建筑结构与控制系统并行设计研究

Improving Collateral Design of Structure and Control System

针对随机激励下的以结构参数为变量、以控制输入力最小化为优化目标的建筑结构和控制系统并行设计问题,设计了一种基于线性矩阵不等式工具的并行优化算法。该算法在以下2个方面突破了现有算法的局限性:①将质量矩阵纳入优化变量,拓宽了优化范围;②采用凸化势能函数处理将控制引入结构设计导致的非凸约束,大大降低了算法复杂度。算例分析显示该算法能有效提高建筑结构的设计效能。

Purpose. The method in Lu and Skelton＇s paper is, in our opinion, still too slow. We now propose a parallel algorithm, based on LMI （Linear Matrix Inequality）, which can be more efficient. Based on LMI, a parallel algorithm, which is used to solve the optimal problem under stochastic activation to get the minimum of control energy by changing the value of structure parameters, is presented to design the structure and control system simultaneously. This algorithm overcomes the deficiency of present methods in two aspects. （1） by introducing the mass matrix into optimal variable, the method broadens the range of the optimization; （2）in order to solve the optimal problem with nonconvex constraint induced by control in structure, we use convexifying potential function to make the nonconvex constraint part to be convex, thus reducing the complexity of the algorithm greatly. Finally we give a numerical example, whose results are given in Table 1 and Figs. 3 and 4 in the full paper;These results prove that our parallel algorithm can improve the efficiency of the collateral design.