an eigenfrequency ranging between 1 and 10 Hz with a step of 0.5 Hz. Therefore, 1197 models of MDOF models were derived. For each of these models, three timeframes of ambient response were selected, leading to the generation of 3591 artificial ambient responses. Figure 3: Bilinear capacity curve of all structural members, where yielding and ultimate states are denoted. Figure 2: The MDOF 2D shear model. In terms of earthquake signals, nine acceleration time histories were carefully chosen to accompany the ambient response signals.