A Comparative Study of the Least Squares Method and the Genetic Algorithm in Deducing Peak Ground Acceleration Attenuation Relationships

In engineering applications, the development of attenuation relationships in a seismic hazard analysis is a useful way to plan for earthquake hazard mitigation. However, finding an optimal solution is difficult using traditional mathematical methods because of the nonlinearity of many relationships. Furthermore, using unweighted regression analysis in which each recording carries an equal weight is often problematic because of the non-uniform distribution of the data with respect to distance. In this study, the least squares method (LSM) and a genetic algorithm (GA) were employed as optimization methods for an attenuation model to compare the robustness and prediction accuracy of the two methods. Different (equal and unequal) weights of each recording were used to compare the adaptability of the weighting for practical application. The unequal weights of each recording were defined as functions of the hypocentral distance or the shortest distance from a station to the fault on the earth’s surface. Finally, regression analysis of horizontal peak ground acceleration (PGA) attenuation model in southwest Taiwan was shown.

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