The optimization of GPS positioning using response surface methodology

The Global Positioning System (GPS) has become a popular sensing system for positioning because it is free and always available and can be used in all weathers. However, the accuracy of GPS is dependent on the measurement factors selected by the surveyor. Therefore, the purpose of this research is to determine the optimal factors of the GPS positioning process. The selected process variables were measurement time and duration, recording interval, and mask angle. To determine the optimum conditions of these factors, a three-level Box–Behnken design was utilized. The results indicated that the optimum conditions of the experimental factors are 13 h as measurement time, 21.77 min as the measurement duration, 22.43 s as the range interval, and 8° as the mask angle.     

Bayesian model selection for complex geological structures using polynomial chaos proxy

Different interpretation of sedimentary environments lead to “scenario uncertainty” where the prior reservoir model has a high level of discrete uncertainty. In a real field application, the scenario uncertainty has a considerable effect on flow response uncertainty and makes the uncertainty quantification problem highly nonlinear. We use clustering methods to address the scenario uncertainty. Our approach to cluster analysis is based on the posterior probabilities of models, known as “Bayesian model selection.” Accordingly, we integrate overall possible parameters in each scenario with respect to their corresponding priors to give the measure of how well a model is supported by observations. We propose a cluster-based reduced terms polynomial chaos proxy to efficiently estimate the posterior probability density function under each cluster and calculate the posterior probability of each model. We demonstrate that the convergence rate of the reduced terms polynomial chaos proxy is significantly improved under each cluster comparing to the non-clustered case. We apply the proposed cluster-based polynomial chaos proxy framework to study the plausibility of three training images based on different geological interpretation of the second layer of synthetic Stanford VI reservoir. We demonstrate that the proposed workflow can be efficiently used to calculate the posterior probability of each scenario and also sample from the posterior facies models within each scenario.     

Dimensionality reduction for production optimization using polynomial approximations

The objective of this paper is to introduce a novel paradigm to reduce the computational effort in waterflooding global optimization problems while realizing smooth well control trajectories amenable for practical deployments in the field. In order to overcome the problems of slow convergence and non-smooth impractical control strategies, often associated with gradient-free optimization (GFO) methods, we introduce a generalized approach which represent the controls by smooth polynomial approximations either by a polynomial function or by a piecewise polynomial interpolation, which we denote as function control method (FCM) and interpolation control method (ICM), respectively. Using these approaches, we aim to optimize the coefficients of the selected functions or the interpolation points in order to represent the well-control trajectories along a time horizon. Our results demonstrate significant computational savings, due to a substantial reduction in the number of control parameters, as we seek the optimal polynomial coefficients or the interpolation points to describe the control trajectories as opposed to directly searching for the optimal control values (bottom hole pressure) at each time interval. We demonstrate the efficiency of the method on two and three-dimensional models, where we found the optimal variables using a parallel dynamic-neighborhood particle swarm optimization (PSO). We compared our FCM-PSO and ICM-PSO to the traditional formulation solved by both gradient-free and gradient-based methods. In all comparisons, both FCM and ICM show very good to superior performances.     

考虑地表径流与地下渗流耦合的斜坡降雨入渗研究

为简化分析，在模拟斜坡降雨入渗暂态渗流时，通常没有考虑入渗和产流的耦合过程。笔者提出了一种新的考虑地表径流与地下渗流耦合的斜坡降雨入渗分析方法，它较好地模拟了入渗和产流的过程，并通过算例，研究了考虑与不考虑该耦合作用对斜坡孔隙水压力分布的影响。     

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least-square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)-PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL-PCE-IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.     

Use of particulate surrogates for assessing microbial mobility in subsurface ecosystems

Mass fluxes from the ground surface can play a vital role in influencing groundwater ecosystems. Rates of delivery may influence intact ecosystem composition, while fluxes of substances associated with anthropogenic activity may critically alter the functioning of associated microbial assemblages. Field-based tracing experiments offer a valuable means of understanding mass transport rates and mechanisms, particularly in complex heterogeneous epikarst systems overlying vulnerable fissured aquifers. A short-term tracer experiment monitoring solute and particle tracer concentrations after they passed through a 10-m-thick sequence of limestone, capped by a thin soil, revealed rapid travel times and variable attenuation rates for the substances employed. Results demonstrated that particle tracers have shorter average travel times and can reach the subsurface in higher concentrations and over shorter times than non-reactive solutes. High recovery rates for the bacterial tracer Ralstonia eutropha H16 contrasted strongly with those of similarly sized fluorescent polystyrene microspheres, highlighting the importance of physico-chemical surface characteristics of particle tracers. Complementary laboratory batch experiments examined the role played by organic and inorganic soil/rock surfaces on particle tracer attenuation. Findings suggest that biofilms may significantly promote transport of particulate material below ground, i.e., the delivery of allochthonous microorganisms to karst groundwater.     

Bearing capacity of strip footings on spatially random soils using sparse polynomial chaos expansion

A probabilistic model is presented to compute the probability density function (PDF) of the ultimate bearing capacity of a strip footing resting on a spatially varying soil. The soil cohesion and friction angle were considered as two anisotropic cross‐correlated non‐Gaussian random fields. The deterministic model was based on numerical simulations. An efficient uncertainty propagation methodology that makes use of a non‐intrusive approach to build up a sparse polynomial chaos expansion for the system response was employed. The probabilistic numerical results were presented in the case of a weightless soil. Sobol indices have shown that the variability of the ultimate bearing capacity is mainly due to the soil cohesion. An increase in the coefficient of variation of a soil parameter (c or φ) increases its Sobol index, this increase being more significant for the friction angle. The negative correlation between the soil shear strength parameters decreases the response variability. The variability of the ultimate bearing capacity increases with the increase in the coefficients of variation of the random fields, the increase being more significant for the cohesion parameter. The decrease in the autocorrelation distances may lead to a smaller variability of the ultimate bearing capacity. Finally, the probabilistic mean value of the ultimate bearing capacity presents a minimum. This minimum is obtained in the isotropic case when the autocorrelation distance is nearly equal to the footing breadth. However, for the anisotropic case, this minimum is obtained at a given value of the ratio between the horizontal and vertical autocorrelation distances. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust optimisation of CO2 sequestration strategies under geological uncertainty using adaptive sparse grid surrogates

Geologic CO₂ sequestration in deep saline aquifers is a promising technique to mitigate the effect of greenhouse gas emissions. Designing optimal CO₂ injection strategy becomes a challenging problem in the presence of geological uncertainty. We propose a surrogate assisted optimisation technique for robust optimisation of CO₂ injection strategies. The surrogate is built using Adaptive Sparse Grid Interpolation (ASGI) to accelerate the optimisation of CO₂ injection rates. The surrogate model is adaptively built with different numbers of evaluation points (simulation runs) in different dimensions to allow automatic refinement in the dimension where added resolution is needed. This technique is referred to as dimensional adaptivity and provides a good balance between the accuracy of the surrogate model and the number of simulation runs to save computational costs. For a robust design, we propose a utility function which comprises the statistical moment of the objective function. Numerical testing of the proposed approach applied to benchmark functions and reservoir models shows the efficiency of the method for the robust optimisation of CO₂ injection strategies under geological uncertainty.     

Stochastic seismic slope stability assessment using polynomial chaos expansions combined with relevance vector machine

This paper presents probabilistic assessment of seismically-induced slope displacements considering uncertainties of seismic ground motions and soil properties.A stochastic ground motion model representing both the temporal and spectral non-stationarity of earthquake shakings and a three-dimensional rotational failure mechanism are integrated to assess Newmark-type slope displacements.A new probabilistic approach that incorporates machine learning in metamodeling technique is proposed,by combining relevance vector machine with polynomial chaos expansions(RVM-PCE).Compared with other PCE methods,the proposed RVM-PCE is shown to be more effective in estimating failure probabilities.The sensitivity and relative influence of each random input parameter to the slope displacements are discussed.Finally,the fragility curves for slope displacements are established for sitespecific soil conditions and earthquake hazard levels.The results indicate that the slope displacement is more sensitive to the intensities and strong shaking durations of seismic ground motions than the frequency contents,and a critical Arias intensity that leads to the maximum annual failure probabilities can be identified by the proposed approach.     

A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database

This work explores the implementation of an adaptive strategy to design sparse ensembles of oceanic simulations suitable for constructing polynomial chaos surrogates. We use a recently developed pseudo-spectral algorithm that is based on a direct application of the Smolyak sparse grid formula and that allows the use of arbitrary admissible sparse grids. The adaptive algorithm is tested using an existing simulation database of the oceanic response to Hurricane Ivan in the Gulf of Mexico. The a priori tests demonstrate that sparse and adaptive pseudo-spectral constructions lead to substantial savings over isotropic sparse sampling in the present setting.     

A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow

We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical and numerical aspects of surface–subsurface flow modeling are presented. This work was supported by National Science Foundation grant DMS-0411413.     

A coupled surface/subsurface flow model accounting for air entrapment and air pressure counterflow

This work introduces the soil air system into integrated hydrology by simulating the flow processes and interactions of surface runoff, soil moisture and air in the shallow subsurface. The numerical model is formulated as a coupled system of partial differential equations for hydrostatic (diffusive wave) shallow flow and two-phase flow in a porous medium. The simultaneous mass transfer between the soil, overland, and atmosphere compartments is achieved by upgrading a fully established leakance concept for overland-soil liquid exchange to an air exchange flux between soil and atmosphere. In a new algorithm, leakances operate as a valve for gas pressure in a liquid-covered porous medium facilitating the simulation of air out-break events through the land surface. General criteria are stated to guarantee stability in a sequential iterative coupling algorithm and, in addition, for leakances to control the mass exchange between compartments. A benchmark test, which is based on a classic experimental data set on infiltration excess (Horton) overland flow, identified a feedback mechanism between surface runoff and soil air pressures. Our study suggests that air compression in soils amplifies surface runoff during high precipitation at specific sites, particularly in near-stream areas.     

Effect of Fenton process on treatment of simulated textile wastewater: optimization using response surface methodology

A large portion of water is consumed during various textile operations thereby discharging wastewaters with pollutants of huge environmental concern. The treatment of such wastewaters has promising impact in the field of environmental engineering. In this work, Fenton oxidation treatment was engaged to treat simulated textile wastewater. Box–Behnken design and response surface methodology were employed to optimize the efficiency of Fenton process. Iron dose, peroxide dose and pH were considered as input variables while the responses were taken as chemical oxygen demand and color removal. A total of 17 experiments were conducted and analyzed using second-order quadratic model. The quadratic models generated for chemical oxygen demand and color removal efficiencies were validated using analysis of variances, and it was found that the experimental data fitted the second-order model quite effectively. Analysis of variances demonstrated high values of coefficient of determination (R ²) for chemical oxygen demand and color removal efficiencies with values of 0.9904 and 0.9963 showing high conformation of predicted values to the experimental ones. Perturbation plots suggested that the iron dosage produced the maximum effect on both chemical oxygen demand and color removal efficiencies. The optimum parameters were determined as Fe²⁺ dose—550 mg/L, H₂O₂ dose—5538 mg/L, pH—3.3 with corresponding chemical oxygen demand and color removal efficiencies of 73.86 and 81.35%. Fenton process was found efficient in treatment of simulated textile wastewater, and optimization using response surface methodology was found satisfactory as well as relevant. From the present study, it can also be concluded that if this method is used as pretreatment integrated with biological treatment, it can lead to eco-friendly solution for treatment of textile wastewaters.     

Up-scaling application of microbial carbonate precipitation: optimization of urease production using response surface methodology and injection modification

In order to reduce the cost of the microbial-induced carbonate precipitation, mixotrophic growth of Sporosarcina pasteurii was carried out at different yeast extract/sodium acetate concentrations and constant chemical oxygen demand for optimal production of urease enzyme. Optimization of cultivation conditions was also investigated using a 3-level central composite design approach based on the response surface methodology. A good agreement between predicted values of enzyme activity and experimental results was observed (R ² value of 0.973). All three chosen independent variables had statistically great effects on the efficiency of urease activity. The maximum activity of 2.98 mM urea min^?1 was achieved at yeast extract concentration of 5 g L^?1, NH₄ concentration of 9.69 g L^?1, and incubation time of 60 h as the optimal conditions. Thereafter, a novel injection procedure as sequencing batch mode injection has been proposed for bacteria and cementation fluid injection at obtained optimal urease activity. After fourth injection of bacteria and cementation fluid, uniform CaCO₃ distribution with unconfined compression strength of 795 kPa was obtained even for poorly graded sand. The presented experimental approach for optimizing urease activity and strength production in porous media can be used to design the treatment protocol for practical engineering applications.     

A semi‐analytical solution of surface flow and subsurface flow on a slope land under a uniform rainfall excess

A new approach is proposed to analyze the surface flow and subsurface flow passing over a pervious ground under a uniform rainfall excess. The flow field is divided into two regions that are called water layer and soil layer. To figure out the hydraulic behavior of overland flow on an inclined plane under a rainfall event, the simplified Navier–Stokes equations are employed for the surface water flow, and the flow inside the soil layer is porous media flow, which is governed by Biot's (1956, 1962) theory of poroelasticity. The velocity distribution of overland flow is nonzero at the ground surface. The relation between water depth and slope length was developed first. The profile of surface water flow was then found backwards from the downstream end of the flow section by the Runge–Kutta method. After that, the flow velocity and flow discharge of each layer could also be obtained via the water depth. Finally, the variation of fluid shear stress inside the soil layer is also discussed. Copyright © 2011 John Wiley & Sons, Ltd.     

Probabilistic evaluation of tunnel face stability in spatially random soils using sparse polynomial chaos expansion with global sensitivity analysis

The sparse polynomial chaos expansion is employed to perform a probabilistic analysis of the tunnel face stability in the spatially random soils. A shield tunnel under compressed air is considered which implies that the applied pressure is uniformly distributed on the tunnel face. Two sets of failure mechanisms in the context of the limit analysis theory with respect to the frictional and the purely cohesive soils are used to calculate the required face pressure. In the case of the frictional soils, the cohesion and the friction angle are modeled as two anisotropic cross-correlated lognormal random fields; for the purely cohesive soils, the cohesion and the unit weight are modeled as two anisotropic independent lognormal random fields. The influences of the spatial variability and of the cross-correlation between the cohesion and the friction angle on the probability density function of the required face pressure, on the sensitivity index and on the failure probability are discussed. The obtained results show that the spatial variability has an important influence on the probability density function as well as the failure probability, but it has a negligible impact on the Sobol’s index.     

Quantifying and relating land-surface and subsurface variability in permafrost environments using LiDAR and surface geophysical datasets

The value of remote sensing and surface geophysical data for characterizing the spatial variability and relationships between land-surface and subsurface properties was explored in an Alaska (USA) coastal plain ecosystem. At this site, a nested suite of measurements was collected within a region where the land surface was dominated by polygons, including: LiDAR data; ground-penetrating radar, electromagnetic, and electrical-resistance tomography data; active-layer depth, soil temperature, soil-moisture content, soil texture, soil carbon and nitrogen content; and pore-fluid cations. LiDAR data were used to extract geomorphic metrics, which potentially indicate drainage potential. Geophysical data were used to characterize active-layer depth, soil-moisture content, and permafrost variability. Cluster analysis of the LiDAR and geophysical attributes revealed the presence of three spatial zones, which had unique distributions of geomorphic, hydrological, thermal, and geochemical properties. The correspondence between the LiDAR-based geomorphic zonation and the geophysics-based active-layer and permafrost zonation highlights the significant linkage between these ecosystem compartments. This study suggests the potential of combining LiDAR and surface geophysical measurements for providing high-resolution information about land-surface and subsurface properties as well as their spatial variations and linkages, all of which are important for quantifying terrestrial-ecosystem evolution and feedbacks to climate.     

Effects of hillslope geometry on surface and subsurface flows

Dividing a catchment to subcatchment or hillslope scales allows for better scrutiny of the changes in spatial distribution of rainfall, soil attributes and plant cover across the catchment. An instantaneous unit hydrograph model is suggested for simulating runoff hydrographs for complex hillslopes. This model is able to estimate surface and subsurface flows of the catchment based on the Dunne-Black mechanism. For this purpose, a saturation model is used to separate the saturated and unsaturated zones in complex hillslopes. The profile curvatures (concave, straight and convex) and plan shapes (convergent, parallel and divergent) of complex hillslopes are considered, in order to compute the travel time of surface and subsurface flows. The model was used for prediction of the direct runoff hydrograph and subsurface flow hydrograph of Walnut Gulch No. 125 catchment in Arizona (USA). Based on results, the geometry of hillslopes can change the peak of the direct runoff hydrograph up to two-fold, either higher or lower. The divergent hillslopes show higher peaks in comparison with the parallel and convergent hillslopes. The highest and lowest peak flows correspond to divergent-concave and convergent-straight hillslopes, respectively.     

Fluoride in groundwater: low-cost separation and stabilization by response surface optimization

A nanomembrane-based hybrid treatment system for separation of fluoride from contaminated groundwater and its subsequent stabilization in a solid matrix through chemical coagulation–precipitation process using response surface optimization for safe disposal were designed and investigated. The continuous flat-sheet cross-flow nanofiltration membrane module with well-screened commercial polyamide composite membrane succeeded in removing 99 % fluoride from water while yielding a pure water flux as high as 158–160 L/m²h of a transmembrane hydraulic pressure of only 14 bars. Such an operating pressure is much lower than that required in reverse osmosis for the same separation. The designed system for the first time provides a total solution to a complex problem in a very simple, compact, flexible, and novel design that ensures continuous, steady, and hassle-free long-term operation without the necessity for frequent replacement of membranes. The approximate cost for production of 1000 L of safe drinking water from fluoride-contaminated groundwater computes to only $ 1.4, indicating affordability in adopting the low-cost, high-flux water purification system by the affected people in many parts of the world.