Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis基于增量动力分析的随机地震激励下非线性结构随机设计优化
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Ni PH, Yuan ZS, Fu JL, Bai YL, Liu L, 2024. Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis. Probabilistic Engineering Mechanics, 78: 103707.DOI: 10.1016/j.probengmech.2024.103707
随着抗震减灾需求日益增加，基于性能的土木结构抗震设计研究受到广泛关注。然而，在考虑地震不确定性下进行复杂结构优化的研究仍然有限。本研究旨在引入一类随机地震激励下非线性结构设计优化的有效方法来求解这一问题。关键创新在于通过增量动力分析 (incremental dynamic analysis, IDA) 近似结构失效概率，从而提出一类双循环优化新方法，用于随机地震条件下的非线性结构设计。外层循环采用序列二次规划优化结构几何变量；内层循环采用增量动力分析进行结构分析以量化地震不确定性，然后将所得失效概率作为外层循环的优化约束。为验证其精度和有效性，利用 OpenSEES 对两个代表性案例进行了数值研究：钢筋混凝土柱和三层钢框架。研究结果表明，增量动力分析可以准确估计非线性结构在随机地震动下的失效概率，所提方法可有地确定最佳几何形状，增强结构在各类失效概率和边界约束下的抗震能力。关键词: 增量动力分析, 非线性结构, 随机设计优化, 随机地震激励, 失效概率, 不确定性量化The increasing demand for mitigating earthquake hazards has prompted substantial research attention towards performance-based seismic design of civil structures. Nevertheless, there remains limited exploration into optimizing complex structures while accounting for seismic uncertainties. This study seeks to address this gap by introducing an effective approach for optimizing designs of nonlinear structures under random seismic excitations. The key innovation lies in approximating structural failure probability through incremental dynamic analysis (IDA), leading to the development of a novel double-loop optimization method tailored for designing nonlinear structures exposed to stochastic seismic loading conditions. In the outer loop, geometric variables of structures are optimized using sequential quadratic programming; within the inner loop, IDA is adopted for structural analysis to quantify seismic uncertainty, and the resulting failure probability is then served as the optimization constraint for the outer loop. To validate its accuracy and efficacy, numerical investigations have been performed on two representative case studies utilizing OpenSees: a reinforced concrete column and a three-story steel frame. The findings affirm that IDA can precisely estimate failure probabilities associated with nonlinear structures experiencing random ground motions and demonstrate that this proposed methodology can effectively determine optimal geometries aimed at enhancing structural resilience against earthquakes across various levels of failure probabilities and bound constraints.Keywords: Incremental dynamic analysis; Nonlinear structures; Stochastic design optimization; Random seismic excitation; Failure probability; Uncertainty quantification.图 1: 基于增量动力分析双循环优化流程的随机地震激励下非线性结构随机设计优化Fig. 1. Stochastic design optimization of nonlinear structures under random seismic excitations through an IDA-based double-loop optimization procedure
Fig. 2. Dimensions of the reinforced concrete (RC) column
Fig. 3. Twenty-two seismic response spectra
Fig. 4. Results of the IDA-based design optimization
Fig. 5. Comparison of the fragility curves of the RC column before and after optimization
图 6: 取不同失效概率作为优化约束的增量动力分析设计优化结果Fig. 6. Results of IDA-based design optimization by setting different failure probabilities P_f as the optimization constraint
图 7: 取不同失效概率作为优化约束的增量动力分析设计优化结果Fig. 7. Results of IDA-based design optimization by setting different failure probabilities P_f as the optimization constraint
图 8: 钢筋混凝土柱优化前后的极限状态 1 易损性曲线对比Fig. 8. Comparison of the LS1 fragility curves of the RC column before and after optimization
Fig. 9. Dimensions and numerical analysis model of a three-story steel frame
Fig. 10. A linear probabilistic seismic demand model
Fig. 11. Comparison of the fragility curves before and after optimization
Fig. 12. Comparison between the IDA curves before and after design optimization
Fig. 13. Results of the IDA-based design optimization
Fig. 14. Results of design optimization with different target failure probabilities
图 15: 取不同失效概率作为优化约束的增量动力分析设计优化结果Fig. 15. Results of IDA-based design optimization by setting different failure probabilities P_f as the optimization constraint
图 16: 优化设计前后的极限状态 1 易损性曲线对比Fig. 16. Comparison of the LS1 fragility curves before and after optimization design
图 17: 设计变量不同范围约束下的增量动力分析设计优化结果Fig. 17. Results of IDA-based design optimization by setting different range constraints for design variables
图 18: 设计变量不同范围约束下的增量动力分析设计优化结果Fig. 18. Results of IDA-based design optimization by setting different range constraints for design variables
图 19: 优化设计前后的极限状态 1 易损性曲线对比Fig. 19. Comparison of the LS1 fragility curves before and after optimization design
作者信息 | Authors
北京工业大学 (Beijing University of Technology) 桥梁工程安全与韧性全国重点实验室
北京工业大学 (Beijing University of Technology) 桥梁工程安全与韧性全国重点实验室
傅金龙 Jin-Long Fu, 通讯作者 (Corresp.)英国伦敦玛丽女王大学 (Queen Mary University of London) 科学与工程学院Email: jinlong.fu@qmul.ac.uk
北京工业大学 (Beijing University of Technology) 桥梁工程安全与韧性全国重点实验室
北京工业大学 (Beijing University of Technology) 桥梁工程安全与韧性全国重点实验室
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
