Kriging groundwater solute concentrations using flow coordinates and nonstationary covariance functions

Rivest, Martine; Marcotte, Denis

doi:10.1016/j.jhydrol.2012.09.027

Cited by 20 publications

(4 citation statements)

References 48 publications

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“…A comparative assessment from the viewpoint of accuracy and computational efficiency can be found in ref [19], where both high and low dimensional input parameter space was considered for a comprehensive analysis. The choice of suitable correlation function is a crucial element for all the Kriging variants [59][60][61]…”

Section: Krigingmentioning

confidence: 99%

Stochastic Oblique Impact on Composite Laminates: A Concise Review and Characterization of the Essence of Hybrid Machine Learning Algorithms

Mukhopadhyay

Naskar

Chakraborty

et al. 2020

Arch Computat Methods Eng

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Due to the absence of adequate control at different stages of complex manufacturing process, material and geometric properties of composite structures are often uncertain. For a secure and safe design, tracking the impact of these uncertainties on the structural responses is of utmost significance. Composite materials, commonly adopted in various modern aerospace, marine, automobile and civil structures, are often susceptible to low-velocity impact caused by various external agents. Here, along with a critical review, we present machine learning based probabilistic and non-probabilistic (fuzzy) low-velocity impact analyses of composite laminates including a detailed deterministic characterization to systematically investigate the consequences of source-uncertainty. While probabilistic analysis can be performed only when complete statistical description about the input variables are available, the non-probabilistic analysis can be executed even in the presence of incomplete statistical input descriptions with sparse data. In this study, the stochastic effects of stacking sequence, twist angle, oblique impact, plate thickness, velocity of impactor and density of impactor are investigated on the crucial impact response parameters such as contact force, plate displacement, and impactor displacement. For efficient and accurate computation, a hybrid polynomial chaos based Kriging (PC-Kriging) approach is coupled with in-house finite element codes for uncertainty propagation in both the probabilistic and non-probabilistic analyses. The essence of this paper is a critical review on the hybrid machine learning algorithms followed by detailed numerical investigation in the probabilistic and non-probabilistic regimes to access the performance of such hybrid algorithms in comparison to individual algorithms from the viewpoint of accuracy and computational efficiency.

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Section: Krigingmentioning

confidence: 99%

Stochastic Oblique Impact on Composite Laminates: A Concise Review and Characterization of the Essence of Hybrid Machine Learning Algorithms

Mukhopadhyay

Naskar

Chakraborty

et al. 2020

Arch Computat Methods Eng

View full text Add to dashboard Cite

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“…Various studies have dealt with techniques that are considered more useful than kriging: Berg and Illman (), for instance, have shown that hydraulic tomography used to map hydraulic conductivity leads to more accurate results than kriging the hydraulic conductivity field, while Shlomi and Michalak () presented an inverse/forward modelling and a transport‐enhanced kriging that perform better than “basic” kriging to represent the spatial distribution of plumes. Various methodologies have been proposed to improve the kriging technique (e.g., Shlomi and Michalak ; Rivest et al ; Schwede and Cirpka ; Rivest and Marcotte ), but “basic” kriging and cokriging are generally still used by geologists and engineers (e.g., Ahmadi and Sedghamiz ; Triki et al ; Sadat Noori et al ), because these methods are easy to implement and they have by now passed from purely academic interest to practical use (Renard ). For this reason, cokriging has been adopted in the present manuscript to offer professionals and public administrations a very simple tool that can be used to integrate different information on aquifers and to perform estimations with the estimation error variance, in order to measure their uncertainty.…”

Section: Introductionmentioning

confidence: 99%

Cokriging Transmissivity, Head and Trajectory Data for Transmissivity and Solute Path Estimation

Butera

Soffia

2016

Groundwater

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In practical situations concerning aquifers, time and/or economic restraints often make it impossible to construct numerical models, and in these cases simple methodologies could be useful, at least for feasibility studies. In this context, the present manuscript deals with the use of a straightforward cokriging method to use data acquired from a monitoring network (transmissivity, piezometric head and trajectory data) in order to obtain useful information about the characteristics of the aquifer. Two issues have been addressed: estimation of the solute path and estimation of the transmissivity. This manuscript, compared with previous works that have applied cokriging, considers that the solute transit data originate from a source of unknown intensity and from an unknown location. The proposed cokriging systems are implemented through already developed covariance and cross-covariance functions, considering a first-order approximation in the log-transmissivity variance. For this reason, numerical Monte Carlo experiments have been performed to test the accuracy of the results of the proposed cokriging procedures in both weakly (σY2=0.16) and mildly (σY2=2) heterogeneous transmissivity aquifers. Since a prerequisite of cokriging is a linear relationship among the involved quantities, more accurate results can be expected in weakly heterogeneous transmissivity fields, where the trajectory, transmissivity and hydraulic head data relations are almost linear. Comparing the numerical results with the analytical solutions, it in fact emerges that cokriging can be very useful for the estimation of a solute path and transmissivity when a limited set of data is available for weakly heterogeneous aquifers.

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“…However, the resulting non-stationary covariance functions appear to be not compactly supported. Applications of non-stationary models using the above models can be found in Paciorek and Schervish (2006), Jun and Stein (2008), Rivest and Marcotte (2012), Shamsipour et al (2013), Liang et al (2013).…”

Section: Introductionmentioning

confidence: 99%

A class of non-stationary covariance functions with compact support

Min

Marcotte

2015

Stoch Environ Res Risk Assess

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This article describes the use of non-stationary covariance functions with compact support to estimate and simulate a random function. Based on the kernel convolution theory, the functions are derived by convolving hyperspheres in R n followed by a Radon transform. The order of the Radon transform controls the differentiability of the covariance functions. By varying spatially the hyperspheres radius one defines non-stationary isotropic versions of the spherical, the cubic and the penta-spherical models. Closed-form expressions for the non-stationary covariances are derived for the isotropic spherical, cubic, and penta-spherical models. Simulation of the different non-stationary models is easily obtained by weighted average of independent standard Gaussian variates in both the isotropic and the anisotropic case. The non-stationary spherical covariance model is applied to estimate the overburden thickness over an area composed of two different geological domains. The results are compared to the estimation with a single stationary model and the estimation with two stationary models, one for each geological domain. It is shown that the non-stationary model enables a reduction of the mean square error and a more realistic transition between the two geological domains.

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Kriging groundwater solute concentrations using flow coordinates and nonstationary covariance functions

Cited by 20 publications

References 48 publications

Stochastic Oblique Impact on Composite Laminates: A Concise Review and Characterization of the Essence of Hybrid Machine Learning Algorithms

Stochastic Oblique Impact on Composite Laminates: A Concise Review and Characterization of the Essence of Hybrid Machine Learning Algorithms

Cokriging Transmissivity, Head and Trajectory Data for Transmissivity and Solute Path Estimation

A class of non-stationary covariance functions with compact support

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