基于混合编码遗传算法和有限元分析的压电结构载荷识别

Load identification of piezoelectric structures by using genetic algorithm and finite element analysis

与传统的优化算法相比,遗传算法不需要计算目标函数的导数信息,便于迭代,可实现全局寻优。因此,本文提出一种采用混合编码的遗传算法与有限元分析相结合,对复合材料层合板、壳进行载荷识别的新方法。在遗传算法求解过程中,设计变量的编码方法选择是其重要环节,二进制编码容易产生连续函数离散化时的映射误差,且其求解精度与染色体的编码长度紧密相关,过长的染色体描述虽可提高精度,但会显著降低算法的求解效率。为此,本文提出采用混合编码的方法进行载荷识别,即用二进制编码表征载荷作用位置,浮点数编码表示载荷的大小。这一方法大大降低了染色体的长度,并显著提高了计算效率和精度。

In this paper, a new approach is presented for solving the problems of load identification, which combines the genetic algorithm（GA） and finite element analysis. As compared with the traditional optimization and search algorithms, GA search from a population of points in the region of the whole solution space, rather than a single point, and can obtain the global optimum. Moreover, GA has the ad vantage of easy implementation, because only an objective function is required and derivatives or other auxiliary information are not necessary. To implement the genetic algorithm for the determination of the optimal design, it is necessary first to devise a general coding system for the representation of the design variables. Most commonly the design variables are coded by a bit-string and the fact that, with this binary representation, the design variables can be coded only as integers, means that there will be usually loss of precision due to the binary representation and the length of each chromosome as well as the population of chromosomes must be very huge in order to obtain a relatively accurate model. In this paper, the location and magnitude of the load are coded with binary string and real number representation, respectively; therefore, the chromosome length will be substantially shorter, which greatly reduces the computational effort.