Cumulative formation of response surface and its use in reliability analysis

An improved response surface method is proposed and applied to the reliability analysis of a stiffened plated structure. The response surface function is formed in a cumulative manner in order to properly account for the second order effects in the response surface with acceptable computational effort involved in the evaluation of the state function. First, a linear response surface is formed by searching for the design point by the first order reliability method. The vector projection technique is used to allocate the sampling points close to the response surface. Then, the linear response surface is improved by adding square terms, and the second order reliability method is employed to search for the design point. All the available sampling points except those generated in the very initial stage are used to obtain a well-conditioned system matrix for regression. Lastly, the obtained response surface is checked for the selected sampling points. If the response surface function is not satisfactory, it is adaptively improved by adding cross terms and removing some of the second order terms. In this way an appropriate incomplete second order response surface can be obtained and used for reliability analysis. Examples are given to demonstrate the features of the proposed method.