基于CMAES杂交算法的钢筋混凝土框架结构优化设计研究
发布时间：2018-08-20 13:10
【摘要】：钢筋混凝土框架结构设计既要满足安全性、适用性、耐久性的结构性要求,又应满足结构体系受力合理、材料用量尽可能少的经济性要求。现行“试算—验证—修改”的设计方法,得到的设计方案不一定是满足规范要求的最优方案。结构优化设计是结构设计理论的重要发展,其思想内涵不仅仅是追求体积最小或重量最轻,更重要的是要达到一种资源合理的优化配置,调和当今城市化进程中,建筑行业发展与经济、资源、环境之间的矛盾。结构优化理论的研究历史悠久,在很多领域得到了成功应用,并且开发了许多具有优化功能的大型有限元软件。然而,针对钢筋混凝土框架结构的优化算法研究及应用还相对匾乏。这一方面是由于钢筋混凝土框架结构优化设计是多工况、多变量、多约束和多目标的复杂的优化问题,且存在大量的不确定性(如荷载、构件材料与尺寸、分析模型等);另一方面传统优化算法挣扎于全局勘探和局部开发能力的平衡,受限于复杂结构分析计算量大的特点。这些都给建立全面、实用的钢筋混凝土框架结构优化设计算法带来了挑战。本文针对钢筋混凝土结构优化设计存在的一系列问题,以CMAES算法为基本工具,在充分分析钢筋混凝土结构优化设计模型的基础上,开展了杂交优化算法的研究。本文主要完成以下创新工作:(1)利用虚功原理,建立结构位移响应与设计变量间的显式关系。在基于位移的抗震设计原理上,提出约束条件的两种形式:目标位移约束条件和约束位移约束条件。采用非线性规划算法和CMAES算法求解优化模型。对比不同目标位移形状对优化结果的影响,给出了基于位移的抗震设计方法的结构优化设计模型。(2)结合DE算法和CMAES算法的性能,构建自适应子群体策略,实现了CMAES群体协助DE群体开发最优解,DE群体协助CMAES群体勘探有潜力区域。提出了自适应子群体杂交算法(Sa S-MA),成功求解了数值试验平台和钢筋混凝土结构线性优化设计问题。与目前公认的算法对比,验证了自适应子群体算法的有效性,分析了算法参数对优化性能的影响,并给出了参数的建议值。(3)充分分析了钢筋混凝土结构非线性优化设计的特点,将设计变量划分为离散变量和连续变量。结合PSO算法和CMAES算法的搜索性能,提出了两阶段自适应杂交算法(AHA)分别优化两类变量。设计了开关操作实现了设计过程的两阶段划分和变量降维。提出了一种处理结构非线性分析失败的约束条件,避免了奇异点对算法性能的影响。建立了应变约束条件,增强了钢筋混凝土结构非线性分析的稳定性。通过两个钢筋混凝土框架的非线性优化设计算例,验证了算法的有效性。(4)根据kriging模型的近似特点,提出了自更新kriging模型。借助于CMAES算法,自更新kriging模型实现了精炼操作。采用自更新kriging模型代替钢筋混凝土结构非线性分析程序,克服了钢筋混凝土结构非线性分析计算量大的缺点。通过两个钢筋混凝土结构非线性优化设计算例,验证了算法的有效性。在对比研究的基础上给出了算法关键参数的建议值。(5)利用大种群规模的CMAES算法和双循环框架,建立了钢筋混凝土框架结构基于可靠度的优化设计方法。为克服双循环可靠度优化设计方法中计算量大的缺点,建立了RBDO-kriging模型,实现设计变量和随机变量的统一近似。采用CMAES算法确定设计变量精炼区域,采用可靠指标法确定随机变量精炼区域,实现了RBDO-kriging模型在CMAES搜索区域内的精炼操作。数值算例和钢筋混凝土结构优化设计算例验证了算法的性能,在对比分析的基础上给出了关键参数的取值建议。
[Abstract]:The design of reinforced concrete frame structure should not only satisfy the structural requirements of safety, applicability and durability, but also satisfy the economic requirements of reasonable stress on the structure system and minimum material consumption. Optimal design is an important development of structural design theory. Its ideological connotation is not only to pursue the smallest volume or the lightest weight, but also to achieve a rational allocation of resources, to reconcile the contradiction between the development of the construction industry and the economy, resources and environment in the process of urbanization. Many fields have been successfully applied and many large-scale finite element software with optimization functions have been developed. However, the research and application of optimization algorithms for reinforced concrete frame structures are relatively scarce. On the other hand, traditional optimization algorithms struggle with the balance of global exploration and local development capability, which is limited by the large amount of calculation and analysis of complex structures. All these give a comprehensive and practical optimization design of reinforced concrete frame structures. In view of a series of problems existing in the optimization design of reinforced concrete structures, this paper takes CMAES algorithm as the basic tool and carries out the research of hybrid optimization algorithm on the basis of fully analyzing the optimization design model of reinforced concrete structures. Based on the displacement-based seismic design principle, two kinds of constraints are proposed: target displacement constraints and constraint displacement constraints. Nonlinear programming algorithm and CMAES algorithm are used to solve the optimization model. (2) Combining the performance of DE algorithm and CMAES algorithm, an adaptive subgroup strategy is constructed to realize the optimal solution of CMAES group assisting DE group and the potential area of DE group assisting CMAES group exploration. The validity of the adaptive subgroup algorithm is verified by comparing with the commonly accepted algorithm. The influence of the algorithm parameters on the optimization performance is analyzed, and the recommended values of the parameters are given. (3) The characteristics of the nonlinear optimization design of reinforced concrete structures are fully analyzed, and the design will be carried out. Variables are divided into discrete variables and continuous variables.Combining the searching performance of PSO algorithm and CMAES algorithm,a two-stage adaptive hybrid algorithm(AHA) is proposed to optimize two types of variables respectively.Switching operation is designed to realize two-stage partitioning and variable dimensionality reduction in the design process.A constraint condition to deal with the failure of structural nonlinear analysis is proposed. In order to avoid the influence of singularities on the performance of the algorithm, the strain constraints are established and the stability of nonlinear analysis of reinforced concrete structures is enhanced. The effectiveness of the algorithm is verified by two examples of nonlinear optimization design of reinforced concrete frames. (4) According to the approximate characteristics of the Kriging model, a self-renewal Kriging model is proposed. In the CMAES algorithm, the self-renewal Kriging model is used to realize the refining operation. The self-renewal Kriging model is used to replace the non-linear analysis program of reinforced concrete structure to overcome the disadvantage of large amount of calculation in the non-linear analysis of reinforced concrete structure. Proposed values of key parameters of the algorithm are given on the basis of comparison study. (5) A reliability-based optimization design method for reinforced concrete frame structures is established by using large population-scale CMAES algorithm and double-cycle frame. To overcome the disadvantage of large amount of calculation in the double-cycle reliability optimization design method, a RBDO-kriging model is established to realize the design. The refinement region of design variables is determined by CMAES algorithm, and the refinement region of random variables is determined by reliability index method. The refinement operation of RBDO-kriging model in the CMAES search region is realized. The performance of the algorithm is verified by numerical examples and optimization design examples of reinforced concrete structures. Based on the analysis, suggestions for the key parameters are given.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU375.4
本文编号：2193725
[Abstract]:The design of reinforced concrete frame structure should not only satisfy the structural requirements of safety, applicability and durability, but also satisfy the economic requirements of reasonable stress on the structure system and minimum material consumption. Optimal design is an important development of structural design theory. Its ideological connotation is not only to pursue the smallest volume or the lightest weight, but also to achieve a rational allocation of resources, to reconcile the contradiction between the development of the construction industry and the economy, resources and environment in the process of urbanization. Many fields have been successfully applied and many large-scale finite element software with optimization functions have been developed. However, the research and application of optimization algorithms for reinforced concrete frame structures are relatively scarce. On the other hand, traditional optimization algorithms struggle with the balance of global exploration and local development capability, which is limited by the large amount of calculation and analysis of complex structures. All these give a comprehensive and practical optimization design of reinforced concrete frame structures. In view of a series of problems existing in the optimization design of reinforced concrete structures, this paper takes CMAES algorithm as the basic tool and carries out the research of hybrid optimization algorithm on the basis of fully analyzing the optimization design model of reinforced concrete structures. Based on the displacement-based seismic design principle, two kinds of constraints are proposed: target displacement constraints and constraint displacement constraints. Nonlinear programming algorithm and CMAES algorithm are used to solve the optimization model. (2) Combining the performance of DE algorithm and CMAES algorithm, an adaptive subgroup strategy is constructed to realize the optimal solution of CMAES group assisting DE group and the potential area of DE group assisting CMAES group exploration. The validity of the adaptive subgroup algorithm is verified by comparing with the commonly accepted algorithm. The influence of the algorithm parameters on the optimization performance is analyzed, and the recommended values of the parameters are given. (3) The characteristics of the nonlinear optimization design of reinforced concrete structures are fully analyzed, and the design will be carried out. Variables are divided into discrete variables and continuous variables.Combining the searching performance of PSO algorithm and CMAES algorithm,a two-stage adaptive hybrid algorithm(AHA) is proposed to optimize two types of variables respectively.Switching operation is designed to realize two-stage partitioning and variable dimensionality reduction in the design process.A constraint condition to deal with the failure of structural nonlinear analysis is proposed. In order to avoid the influence of singularities on the performance of the algorithm, the strain constraints are established and the stability of nonlinear analysis of reinforced concrete structures is enhanced. The effectiveness of the algorithm is verified by two examples of nonlinear optimization design of reinforced concrete frames. (4) According to the approximate characteristics of the Kriging model, a self-renewal Kriging model is proposed. In the CMAES algorithm, the self-renewal Kriging model is used to realize the refining operation. The self-renewal Kriging model is used to replace the non-linear analysis program of reinforced concrete structure to overcome the disadvantage of large amount of calculation in the non-linear analysis of reinforced concrete structure. Proposed values of key parameters of the algorithm are given on the basis of comparison study. (5) A reliability-based optimization design method for reinforced concrete frame structures is established by using large population-scale CMAES algorithm and double-cycle frame. To overcome the disadvantage of large amount of calculation in the double-cycle reliability optimization design method, a RBDO-kriging model is established to realize the design. The refinement region of design variables is determined by CMAES algorithm, and the refinement region of random variables is determined by reliability index method. The refinement operation of RBDO-kriging model in the CMAES search region is realized. The performance of the algorithm is verified by numerical examples and optimization design examples of reinforced concrete structures. Based on the analysis, suggestions for the key parameters are given.
【学位授予单位】：华南理工大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TU375.4
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