缩短数值优化寻优过程计算机时的一种有效方法

An Efficient Method of Reduce Computer Time for Numerical Optimization

为了改良大型系统的频谱而作的设计修改,通常需要多次求解大型特征值问题,而这一计算机过程十分冗繁费时。本文提出的方法,不仅有效地解决了这一繁难,还可预言设计修改对多自由度机械系统的影响。本文介绍了采用有限单元预处理方法和泰勒级数近似方法把特征值和特征矢量近似地表达为设计变动量的一个函数。这样,进行最优化再设计的迭代过程,总共只需要O(n^2)次计算。相对于特征值问题的O(n^3)次计算工作量,本文的方法大大缩短了计算机时。分析计算实例证明了这一近似方法适用于很广范围内的设计变动。

The design modifications for improving the frequency spectrum of a systemrequire usually many solutions of large eigenvalue problems, this has been computa-tionally burdensome. An efficient method introduced here is not only solving problem properly, butalso able to predict the effect of design modifications on the mechanical systemwith a large number of DOF. Using a finite element preprocessor and the Taylorseries, the eigenvalues and eigenvectors may be presented as a function of designchanges. The optimization process for redesigning requires only O(n^2) calculations,opposed to O(n^3) for every eigenvalue problem, this method is more efficient. Applied examples indicated this approximations are useful over a wide range of design changes.