中文摘要：

针对自适应压电桁架结构振动控制，建立了作动器／传感器优化配置数学模型，并提出一种优化配置的新方法。为了减少结构分析次数，该方法将近似概念、对偶法和遗传算法相结合，首先采用多点近似技术建立原问题的序列近似问题，再对近似问题中的作动器／传感器位置离散变量和控制增益连续变量采用遗传算法和对偶方法分别寻优的分层优化策略。为了提高近似问题对原问题的逼近程度，本文提出一种适于离散变量结构优化的分段多点近似函数。算例表明本文方法能够以很少的结构分析次数得到最优解。

英文摘要：

A mathematical model of actuators/sensors optimized placements is built up for vibration control of adaptive piezoelectric truss structure, and a new method of optimal placements is proposed in this paper. In the method, the approximation concepts, dual method and genetic algorithm are adopted to decrease the number of structural analysis. Firstly, a series of approximate problems are created through the multi-point approximate function, and then a layered optimization method is used, in the outside layer the actuator placement variables are optimized through the genetic algorithm, and in the inside layer the control augment variables are optimized through the dual method. In order to improve the approximation quality to the original problem, a new combined multi-point approximation is proposed to create the first-level approximate problems. The results of a truss example show that the proposed method can bring out the optimum solutions after an extremely few times of structural analysis.