Optimal objective function for simulating endurance time excitations

Endurance Time (ET) method is a dynamic analysis procedure in which increasing excitations are imposed on structures; these excitations are known as Endurance Time Excitation Functions (ETEF). This study presents a method to determine an optimal objective function for simulating ETEFs including unconstrained optimization problems. In optimization problems, equations are defined in terms of an objective function. In the problem of simulating ETEFs, the objective function can be defined in many different ways regarding the considered intensity measures and respective weighting factors. In addition, the type of calculating residuals (absolute way or relative way) diversifies the objective function definitions. The proposed method for determining the optimal objective function includes quantifying the accuracy of ETEFs in a scalar quantity regardless of their objective functions and introducing an approach to attenuate the dependence of results on the initial points of optimizations. The proposed method is applied, and results are then presented. It is observed that considering only acceleration spectra and calculating residuals in a relative way lead to more accurate ETEFs.