AN ADAPTIVE RESPONSE SURFACE METHOD WITH CROSS TERMS

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.