一种确定压电传感器位置的拓扑优化方法

基于可观矩阵奇异值单元灵敏度的思想，提出了确定智能压电传感器安放位置的一种拓扑优化方法。为了获得智能结构压电传感器的优化位置，首先采用有限元方法对原系统进行了特征问题分析；第二利用奇异值分解法讨论了智能结构模态可观性的度量问题；第三推导了可观矩阵奇异值单元灵敏度公式；第四以奇异值单元灵敏度作为度量和准则并且给出一个门槛值，根据门槛值可以确定压电传感器优化位置；最后利用算例来说明本文方法的有效性。

A Topological Optimal Method of Determining Locations of The Piezoelectric Sensors

On the basis of element sensitivities of the observable matrix singular-values,a technique to determine the locations of piezoelectric sensors of intelligent structures is presented in this paper In order to obtain optimal locations of sensors of intelligent structures,steps are taken as follows:firstly,a modal analysis of the initial structure is carried out with piezoelectric sensors on the given domain ;secondly,the observable modes corresponding to singular-values are taken with the singular-value decomposition method;thirdly,formulation of the element sensitivity of the singular-value of controllability is developed;fourthly,the element sensitivity of the singular-values is chosen as the measure and the criterion to determine optimal locations of sensors A threshold value is given and optimal procedure is presented to determine which sensor element needs to be kept/removed based on the sensitivity information Locations of sensors are determined as the point where the element sensitivities of the singular-values are maximum One numerical example is taken to illustrate the applications of the present method