An adaptive SVR-HDMR model for approximating high dimensional problems

2015 ◽  
Vol 32 (3) ◽  
pp. 643-667 ◽  
Author(s):  
Zhiyuan Huang ◽  
Haobo Qiu ◽  
Ming Zhao ◽  
Xiwen Cai ◽  
Liang Gao
Keyword(s):  
Support Vector Regression ◽  
Direct Method ◽  
Model Representation ◽  
Computational Time ◽  
High Dimensional ◽  
Support Vector ◽  
High Dimensional Model Representation ◽  
Model Assessment ◽  
Dimensional Model ◽  
Content Type

Purpose – Popular regression methodologies are inapplicable to obtain accurate metamodels for high dimensional practical problems since the computational time increases exponentially as the number of dimensions rises. The purpose of this paper is to use support vector regression with high dimensional model representation (SVR-HDMR) model to obtain accurate metamodels for high dimensional problems with a few sampling points. Design/methodology/approach – High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for improving the efficiency of deducing high dimensional input-output system behavior. Support vector regression (SVR) method can approximate the underlying functions with a small subset of sample points. Dividing Rectangles (DIRECT) algorithm is a deterministic sampling method. Findings – This paper proposes a new form of HDMR by integrating the SVR, termed as SVR-HDMR. And an intelligent sampling strategy, namely, DIRECT method, is adopted to improve the efficiency of SVR-HDMR. Originality/value – Compared to other metamodeling techniques, the accuracy and efficiency of SVR-HDMR were significantly improved. The SVR-HDMR helped engineers understand the essence of underlying problems visually.

A bisection-sampling-based support vector regression–high-dimensional model representation metamodeling technique for high-dimensional problems

2016 ◽  
Vol 231 (12) ◽  
pp. 2173-2186 ◽  
Author(s):  
Yaping Ju ◽  
Geoff Parks ◽  
Chuhua Zhang
Keyword(s):  
Support Vector Regression ◽  
Computational Cost ◽  
Model Representation ◽  
High Dimensional ◽  
Support Vector ◽  
High Dimensional Model Representation ◽  
Dimensional Model ◽  
Comparison Results ◽  
Modeling Accuracy ◽  
Metamodeling Technique

A major challenge of metamodeling in simulation-based engineering design optimization is to handle the “curse of dimensionality,” i.e. the exponential growth of computational cost with increase of problem dimensionality. Encouragingly, it has been reported recently that a high-dimensional model representation assisted by a radial basis function is capable of deriving high-dimensional input–output relationships at dramatically reduced computational cost. In this article, support vector regression is employed as an alternative to be coupled with high-dimensional model representation for the metamodeling of high-dimensional problems. In particular, the bisection sampling method is proposed to be used in the metamodeling process to generate high-quality training samples. Testing and comparison results show that the developed bisection-sampling-based support vector regression–high-dimensional model representation metamodeling technique can achieve high modeling accuracy with a smaller number of training sample evaluations. For the problem examined in this study, the bisection-sampling-based support vector regression–high-dimensional model representation enables high modeling accuracy and linear computational complexity as the problem dimensionality increases. Analysis of this performance advantage shows that the use of bisection method enables the developed metamodeling technique to be more effective in dealing with high-dimensional problems.

Structural Reliability Analysis with Multi-Failure Models Using High-Dimensional Model Representation

2013 ◽  
Vol 351-352 ◽  
pp. 1648-1651
Author(s):  
Wei Tao Zhao ◽  
Lei Jia ◽  
Cheng Kui Niu
Keyword(s):  
Failure Probability ◽  
Parallel System ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
State Function ◽  
Model Assessment ◽  
Series System ◽  
Dimensional Model ◽  
Failure Models

Based on the high dimensional model representation (HDMR) and Monte Carlo simulation (MCS), this paper presents the improved method used to evaluate the failure probability of the system with multi-failure models. The HDMR is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. Once the limit state function is defined by using the HDMR, the failure probability can be obtained by using the MCS without increasing computational efforts. The series and parallel system are considered in this paper, a numerical example is presented to demonstrate the efficiency and the accuracy of the proposed method. It is shown that the efficiency of the HDMR are both high in terms of series system and parallel system, the accuracy can be acceptable with respect to series system, and the accuracy can not be acceptable with respect to parallel system.

Fragility curves production by seismic improvement of the high-dimensional model representation method

2019 ◽  
Vol 37 (1) ◽  
pp. 120-143
Author(s):  
Payam Asadi ◽  
Hosein Sourani
Keyword(s):  
Fragility Curves ◽  
Random Variables ◽  
Performance Level ◽  
Model Representation ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Response Functions ◽  
Dimensional Model ◽  
Content Type ◽  
Representation Method

Purpose In the absence of random variables, random variables are generated by the Monte Carlo (MC) simulation method. There are some methods for generating fragility curves with fewer nonlinear analyses. However, the accuracy of these methods is not suitable for all performance levels and peak ground acceleration (PGA) range. This paper aims to present a method through the seismic improvement of the high-dimensional model representation method for generating fragility curves while taking advantage of fewer analyses by choosing the right border points. Design/methodology/approach In this method, the values of uncertain variables are selected based on the results of the initial analyses, the damage limit of each performance level or according to acceptable limits in the design code. In particular, PGAs are selected based on the general shape of the fragility curve for each performance limit. Also, polynomial response functions are estimated for each accelerogram. To evaluate the accuracy, fragility curves are estimated by different methods for a single degree of freedom system and a reinforced concrete frame. Findings The results indicated that the proposed method can not only reduce the computational cost but also has a higher accuracy than the other methods, compared with the MC baseline method. Originality/value The proposed response functions are more consistent with the actual values and are also congruent with each performance level to increase the accuracy of the fragility curves.

Sign in / Sign up

Export Citation Format

Share Document