计算机试验的分步优化设计研究  

Study on Optimal Design of Computer Experiments by Stages

作　　者：黄靓[1] 易伟建[1] 汪优[2] 

机构地区：[1]湖南大学土木工程学院,湖南长沙410082 [2]中南大学土木建筑学院,湖南长沙410075

出　　处：《湖南大学学报（自然科学版）》2007年第8期65-69,共5页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(50378034);高校博士点专项基金资助项目(20030532020)

摘　　要：针对传统的计算机试验优化设计计算费时的不足,一方面改进了原始的随机进化寻优算法,以兼顾深度搜索与广度搜索;另一方面提出了分步试验优化设计的思路,逐步分批地布置试验样本点,化整为零地减小搜索空间;最后采用径向基神经网络替代模型,以均匀试验设计为例,检验分步试验优化设计方法的有效性.计算实践表明,改进算法可平均节省50%左右的机时,寻找到与原始算法结果相差约1%的最优值;分步试验设计较一步试验设计可减少40%-60%左右的机时,数值实验表明,随着试验样本点数量的递增,由不同试验设计所产生的替代模型的误差将趋于一致,分步试验设计尤其适合基于大规模试验样本点的替代模型。Considering the high computational cost of traditional optimal design of computer experiments, the original stochastic evolutionary algorithm was improved by balancing the depth searching and broadness searching. And optimal experiment design by steps was provided, which divided full searching space into subspaces and arranged samplings in batches. The influences of experiment design by steps on RBF network metamodel were also measured by numerical tests. The training sampling set of RBF network wss decided upon by uniform design. The computer practice shows that the improved algorithm can decrease about 50 % time cost at an average to find optimal values, which are about 1% different from what the original algorithm finds. The theory analyses show that the complements of experiment design by steps can decrease about 40% -60% machine time,compared with the traditional experiment design, which is confirmed by computer examples. Numerical tests show that, with the increment of samplings, the errors of metamodel resulted from different experiment designs will be consistent. Numerical tests also show that experiment design by steps will be suitable for the metamodels that need largescale experiment samplings.

关 键 词：结构可靠性 计算机试验 优化设计 随机进化算法 替代模型 

分 类 号：TB114[理学—概率论与数理统计] TU375[理学—数学]