Predicting peak ground acceleration of an earthquake by using the machine learning program Lagramge

This bachelor’s thesis deals with testing the equation discovery system Lagramge when applied to a specific engineering problem of modelling the earthquake’s peak ground acceleration. The Lagramge system uses context-free grammar formalism which contains rules for building equations and limits the hypothesis space of possible equations. We developed three different grammars, each incorporating a different level of domain specific knowledge, which included 68 published equations. In the experiments a database of 3550 strong motion earthquake recordings was used and for the purpose of cross validation split 10 times into 90 % learning and 10 % testing sets. The algorithm employed exhaustive and/or heuristic search methods in all three hypothesis spaces and evaluated the equations on the learning and testing datasets using the\ud mean squared error criterion. From each of 4 experiments three best equations were selected on the basis of quantitative criterion and compared with each other and with the equations from the Next Generation Attenuation study as well as with the equation developed by the European\ud authors Akkar and Bommer. We found out that inclusion of the domain specific knowledge which is neither too specific nor too general improves the quality of the results. In addition to this, influences of other input parameters guiding the process of equation discovery were examined. The results of this study show that the Lagramge system could also be applied to similar problems in earthquake engineering as well as to other fields of engineering