Alternative Kriging-HDMR optimization method with expected improvement sampling strategy

2017 ◽  
Vol 34 (6) ◽  
pp. 1807-1828 ◽  
Author(s):  
Enying Li ◽  
Fan Ye ◽  
Hu Wang
Keyword(s):  
Standard Deviation ◽  
Sampling Strategy ◽  
Suggested Method ◽  
Expected Improvement ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Analysis Tool ◽  
Model Assessment ◽  
Content Type ◽  
Kriging Predictor

Purpose The purpose of study is to overcome the error estimation of standard deviation derived from Expected improvement (EI) criterion. Compared with other popular methods, a quantitative model assessment and analysis tool, termed high-dimensional model representation (HDMR), is suggested to be integrated with an EI-assisted sampling strategy. Design/methodology/approach To predict standard deviation directly, Kriging is imported. Furthermore, to compensate for the underestimation of error in the Kriging predictor, a Pareto frontier (PF)-EI (PFEI) criterion is also suggested. Compared with other surrogate-assisted optimization methods, the distinctive characteristic of HDMR is to disclose the correlations among component functions. If only low correlation terms are considered, the number of function evaluations for HDMR grows only polynomially with the number of input variables and correlative terms. Findings To validate the suggested method, various nonlinear and high-dimensional mathematical functions are tested. The results show the suggested method is potential for solving complicated real engineering problems. Originality/value In this study, the authors hope to integrate superiorities of PFEI and HDMR to improve optimization performance.

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.

Polynomial Representation of the Gaussian Process

2018 ◽  
Author(s):  
Jesper Kristensen ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Gaussian Process ◽  
Basis Functions ◽  
Training Data ◽  
Computational Time ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Analysis Tool ◽  
Sobol Indices ◽  
Robust Fitting ◽  
Uncertainty Estimates

Gaussian Process (GP) regression is a well-established probabilistic meta-modeling and data analysis tool. The posterior distribution of the GP parameters can be estimated using, e.g., Markov Chain Monte Carlo (MCMC). The ability to make predictions is a key aspect of using such surrogate models. To make a GP prediction, the MCMC chain as well as the training data are required. For some applications, GP predictions can require too much computational time and/or memory, especially for many training data points. This motivates the present work to represent the GP in an equivalent polynomial (or other global functional) form called a portable GP. The portable GP inherits many benefits of the GP including feature ranking via Sobol indices, robust fitting to non-linear and high-dimensional data, accurate uncertainty estimates, etc. The framework expands the GP in a high-dimensional model representation (HDMR). After fitting each HDMR basis function with a polynomial, they are all added together to form the portable GP. A ranking of which basis functions to use in the fitting process is automatically provided via Sobol indices. The uncertainty from the fitting process can be propagated to the final GP polynomial estimate. In applications where speed and accuracy are paramount, spline fits to the basis functions give very good results. Finally, portable BHM provides an alternative set of assumptions with regards to extrapolation behavior which may be more appropriate than the assumptions inherent in GPs.

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.

Structural Reliability Evaluation Using Enhanced HDMR

2008 ◽  
Author(s):  
B. N. Rao ◽  
Rajib Chowdhury
Keyword(s):  
Failure Probability ◽  
Structural Reliability ◽  
Limit State ◽  
Statistical Simulation ◽  
Higher Order ◽  
Complex Model ◽  
High Dimensional ◽  
Approximation Technique ◽  
High Dimensional Model Representation ◽  
Model Assessment

This paper presents a new computational tool for predicting failure probability of randomly parametered structural/mechanical systems based on high dimensional model representation (HDMR) generated from low order function components. 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. When first-order HDMR approximation of the original high dimensional implicit limit state/performance function is not adequate to provide desired accuracy to the predicted failure probability, this paper presents an enhanced HDMR (eHDMR) method to represent the higher order terms of HDMR expansion by expressions similar to the lower order ones with monomial multipliers. The accuracy of the HDMR expansion can be significantly improved using preconditioning with a minimal number of additional input-output samples without directly invoking the determination of second- and higher order HDMR terms. This study aims to assess how accurately and efficiently eHDMR approximation technique can capture complex model output uncertainty. As a part of this effort, the efficacy of HDMR approximation, which is recently applied to reliability analysis, is also demonstrated. Once the approximate form of implicit response function is defined using HDMR/eHDMR, the failure probability can be obtained by statistical simulation.

Time-based reflow soldering optimization by using adaptive Kriging-HDMR method

2016 ◽  
Vol 28 (2) ◽  
pp. 101-113 ◽  
Author(s):  
Liming Chen ◽  
Enying Li ◽  
Hu Wang
Keyword(s):  
Design Variable ◽  
Optimization Method ◽  
Expected Improvement ◽  
High Dimensional ◽  
Dimensional Problem ◽  
Reflow Soldering ◽  
Content Type ◽  
Soldering Process ◽  
High Dimensional Problem ◽  
Adaptive Kriging

Purpose Reflow soldering process is an important step of the surface mount technology. The purpose of this paper is to minimize the maximum warpage of shielding frame by controlling reflow soldering control parameters. Design/methodology/approach Compared with other reflow-related design methods, both time and temperate of each extracted time region are considered. Therefore, the number of design variable is increased. To solve the high-dimensional problem, a surrogate-assisted optimization (SAO) called adaptive Kriging high-dimensional representation model (HDMR) is used. Findings Therefore, the number of design variable is increased. To solve the high-dimensional problem, a surrogate-assisted optimization (SAO) called HDMR is used. The warpage of shield frame is significantly reduced. Moreover, the correlations of design variables are also disclosed. Originality/value Compared with the original Kriging HDMR, the expected improvement (EI) criterion is used and a new projection strategy is suggested to improve the efficiency of optimization method. The application suggests that the adaptive Kriging HDMR has potential capability to solve such complicated engineering problems.

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.

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