Prediction of inelastic displacement ratios for evaluation of degrading SDOF systems: A comparison of the scaled conjugate gradient and Bayesian regularized artificial neural network modeling

Abstract

Inelastic displacement demand is an important part of the performance-based design and it should be estimated realistically to determine a reliable seismic performance of a structure. In this context, the coefficient method is an easy and practical method for this estimation. The coefficient method is a method that is used to estimate inelastic displacement demand by the multiplication of the elastic displacement demand and inelastic displacement ratio. Thus, it is clear that a reliable estimation of inelastic displacement demand depends on a reliable inelastic displacement ratio. After a reliable estimation of the inelastic displacement ratio, it is essential to propose an equation for the usage of engineering practice. Although nonlinear regression analysis is preferred in the literature as a classical method to estimate an equation, the Artificial Neural Network method is a new and modern way that can be used in the esti-mation of inelastic displacement ratio. In this study, Artificial Neural Network models have been proposed by using data of inelastic displacement ratios of Single Degree of Freedom systems with stiffness and strength degrading peak-oriented hysteretic model and collapse potential by performing nonlinear time history analyses. Firstly, a large number of trials have been conducted to obtain an optimum Artificial Neural Network model. The results of Ar-tificial Neural Network models have been compared to the results of equation estimated by using nonlinear regression analysis and given in the previous studies. According to the results, Artificial Neural Network models give closer values to the inelastic displacement ratios of time history analysis than nonlinear regression analysis. Especially, the Bayesian Regulariza-tion Backpropagation model of the Artificial Neural Network method with two hidden layers achieved the best performance among the other Artificial Neural Network models. It can be said that Artificial Neural Network methods can be used to estimate inelastic displacement ratio since it yields better accuracy than previous techniques for different parameters.

Keywords

• Artificial Neural Network
• Degradation
• Dynamic Instability
• Inelastic Displacement Ratio
• Nonlinear Regression Analysis
• Nonlinear Time History Analysis

References

1. REFERENCES
2. [1] Newmark NM. Effect of inelastic behavior on the response of simple systems to earthquake motions. In: Proceedings of the 2nd World Conference on Earthquake Engineering; 1960; Tokyo, Japan. p. 895912.
3. [2] Shimazaki K, Sozen MA. Seismic drift of reinforced concrete structures. Tokyo: Hazama-gumi; 1984.
4. [3] Qi X, Moehle JP. Displacement design approach for reinforced concrete structures subjected to earthquakes. Berkeley (CA): Earthquake Engineering Research Center, College of Engineering, University of California; 1991.
5. [4] Miranda E. Seismic evaluation and upgrading of existing structures [Dissertation Thesis]. Berkeley (CA): University of California; 1991.
6. [5] Miranda E. Evaluation of seismic design criteria for highway bridges. Earthquake Spectra 1993;9:233250. [CrossRef]
7. [6] Miranda E. Evaluation of site-dependent inelastic seismic design spectra. J Struct Eng 1993;119:13191338. [CrossRef]
8. [7] Miranda E. Inelastic displacement ratios for structures on firm sites. J Struct Eng 2000;126(10):11501159. [CrossRef]

9. [8] Ruiz-García J, Miranda E. Inelastic displacement ratios for evaluation of existing structures. Earthquake Eng Struct Dyn 2003;32:12371258. [CrossRef]
10. [9] Vidic T, Fajfar P, Fischinger M. Consistent inelastic design spectra: strength and displacement. Earthquake Eng Struct Dyn 1994;23:507521. [CrossRef]
11. [10] Aydinoglu MN, Kacmaz U. Strength-based displacement amplification spectra for inelastic seismic performance evaluation. Istanbul: Bogazici University, Department of Earthquake Engineering; 2002 Report No.: 2002/2.
12. [11] Chopra AK, Chintanapakdee C. Inelastic deformation ratios for design and evaluation of structures: single-degree-of-freedom bilinear systems. J Struct Eng 2004;130:13091319. [CrossRef]
13. [12] Eser M, Aydemir C, Ekiz I. Inelastic displacement ratios for structures with foundation flexibility. KSCE J Civ Eng 2012;16:155162. [CrossRef]
14. [13] Durucan C, Durucan AR. Ap/Vp specific inelastic displacement ratio for the seismic response estimation of SDOF structures subjected to sequential near fault pulse type ground motion records. Soil Dyn Earthquake Eng 2016;89:163170. [CrossRef]
15. [14] Zhai CH, Wen WP, Zhu TT, Li S, Xie LL. Inelastic displacement ratios for design of structures with constant damage performance. Eng Struct 2013;52:5363. [CrossRef]
16. [15] Wen WP, Zhai CH, Li S, Chang Z, Xie LL. Constant damage inelastic displacement ratios for the near-fault pulse-like ground motions. Eng Struct 2014;59:599607. [CrossRef]
17. [16] Ibarra LF, Medina RA, Krawinkler H. Hysteretic models that incorporate strength and stiffness deterioration. Earthquake Eng Struct Dyn 2005;34:148914511. [CrossRef]
18. [17] Braz-César MT, Oliveira DV, Barros RC. Comparison of cyclic response of reinforced concrete infilled frames with experimental results. In: Proceedings of the 14th World Conference on Earthquake Engineering; 2008; Beijing, China.
19. [18] Luo H, Paal SG. Machine learning–based backbone curve model of reinforced concrete columns subjected to cyclic loading reversals. J Comput Civ Eng 2018;32:04018042. [CrossRef]
20. [19] Chintanapakdee C, Jaiyong A. Estimation of peak roof displacement of degrading structures. In: Proceedings of the 15th World Conference on Earthquake Engineering; 2012; Lisbon, Portugal.
21. [20] Nassar AA. Seismic demands for SDOF and MDOF systems [thesis]. Stanford (CA): Stanford University; 1991.
22. [21] Rahnama M, Krawinkler H. Effects of soft soils and hysteresis models on seismic design spectra. Stanford (CA): John A. Blume Earthquake Engineering Center, Stanford University; 1993. Report No.: 107.
23. [22] Seneviretna GDPK, Krawinkler H. Evaluation of inelastic MDOF effects for seismic design. Stanford (CA): John A. Blume Earthquake Engineering Center, Stanford University; 1997. Report No.: 120.
24. [23] Gupta B, Kunnath SK. Effect of hysteretic model parameters on inelastic seismic demands. In: Proceedings of the 6th US National Conference on Earthquake Engineering; 1998 May; Seattle, WA. p. 1-12.
25. [24] Song JK, Pincheira JA. Spectral displacement demands of stiffness-and strength-degrading systems. Earthquake Spectra 2000;16:817851. [CrossRef]
26. [25] Pekoz HA, Pincheira JA. Seismic Response of Strength and Stiffness Degrading Single Degree of Freedom Systems. In: Proceedings of the 13th World Conference on Earthquake Engineering; 2004 Aug 1-6; Vancouver, BC, Canada.
27. [26] Chenouda M, Ayoub A. Inelastic displacement ratios of degrading systems. J Struct Eng 2008;134:10301045. [CrossRef]
28. [27] Lumantarna E, Lam N, Wilson J, Griffith M. Inelastic displacement demand of strength-degraded structures. J Earthquake Eng 2010;14:487511. [CrossRef]
29. [28] Borekci M, Kırçıl MS, Ekiz I. Inelastic displacement ratios for evaluation of degrading peak-oriented SDOF systems. Period Polytech Civ Eng 2018;62:3347. [CrossRef]
30. [29] Xie Y, Ebad Sichani M, Padgett JE, DesRoches R. The promise of implementing machine learning in earthquake engineering: A state-of-the-art review. Earthquake Spectra 2020;36:17691801. [CrossRef]
31. [30] Dwairi HM, Tarawneh AN. Artificial neural networks prediction of inelastic displacement demands for structures built on soft soils. Innov Infrastruct Solut 2022;7:4. [CrossRef]
32. [31] Wei M, Hu X, Yuan H. Residual displacement estimation of the bilinear SDOF systems under the near-fault ground motions using the BP neural network. Adv Struct Eng 2022;25:552571. [CrossRef]
33. [32] Clough RW. Effect of stiffness degradation on earthquake ductility requirements. In: Proceedings of the Japan Earthquake Engineering Symposium; 1966.
34. [33] Mahin SA, Bertero VV. An evaluation of some methods for predicting seismic behavior of reinforced concrete buildings. Berkeley (CA): University of California, Earthquake Engineering
35. Research Center; 1975. [34] Ibarra LF. Global collapse of frame structures under seismic excitations [thesis]. Stanford (CA): Stanford University; 2004.
36. [35] Miranda E, Akkar SD. Dynamic instability of simple structural systems. J Struct Eng 2003;129(12):17221726. [CrossRef]
37. [36] Ayoub A, Chenouda M. Response spectra of degrading structural systems. Eng Struct 2009;31:13931402. [CrossRef]
38. [37] Bernal D. Instability of buildings during seismic response. Eng Struct 1998;20:496502. [CrossRef]
39. [38] Villaverde R. Methods to assess the seismic collapse capacity of building structures: State of the art. J Struct Eng 2007;133:5766. [CrossRef]
40. [39] Borekci M, Kirçil MS, Ekiz I. Collapse period of degrading SDOF systems. Earthquake Eng Eng Vib 2014;13:681694. [CrossRef]
41. [40] Hagan MT, Menhaj MB. Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Netw 1994;5:989993. [CrossRef]
42. [41] MacKay DJC. Bayesian model comparison and backprop nets. In: Advances in Neural Information Processing Systems 4. 1991.
43. [42] Burden F, Winkler D. Bayesian regularization of neural networks. In: Artificial Neural Networks: Methods and Applications. 2009. p. 2342. [CrossRef]
44. [43] Foresee FD, Hagan MT. Gauss-Newton approximation to Bayesian learning. In: Proceedings of the International Conference on Neural Networks (ICNN'97); 1997 Jun 12; Houston, TX. IEEE. vol. 3, p. 19301935.