Structural optimization using Kriging approximation

Sakata, Sei-ichiro; Ashida, Fumihiro; Zako, Masaru

doi:10.1016/s0045-7825(02)00617-5

Cited by 183 publications

(78 citation statements)

References 10 publications

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“…In this study, types of semivariograms are from the Gaussian semivariogram model because the Gaussian semivariogram model generates a relatively smooth estimated surface [57]. It is widely used in the field of approximate optimization [58].…”

Section: The Ordinary Kriging Methodsmentioning

confidence: 99%

A Comparison of Markov Chain Random Field and Ordinary Kriging Methods for Calculating Soil Texture in a Mountainous Watershed, Northwest China

Zhang

et al. 2018

Sustainability

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Accurate mapping the spatial distribution of different soil textures is important for eco-hydrological studies and water resource management. However, it is quite a challenge to map the soil texture in data scarce, hard to access mountainous watersheds. This paper compares a nonlinear method, the Markov chain random field (MCRF) with a classical linear method, ordinary kriging (OK) for calculating the soil texture at different search radiuses in the upstream region of the Heihe River Watershed. Results show that soil texture values that were calculated by the OK method tends to predict soil texture values within a certain range (sand (12.098~40.317), silt (47.847~71.231), and clay (12.781~19.420)) because of the smoothing effect, thus leading to greater accuracy in predicting the major soil texture type (silt loam). Nonetheless, the MCRF method considers the interclass relationships between sampling points, leading to greater accuracy in predicting minor types (loam and sandy loam). Meanwhile, the OK method performed best for all the types at the radius of 65 km influenced by the densities of all the sampling points, while the best performance of the MCRF method differs with radiuses as the largest densities varying for different soil types. For loam and sandy loam, the OK method ignored them, thus the MCRF method is more suitable in mountainous areas with high soil heterogeneity.

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Section: The Ordinary Kriging Methodsmentioning

confidence: 99%

A Comparison of Markov Chain Random Field and Ordinary Kriging Methods for Calculating Soil Texture in a Mountainous Watershed, Northwest China

Zhang

et al. 2018

Sustainability

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“…Although a different surrogate modeling method such as a simple polynomial or a radial basis function could conceivably be used within this framework, kriging is used due to its ability to more accurately represent complicated responses while providing an error estimate of the predictor. First used by geologists in the estimation of mineral concentrations, it has since been popularized by Sacks et al [12] in the creation of surrogate models of deterministic computational experiments and has been used successfully in the optimization of a number of different design problems [13][14][15][16].…”

Section: B Krigingmentioning

confidence: 99%

Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization

et al. 2010

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When carrying out design searches, traditional variable screening techniques can find it extremely difficult to distinguish between important and unimportant variables. This is particularly true when only a small number of simulations are combined with a parameterization that results in a large number of variables of seemingly equal importance. Here, the authors present a variable reduction technique that employs proper orthogonal decomposition to filter out undesirable or badly performing geometries from an optimization process. Unlike traditional screening techniques, the presented method operates at the geometric level instead of the variable level. The filtering process uses the designs that result from a geometry parameterization instead of the variables that control the parameterization. The method is shown to perform well in the optimization of a two-dimensional airfoil for the minimization of drag-to-lift ratio, producing designs better than those resulting from traditional krigingbased surrogate model optimization and with a significant reduction in surrogate tuning cost.

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“…This may be the same as the objective function of the problem being optimized, but often is not, in an effort to increase efficiency. Within survivor selection, we use the Kriging method to select one individual 49 (and reject the others). We progressively generate a new population b (g+1) with l individuals.…”

Section: Survivor Selectionmentioning

confidence: 99%

“…It recycles the already calculated functions to better approximate the function over the optimization domain. For this, the Kriging method 49 is used. This method provides both an estimation of the function value at any point but also the confidence interval of this estimation.…”

Section: Survivor Selectionmentioning

confidence: 99%

Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm

et al. 2009

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A novel optimization approach, capable of extracting the mechanical properties of an elasto-plastic material from indentation data, is proposed. Theoretical verification is performed on two simulated configurations. The first is based on the analysis of the load-displacement data and the topography of the residual imprint of a single conical indenter. The second is based on the load-displacement data obtained from two conical indenters with different semi-angles. In both cases, a semi-analytical approach [e.g., Dao et al., Acta Mater. 49, 3899 (2001) and Bucaille et al., Acta Mater. 51, 1663] is used to estimate Young's modulus, yield stress, and strain hardening coefficient from the load-displacement data. An inverse finite element model, based on a commercial solver and a newly developed optimization algorithm based on a robust stochastic methodology, uses these approximate values as starting values to identify parameters with high accuracy. Both configurations use multiple data sets to extract the elastic-plastic material properties; this allows the mechanical properties of materials to be determined in a robust way.

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Structural optimization using Kriging approximation

Cited by 183 publications

References 10 publications

A Comparison of Markov Chain Random Field and Ordinary Kriging Methods for Calculating Soil Texture in a Mountainous Watershed, Northwest China

A Comparison of Markov Chain Random Field and Ordinary Kriging Methods for Calculating Soil Texture in a Mountainous Watershed, Northwest China

Geometric Filtration Using Proper Orthogonal Decomposition for Aerodynamic Design Optimization

Determination of plastic properties of metals by instrumented indentation using a stochastic optimization algorithm

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