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In this study, a novel optimization method based on Imperialist Competitive Algorithm (ICA) was proposed to simulate endurance time (ET) excitations. These excitations are monotonically intensifying acceleration time histories that are used as dynamic loading for seismic response analysis and design. The ICA as a population-based evolutionary algorithm was used in this study and the discrete wavelet transform was also employed to reduce the number of optimization variables. Optimal parameter values of the ICA algorithm for simulating ETEFs were evaluated and were utilized to simulate ET excitations. In order to increase the capability of ICA and provide further search in the optimization space, this algorithm was combined with simulated annealing (SA). The new excitation results were compared with the current practice for simulation of ET excitations. It was shown that the proposed ICA-SA method leads to more accurate ET excitations than the classical optimization methods.

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The main objective of this study is the development of endurance time (ET) excitations in order to take structural response uncertainty into account for use in performance-based earthquake engineering. There are several uncertainties in earthquake engineering, including earthquake occurrence, structural response, damage, and loss.In the current research, structural response uncertainty is directly included in the ET method, which is an analysis method used for performing structural behavior assessment under seismic actions. Conventional practice of the ET method does not provide any information about seismic response distribution. Despite the simplicity of the ET method, it is an accurate dynamic analysis approach in which structures are subjected to predesigned intensifying acceleration functions, also known as ET excitation functions (ETEFs). In this study, the ETEF generating procedure is modified in order to include the exceedance probability of structural responses observed at an intensity measure. This proposed method is applied to generate new ETEFs; then they are utilized in assessing distribution responses in three structure case studies. Finally, response distributions obtained by the ET method are compared with incremental dynamic analysis so as to investigate the proposed method efficiency. Results show that response probabilistic distributions that are predicted using the ET method match those obtained by incremental dynamic analysis. KEYWORDS endurance time method, engineering demand parameter, performance-based earthquake engineering, record-to-record variability, seismic response analysis, uncertainty 1 | INTRODUCTIONThe main objective of this study is the development of endurance time (ET) excitations in order to take structural response uncertainty into account for use in performance-based earthquake engineering (PBEE). There are several uncertainties in earthquake engineering, including earthquake occurrence, structural response, damage, and losses. In the current study, structural response uncertainty is directly included in the ET method. The mentioned method is an analysis technique used for performing structural behavior assessment under seismic actions. Traditional practice of the ET method does not provide any information about seismic response distribution. Accounting for uncertainties is an essential need for modern PBEE in evaluating structural system performance.In a promising PBEE methodology developed by the Pacific Earthquake Engineering (PEER) center, uncertainty in different analytical stages is taken into account for determining any facility performances. [1,2] The performance assessment is divided into four analytical stages: probabilistic seismic hazard analysis, structural response assessment, damage analysis, and loss analysis. In PEER framework, the mean annual rate of a decision