Gaussian Process Model – An Exploratory Study in the Response Surface Methodology

Costa, Nuno; Lourenço, João

doi:10.1002/qre.1940

Cited by 20 publications

(8 citation statements)

References 92 publications

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“…The related literature proposes different approaches in the modeling of surface response instead of polynomial models. For example, regression of Gaussian processes has been proposed, since these models can model complex functions [141,154]. Also, the use of SVM regression as a prediction model has been proposed [155].…”

Section: Response Surface Methodology (Rsm)mentioning

confidence: 99%

Trends in Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing

2019

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Multiphase systems are important in minerals processing, and usually include solid–solid and solid–fluid systems, such as in wet grinding, flotation, dewatering, and magnetic separation, among several other unit operations. In this paper, the current trends in the process system engineering tasks of modeling, design, and optimization in multiphase systems, are analyzed. Different scales of size and time are included, and therefore, the analysis includes modeling at the molecular level (molecular dynamic modeling) and unit operation level (e.g., computational fluid dynamic, CFD), and the application of optimization for the design of a plant. New strategies for the modeling, design, and optimization of multiphase systems are also included, with a strong focus on the application of artificial intelligence (AI) and the combination of experimentation and modeling with response surface methodology (RSM). The integration of different modeling techniques such as CFD with discrete element simulation (DEM) and response surface methodology (RSM) with artificial neural networks (ANN) is included. The paper finishes with tools to study the uncertainty, both epistemic and stochastic, based on uncertainty and global sensitivity analyses, which is present in all mineral processing operations. It is shown that all of these areas are very active and can help in the understanding, operation, design, and optimization of mineral processing that involves multiphase systems. Future needs, such as meso-scale modeling, are highlighted.

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Section: Response Surface Methodology (Rsm)mentioning

confidence: 99%

Trends in Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing

2019

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“…GP models have successful applications in various research fields, such as statistical process control and advanced manufacturing processes. 35,36 As a nonparametric model, GP can accurately estimate the relationship models from experimental data without prior information. 21 There are two given × 1 vectors for output responses = ( 1 , … , ) and input variables = ( 1 , … , ) .…”

Section: Gp Modelmentioning

confidence: 99%

“…The first is the RPD method, which integrated the QL function and uncertainty quantification technique. 35,42,50 The second is the commonly used RBRDO method based on GP models with MLE technique. 10,30 33 The optimal solutions of different methods are substituted into the real model for verification.…”

Section: Experimental Analysis For a Micro-drilling Processmentioning

confidence: 99%

“…In engineering practice, output responses of the process are usually used to reflect the quality characteristics, 35 such as the reaction time in chemical experiments, the surface roughness in the high‐speed wire‐cut electrical discharge machining process, and the taper of holes in the laser drilling process. RPD can be used to find the optimal solutions that can make the response meets the target (

T

) of quality characteristic.…”

Section: The Proposed Approachmentioning

confidence: 99%

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Life‐cycle reliability‐based robust design optimization for GP model with response uncertainty

Feng

Wang

et al. 2021

Quality & Reliability Eng

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Reliability-based robust design optimization (RBRDO) is a crucial tool for lifecycle quality improvement. Gaussian process (GP) model is an effective alternative modeling technique that is widely used in robust parameter design. However, there are few studies to deal with reliability-based design problems by using GP model. This article proposes a novel life-cycle RBRDO approach concerning response uncertainty under the framework of GP modeling technique. First, the hyperparameters of GP model are estimated by using the Gibbs sampling procedure. Second, the expected partial derivative expression is derived based on GP modeling technique. Moreover, a novel failure risk cost function is constructed to assess the life-cycle reliability. Then, the quality loss function and confidence interval are constructed by simulated outputs to evaluate the robustness of optimal settings and response uncertainty, respectively. Finally, an optimization model integrating failure risk cost function, quality loss function, and confidence interval analysis approach is constructed to find reasonable optimal input settings. Two case studies are given to illustrate the performance of the proposed approach. The results show that the proposed approach can make better trade-offs between the quality characteristics and reliability requirements by considering response uncertainty.

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“…Because of the disadvantage of over‐reliance on a large number of finite element samples by iterative method, Box et al 3 first proposed the experimental design of the response surface method. Many authors have used the response surface method for finite element model correction and for proposing improved methods 4–10 . The traditional response surface method mainly uses regression analysis to establish the response surface model instead of the complex finite element model; then, it approximates the target value.…”

Section: Introductionmentioning

confidence: 99%

Prediction method of bridge static deformation based on dynamic test

Pan

Hong

et al. 2020

Structural Concrete

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To solve the high cost of bridge load tests, considerable influence on traffic, and damage to bridge structure in the process of problem detection and maintenance of existing bridges, we use the method of improved Gaussian process response surface to explore the prediction of the rigidity and unit weight of existing bridges to produce high‐precision predictions of the existing bridge static test. The Gaussian process response surface method in Bayesian principle is adopted to optimize and correct the model. Because Gaussian process is a non‐parameter model with high sensitivity, reliable accuracy, and small calculation, it avoids repeatedly using finite element model. This makes the efficiency of finite element correction improve significantly. A continuous beam bridge is adopted as a study case. In sample selection, an improved uniform design method based on weighting is designed to improve the learning efficiency and prediction accuracy of the model while using ANSYS to analyze and predict the typical bridge. The analysis of the date of the bridge dynamic test is used to correct the finite element model, obtain the actual parameters of the bridge structure, and predict the measured data of the bridge static load test based on the modified finite element model.

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Gaussian Process Model – An Exploratory Study in the Response Surface Methodology

Cited by 20 publications

References 92 publications

Trends in Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing

Trends in Modeling, Design, and Optimization of Multiphase Systems in Minerals Processing

Life‐cycle reliability‐based robust design optimization for GP model with response uncertainty

Prediction method of bridge static deformation based on dynamic test

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