Statistical Tests for Cross-Validation of Kriging Models

Kleijnen, J.P.C.; Beers, Wim van

doi:10.2139/ssrn.3395872

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…They also provided an extensive review on model selection strategies, including model fitness and validation, as well as guidelines for the choice of surrogate model for modelling, feasibility analysis, and optimization purposes. For new statistical tests for leave-one-out cross-validation of Kriging models, the reader is referred to Kleijnen and van Beers [93].…”

Section: Selection Of Experimental Design and Analysis Methodsmentioning

confidence: 99%

Energy-Efficiency Assessment and Improvement—Experiments and Analysis Methods

Costa

Fontes

2020

Sustainability

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Some (non)manufacturing industries are becoming more energy efficient, but many of them are losing cost-effective energy-savings opportunities, namely, by lack of knowledge or underestimation of good engineering and management practices as well as guidance on techniques or tools for that purpose. This study points out that Design of Experiments is a tool that cannot be ignored by managers and other technical staff, namely, by those who have the responsibility to eliminate energy waste and promote energy-efficiency improvement in industry, mainly in energy-intensive manufacturing industries. A review on Design of Experiments for physical and simulation experiments, supported on carefully selected references, is provided, since process and product improvement at the design and manufacturing stages increasingly rely on virtual tests and digital simulations. However, the expense of running experiments in complex computer models is still a relevant issue, despite advances in computer hardware and software capabilities. Here, experiments were statistically designed, and several easy-to-implement yet effective data analysis methods were employed for identifying the variables that must be measured with more accurate devices and methods to better estimate the energy efficiency or improve it in a billets reheating furnace. A simulation model of this type of furnace was used to run the experiments and the results analysis shows that variables with practical effect on the furnace’s energy efficiency are the percentage of oxygen in the combustion gases, the fuel flow in the burners, and the combustion air temperature.

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Section: Selection Of Experimental Design and Analysis Methodsmentioning

confidence: 99%

Energy-Efficiency Assessment and Improvement—Experiments and Analysis Methods

Costa

Fontes

2020

Sustainability

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“…The special case

K = n

is referred to as leave‐one‐out (LOO) cross‐validation. In practice, other leave‐one‐out strategies can be developed and applied 25 …”

Section: Validation Criteria For Model Selectionmentioning

confidence: 99%

“…In practice, other leave-one-out strategies can be developed and applied. 25 All the quantitative and graphical indicators of validation presented in the following can be applied indifferently on a test sample or by cross-validation. They will be formulated here by LOO cross-validation, considering the notations ẑ−𝑖 and ŝ2…”

Section: Estimation Procedures For Validation Criteriamentioning

confidence: 99%

Model selection based on validation criteria for Gaussian process regression: An application with highlights on the predictive variance

Demay¹,

Iooss

Gratiet³

et al. 2021

Quality & Reliability Eng

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The manufacturing quality of industrial pieces is linked with the intrinsic concentration field of certain chemical species. Thus, from punctual measurements sparsely distributed on the piece, a robust estimation of the maximum concentration is very valuable. To this aim, Gaussian Process regression models may be used, providing useful confidence interval at each interpolation location. However, the specification of the underlying covariance function from sparse data may be arduous, both in terms of function form and hyperparameters. This specification problem, also referred to as a model selection problem, may be addressed in several ways, from expert knowledge to numerical estimation. Regarding the covariance function form, the predictivity coefficient Q2$Q^2$ is commonly used as a primary criteria and focuses on the prediction capabilities of the model predictor. In this paper, other criteria related to the correctness of the model variance, covariance and more generally to the whole conditional distribution are added. This methodology is applied on the Kriging of chemical measurements spatially distributed on circular domains, where several classical covariance functions are fitted and compared. The results highlight the need to include the above mentioned criteria to get a predictive model with robust uncertainty. The Kriging models are then used to quantify the uncertainty on the highest concentration via the use of conditional simulations.

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“…

D_{s} = \frac{y_{s} - {\overset{falsê}{y}}_{- s}}{\sqrt{\frac{1}{l} \sum_{s = 1}^{l} {((), y_{s} - {\overset{falsê}{y}}_{- s})}^{2}}} ((), s = 1, 2, \dots, l)

where y s and

{\overset{falsê}{y}}_{- s}

are the prediction for s th sample point using original Kriging surrogate and surrogate constructed with removing s th sample, respectively. Note that the surrogate is accepted when most of the standardized residuals are located in the acceptable range of [−3, 3], see References 56,70. Details of the statistical procedure required for leave‐one‐out cross‐validation are provided in Reference 70.…”

Section: Surrogate‐based Robust Simulation‐optimization (Two‐layer Sumentioning

confidence: 99%

“…Note that the surrogate is accepted when most of the standardized residuals are located in the acceptable range of [−3, 3], see References 56,70. Details of the statistical procedure required for leave‐one‐out cross‐validation are provided in Reference 70.…”

Section: Surrogate‐based Robust Simulation‐optimization (Two‐layer Sumentioning

confidence: 99%

Robust tuning and sensitivity analysis of stochastic integer andfractional‐order PIDcontrol systems: application ofsurrogate‐basedrobustsimulation‐optimization

Parnianifard

Fakhfakh

Kotti

et al. 2020

Int J Numerical Modelling

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This paper aims to make a trade‐off between performance and robustness in stochastic control systems with probabilistic uncertainties. For this purpose, we develop a surrogate‐based robust simulation‐optimization approach for robust tuning and analyzing the sensitivity of stochastic controllers. Kriging surrogate is combined with robust design optimization to construct a robust simulation‐optimization model in the class of dual response surfaces. Randomness in simulation experiments due to uncertainty is analyzed through bootstrapping technique by computing confidence regions for the estimation of Pareto frontier. Results confirmed a proper trade‐off between the model's performance with the measure of expected Integral Squared Error (ISE) and robustness against uncertainty in the plant's physical parameters. Finally, the proposed method is evaluated in terms of accuracy, computational cost, and simplicity particularly in comparison with some common existed techniques in the tuning of the Proportional‐Integral‐Derivative (PID) and Fractional‐Order PID (FOPID) controllers.

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Statistical Tests for Cross-Validation of Kriging Models

Cited by 6 publications

References 15 publications

Energy-Efficiency Assessment and Improvement—Experiments and Analysis Methods

Energy-Efficiency Assessment and Improvement—Experiments and Analysis Methods

Model selection based on validation criteria for Gaussian process regression: An application with highlights on the predictive variance

Robust tuning and sensitivity analysis of stochastic integer andfractional‐order PIDcontrol systems: application ofsurrogate‐basedrobustsimulation‐optimization

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