动力吸振器的多目标优化和多属性决策研究

Multi-objective optimization and multi-attribute decision making study of dynamic vibration absorber

在结构振动控制中,为了最大限度发挥吸振器的耗能减振作用,需要寻找吸振器的最优参数,即最优频率比、最优阻尼比和最优质量比,使得结构在不同的频率激励下获得最好的减振效果。本文将基于进化算法的多目标优化技术与多属性决策方法联合运用,针对主系统存在阻尼的减振系统,研究了动力吸振器的优化和决策问题。对于多目标优化问题,采用改进的非支配解排序的多目标进化算法(NSGA Ⅱ),求出Pareto最优解,由这些Pareto最优解构成决策矩阵,使用客观赋权的信息熵方法对最优解的属性进行权值计算,然后用逼近理想解的排序方法(TOPSIS)进行多属性决策(MADM)研究,对Pareto最优解给出排序。文中给出了4个设计参数、3个目标函数的动力吸振器优化设计算例。

When dynamic vibration absorber （DVA） is used in structural passive control, its optimal parameters, such as frequency ratio, damping ratio and mass ratio should be computed to reduce the vibration of main system. A hybrid approach for multi-objective optimization study of DVA is proposed in present analysis. In the first stage, a Non-dominated Sorting Genetic Algorithm Ⅱ （NSGA Ⅱ） is employed to approximate the set of Pareto solution through an evolutionary optimization process. In the subsequent stage, a multi-attribute decision making （MADM） approach is adopted to rank these solutions from best to worst and to determine the best solution in a deterministic environment with a single decision maker. A DVA example, in which four design parameters and three optimization objectives are included, is conducted to illustrate the analysis process in present study. Pareto frontiers are obtained and the ranking of Pareto solution is based on entropy weighting and TOPSIS method.