基于CMAES雜交算法的鋼筋混凝土框架結(jié)構(gòu)優(yōu)化設(shè)計研究
發(fā)布時間：2018-08-20 13:10
【摘要】：鋼筋混凝土框架結(jié)構(gòu)設(shè)計既要滿足安全性、適用性、耐久性的結(jié)構(gòu)性要求,又應(yīng)滿足結(jié)構(gòu)體系受力合理、材料用量盡可能少的經(jīng)濟性要求。現(xiàn)行“試算—驗證—修改”的設(shè)計方法,得到的設(shè)計方案不一定是滿足規(guī)范要求的最優(yōu)方案。結(jié)構(gòu)優(yōu)化設(shè)計是結(jié)構(gòu)設(shè)計理論的重要發(fā)展,其思想內(nèi)涵不僅僅是追求體積最小或重量最輕,更重要的是要達到一種資源合理的優(yōu)化配置,調(diào)和當今城市化進程中,建筑行業(yè)發(fā)展與經(jīng)濟、資源、環(huán)境之間的矛盾。結(jié)構(gòu)優(yōu)化理論的研究歷史悠久,在很多領(lǐng)域得到了成功應(yīng)用,并且開發(fā)了許多具有優(yōu)化功能的大型有限元軟件。然而,針對鋼筋混凝土框架結(jié)構(gòu)的優(yōu)化算法研究及應(yīng)用還相對匾乏。這一方面是由于鋼筋混凝土框架結(jié)構(gòu)優(yōu)化設(shè)計是多工況、多變量、多約束和多目標的復(fù)雜的優(yōu)化問題,且存在大量的不確定性(如荷載、構(gòu)件材料與尺寸、分析模型等);另一方面?zhèn)鹘y(tǒng)優(yōu)化算法掙扎于全局勘探和局部開發(fā)能力的平衡,受限于復(fù)雜結(jié)構(gòu)分析計算量大的特點。這些都給建立全面、實用的鋼筋混凝土框架結(jié)構(gòu)優(yōu)化設(shè)計算法帶來了挑戰(zhàn)。本文針對鋼筋混凝土結(jié)構(gòu)優(yōu)化設(shè)計存在的一系列問題,以CMAES算法為基本工具,在充分分析鋼筋混凝土結(jié)構(gòu)優(yōu)化設(shè)計模型的基礎(chǔ)上,開展了雜交優(yōu)化算法的研究。本文主要完成以下創(chuàng)新工作:(1)利用虛功原理,建立結(jié)構(gòu)位移響應(yīng)與設(shè)計變量間的顯式關(guān)系。在基于位移的抗震設(shè)計原理上,提出約束條件的兩種形式:目標位移約束條件和約束位移約束條件。采用非線性規(guī)劃算法和CMAES算法求解優(yōu)化模型。對比不同目標位移形狀對優(yōu)化結(jié)果的影響,給出了基于位移的抗震設(shè)計方法的結(jié)構(gòu)優(yōu)化設(shè)計模型。(2)結(jié)合DE算法和CMAES算法的性能,構(gòu)建自適應(yīng)子群體策略,實現(xiàn)了CMAES群體協(xié)助DE群體開發(fā)最優(yōu)解,DE群體協(xié)助CMAES群體勘探有潛力區(qū)域。提出了自適應(yīng)子群體雜交算法(Sa S-MA),成功求解了數(shù)值試驗平臺和鋼筋混凝土結(jié)構(gòu)線性優(yōu)化設(shè)計問題。與目前公認的算法對比,驗證了自適應(yīng)子群體算法的有效性,分析了算法參數(shù)對優(yōu)化性能的影響,并給出了參數(shù)的建議值。(3)充分分析了鋼筋混凝土結(jié)構(gòu)非線性優(yōu)化設(shè)計的特點,將設(shè)計變量劃分為離散變量和連續(xù)變量。結(jié)合PSO算法和CMAES算法的搜索性能,提出了兩階段自適應(yīng)雜交算法(AHA)分別優(yōu)化兩類變量。設(shè)計了開關(guān)操作實現(xiàn)了設(shè)計過程的兩階段劃分和變量降維。提出了一種處理結(jié)構(gòu)非線性分析失敗的約束條件,避免了奇異點對算法性能的影響。建立了應(yīng)變約束條件,增強了鋼筋混凝土結(jié)構(gòu)非線性分析的穩(wěn)定性。通過兩個鋼筋混凝土框架的非線性優(yōu)化設(shè)計算例,驗證了算法的有效性。(4)根據(jù)kriging模型的近似特點,提出了自更新kriging模型。借助于CMAES算法,自更新kriging模型實現(xiàn)了精煉操作。采用自更新kriging模型代替鋼筋混凝土結(jié)構(gòu)非線性分析程序,克服了鋼筋混凝土結(jié)構(gòu)非線性分析計算量大的缺點。通過兩個鋼筋混凝土結(jié)構(gòu)非線性優(yōu)化設(shè)計算例,驗證了算法的有效性。在對比研究的基礎(chǔ)上給出了算法關(guān)鍵參數(shù)的建議值。(5)利用大種群規(guī)模的CMAES算法和雙循環(huán)框架,建立了鋼筋混凝土框架結(jié)構(gòu)基于可靠度的優(yōu)化設(shè)計方法。為克服雙循環(huán)可靠度優(yōu)化設(shè)計方法中計算量大的缺點,建立了RBDO-kriging模型,實現(xiàn)設(shè)計變量和隨機變量的統(tǒng)一近似。采用CMAES算法確定設(shè)計變量精煉區(qū)域,采用可靠指標法確定隨機變量精煉區(qū)域,實現(xiàn)了RBDO-kriging模型在CMAES搜索區(qū)域內(nèi)的精煉操作。數(shù)值算例和鋼筋混凝土結(jié)構(gòu)優(yōu)化設(shè)計算例驗證了算法的性能,在對比分析的基礎(chǔ)上給出了關(guān)鍵參數(shù)的取值建議。
[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.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TU375.4
本文編號：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.
【學(xué)位授予單位】：華南理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2014
【分類號】：TU375.4
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相關(guān)期刊論文 前2條
1 Eysa Salajegheh;Saeed Gholizadeh;Mohsen Khatibinia;;Optimal design of structures for earthquake loads by a hybrid RBF-BPSO method[J];Earthquake Engineering and Engineering Vibration;2008年01期
2 劉波;王凌;金以慧;;差分進化算法研究進展[J];控制與決策;2007年07期
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