Weighted Least Square Support Vector
Regression Method with GGP-Based
Sequential Sampling
Yang Guo
1 , Jiang Cao
1 , Qi Ouyang
2(&)
, and Shaochi Cheng
1
1 PLA Academy of Military Science, Beijing 10091, China
guoyangnudt@gmail.com
2 Beijing Aerospace Control Center, Beijing 10094, China
oyqnudt@hotmail.com
Abstract. Approximation models are widely used in engineering reliability
analysis due to the enormously expensive computation cost of limit state
functions. In this paper, the weighted least-squared support vector regression
(WLSSVR) method is used for model approximation. Sequential modeling is
also considered to reduce the training sample number. A WLSSVR method with
great gradient point (GGP)-based sequential sampling strategy is established and
tested. The results show that the proposed method improves the global
approximation accuracy.
Keywords: Support vector machine Á WLSSVR Á Sequential modeling Á
Greatest gradient point
1 Introduction
In order to reduce the computational burden in reliability analysis, approximation
methods are always be applied to construct a simple and inexpensive approximate
model as a replacement of the complex limit state function. Various types of
approximation methods have been applied to reliability analysis, for instance, the
response surface method (regression polynomial, RSM) [1–6], polynomial chaos
expansion (PCE) [7–10], kriging [11–14], neural network (NN) [15–18] and support
vector machines (SVM) [19]. As SVM and its improved variant least square support
vector machine (LSSVM) method [19] are powerful tool that can provide good
approximation accuracy and robustness [20], they have been widely studied in recent
researches [21–30].
The performance of SVM/LSSVM is highly depended on the training samples. An
effective way to choose the appropriate training samples is to use sequential modeling
technology. In this paper, weighted least square support vector machines (WLSSVM )
method [19] is used for model approximation. Section 2 gives a brief introduction of
WLSSVR method. In Sect. 3, a great gradient point (GGP)-based sampling strategy is
developed. This sampling strategy can improve the approximate ability of WLSSVR
method for highly nonlinear limit state function. Section 4 presents the application
examples of the proposed method.
© Springer Nature Singapore Pte Ltd. 2020
Q. Liang et al. (Eds.): Artificial Intelligence in China, LNEE 572, pp. 212–219, 2020.
https://doi.org/10.1007/978-981-15-0187-6_24
Regression Method with GGP-Based
Sequential Sampling
Yang Guo
1 , Jiang Cao
1 , Qi Ouyang
2(&)
, and Shaochi Cheng
1
1 PLA Academy of Military Science, Beijing 10091, China
guoyangnudt@gmail.com
2 Beijing Aerospace Control Center, Beijing 10094, China
oyqnudt@hotmail.com
Abstract. Approximation models are widely used in engineering reliability
analysis due to the enormously expensive computation cost of limit state
functions. In this paper, the weighted least-squared support vector regression
(WLSSVR) method is used for model approximation. Sequential modeling is
also considered to reduce the training sample number. A WLSSVR method with
great gradient point (GGP)-based sequential sampling strategy is established and
tested. The results show that the proposed method improves the global
approximation accuracy.
Keywords: Support vector machine Á WLSSVR Á Sequential modeling Á
Greatest gradient point
1 Introduction
In order to reduce the computational burden in reliability analysis, approximation
methods are always be applied to construct a simple and inexpensive approximate
model as a replacement of the complex limit state function. Various types of
approximation methods have been applied to reliability analysis, for instance, the
response surface method (regression polynomial, RSM) [1–6], polynomial chaos
expansion (PCE) [7–10], kriging [11–14], neural network (NN) [15–18] and support
vector machines (SVM) [19]. As SVM and its improved variant least square support
vector machine (LSSVM) method [19] are powerful tool that can provide good
approximation accuracy and robustness [20], they have been widely studied in recent
researches [21–30].
The performance of SVM/LSSVM is highly depended on the training samples. An
effective way to choose the appropriate training samples is to use sequential modeling
technology. In this paper, weighted least square support vector machines (WLSSVM )
method [19] is used for model approximation. Section 2 gives a brief introduction of
WLSSVR method. In Sect. 3, a great gradient point (GGP)-based sampling strategy is
developed. This sampling strategy can improve the approximate ability of WLSSVR
method for highly nonlinear limit state function. Section 4 presents the application
examples of the proposed method.
© Springer Nature Singapore Pte Ltd. 2020
Q. Liang et al. (Eds.): Artificial Intelligence in China, LNEE 572, pp. 212–219, 2020.
https://doi.org/10.1007/978-981-15-0187-6_24