多目标模糊优化在桥梁设计中的应用

发布时间：2018-02-11 19:12

本文关键词： 多目标模糊优化遗传算法优化设计　出处：《重庆师范大学》2017年硕士论文　论文类型：学位论文

【摘要】：在现实生活中,一个复杂的系统往往具有多样性、多维性、多准则性和不确定性。处理这些问题时,多目标模糊优化就成了一种非常重要的数学工具。本文以桥梁优化设计为背景,研究了桥梁设计中以工程造价最小且全截面刚度最大(截面模量最大)为目标函数的多目标模糊优化模型,并给出了两类桥型的工程算例,进行了模型求解。所得结果与传统设计方法比对具有较强的经济实用价值。本文首先从多目标模糊优化的研究背景与意义入手,详细地阐述了模糊优化设计的基本概况,并概括了多目标模糊优化理论的研究现状,着重探讨了多目标模糊优化理论在桥梁设计中的应用。然后归纳总结了桥梁多目标模糊优化求解的一般步骤,并以等截面普通钢筋混凝土简支T梁和等截面小钢箱梁为例,分析了桥梁设计中的设计变量、目标函数、约束条件这三大要素,建立了等截面普通钢筋混凝土简支T梁和小钢箱梁模糊优化的多目标模糊优化模型。最后以等截面普通钢筋混凝土简支T梁和等截面小钢箱梁为工程算例,并利用二级综合模糊评判法求解最优水平截集,构造模糊目标集、隶属函数,并用遗传算法求解全局最优解,将多目标模糊优化求解的结果与传统经验模型的结果进行了对比。
[Abstract]:In real life, a complex system often has diversity, multidimensionality, multicriteria and uncertainty. Multi-objective fuzzy optimization has become a very important mathematical tool. In this paper, a multi-objective fuzzy optimization model with minimum engineering cost and maximum cross-section stiffness (maximum cross-section modulus) as objective function is studied, and two kinds of bridge engineering examples are given. The model is solved. Compared with the traditional design method, the results obtained are of great economic and practical value. Firstly, this paper starts with the background and significance of multi-objective fuzzy optimization, and expounds the basic situation of fuzzy optimization design in detail. The research status of multi-objective fuzzy optimization theory is summarized, and the application of multi-objective fuzzy optimization theory in bridge design is emphatically discussed. Then, the general steps of solving multi-objective fuzzy optimization theory are summarized. Taking the T-beam and small steel box girder with equal section as examples, the design variables, objective function and constraint conditions of bridge design are analyzed. A multi-objective fuzzy optimization model for the fuzzy optimization of simple supported T beam and small steel box girder with equal section is established. Finally, an engineering example of T beam and small steel box girder with equal section is presented. The two-level comprehensive fuzzy evaluation method is used to solve the optimal horizontal cut set, the fuzzy objective set and membership function are constructed, and the global optimal solution is solved by genetic algorithm. The results of multi-objective fuzzy optimization are compared with those of the traditional empirical model.
【学位授予单位】：重庆师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159;U442.5

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