scispace - formally typeset
Journal ArticleDOI: 10.1080/0305215X.2020.1739280

A unified ensemble of surrogates with global and local measures for global metamodelling

04 Mar 2021-Engineering Optimization (Taylor & Francis)-Vol. 53, Iss: 3, pp 474-495
Abstract: Surrogate models are widely used in engineering design and optimization to substitute computationally expensive simulations for efficient approximation of system behaviours. However, since actual s...

... read more

Citations
  More

9 results found


Journal ArticleDOI: 10.1016/J.YMSSP.2021.107727
Jian Zhang1, Xinxin Yue1, Jiajia Qiu, Lijun Zhuo1  +1 moreInstitutions (1)
Abstract: Polynomial chaos expansion (PCE) is widely used in a variety of engineering fields for uncertainty and sensitivity analyses. The computational cost of full PCE is unaffordable due to the ‘curse of dimensionality’ of the expansion coefficients. In this paper, a novel methodology for developing sparse PCE is proposed by making use of the efficiency of greedy coordinate descent (GCD) in sparsity exploitation and the capability of Bregman iteration in accuracy enhancement. By minimizing an objective function composed of the l 1 norm (sparsity) of the polynomial chaos (PC) coefficients and regularized l 2 norm of the approximation fitness, the proposed algorithm screens the significant basis polynomials and builds an optimal sparse PCE with model evaluations much fewer than unknown coefficients. To validate the effectiveness of the developed algorithm, several benchmark examples are investigated for global sensitivity analysis (GSA). A detailed comparison is made with the well-established orthogonal matching pursuit (OMP), least angle regression (LAR) and two adaptive algorithms. Results show that the proposed method is superior to the benchmark methods in terms of accuracy while maintaining a better balance among accuracy, complexity and computational efficiency.

... read more

Topics: Polynomial chaos (58%), Coordinate descent (57%), Matching pursuit (52%) ... read more

3 Citations


Journal ArticleDOI: 10.1007/S00158-021-02866-7
Xinxin Yue1, Jian Zhang1, Weijie Gong1, Min Luo2  +1 moreInstitutions (2)
Abstract: Metamodel-based high-dimensional model representation (HDMR) has recently been developed as a promising tool for approximating high-dimensional and computationally expensive problems in engineering design and optimization. However, current stand-alone Cut-HDMRs usually come across the problem of prediction uncertainty while combining an ensemble of metamodels with Cut-HDMR results in an implicit and inefficient process in response approximation. To this end, a novel stand-alone Cut-HDMR is proposed in this article by taking advantage of the explicit polynomial chaos expansion (PCE) and hierarchical Cut-HDMR (named PCE-HDMR). An intelligent dividing rectangles (DIRECT) sampling method is adopted to adaptively refine the model. The novelty of the PCE-HDMR is that the proposed multi-hierarchical algorithm structure by integrating PCE with Cut-HDMR can efficiently and robustly provide simple and explicit approximations for a wide class of high-dimensional problems. An analytical function is first used to illustrate the modeling principles and procedures of the algorithm, and a comprehensive comparison between the proposed PCE-HDMR and other well-established Cut-HDMRs is then made on fourteen representative mathematical functions and five engineering examples with a wide scope of dimensionalities. The results show that the proposed PCE-HDMR has much superior accuracy and robustness in terms of both global and local error metrics while requiring fewer number of samples, and its superiority becomes more significant for polynomial-like functions, higher-dimensional problems, and relatively larger PCE degrees.

... read more

2 Citations


Journal ArticleDOI: 10.1016/J.ENGANABOUND.2021.08.023
Abstract: This research presents a novel algorithm for robust topology optimization of continuous structures under material and loading uncertainties by combining an evolutionary structural optimization (ESO) method with an extended finite element method (XFEM). Conventional topology optimization approaches (e.g. ESO) often require additional post-processing to generate a manufacturable topology with smooth boundaries. By adopting the XFEM for boundary representation in the finite element (FE) framework, the proposed method eliminates this time-consuming post-processing stage and produces more accurate evaluation of the elements along the design boundary for ESO-based topology optimization methods. A truncated Gaussian random field (without negative values) using a memory-less translation process is utilized for the random uncertainty analysis of the material property and load angle distribution. The superiority of the proposed method over Monte Carlo, solid isotropic material with penalization (SIMP) and polynomial chaos expansion (PCE) using classical finite element method (FEM) is demonstrated via two practical examples with compliances in material uncertainty and loading uncertainty improved by approximately 11% and 10%, respectively. The novelty of the present method lies in the following two aspects: (1) this paper is among the first to use the XFEM in studying the robust topology optimization under uncertainty; (2) due to the adopted XFEM for boundary elements in the FE framework, there is no need for any post-processing techniques. The effectiveness of this method is justified by the clear and smooth boundaries obtained.

... read more

Topics: Topology optimization (64%), Extended finite element method (60%), Finite element method (56%) ... read more

2 Citations


Open accessJournal ArticleDOI: 10.1155/2021/8857417
Huanwei Xu1, Xin Zhang1, Hao Li1, Ge Xiang1Institutions (1)
Abstract: An ensemble of surrogate models with high robustness and accuracy can effectively avoid the difficult choice of surrogate model. However, most of the existing ensembles of surrogate models are constructed with static sampling methods. In this paper, we propose an ensemble of adaptive surrogate models by applying adaptive sampling strategy based on expected local errors. In the proposed method, local error expectations of the surrogate models are calculated. Then according to local error expectations, the new sample points are added within the dominating radius of the samples. Constructed by the RBF and Kriging models, the ensemble of adaptive surrogate models is proposed by combining the adaptive sampling strategy. The benchmark test functions and an application problem that deals with driving arm base of palletizing robot show that the proposed method can effectively improve the global and local prediction accuracy of the surrogate model.

... read more

Topics: Surrogate model (62%), Adaptive sampling (55%), Kriging (50%)

1 Citations


Open accessJournal ArticleDOI: 10.3390/MATH8101721
07 Oct 2020-
Abstract: Surrogate modeling techniques are widely used to replace the computationally expensive black-box functions in engineering. As a combination of individual surrogate models, an ensemble of surrogates is preferred due to its strong robustness. However, how to select the best quantity and variety of surrogates for an ensemble has always been a challenging task. In this work, five popular surrogate modeling techniques including polynomial response surface (PRS), radial basis functions (RBF), kriging (KRG), Gaussian process (GP) and linear shepard (SHEP) are considered as the basic surrogate models, resulting in twenty-six ensemble models by using a previously presented weights selection method. The best ensemble model is expected to be found by comparative studies on prediction accuracy and robustness. By testing eight mathematical problems and two engineering examples, we found that: (1) in general, using as many accurate surrogates as possible to construct ensemble models will improve the prediction performance and (2) ensemble models can be used as an insurance rather than offering significant improvements. Moreover, the ensemble of three surrogates PRS, RBF and KRG is preferred based on the prediction performance. The results provide engineering practitioners with guidance on the superior choice of the quantity and variety of surrogates for an ensemble.

... read more

Topics: Ensemble forecasting (58%)

1 Citations


References
  More

30 results found


Open accessBook
31 Mar 1995-
Abstract: Preface. 1. Introduction. 2. Finite Element Modelling. 3. Vibration Testing. 4. Comparing Numerical Data with Test Results. 5. Estimation Techniques. 6. Parameters for Model Updating. 7. Direct Methods Using Modal Data. 8. Iterative Methods Using Modal Data. 9. Methods Using Frequency Domain Data. 10. Case Study: an Automobile Body M. Brughmans, J. Leuridan, K. Blauwkamp. 11. Discussion and Recommendations. Index.

... read more

2,100 Citations


Journal ArticleDOI: 10.1115/1.2429697
Gongming Wang1, Songqing Shan1Institutions (1)
01 Jan 2006-
Abstract: Computation-intensive design problems are becoming increasingly common in manufacturing industries. The computation burden is often caused by expensive analysis and simulation processes in order to reach a comparable level of accuracy as physical testing data. To address such a challenge, approximation or metamodeling techniques are often used. Metamodeling techniques have been developed from many different disciplines including statistics, mathematics, computer science, and various engineering disciplines. These metamodels are initially developed as “surrogates” of the expensive simulation process in order to improve the overall computation efficiency. They are then found to be a valuable tool to support a wide scope of activities in modern engineering design, especially design optimization. This work reviews the state-of-the-art metamodel-based techniques from a practitioner’s perspective according to the role of metamodeling in supporting design optimization, including model approximation, design space exploration, problem formulation, and solving various types of optimization problems. Challenges and future development of metamodeling in support of engineering design is also analyzed and discussed.Copyright © 2006 by ASME

... read more

Topics: Metamodeling (65%), Metadata modeling (63%), Engineering optimization (60%) ... read more

1,374 Citations


Journal ArticleDOI: 10.2514/1.8650
01 Apr 2005-AIAA Journal
Abstract: The use of kriging models for approximation and metamodel-based design and optimization has been steadily on the rise in the past decade. The widespread usage of kriging models appears to be hampered by (1) the lack of guidance in selecting the appropriate form of the kriging model, (2) computationally efficient algorithms for estimating the model’s parameters, and (3) an effective method to assess the resulting model’s quality. In this paper, we compare (1) Maximum Likelihood Estimation (MLE) and Cross-Validation (CV) parameter estimation methods for selecting a kriging model’s parameters given its form and (2) and an R 2 of prediction and the corrected Akaike Information Criterion for assessing the quality of the created kriging model, permitting the comparison of different forms of a kriging model. These methods are demonstrated with six test problems. Finally, different forms of kriging models are examined to determine if more complex forms are more accurate and easier to fit than simple forms of kriging models for approximating computer models.

... read more

Topics: Variogram (65%), Kriging (61%), Akaike information criterion (55%)

757 Citations


Journal ArticleDOI: 10.1007/S00158-006-0051-9
Abstract: The custom in surrogate-based modeling of complex engineering problems is to fit one or more surrogate models and select the one surrogate model that performs best. In this paper, we extend the utility of an ensemble of surrogates to (1) identify regions of possible high errors at locations where predictions of surrogates widely differ, and (2) provide a more robust approximation approach. We explore the possibility of using the best surrogate or a weighted average surrogate model instead of individual surrogate models. The weights associated with each surrogate model are determined based on the errors in surrogates. We demonstrate the advantages of an ensemble of surrogates using analytical problems and one engineering problem. We show that for a single problem the choice of test surrogate can depend on the design of experiments.

... read more

Topics: Surrogate data (66%), Surrogate model (65%), Kriging (50%)

504 Citations


Proceedings ArticleDOI: 10.1115/DETC2003/DAC-48759
01 Jan 2003-
Abstract: A variety of metamodeling techniques have been developed in the past decade to reduce the computational expense of computer-based analysis and simulation codes. Metamodeling is the process of building a model of a model to provide a fast surrogate for a computationally expensive computer code. Common metamadeling techniques include response surface methodology, kriging, radial basis functions, and multivariate adaptive regression splines. In this paper, we investigate support vector regression (SVR) as an alternative technique for approximating complex engineering analyses. The computationally efficient theory behind SVR is reviewed, and SVR approximations are compared against the aforementioned four mefamodeling techniques using a test bed of 26 engineering analysis functions. SVR achieves more accurate and more robust function approximations than the four metamodeling techniques, and shows great potential for metamodeling applications, adding to the growing body of promising empirical performance of SVR.

... read more

460 Citations


Performance
Metrics
No. of citations received by the Paper in previous years
YearCitations
20221
20217
20201