CAJ | 학술논문

对比分析了Kriging、径向基函数、多项式响应面三种代理模型在不同样本点比例和不同样本点空间分布下对4类典型数学函数的拟合精度和推广能力.研究结果表明,Kriging模型对典型数学函数具有较好的适用性和推广能力,径向基函数次之,多项式响应面的适应能力不足.在此基础上,基于Kriging方法构造了船舶双层底板架强度和稳定性计算代理模型,讨论了低样本点比例下Kriging模型代替有限元计算分析的适用性以及不同样本点空间分布对代理模型近似误差的影响.计算结果表明,在低样本点比例下一个均匀齐整的样本点空间分布更利于保证代理模型的精度.在所选取的样本点比例下Kriging模型对船舶板架强度和稳定性计算的适用性较好,近似误差满足工程精度要求.
대비분석료Kriging、경향기함수、다항식향응면삼충대리모형재불동양본점비례화불동양본점공간분포하대4류전형수학함수적의합정도화추엄능력.연구결과표명,Kriging모형대전형수학함수구유교호적괄용성화추엄능력,경향기함수차지,다항식향응면적괄응능력불족.재차기출상,기우Kriging방법구조료선박쌍층저판가강도화은정성계산대리모형,토론료저양본점비례하Kriging모형대체유한원계산분석적괄용성이급불동양본점공간분포대대리모형근사오차적영향.계산결과표명,재저양본점비례하일개균균제정적양본점공간분포경리우보증대리모형적정도.재소선취적양본점비례하Kriging모형대선박판가강도화은정성계산적괄용성교호,근사오차만족공정정도요구.
@@@@A comparison between Kriging model, radial basis function and response surface method is conducted for their approximate performance and generalization ability by means of fitting typical mathematical functions under different sample proportions and different sample distributions. The results show that Kriging model is proved to possess the best applicability and generalization ability in fitting typical mathematical functions, followed by radial basis function, while response surface lacks of adapting ability. Then, with Kriging surrogate model, strength and stability calculation of double bottom grillages is carried out and the usability of Kriging model is studied, as well as the effect of sample distributions on the performance of approximation is comparatively analyzed in the case of small sample proportion. The results indicate that an even and uniform sample distribution benefits the accuracy of surrogate model under circumstance of small sample proportion;Kriging model with small sample proportion has good performance in surrogating strength and stability calculations of grillage, its approximation error meets the requirement of engineering application.