多级递阶工程结构系统抗地震设计的全局优化

GLOBAL OPTIMIZATION OF ANTI-SEISMIC DESIGN FOR MULTILEVEL HIERARCHICAL ENGINEERING STRUCTURE SYSTEMS

多级递阶工程结构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系列,表征了常见建设项目的一般性分布。以结构设防烈度为决策变量、地震灾害的多级设防为工程背景,建立了该系统全局优化的数学模型;考虑到系统的结构特点和目标函数的离散性,提出二个层次的优化计算方法,其中递级凝聚法用于大系统建模分析,改进的离散型共轭梯度法和改进的离散型 Lagrange 直接法分别执行具体的最优或次优化计算;算例讨论了复杂项目在抗震设防标准、工程造价和总投资分配方面的优化决策。上述概念、原则与方法为复杂工程的系统化设计、土木工程问题的科学决策提供了理论分析的基础。

The multilevel hierarchical engineering structure system is defined as a structural series of multilevel branching and general distribution of structures, that is characterized by main engineering structures in a complex construction project of functionally logical relationships. Under the engineering background of multilevel aseismic design and the case where structural earthquake fortification intensities are used as variables, programming models for the global optimization of the system are established in this paper. Meanwhile, two levels of global optimization methods, including a hierarchical condensation method and two modified minimizing approaches, are put forward to overcome the discreteness of objective functions as well as the complexity of the system. The former is employed for the analysis of system modeling; and the latter, with a modified conjugate gradient method and a modified Lagrange direct method, is utilized to evaluate unconstrained and constrained minimization, respectively. An example is presented to demonstrate the optimization of the near-optimum earthquake fortification criterion, construction cost, and allocation of total investment of a complex construction project. Concepts, principles and methods proposed in this paper can provide a basis of theoretical analysis of the systematized design of complex construction projects, and the scientific decision-making in civil engineering as well.