# Machine Learning Algorithms for the Prediction of the Seismic Response of Rigid Rocking Blocks
###### Abstract  
A variety of structural members and non-structural components, including bridge piers, museum artifacts, furniture, or electrical and mechanical equipment, can uplift and rock under ground motion excitations. Given the inherently non-linear nature of rocking behavior, employing machine learning algorithms to predict rocking response presents a notable challenge. In the present study, the performance of supervised ML algorithms in predicting the maximum seismic response of free-standing rigid blocks subjected to ground motion excitations is evaluated. As such, both regression and classification algorithms were developed and tested, aiming to model the finite rocking response and rocking overturn. From this point of view, it is essential to estimate the maximum rocking rotation and to efficiently classify its magnitude by successfully assigning respective labels. To this end, a dataset containing the response data of 1100 rigid blocks subjected to 15,000 ground motion excitations, was employed. The results showed high accuracy in both the classification (95% accuracy) and regression (coefficient of determination \(R^{2}=0.89\)) tasks. rocking blocks; machine learning; artificial neural network; decision tree; gradient boosting +
Footnote †: journal: Medical  
From this point of view, estimating the maximum rocking response is essential. Nonetheless, achieving this objective is not a straightforward endeavor, primarily attributable to the pronounced non-linearity inherent in the motion, which arises from the negative stiffness characteristic of the rocking oscillator [2]. It is apparent that even minor alterations in the parameters of the rocking oscillator or in the attributes of the ground motion record yield entirely distinct responses [23]. Hence, the seismic response of rocking systems should be assessed within a probabilistic framework [24; 25; 26; 27; 28; 29; 30; 31]. To this end, it is necessary to perform a vast number of non-linear time history analyses to assess the probabilistic distribution of seismic demands. It is evident that non-linear time history analysis of structures is a time-consuming process that also requires high computational resources. To overcome this bottleneck, a substantial research effort in the field of soft computing methods for the rapid evaluation of the seismic response of structures has been undertaken over the past two decades. The majority of machine learning (ML) applications in this field primarily focus on predicting seismic demands for various types of structures, including reinforced concrete [32; 33; 34], steel [35; 36; 37], and timber [38] buildings, as well as bridges [39]. For bridges, in particular, methods such as convolutional neural networks (CNNs), in conjunction with signal processing, have been implemented for early damage detection and warning [40]. In addition to capturing the precise values of engineering demand parameters (EDPs), the capability of machine learning methods to classify seismic responses into levels corresponding to different damage limit states has been investigated [41; 42; 43]. Given that assessing the seismic performance of structures in terms of fragility is the basis of performance-based earthquake engineering, numerous applications of ML methods in seismic fragility and risk have also been presented in the literature [44; 45; 46]. Although there is a plethora of ML implementations on fixed-based or seismically isolated structures, there is a lack of implementations on rocking structures. To the best of the authors' knowledge, there are only four studies that utilize ML algorithms to predict the response of rocking oscillators. Specifically, [PERSON] et al. [47] developed an ANN to predict the overturning response of rigid blocks under pulses, while [PERSON] et al. [48] proposed an ANN with adaptive training to predict the time-history response of a rocking block. Moreover, [PERSON] et al.