TY - JOUR

T1 - Multiple response surfaces method with advanced classification of samples for structural failure function fitting

AU - Jiang, Youbao

AU - Zhao, Linjie

AU - Beer, Michael

AU - Patelli, Edoardo

AU - Broggi, Matteo

AU - Luo, Jun

AU - He, Yihua

AU - Zhang, Jianren

N1 - Funding information: The research is supported by the National Natural Science Foundation of China (Grant No. 51678072 ), National Key Basic Research Program of China (973 Program) (Grant No. 2015CB057705 ) and China Scholarship Council (Grant No. 201308430311 ). This support is gratefully acknowledged.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - 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.

AB - 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.

KW - Correct classification

KW - Failure function

KW - Multiple response surfaces

KW - Sector division

KW - Structural reliability

KW - Support vector

UR - http://www.scopus.com/inward/record.url?scp=84998854298&partnerID=8YFLogxK

U2 - 10.1016/j.strusafe.2016.10.002

DO - 10.1016/j.strusafe.2016.10.002

M3 - Article

AN - SCOPUS:84998854298

VL - 64

SP - 87

EP - 97

JO - Structural Safety

JF - Structural Safety

SN - 0167-4730

ER -