Optimal objective function for simulating endurance time excitations

Document Type : Article


Department of Civil Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9313, Iran


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 find the optimal objective function for simulating ETEFs which unconstrained optimization problems are. In optimization problems, equations are defined in term of an objective function. In the problem of simulating ETEFs, the objective function can be defined in many different ways regarding considered intensity measures and respective weighting factors. In addition, the type of calculating residuals (absolute way or relative way) diversifies objective function definitions. The proposed method for determining optimal objective function includes quantifying the accuracy of ETEFs in a scalar quantity regardless of their objective functions and introducing an approach to overcome the dependence of results on 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 the relative way creates more accurate ETEFs.


Main Subjects

1. Estekanchi, H.E., Vafai, A., and Sadeghazar, M. Endurance time method for seismic analysis and design of structures", Scientia Iranica, 11(4), pp. 361{370 (2004). 2. Krawinkler, H. and Seneviratna, S. Pros and cons of a pushover analysis of seismic performance evaluation", Eng. Struct., 20(4{6), pp. 452{464 (1998). 3. Federal Emergency Management Agency (FEMA), Pre-Standard and Commentary for the Seismic Rehabilitation of Buildings, FEMA{356, Washington, DC (2000). 4. Federal Emergency Management Agency (FEMA), NEHRP Guidelines for Seismic Rehabilitation of Buildings, Report FEMA{273, Washington, DC (1997). 5. Vamvatsikos, D. and Cornell, C.A. Incremental dynamic analysis", Earthq. Eng. Struct. D, 31(3), pp. 491{514 (2002). 6. Kiani, J. and Khanmohammadi, M. New approach for selection of real input ground motion records for incremental dynamic analysis (IDA)", J. Struct. Eng., 19, pp. 592{623 (2015). 7. Riahi, H.T., Estekanchi, H.E., and Vafai, A. Application of endurance time method in nonlinear seismic analysis of SDOF Systems", J. App. Sci., 9(10), pp. 1817{1832 (2009). 8. Riahi, H.T., Estekanchi, H.E., and Vafai, A. Seismic assessment of steel frames with the endurance time method", J. Construct. Steel. Res., 66(6), pp. 780{792 (2010). 9. Mirzaee, A. and Estekanchi, H.E. Performance-based seismic retro_tting of steel frames by endurance time method", Earthquake Spectra, 31(1), pp. 383{402 (2015). 10. Rahimi, E. and Estekanchi, H.E. Collapse assessment of steel moment frames using endurance time method", Earthq. Eng. Eng. Vib., 14(2), pp. 347{360 (2015). 11. Basim, M.C. and Estekanchi, H.E. Application of endurance time method in performance-based optimum design of structures", Struct. Saf., 56, pp. 52{67 (2015). 12. Tafakori, E., Pourzeynali, S., and Estekanchi, H.E. Probabilistic seismic loss estimation via endurance time method", Earthq. Eng. Eng. Vib., 16(1), pp. 233{ 245 (2017). 13. Chiniforush, A.A., Estekanchi, H., and Dolatshahi, K.M. Application of endurance time analysis in seismic evaluation of an unreinforced masonry monument", J. Struct. Eng., 23(3), pp. 827{841 (2016). 14. Vaezi, D., Estekanchi, H.E., and Vafai, A. A parametric study of seismic response in anchored steel tanks with endurance time method", Scientia Iranica, 21(5), pp. 1608{1619 (2014). 15. Nozari, A. and Estekanchi, H.E. Optimization of endurance time acceleration functions for seismic assessment of structures", Int. J. Optim. Civ. Eng., 2, pp. 257{277 (2011). M. Mashayekhi et al./Scientia Iranica, Transactions A: Civil Engineering 27 (2020) 1728{1739 1739 16. Kaveh, A. and Mahdavi, V.R. Generation of endurance time acceleration functions using the wavelet transform", Int. J. Optim. Civ. Eng., 2(2), pp. 203{ 219 (2012). 17. Kaveh, A., Kalateh, M., and Estekanchi, H.E. Production of endurance time excitation function: The CMA evolution strategy approach", Iranian Journal of Science and Technology, Transaction of Civil Engineering, 37, pp. 383{394 (2013). 18. Mashayekhi, M. and Estekanchi, H.E. Investigation of strong-motion duration consistency in endurance time excitation functions", Scientia Iranica, 20(4), pp. 1085{1093 (2013). 19. Mashayekhi, M. and Estekanchi, H.E. Investigation of non-linear cycles' properties in structures subjected to endurance time excitation functions", Int. J. Optim. Civ. Eng., 3(2), pp. 239{257 (2013). 20. Mashayekhi, M. and Estekanchi, H.E. Signi_cance of e_ective number of cycle in endurance time", Asian Journal of Civil Engineering (Building and Housing), 13(5), pp. 647{657 (2012). 21. Federal Emergency Management Agency (FEMA), Quanti_cation of Building Seismic Performance Factors, FEMA P-695, Washington, D.C (2009). 22. Mor_e, J.J. and Sorensen, D.C. Computing a trust region step", SIAM. J. Sci. Stat. Comput., 3, pp. 553{ 572 (1983). 23. Mashayekhi, M., Estekanchi, H.E., and Vafai, H. Simulation of endurance time excitations using increasing sine functions", Int. J. Optim. Civ. Eng., 9(1), pp. 65{ 77 (2018).