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An assessment of radio network coverage, usually in the form of a measurement campaign, is essential for multi-base-station (multi-BS) network deployment and maintenance. It can be conducted by a network operator or its served consumers. However, the number of measurement points and their locations may not be known in advance for an efficient and accurate evaluation. The main goal of this study is to propose a new methodology for understanding the selection of measurement points during coverage and signal quality assessment. It is particularly tailored to multi-BS low-power wide-area network (LPWAN) deployments without explicit knowledge of BS locations. To this aim, we first conduct a large-scale measurement campaign for three popular LPWAN technologies, namely, NB-IoT, Sigfox, and LoRaWAN. Utilizing this baseline data, we develop a procedure for identifying the minimum set of measurement points for the coverage assessment with a given accuracy as well as study which interpolation algorithms produce the lowest approximation error. Our results demonstrate that a random choice of measurement points is on par with their deterministic selection. Out of the candidate interpolation algorithms, Kriging method offers attractive performance in terms of the absolute error for NB-IoT deployments. By contrast, for Sigfox and LoRaWAN infrastructures, less complex techniques, such as Natural-neighbor, Linear interpolation, or Inverse-Distance Weighting, can achieve comparable (and occasionally even better) accuracy levels. acceptedVersion

Context. Piecewise linear approximation of curves has a large number of applications in computer algorithms, as the reconstruction of objects of complex shapes on monitors, CNC machines and 3D printers. In many cases, it is required to have the smallest number of segments for a given accuracy. Objective. The objective of this paper is to improve the method of asymptotically optimal piecewise linear interpolation of plane parametric curves. This improvement is based to research influence of the method parameters and algorithms to distributions of approximation errors. Method. An asymptotically optimal method of curves interpolation is satisfied to the condition of minimum number of approximation units. Algorithms for obtaining the values of the sequence of approximation nodes are suggested. This algorithm is based on numerical integration of the nodes regulator function with linear and spline interpolation of its values. The method of estimating the results of the curve approximation based on statistical processing of line segments sequence of relative errors is substantiated. Modeling of real curves approximation is carried out and influence of the sampling degree of integral function – the nodes regulator on distribution parameters of errors is studied. The influence is depending on a method of integral function interpolation. Results. Research allows to define necessary the number of discretization nodes of the integral function in practical applications. There have been established that with enough sampling points the variance of the error’s distribution stabilizes and further increasing this number does not significantly increase the accuracy of the curve approximation. In the case of spline interpolation of the integral function, the values of the distribution parameters stabilized much faster, which allows to reduce the number of initial sampling nodes by 5–6 times having similar accuracy. Conclusions. Modelling of convex planar parametric curves reconstruction by an asymptotically optimal linear interpolation algorithm showed acceptable results without exceeding the maximum errors limit in cases of a sufficient discretization of the integral function. The prospect of further research is to reduce the computational complexity when calculating the values of the integral distribution function by numerical methods, and to use discrete analogues of derivatives in the expression of this function.

The paper is based on using methods of continuous mathematics in discrete problems. Three new approaches to solving scheduling theory problems are considered, namely, a metric approach, an interpolation approach, and a combined one (metric interpolation). Metric interpolation is a mix of the other two approaches and combines their advantages. Each of these approaches permits one to reduce the time required for solving the corresponding problems and calculate the values of the guaranteed absolute error of the objective function.

This paper presents a new predictor–corrector numerical scheme suitable for fractional differential equations. An improved explicit Atangana–Seda formula is obtained by considering the neglected terms and used as the predictor stage of the proposed method. Numerical formulas are presented that approximate the classical first derivative as well as the Caputo, Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. Simulation results are used to assess the approximation error of the new method for various differential equations. In addition, a case study is considered where the proposed scheme is used to obtain numerical solutions of the Gierer–Meinhardt activator–inhibitor model with the aim of assessing the system’s dynamics.

Polarization tensor (PT) has been widely used in engineering application, particularly in electric and magnetic field areas. In this case, suitable method must be employed in the evaluation of PT in order to make sure that the tensor obtained is higher in its accuracy. Our aim in this paper is to provide simple and easy implemented method to compute first order PT which is based on Gaussian quadrature numerical integration involving linear interpolation. This study provides the comparison between two different orders of Gaussian quadrature, which is order one and order three. The numerical technique of higher order Gaussian quadrature as PT being calculated offer more accurate and higher in its convergence. Relative error for PT is calculated by using provided analytical solution and higher order Gaussian quadrature gives high accuracy and convergence compared to lower order Gaussian quadrature. In this study, the validation of the results obtained by using our proposed method is provided by comparing it with the analytical solution derived from previous researcher. We illustrate the behavior of a tensor of a sphere and ellipsoid with graphical representation.

With the increasing integration of various renewable energy resources into electric power systems, the stochastic power flow calculation, which falls into the uncertainty propagation (UP) problems, has attracted renewed interest recently. The adaptive sparse pseudospectral approximation method (A-SPAM) is highly efficient to solve UP problems. However, there still exist two major drawbacks: 1) its global error estimate is not accurate enough to evaluate the actual approximation error; and 2) it is intended for single-output systems and there is no efficient method for its application in multi-output systems. In order to overcome these two defects, in this study a new adaptive sparse pseudospectral approximation method (NA-SPAM) is proposed based on two improvements on A-SPAM. First, a new global error estimate is presented which features much higher estimation accuracy. Second, a revised version of error estimates is given based on unification of the index set, which apparently improves the calculation efficiency for multi-output problems. At last, the effectiveness of the two improvements and NA-SPAM is validated by mathematical and practical cases.

Calculation of water influx into petroleum reservoir is a tedious evaluation with significant reservoir engineering applications. The classical approach developed by van Everdingen–Hurst (vEH) based on diffusivity equation solution had been the fulcrum for water influx calculation in both finite and infinite-acting aquifers. The vEH model for edge-water drive reservoirs was modified by Allard and Chen for bottom-water drive reservoirs. Regrettably, these models solution variables: dimensionless influx ($$W_{{{\text{eD}}}}$$WeD) and dimensionless pressure ($$P_{D}$$PD) were presented in tabular form. In most cases, table look-up and interpolation between time entries are necessary to determine these variables, which makes the vEH approach tedious for water influx estimation. In this study, artificial neural network (ANN) models to predict the reservoir-aquifer variables$$W_{{{\text{eD}}}}$$WeDand$$P_{D}$$PDwas developed based on the vEH datasets for the edge- and bottom-water finite and infinite-acting aquifers. The overall performance of the developed ANN models correlation coefficients (R) was 0.99983 and 0.99978 for the edge- and bottom-water finite aquifer, while edge- and bottom-water infinite-acting aquifer was 0.99992 and 0.99997, respectively. With new datasets, the generalization capacities of the developed models were evaluated using statistical tools: coefficient of determination (R2),R, mean square error (MSE), root-mean-square error (RMSE) and absolute average relative error (AARE). Comparing the developed finite aquifer models predicted$$W_{{{\text{eD}}}}$$WeDwith Lagrangian interpolation approach resulted inR2,R, MSE, RMSE and AARE of 0.9984, 0.9992, 0.3496, 0.5913 and 0.2414 for edge-water drive and 0.9993, 0.9996, 0.1863, 0.4316 and 0.2215 for bottom-water drive. Also, infinite-acting aquifer models (Model-1) resulted inR2,R, MSE, RMSE and AARE of 0.9999, 0.9999, 0.5447, 0.7380 and 0.2329 for edge-water drive, while bottom-water drive had 0.9999, 0.9999, 0.2299, 0.4795 and 0.1282. Again, the edge-water infinite-acting model predicted$$W_{{{\text{eD}}}}$$WeDand Edwardson et al. polynomial estimated$$W_{eD}$$WeDresulted in theR2value of 0.9996,Rof 0.9998, MSE of 4.740 × 10–4, RMSE of 0.0218 and AARE of 0.0147. Furthermore, the developed ANN models generalization performance was compared with some models for estimating$$P_{D}$$PD. The results obtained for finite aquifer model showed the statistical measures:R2,R, MSE, RMSE and AARE of 0.9985, 0.9993, 0.0125, 0.1117 and 0.0678 with Chatas model and 0.9863, 0.9931, 0.1411, 0.3756 and 0.2310 with Fanchi equation. The infinite-acting aquifer model had 0.9999, 0.9999, 0.1750, 0.0133 and 7.333 × 10–3with Edwardson et al. polynomial, then 0.9865, 09,933, 0.0143, 0.1194 and 0.0831 with Lee model and 0.9991, 0.9996, 1.079 × 10–3, 0.0328 and 0.0282 with Fanchi model. Therefore, the developed ANN models can predict$$W_{{{\text{eD}}}}$$WeDand$$P_{D}$$PDfor the various aquifer sizes provided by vEH datasets for water influx calculation.

Global navigation satellite system (GNSS) and interferometric synthetic aperture radar (InSAR) data are integrated to extract the 3-D surface deformations, which are of great significance for studying geological hazards. In this study, two major problems are focused on integration. For one thing, we propose an iterated almost unbiased estimation (IAUE) method to estimate the variance components of GNSS and InSAR for the case where the estimation of variance components of multisource data by traditional variance component estimation methods may be negative and inaccurate. For another, considering that heterogeneous data errors may lead to unstable 3-D solutions, we propose adding the Laplacian smoothness constraint (LSC) to the function model, which can smooth the solutions by minimizing the second derivative of the displacements. These two methods are abbreviated as IAUE-LSC. In the simulation experiment, the performance of traditional Helmert variance component estimation is first compared with IAUE. IAUE can not only converge more quickly, but also avoid negative variances. Furthermore, we find that the excessively large relative error ratio between GNSS and InSAR is an essential factor leading to the instability of the 3-D solutions. The IAUE-LSC method is immune to this instability and can obtain more stable results. In addition, the 2018 Hawaii case demonstrates that IAUE achieves improvements of 2.58, 2.77, and 7.69 cm in the east, north, and up directions relative to the traditional weighted least-squares method, while the combined IAUE-LSC achieves improvements of 2.29, 0.32, and 1.68 cm compared to the IAUE alone.

The present attempt is made to propose a new class of numerical techniques for finding numerical solutions of ODE. The proposed numerical techniques are based on interpolation of a polynomial. Currently constructed numerical techniques use the additional information(s) of derivative(s) on particular grid point(s). The advantage of the presently proposed numerical techniques is that these techniques are implemented in one step and can provide highly accurate solution and can be constructed on fewer amounts of grid points but has the disadvantage of finding derivative(s). It is to be noted that the high order techniques can be constructed using just two grid points. Presently proposed fourth order technique is A-stable but not L-stable. The order and maximum absolute error are found for a fourth order technique. The fourth order technique is employed to solve the Darcy-Forchheimer fluid-flow problem which is transformed further to a third-order non-linear boundary value problem on the semi-infinite domain.

This brief presents a memory based fast binary logarithmic converter based on a piecewise linear approximation technique. The proposed method is simple and arithmetic operation-less, which achieves 10−4 to 10−3 maximum absolute error (MAE) while maintaining a high speed. The approach partitions the logarithmic curve of the fractional component into $2^{L}$ uniform regions and a block RAM (size $2^{L} \times $ bits) stores the approximate value of each sub-region. For any number, most significant $L$ bits of the fractional component address the memory location of the logarithmic converter. The hardware synthesis result, implemented with 26 bits fractional precision on Virtex-6 field-programmable gate array device, shows 75% improvement in MAE and 27% decrease in critical path delay compared to the current state-of-the-art techniques in the worst-case scenario. In Otsu’s image thresholding algorithm, the proposed logarithmic converter with 3.08 ( $=2^{8} \times 12$ ) kbits memory size adequately meets the accuracy requirement for improved image segmentation.

Efficient hardware implementations routinely approximate mathematical functions with look-up tables, while keeping the error of the approximation under control. For a certain class of commonly occurring 1D functions, namely monotonically increasing or decreasing functions, we found that it is possible to approximate such functions by repeated application of a very low resolution 1D look-up table. There are many advantages to cascading multiple identical LUTs, including the promise of a very simple hardware design and the use of standard linear interpolation. Further, the complexity associated with unequal bin sizes can be avoided. We show that for realistic applications, including gamma correction, high dynamic range encoding and decoding curves, as well as tone mapping and inverse tone mapping applications, multiple cascaded look-up tables can reduce the approximation error by more than 50% compared to a single look-up table with the same total memory footprint.

A metamodeling technique based on Bivariate Cut High Dimensional Model Representation (Bivariate Cut HDMR) is implemented for a semiconductor packaging design problem with 10 design variables. Bivariate Cut-HDMR constructs a metamodel by considering only up to second-order interactions. The implementation uses three uniformly distributed sample points (s = 3) with quadratic spline interpolation to construct the component functions of Bivariate Cut-HDMR, which can be used to make a direct comparison with a metamodel based on Central Composite Design (CCD). The performance of Bivariate Cut-HDMR is evaluated by two well-known error metrics: R-squared and Relative Average Absolute Error (RAAE). The results are compared with the performance of CCD. Bivariate Cut HDMR does not compromise the accuracy compared to CCD, although the former uses only one-fifth of sample points (201 sample points) required by the latter (1045 sample points). The sampling schemes and the predictions of cut-planes and boundary-planes are discussed to explain possible reasons for the outstanding performance of Bivariate Cut HDMR.

A new Mean Sea Surface (MSS) model called Shandong University of Science and Technology Antarctic Mean Sea Surface model (SDUST_ANT MSS) in the Antarctic Ocean is presented and validated in this paper. The SDUST_ANT MSS updates the DTU18 MSS with 6 years of Exact Repeat Mission (ERM) and Geodetic Mission (GM) data from HY-2A. Collinear adjustment was applied to all the ERM data to obtain the along-track mean sea surface height. Oceanic variability has been removed from the GM data. Crossover adjustment was applied to both the ERM and GM data. We constructed the HY-2A_MSS using HY-2A altimetry data based on optimal interpolation method. Several types of errors (such as white noise, residual effect of oceanic variability, and long wavelength bias) have been taken into account for the determination of MSS using optimal interpolation method. The SDUST_ANT MSS was constructed by mapping HY-2A_MSS onto the DTU18 MSS. The SDUST_ANT MSS was compared with DTU18 MSS and CNES_CLS15 MSS. At wavelengths below 150 km, differences between models are consistent with seafloor topographic gradient. At wavelengths above 150 km, differences are affected by the mesoscale activities and the altimetry errors in coastal areas. The errors of the three models, as indicated by their power spectral densities (PSDs), are of similar orders of magnitude. The absolute error is slightly smaller in SDUST_ANT than in CNES_CLS15 or DTU18.

As one of the most important meteorological elements, temperature is an indispensable meteorological parameter for the atmospheric correction of spaceborne LiDAR ranging. Given a limited number of surface meteorological observation stations, the temperature values for all region of LiDAR observation need to be interpolated using appropriate spatial interpolation methods. In this paper, based on the monthly surface observation values in individual years (1981–2010) of Sichuan province observation stations, we firstly analyze the effects of three common interpolation methods, including inverse distance weighting (IDW), ordinary kriging (OK) and gradient plus inverse distance squared (GIDS). To solve the problem of low interpolation accuracy in severely undulating terrain area, an improved gradient distance inverse square method based on the adiabatic lapse rate (GIDS-ALR) is proposed. The experimental results show that the GIDS-ALR has an obvious improvement in the effect of severely undulating terrain, where the absolute error has been improved by more than 43% in average. Additionally, the temperature-interpolated MAE is reduced by more than 30%. The effectiveness and applicability of the proposed method is verified in this paper.

Surface fuel loading is a key factor in controlling wildfires and planning sustainable forest management. Spatially explicit maps of surface fuel loading can highlight the risks of a forest fire. Geospatial information is critical in enabling careful use of deliberate fire setting and also helps to minimize the possibility of heat conduction over forest lands. In contrast to lidar sensing and/or optical sensing based methods, an approach of integrating in-situ fuel inventory data, geospatial interpolation techniques, and multiple linear regression methods provides an alternative approach to surface fuel load estimation and mapping over mountainous forests. Using a stratified random sampling based inventory and cokriging analysis, surface fuel loading data of 120 plots distributed over four kinds of fuel types were collected in order to develop a total surface fuel loading model (lntSFL-BioTopo model) and a fine surface fuel model (lnfSFL-BioTopo model) for generating tSFL and fSFL maps. Results showed that the combination of topographic parameters such as slope, aspect, and their cross products and the fuel types such as pine stand, non-pine conifer stand, broadleaf stand, and conifer–broadleaf mixed stand was able to appropriately describe the changes in surface fuel loads over a forest with diverse terrain morphology. Based on a cross-validation method, the estimation of tSFL and fSFL of the study site had an RMSE of 3.476 tons/ha and 3.384 tons/ha, respectively. In contrast to the average loading of all inventory plots, the estimation for tSFL and fSFL had a relative error of 38% (PRMSE). The reciprocal of estimation bias of both SFL-BioTopo models tended to be an exponential growth function of the amount of surface fuel load, indicating that the estimation accuracy of the proposed method is likely to be improved with further study. In the regression modeling, a natural logarithm transformation of the surface fuel loading prevented the outcome of negative estimates and thus improved the estimation. Based on the results, this paper defined a minimum sampling unit (MSU) as the area for collecting surface fuels for interpolation using a cokriging model. Allocating the MSUs at the boundary and center of a plot improved surface fuel load prediction and mapping.

Energy-efficient thermal management of data centers based on dynamic optimization and provisioning of cooling resources requires rapid (nearly real-time) predictions of temperatures within data centers. This work for the first time compares multiple Data-Driven Models (DDMs) to achieve such rapid temperature predictions. DDM typically employs statistical or machine learning-based tools, in combination with physics-based modeling and/or experimental data to predict system behavior. In general, DDM approaches are well-suited to systems that have multiple operational states based on interactions between the many electrical, mechanical and control parameters typical of data centers. This study compares the performance of three different DDM methods, namely Artificial Neural Networks (ANN), Support Vector Regression (SVR), Gaussian Process Regression (GPR) in predicting both steady-state and transient rack inlet air temperature distributions in data centers. Additionally, Proper Orthogonal Decomposition (POD) was considered for transient modeling. The data used for training and analysis were obtained by performing 300 offline numerical simulations with a room-level, experimentally validated computational fluid dynamics/heat transfer (CFD/HT) model. The performance of the four data-driven models was evaluated based on the absolute mean error for interpolation and extrapolation, and the adaptability of the models to changes in physical domain (data center room) configuration. Additionally, the impact of the size of the training data set on prediction accuracy is also compared for the four models. For the steady-state case study, the predictions for ANN, SVR and GPR models are in good agreement with CFD/HT simulations, with the GPR model having the smallest overall average prediction error of 0.6 °C in rack inlet air temperature, corresponding to a relative error of 2.7% with respect to rack inlet temperature measured in °C. It was found that for all the frameworks the prediction error increases when the size of training data set was less than 300 samples. The GPR model had the best accuracy for smaller training data sets compared with the other models, with an average prediction error for rack inlet temperatures

In fluid-structure interaction (FSI) problems, accuracy of the data transfer between fluid-structure interfaces is mainly attributed to the element type and discretization density of grids in both fluid and structure domains. To remedy the inaccuracy caused by the prevalently applied solo elemental node interpolation strategy, a novel interpolation method is proposed in the present study. The approach is based on the radial basis function and introduces a weight coefficient through which the centroid and nodes of an element are joined. This way, the interpolation will be conducted in accordance to a weighted summation of both terms. Before it is applied to practice relevant engineering examples, the validity of the formulated approach is first examined by simple 2D and further 3D case studies. Studies have clearly illustrated that, compared to pure element centroid or nodes based interpolation schemes, the established approach is insensitive to the pressure distribution. Meanwhile, in these cases the influence of selected basis functions and mesh densities have been examined in detail. Based on the knowledge gained from these case studies, it further investigated a problem emerged from high-speed trains in which the CFD simulation is validated by the field experiment and the task is to transfer data from the fluid domain to the structure domain. Result of the study shows that for the high speed train model considered which has complicated non-matching grids, the accuracy of data transfer in fluid-structure interaction is highly improved and the maximum of global relative error achieves 2.62%.

This paper presents a novel technique based on the current steering technique for the generation of a reconfigurable current that approximates the linear, squaring, cubic, and exponential and their descending analog functions. The proposed implementation can be easily programmed to generate these functions by simply reconfiguring the weighting factors of current sources and offers an extendable input voltage range keeping excellent accuracy. The circuit topology has been fabricated using $0.18~\mu \text{m}$ TSMC CMOS process under 1.8 V supply voltage. Measurements results validate the theoretical analysis giving for 400 mV input voltage range while keeping small relative approximation errors, 0.3%, 1%, 1.9%, and 0.7% for linear, squaring, cubic, and exponential, respectively.

We present a beat-to-beat heart rate tracking algorithm that is designed especially to handle the nonstationary motion artifacts often encountered using photoplethysmographic (PPG) signals acquired from smartwatches or a forehead-worn device, during intense exercise. To date, many algorithms have been based on tracking heart rates during intense exercise using an 8-second average of heart rates, which does not accurately capture the large variation in instantaneous heart rates during exercise. In this paper, we propose a novel technique that can accurately estimate heart rates from wearable PPG signals with subjects running on a treadmill and making other sudden movements. The proposed algorithm includes three parts: 1) time-frequency spectrum estimation of PPG and accelerometer signals, 2) motion artifact removal by subtraction of the time-frequency spectra of the accelerometer signals from the PPG signals, and 3) postprocessing to further reject motion artifact-affected heart rates followed by interpolation of removed heart beats using a cubic spline approach. The proposed approach was compared to one of the recent and most accurate algorithms. The results of the proposed and compared algorithms were evaluated with two datasets (IEEE Signal Processing Cup (N=12) and our own dataset (N=10)) obtained from a smartwatch and a forehead PPG sensor with subjects running on a treadmill. The reference heart rates were obtained from a chest-worn ECG. Our method, using a 12 second windowed segment, resulted in an average absolute error of only 2.94 beats per minute and an average relative error of 2.42 beats per minute, which are a 71% and 94% improvement, respectively, over the compared algorithm.

In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques.

Spatial regression or interpolation is widely used for predictive soil pollution mapping, which aims to estimate all unobserved soil pollution based on a finite number of sample points. However, it may be unreasonable to use spatial regression or interpolation directly for an environmental soil dataset with outliers, because the mechanism generating outlier datasets is always different from that generating normal datasets, which necessitates handling outliers separately. Therefore, a hybrid approach for estimating unknown soil pollution concentrations is developed in this paper. The hybrid approach comprises three main steps: First, spatial outlier detection is used to uncover abnormal sample points and the study area is then divided into the normal and outlier areas. Second, spatial regression and interpolation are applied to analyze the normal and outlier datasets, respectively. Finally, the results of the predictive soil pollution mapping are derived from the prediction combination of spatial regression and interpolation. An environmental dataset recording heavy metal Cd and As concentrations at Huizhou, China was selected to verify the performance of the proposed approach. The numbers of identified outlier points of heavy metal Cd and As concentrations were 16 and 13. For the prediction result of Cd, the mean square error (MSE) and mean relative error (MRE) of the hybrid approach were about 0.028 and 0.332, respectively. For the prediction result of As, the MSE and MRE of the hybrid approach were about 3.834 and 0.366, respectively. All of these values were smaller than those of models used for comparison. The result of the comparative analysis demonstrates the feasibility and effectiveness of the proposed approach.