Arch bridge axis optimization design based on Kriging-SBO

MAO Xingbo; SHENG Dongfa; LI Zhongjun; ZHU Jun

doi:10.13471/j.cnki.acta.snus.2022D063

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Arch bridge axis optimization design based on Kriging-SBO

Research articles | 更新时间：2023-11-01

- Arch bridge axis optimization design based on Kriging-SBO
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 4, Pages: 139-146(2023)
- 作者机构：
  
  西南林业大学土木工程学院，云南昆明 650224
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022D063
  CLC： U448.22
- Published：25 July 2023，
  
  Received：08 June 2022，
  
  Accepted：08 November 2022
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毛星波,盛冬发,李忠君等.基于Kriging-SBO算法的拱桥拱轴线优化设计[J].中山大学学报(自然科学版),2023,62(04):139-146.

MAO Xingbo,SHENG Dongfa,LI Zhongjun,et al.Arch bridge axis optimization design based on Kriging-SBO[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(04):139-146.
毛星波,盛冬发,李忠君等.基于Kriging-SBO算法的拱桥拱轴线优化设计[J].中山大学学报(自然科学版),2023,62(04):139-146. DOI： 10.13471/j.cnki.acta.snus.2022D063.

MAO Xingbo,SHENG Dongfa,LI Zhongjun,et al.Arch bridge axis optimization design based on Kriging-SBO[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(04):139-146. DOI： 10.13471/j.cnki.acta.snus.2022D063.

摘要

为对比设计空间内的所有拱轴方案，得到最佳及可能存在的其他较好可行拱轴设计，以拱轴应力分布为优化目标，提出一套基于Kriging代理模型的拱轴优化方法。该方法用Kriging模型来显式表达应力优化目标与设计变量之间的隐函数关系，同时采用以改善期望准则（EI准则）为加点准则、粒子群优化（PSO， particle swarm optimization）算法为子优化求解算法的SBO（surrogate-based optimization）算法作为目标函数的寻优算法。对圆弧、抛物、悬链，以及3次样条拱轴曲线函数进行分析，确定了这4种常用拱轴线的待优化设计变量；同时给出了表征拱轴全局应力水平的目标函数值的计算方法和拱轴优化的具体流程。最后，对工程算例进行了探索优化，并对优化细节与结果进行了说明与讨论。结果表明：这一方法能得到设计空间内最佳及其他较好可行拱轴设计，其中最佳设计的3次样条拱轴线使算例拱轴最大应力减小67%，关键截面应力方差减小97%。研究能为拱轴选形提供更多选择，也对以应力为目标的拱桥拱轴线优化具有参考意义。

Abstract

To optimize the design of the arch axis of bridges， we propose a scheme with a set of Kriging surrogate models focusing on the stress distribution of axes. The Kriging model is used to express the implicit function relationship between stress-optimizing objective and design variables. Meanwhile， the Surrogate-Based Optimization （SBO） algorithm with Expected Improvement （EI） criterion is adopted as the infill sampling criterion and the Particle Swarm Optimization （PSO） algorithm is selected as a sub-optimization algorithm. By analyzing the curve functions of circle， parabolic， catenary， and cubic spline， the variables to be optimized for these common arch axes were determined. The calculation method of objective function value which can represent the global stress level of the arch axis and the specific flow of optimization are presented. An engineering example is analyzed which verifies the feasibility of the scheme. The results show that the best arch-axis design of cubic spline reduces the maximum stress of the arch by 67% and the stress variance of the key section by 97%. Our study provides more options for the shape design of arch bridges and also has reference significance for the optimization of the arch axis with stress as the target.

关键词

桥梁工程拱轴优化Kriging模型改善期望准则粒子群优化算法

Keywords

bridge engineeringoptimization of arch axisKriging modelexpected improvement criterionparticle swarm optimization

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