Multiple response surfaces method with advanced classification of samples for structural failure function fitting

The current response surface methods based on classifier usually fail to classify all samples correctly, thus neglect the effects of the misclassified samples on the fitting function. To overcome this issue, an improved multiple response surfaces method is proposed. It is mainly based on the techniques of sector division and correct classification of samples. The main steps are: (1) compute a normalized inner product coefficient between the closest sample to the origins and any other one, and sort samples by the coefficient values; (2) select a reasonable number of sorted samples (i.e. range of normalized inner product coefficient) for each sector to assure that the samples in the sector can be classified correctly; (3) divide the overall space into multiple sectors based on such ranges and execute an approximation sector by sector based on support vector machines. A main merit of this method is that it can approximate implicit failure functions well as the number of samples is large enough due to the features of the correct classification of all samples. In addition, it can be applied to both single failure functions and multiple failure functions (explicit ones and enveloped ones). Numerical examples show that the proposed method can achieve a good fitting of implicit failure functions, and the reliability results are accurate, too. (C) 2016 Elsevier Ltd. All rights reserved.