Kriging for indirect measurement, with application to flow measurement

International audienceKriging, a technique originating from geostatistics, is employed to build black-box models to be used to predict a quantity of interest based on the values taken by some experimental factors. This attractive alternative to more popular techniques such as neural networks is first presented. It is then applied to the measurement of the flow in a water pipe from the observation of speed at given points of a cross section. A pure black-box model turns out not to be satisfactory, and two approaches are suggested for incorporating prior knowledge. The second one, which is more systematic also turns out to provide much better performance

Modelling environmental factors correlated with podoconiosis: a geospatial study of non-filarial elephantiasis

Introduction The precise trigger of podoconiosis — endemic non-filarial elephantiasis of the lower legs — is unknown. Epidemiological and ecological studies have linked the disease with barefoot exposure to red clay soils of volcanic origin. Histopathology investigations have demonstrated that silicon, aluminium, magnesium and iron are present in the lower limb lymph node macrophages of both patients and non-patients living barefoot on these clays. We studied the spatial variation (variations across an area) in podoconiosis prevalence and the associated environmental factors with a goal to better understanding the pathogenesis of podoconiosis. Methods Fieldwork was conducted from June 2011 to February 2013 in 12 kebeles (administrative units) in northern Ethiopia. Geo-located prevalence data and soil samples were collected and analysed along with secondary geological, topographic, meteorological and elevation data. Soil data were analysed for chemical composition, mineralogy and particle size, and were interpolated to provide spatially continuous information. Exploratory, spatial, univariate and multivariate regression analyses of podoconiosis prevalence were conducted in relation to primary (soil) and secondary (elevation, precipitation, and geology) covariates. Results Podoconiosis distribution showed spatial correlation with variation in elevation and precipitation. Exploratory analysis identified that phyllosilicate minerals, particularly clay (smectite and kaolinite) and mica groups, quartz (crystalline silica), iron oxide, and zirconium were associated with podoconiosis prevalence. The final multivariate model showed that the quantities of smectite (RR = 2.76, 95% CI: 1.35, 5.73; p = 0.007), quartz (RR = 1.16, 95% CI: 1.06, 1.26; p = 0.001) and mica (RR = 1.09, 95% CI: 1.05, 1.13; p < 0.001) in the soil had positive associations with podoconiosis prevalence. Conclusions More quantities of smectite, mica and quartz within the soil were associated with podoconiosis prevalence. Together with previous work indicating that these minerals may influence water absorption, potentiate infection and be toxic to human cells, the present findings suggest that these particles may play a role in the pathogenesis of podoconiosis and acute adenolymphangitis, a common cause of morbidity in podoconiosis patients

Stochastic rainfall interpolation and downscaling

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Estimating rainfall and water balance over the Okavango River Basin for hydrological applications

A historical database for use in rainfall-runoff modeling of the Okavango River Basin in Southwest Africa is presented. The work has relevance for similar data-sparse regions. The parameters of main concern are rainfall and catchment water balance which are key variables for subsequent studies of the hydrological impacts of development and climate change. Rainfall estimates are based on a combination of in-situ gauges and satellite sources. Rain gauge measurements are most extensive from 1955 to 1972, after which they are drastically reduced due to the Angolan civil war. The sensitivity of the rainfall fields to spatial interpolation techniques and the density of gauges was evaluated. Satellite based rainfall estimates for the basin are developed for the period from 1991 onwards, based on the Tropical Rainfall Measuring Mission (TRMM) and Special Sensor Microwave Imager (SSM/I) data sets. The consistency between the gauges and satellite estimates was considered. A methodology was developed to allow calibration of the rainfall-runoff hydrological model against rain gauge data from 1960-1972, with the prerequisite that the model should be driven by satellite derived rainfall products for the 1990s onwards. With the rain gauge data, addition of a single rainfall station (Longa) in regions where stations earlier were lacking was more important than the chosen interpolation method. Comparison of satellite and gauge rainfall outside the basin indicated that the satellite overestimates rainfall by 20%. A non-linear correction was derived used by fitting the rainfall frequency characteristics to those of the historical rainfall data. This satellite rainfall dataset was found satisfactory when using the Pitman rainfall-runoff model (Hughes et al., this issue). Intensive monitoring in the region is recommended to increase accuracy of the comprehensive satellite rainfall estimate calibration procedur

Global Modeling and Prediction of Computer Network Traffic

We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It arises from a limit approximation of the traffic fluctuations as the time--scale and the number of users sharing the network grow. The resulting probability model is comprised of a Gaussian and/or a stable, infinite variance components. They can be succinctly described and handled by certain 'space-time' random fields. The model is validated against simulated and real data. It is then applied to predict traffic fluctuations over unobserved links from a limited set of observed links. Further, applications to anomaly detection and network management are briefly discussed

Performance study of gradient-enhanced Kriging

The use of surrogate models for approximating computationally expensive simulations has been on the rise for the last two decades. Kriging-based surrogate models are popular for approximating deterministic computer models. In this work, the performance of Kriging is investigated when gradient information is introduced for the approximation of computationally expensive black-box simulations. This approach, known as gradient-enhanced Kriging, is applied to various benchmark functions of varying dimensionality (2D-20D). As expected, results from the benchmark problems show that additional gradient information can significantly enhance the accuracy of Kriging. Gradient-enhanced Kriging provides a better approximation even when gradient information is only partially available. Further comparison between gradient-enhanced Kriging and an alternative formulation of gradient-enhanced Kriging, called indirect gradient-enhanced Kriging, highlights various advantages of directly employing gradient information, such as improved surrogate model accuracy, better conditioning of the correlation matrix, etc. Finally, gradient-enhanced Kriging is used to model 6- and 10-variable fluid-structure interaction problems from bio-mechanics to identify the arterial wall's stiffness

Recent advances in low-cost particulate matter sensor: calibration and application

Particulate matter (PM) has been monitored routinely due to its negative effects on human health and atmospheric visibility. Standard gravimetric measurements and current commercial instruments for field measurements are still expensive and laborious. The high cost of conventional instruments typically limits the number of monitoring sites, which in turn undermines the accuracy of real-time mapping of sources and hotspots of air pollutants with insufficient spatial resolution. The new trends of PM concentration measurement are personalized portable devices for individual customers and networking of large quantity sensors to meet the demand of Big Data. Therefore, low-cost PM sensors have been studied extensively due to their price advantage and compact size. These sensors have been considered as a good supplement of current monitoring sites for high spatial-temporal PM mapping. However, a large concern is the accuracy of these low-cost PM sensors. Multiple types of low-cost PM sensors and monitors were calibrated against reference instruments. All these units demonstrated high linearity against reference instruments with high R2 values for different types of aerosols over a wide range of concentration levels. The question of whether low-cost PM monitors can be considered as a substituent of conventional instruments was discussed, together with how to qualitatively describe the improvement of data quality due to calibrations. A limitation of these sensors and monitors is that their outputs depended highly on particle composition and size, resulting in as high as 10 times difference in the sensor outputs. Optical characterization of low-cost PM sensors (ensemble measurement) was conducted by combining experimental results with Mie scattering theory. The reasons for their dependence on the PM composition and size distribution were studied. To improve accuracy in estimation of mass concentration, an expression for K as a function of the geometric mean diameter, geometric standard deviation, and refractive index is proposed. To get rid of the influence of the refractive index, we propose a new design of a multi-wavelength sensor with a robust data inversion routine to estimate the PM size distribution and refractive index simultaneously. The utility of the networked system with improved sensitivity was demonstrated by deploying it in a woodworking shop. Data collected by the networked system was utilized to construct spatiotemporal PM concentration distributions using an ordinary Kriging method and an Artificial Neural Network model to elucidate particle generation and ventilation processes. Furthermore, for the outdoor environment, data reported by low-cost sensors were compared against satellite data. The remote sensing data could provide a daily calibration of these low-cost sensors. On the other hand, low-cost PM sensors could provide better accuracy to demonstrate the microenvironment