摘要
"精度"和"效率"是近似方法的重要评价指标。传统的二次多项式响应面法,无论是不含交叉项的二次多项式还是完全二次多项式均不能兼顾"效率"和"精度"。为此,该文中提出了一类可在两者之间达到较好平衡的自适应响应面法。一方面,为确保响应面形式更具合理性,通过严格的数学推导给出了极限状态曲面中交叉项是否存在的判断准则,将该准则与完全二次多项式相结合即可确定合理的、自适应的响应面形式;另一方面,针对该判断准则,构造了与之对应的实现算法,并结合可靠度问题的特点,将算法进一步完善;为克服此算法选点中心位于均值点的特性,引入了样本点选取的迭代方案对其改进。最后,该文中通过一个数学算例和一个工程算例分别对建议方法及算法进行验证,结果表明:1)交叉项存在的判断准则准确、有效;2)对于较为简单的二次极限状态曲面,建议方法可以真实还原;3)对于涉及一般极限状态曲面的可靠度问题,建议方法具有颇为理想的精度和较高的效率。
Accuracy and efficiency are important evaluation indexes of the approximate method.However,both accuracy and efficiency could not be considered at the same time using the traditional quadratic response surface method with cross terms or not.In order to overcome this problem,an adaptive response surface method is proposed as an equilibrium point between the accuracy and efficiency.On the one hand,in order to ensure the reasonability of the format of response surface,a criterion for judging the existence of cross terms is derived mathematically in the present work.By combing this criterion with quadratic polynomial of all possible terms via an indicative function,an adaptive response surface is proposed,which is more rational than traditional response surface.On the other hand,an implementation algorithm for judging criterion is induced and then improved by increasing experimental points according to the characters of reliability case.Then,an iterative scheme for selecting points is introduced to improve the precision.Finally,the proposed method is verified by a mathematical example and an engineering example.It is can be found from the results that： 1） The criterion is accurate and effective;2） The proposed response surface can reproduce the limit state surface if it is a quadratic polynomial;3） The proposed method is of fair accuracy and high efficiency for reliability analysis.
出处
《工程力学》
EI
CSCD
北大核心
2013年第4期68-72,共5页
Engineering Mechanics
基金
国家自然科学基金项目(50908243)
重庆市自然科学基金项目(CSTC
2009BB4191)
"十一五"国家重大专项水体污染控制与治理课题项目(2008zx71315-001)
关键词
结构可靠度
自适应响应面法
二次多项式
交叉项
选点方案
structural reliability
adaptive response surface method
quadratic polynomial
cross terms
scheme for selecting points
