多级递阶工程系统抗地震设计全局优化的对偶分解法
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摘要
多级递阶工程系统是复杂工程项目的主要工程结构依照功能逻辑关系所构成的多层次分支结构体系,表征了常见复杂项目的一般性分布。以结构设防烈度为优化指标,以抗地震设计为工程背景,本文针对该系统结构特点,提出全局优化方法两个层次划分的概念;然后从Lagrange对偶理论出发,提出第一层次的对偶分解法和分解-协调法,结合第二层次的离散型最优化方法,分别实现大系统约束、无约束全局优化的有效计算。算例讨论了复杂项目在最优设防标准、最优造价和总投资最优分配三个方面的工程决策,并与其他方法的结果作了比较。上述概念与方法使大系统整体优化空间达到高度的降维,为复杂工程项目的系统化设计、工程问题的科学决策奠定了理论分析的基础。
The multilevel hierarchical engineering system is defined as a multilevel branching structural series, that consists of main engineering structures in a complex engineering project by functionally logical relations.It indicates the general distribution of the common complex projects. Under the engineering background of anti seismic design and the case where structural earthquake fortification intensities are used as variables, the concept that two levels of minimizing approaches will be introduced into processes of the global optimization of the complicated system is proposed in this paper. Meanwhile, according to Lagrange dual theory, two methods on the first level, the dual decomposition method and the decomposition coordination method, are put forward and employed, combined with those discrete methods on the second level, for the evaluation of unconstrained and constrained global minimization respectively. An example is presented to demonstrate the high efficiency and accuracy of the proposed methods in the practical use of the globally optimal decision for the global earthquake protection criterion, construction cost, and allocation of total investment of a complex engineering project. Concepts and methods proposed in this paper greatly reduce the spatial dimension to be solved, and would provide a basis of theoretical analysis for the systematizing design of complex engineering projects and scientific decisions in engineering as well.
The multilevel hierarchical engineering system is defined as a multilevel branching structural series, that consists of main engineering structures in a complex engineering project by functionally logical relations.It indicates the general distribution of the common complex projects. Under the engineering background of anti seismic design and the case where structural earthquake fortification intensities are used as variables, the concept that two levels of minimizing approaches will be introduced into processes of the global optimization of the complicated system is proposed in this paper. Meanwhile, according to Lagrange dual theory, two methods on the first level, the dual decomposition method and the decomposition coordination method, are put forward and employed, combined with those discrete methods on the second level, for the evaluation of unconstrained and constrained global minimization respectively. An example is presented to demonstrate the high efficiency and accuracy of the proposed methods in the practical use of the globally optimal decision for the global earthquake protection criterion, construction cost, and allocation of total investment of a complex engineering project. Concepts and methods proposed in this paper greatly reduce the spatial dimension to be solved, and would provide a basis of theoretical analysis for the systematizing design of complex engineering projects and scientific decisions in engineering as well.
引文
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犤6犦JinghuaZhuandHuiyuXue.TransientAnalysisofGeomet-ricallyLinearandNonlinearStructuresbyaCombinedFinite-element-Riccati-transferSubstructureMethod犤J犦.Int.J.NumericalMethodsinEngineering,1993,36(9):1509-1518.
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犤11犦朱靖华,王光远.多级递阶工程结构系统抗地震设计全局优化的科学机制犤J犦.系统工程增刊,2001:8-15.
犤2犦朱靖华.多级递阶工程系统的全局优化犤D犦.哈尔滨工业大学,1999.
犤3犦王光远,顾平,吕大刚.基于规范和最优设防烈度的抗地震结构优化设计犤J犦.土木工程学报,1999,(2).
犤4犦王光远.简单工程系统抗地震设计全局优化的直接解法犤J犦.土木工程学报,1998,(6):7-15.
犤5犦王光远,朱靖华.简单复合工程系统抗地震设计的全局优化犤J犦.哈尔滨建筑大学学报,1999,(3):1-7.
犤6犦JinghuaZhuandHuiyuXue.TransientAnalysisofGeomet-ricallyLinearandNonlinearStructuresbyaCombinedFinite-element-Riccati-transferSubstructureMethod犤J犦.Int.J.NumericalMethodsinEngineering,1993,36(9):1509-1518.
犤7犦MJamshidi.LargeScaleSystemsModelingandControl犤M犦.NorthHolland,NewYork,1983:63-124.
犤8犦王光远,朱靖华.地震作用下串、并联工程系统中结构失效相关性的近似处理犤J犦.地震工程与工程振动,1998,(4):15-24.
犤9犦IJNagrath,MGopal.ControlSystemsEngineering犤M犦.HalstedPress,ADivisionofJohnWiley&Sons,Inc.,NewYork,1982:73-128.
犤10犦朱道立.大系统优化理论与应用犤M犦.上海:上海交通大学出版社,1987:175-179.
犤11犦朱靖华,王光远.多级递阶工程结构系统抗地震设计全局优化的科学机制犤J犦.系统工程增刊,2001:8-15.
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