Information theory-guided machine learning to estimate seismic response of non-linear SDOF structures

This study presents a parametric numerical analysis for the selection of the best seismic parameters characterising seismic records to model the dynamic response of non-linear single-degree-of-freedom (SDOF) structural systems by using Machine Learning (ML) techniques. This analysis is carried out using appropriate indices within Information Theory (IT), which allow for estimation of the amount of usable information from input data. Specifically, 400 artificial seismic excitations were generated, and, for each one, 23 seismic parameters were evaluated. Subsequently, step-by-step numerical analyses were conducted to study the seismic responses of 1000 equivalent elastic perfectly-plastic SDOF systems with different mechanical properties. The "conditional information" index was thus evaluated for both peak relative displacement and hysteretic energy response, given the input values of specific seismic parameters. The same data were treated using supervised learning techniques with 20 ML algorithms: linear regression, decision trees, support vector machine (SVM), boosted trees, bagged trees and artificial neural networks (ANN). Each analysis considered the identical set of seismic parameters, used for the conditional information index, to verify whether a higher theoretical amount of information, obtainable from the input parameters, can lead to a more efficient ML modelling. Finally, the most effective model estimation, derived from a single ML algorithm with the best combination of the input parameters, have been compared with the results of the parametric step-by-step analyses performed for some natural ground motions. The results validate the proposals and show that a higher amount of information, gained from the input parameters, generally corresponds to a better performance estimation of the ML models. This allows for the identification of which and how many seismic parameters should be considered as the best-performing combination of the input parameters for the modelling algorithm. Furthermore, when the training phase is suitably calibrated, considering the specific site hazard and the best seismic parameters, the ML model can effectively estimate the seismic performance. This highlights considerable potentials of integrating ML techniques within the performance-based seismic design approach.