Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias

Amouzgar, Kaveh; Strömberg, Niclas

doi:10.1007/s00158-016-1569-0

Cited by 45 publications

(26 citation statements)

References 24 publications

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“…The simplest approach to surrogate based optimization is to build a fixed surrogate model based on an initial sampling plan. Different Design of Experiments (DoE) techniques, as the Latin Hipercube Sampling and Hammersley Sequence Sampling (HSS), can be used to generate this sampling plan (Forrester et al, 2008;Amouzgar and Strömberg, 2016). The fixed surrogate is used to in all optimization iterations (or generations in GA).…”

Section: Sequential Approximate Optimizationmentioning

confidence: 99%

Sequential approximate optimization of composite structures using radial basis functions

Balreira¹,

Moura²,

Parente³

2018

Proceedings of the 4th Brazilian Conference on Composite Materials

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The use of optimization techniques is necessary in order to explore the full potential of laminated composite structures. Unfortunately, the computational cost of the optimization process can be very high when numerical methods are used to carry out the structural analysis. This work addresses the use of surrogate models to reduce the computational cost to optimize composite structures. The PSO algorithm is used for optimization and a sequence of surrogate models, based on the use of Radial Basis Functions, is used to approximate the structural responses. The accuracy of the proposed approach is assessed using a set of laminate optimization problems and very good results were obtained.

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Section: Sequential Approximate Optimizationmentioning

confidence: 99%

Sequential approximate optimization of composite structures using radial basis functions

Balreira¹,

Moura²,

Parente³

2018

Proceedings of the 4th Brazilian Conference on Composite Materials

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“…This is done in the numerical implementation. Our RBDO problem reads In that latter work, we also let f and g be given as surrogate models using a new approach for radial basis function networks recently suggested and evaluated in Amouzgar and Strömberg (2016). In this work, we focus on the derivation and performance of the proposed second order RBDO approach and therefore only consider explicit analytical expressions on f and g. Surrogate model based RBDO can e.g.…”

Section: Pr[h(y ) < 0] ≈ (−β Hl )mentioning

confidence: 99%

Reliability-based design optimization using SORM and SQP

Strömberg

2017

Struct Multidisc Optim

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In this work a second order approach for reliabilitybased design optimization (RBDO) with mixtures of uncorrelated non-Gaussian variables is derived by applying second order reliability methods (SORM) and sequential quadratic programming (SQP). The derivation is performed by introducing intermediate variables defined by the incremental iso-probabilistic transformation at the most probable point (MPP). By using these variables in the Taylor expansions of the constraints, a corresponding general first order reliability method (FORM) based quadratic programming (QP) problem is formulated and solved in the standard normal space. The MPP is found in the physical space in the metric of Hasofer-Lind by using a Newton algorithm, where the efficiency of the Newton method is obtained by introducing an inexact Jacobian and a line-search of Armijo type. The FORM-based SQP approach is then corrected by applying four SORM approaches: Breitung, Hohenbichler, Tvedt and a recent suggested formula. The proposed SORMbased SQP approach for RBDO is accurate, efficient and robust. This is demonstrated by solving several established benchmarks, with values on the target of reliability that are considerable higher than what is commonly used, for mixtures of five different distributions (normal, lognormal, Gumbel, gamma and Weibull). Established benchmarks are also generalized in order to study problems with large number of variables and several constraints. shown that the proposed approach efficiently solves a problem with 300 variables and 240 constraints within less than 20 CPU minutes on a laptop. Finally, a most well-know deterministic benchmark of a welded beam is treated as a RBDO problem using the proposed SORM-based SQP approach.

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“…Some of the most recognized models that are used widely are the response surface models [23,24,25,26,27]. Extensive surveys and reviews of different meta-modeling methods and their applications are given in previous studies [28,29,30]. On the other hand [31], RSM and RBF were studied to find the best method for modeling highly nonlinear responses found in impact-related problems.…”

Section: Introductionmentioning

confidence: 99%

Multiple Modeling Techniques for Assessing Sesame Oil Extraction under Various Operating Conditions and Solvents

Osman

Shigidi

Arabi

2019

Foods

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This paper compares four different modeling techniques: Response Surface Method (RSM), Linear Radial Basis Functions (LRBF), Quadratic Radial Basis Functions (QRBF), and Artificial Neural Network (ANN). The models were tested by monitoring their performance in predicting the optimum operating conditions for Sesame seed oil extraction yields. Experimental data using three different solvents—hexane, chloroform, and acetone—with varying ratios of solvents to seeds, all under different temperatures, rotational speeds, and mixing times, were modeled by the three proposed techniques. Efficiency for model predictions was examined by monitoring error value performance indicators (R2, R2adj, and RMSE). Results showed that the applied modeling techniques gave good agreements with experimental data regardless of the efficiency of the solvents in oil extraction. On the other hand, the ANN model consistently performed more accurate predictions with all tested solvents under all different operating conditions. This consistency is demonstrated by the higher values of R2 and R2adj ratio equals to one and the very low value of error of RMSE (2.23 × 10−3 to 3.70 × 10−7), thus concluding that ANN possesses a universal ability to approximate nonlinear systems in comparison to other models.

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Radial basis functions as surrogate models with a priori bias in comparison with a posteriori bias

Cited by 45 publications

References 24 publications

Sequential approximate optimization of composite structures using radial basis functions

Sequential approximate optimization of composite structures using radial basis functions

Reliability-based design optimization using SORM and SQP

Multiple Modeling Techniques for Assessing Sesame Oil Extraction under Various Operating Conditions and Solvents

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