# Machine Learning Algorithms for the Prediction of the Seismic Response of Rigid Rocking Blocks
## 2 Materials and Methods
### Dataset Description  
In order to evaluate the efficiency of ML algorithms to predict the maximum rocking response of free-standing rigid blocks, 1100 rocking blocks are considered in total. As indicated in Equation (2), it is evident that the frequency parameter \(p\) and the slenderness \(\alpha\) are the structural parameters that affect the rocking response. Therefore, these two parameters are adopted as the input features that characterize the examined blocks. The rocking blocks under examination were created by combining 100 equally spaced values of the frequency parameter (\(p\)), which spans from 0.7 s\({}^{-1}\) to 7 s\({}^{-1}\), and 11 equally spaced values of the slenderness parameter (\(\tan(\alpha)\)), ranging from 0.05 to 0.30. The adopted range of the frequency parameter corresponds to blocks with semi-diagonals ranging from 0.15 m to 15 m. Thus, the considered database describes the dynamic response of structures ranging from small-sized building contents to rocking bridge priors. In order to create the data set, the considered blocks are subjected to 5000 natural ground motion acceleration records. Since the slender enough rocking blocks are prone to rocking overturn, the selection of ground motions is based on a minimum peak ground acceleration (PGA) value of 0.05 g to enforce uplift without overturn. Additionally, each record is scaled using three scale factors with values 0.5, 1, and 2. The scaling is performed to derive the full range of possible responses of the examined blocks. The ground motion records set comprises an extensive assortment of seismic data, covering a wide spectrum of seismic events. With \(V_{s,30}\)[51] values ranging from 100 m/s to 2000 m/s, which correspond to soil classes ranging from A to D, the set accommodates diverse soil conditions. Furthermore, the \(R_{rup}\) spans from 0.07 km to 185 km, while the magnitude \(M_{up}\) ranges from 3.2 to 7.9. Moreover, the database encompasses records for all faulting types, offering a comprehensive perspective on seismic activity. Seismic excitations are highly intricate and necessitate a substantial volume of data for comprehensive characterization. The definition of various ground motion parameters, known as intensity measures (IMs), simplifies the representation of strong ground motions and establishes a connection between seismic hazards and the structural data essential for solving earthquake engineering challenges. Within the realm of earthquake engineering, the most significant features of ground motion encompass amplitude, frequency content, and duration. From this point of view, the 18 IMs listed in Table 1 are considered as input features for the description of the ground motion signal. In Table 1, \(v_{g}(t)\) and \(d_{g}(t)\) are the ground velocity and displacement; \(C_{i}\), \(f_{i}\) are the Fourier amplitudes of the excitation accelerogram and the discrete Fourier transform frequencies, and \(t_{\text{tot}}\), \(t_{\text{sig}}\) are the total and \"significant\" [52] durations of the ground excitation respectively. For the creation of the dataset, 15,000 time history analyses for each block were conducted, as mentioned above. From the resulting responses, only those where the rocking response was initiated were retained. Also, note that the classification problem of whether or not a rocking response is initiated does not necessitate the use of ML methods since the critical ground acceleration is given by (1). Thus, we obtained 5,782,400 responses in total. From these, in 2,525,847 cases, the excitation resulted in the overturning of the block, while in 3,256,553 it did not. Thus, the class ratio was approximately 56:44, i.e., the dataset did not suffer from the so-called class imbalance problem, which can severely impact the performance of ML algorithms [53; 54]. Finally, the maximum seismic rocking rotation was measured, but only for those instances where the block did not overturn.