Fuzzy Multivariate Regression Models for Seismic Assessment of Rocking Structures

The assessment of rocking response is a challenging task due to its high nonlinearity. The present study investigates two methodologies to evaluate finite rocking rotations and overturn of three typical rocking systems. In particular, fuzzy linear regression (FLR) with triangular fuzzy numbers and a hybrid model combining logistic regression and fuzzy logic were adopted. To this end, three typical rocking structures were considered, and nonlinear time history analyses were performed to obtain their maximum response. Eighteen seismic intensity measures (IMs) extracted from recorded seismic accelerograms were considered to predict the responses. In the absence of rocking overturn, the finite rocking rotations and similarity ratios were calculated by adopting the FLR method. Moreover, extensive analysis was performed to evaluate the influence of each IM on the model's predictions. On the other hand, rocking overturn was evaluated by logistic regression to compute the probability of collapse, followed by the FLR method to estimate the similarity between the different rocking-based structural systems. The root mean square error (RMSE) parameter and the log loss function were determined for every model to assess the predictions that emerged from the two fuzzy methods. As indicated, both methods demonstrated satisfactory results, presenting minimal deviations from the observed values. Finally, in the case of finite rocking rotation predictive models, remarkably high similarity ratios were observed among the various structures, with a median value of 0.96.