Classical Interpolation Methods Research Articles

Применение машинного обучения методом случайного леса и систем управления большими пространственными данными для восстановления рядов данных вегетационных индексов

This article discusses the content and results of the work devoted to the development of a machine learning model that allows for data incompleteness recovery using cloud computing. The problem is considered using the example of a study devoted to data modeling to fill in missing values of vegetation indices based on open data catalogs of cloud computing platforms. The proposed methodology is based on the use of a multi-year periodic sampling of vegetation index values and model training on large amounts of data to improve the quality of series reconstruction. The approach indicated in the work allows for higher accuracy than using classical interpolation methods for data recovery, which makes the modeled values suitable for use in solving various practical problems. The proposed method is implemented using the example of restoring the values of the Normalized Difference Vegetation Index used for monitoring and evaluating the state of vegetation cover. Arrays of values obtained from the catalogs of the Google Earth Engine cloud environment intended for processing and analyzing data from remote sensing of the Earth (on the territory of the central part of the Novgorod Region) were used as initial data. To accelerate the learning process of the model and increase efficiency and productivity, the capabilities of the Google Colaboratory platform were used, which made it possible not to use local computing capacity and do not use specialized software in the study. This approach can be adapted to reconstruct other indexes or resolve data incompleteness in various subject areas, which emphasizes its versatility and potential practical application.

Carbon Footprint Optimization with Data Resolution Conversion via Kalman Filter for Smart Energy Hub

The severe climate changes due to global warming pushed the world to strive to reduce carbon emissions. And transitioning to renewable energy sources is essential for achieving sustainability and combating climate change. This study aims to minimize the carbon emissions for a proposed smart energy hub. This paper prioritizes the minimization of carbon emissions, considering the minimization of operational running costs, and the maximization of profit. In this paper, two optimization scenarios were studied to compare the results. In the first scenario, the minimization of carbon emissions was achieved. In the second scenario, the minimization of running costs and the maximization of profit from the hub assets were studied. The proposed model was designed in MATLAB. Then, the results were verified by CPLEX and validated by RTDS. The multi-objective model was presented to obtain the optimal operation. The mitigation of data uncertainty was achieved by applying the Kalman filter. In this work, a novel method was proposed for the estimation of the quarter-hour resolution data from the hourly ones via the Kalman filter rather than by applying the classic polynomial interpolation methods.

SR4KVQA: Video quality assessment database and metric for 4K super-resolution

The quality assessment for 4K super-resolution (SR) videos can be conducive to the optimization of video SR algorithms. To improve the subjective and objective consistency of the SR quality assessment, a 4K video database and a blind metric are proposed in this paper. In the database SR4KVQA, there are 30 4K pristine videos, from which 600 SR 4K distorted videos with mean opinion score (MOS) labels are generated by three classic interpolation methods, six SR algorithms based on the deep neural network (DNN), and two SR algorithms based on the generative adversarial network (GAN). The benchmark experiment of the proposed database indicates that video quality assessment (VQA) of the 4K SR videos is challenging for the existing metrics. Among those metrics, the Video-Swin-Transformer backbone demonstrates tremendous potential in the VQA task. Accordingly, a blind VQA metric based on the Video-Swin-Transformer backbone is established, where the normalized loss function and optimized spatio-temporal sampling strategy are applied. The experiment result manifests that the Pearson linear correlation coefficient (PLCC) and Spearman rank-order correlation coefficient (SROCC) of the proposed metric reach 0.8011 and 0.8275 respectively on the SR4KVQA database, which outperforms or competes with the state-of-the-art VQA metrics. The database and the code proposed in this paper are available in the GitHub repository, https://github.com/AlexReadyNico/SR4KVQA.

Towards a Unified Approach for Continuously-Variable Impedance Control of Powered Prosthetic Legs over Walking Speeds and Inclines.

Research in powered prosthesis control has explored the use of impedance-based control algorithms due to their biomimetic capabilities and intuitive structure. Modern impedance controllers feature parameters that smoothly vary over gait phase and task according to a data-driven model. However, these recent efforts only use continuous impedance control during stance and instead utilize discrete transition logic to switch to kinematic control during swing, necessitating two separate models for the different parts of the stride. In contrast, this paper presents a controller that uses smooth impedance parameter trajectories throughout the gait, unifying the stance and swing periods under a single, continuous model. Furthermore, this paper proposes a basis model to represent intertask relationships in the impedance parameters-a strategy that has previously been shown to improve model accuracy over classic linear interpolation methods. In the proposed controller, a weighted sum of Fourier series is used to model the impedance parameters of each joint as continuous functions of gait cycle progression and task. Fourier series coefficients are determined via convex optimization such that the controller best reproduces the joint torques and kinematics in a reference able-bodied dataset. Experiments with a powered knee-ankle prosthesis show that this simpler, unified model produces competitive results when compared to a more complex hybrid impedance-kinematic model over varying walking speeds and inclines.

Local physical gradient-based coupling information interpolate method and application on double-wall turbine blade multidisciplinary analysis

A novel generalization interpolate modification method based on local gradient is presented. The main idea was to remove the sample points located in the gradient direction away from the unknown points compared to the sample points located in the perpendicular direction. This method first uses the Taylor expansion to construct a set of equations and solves the local physical gradient. Subsequently, a scale vector is derived to modify the interpolate space. Three classical interpolation methods were modified: Inverse Distance Weighted (IDW), Radial Basis Function (RBF), and Kriging method. The results of the test functions prove that the proposed method can effectively decrease the interpolate error regardless of low or high dimensional interpolate problem and irrespective of the sample point size. Surface and volume interpolate validations demonstrate that the local gradient generates a large interpolate error, and the modified method can essentially diminish this error with a maximum reduction of 9.94 %. Subsequently, this method is applied to implement a multidisciplinary analysis of a practical double-wall cooling blade with a large physical gradient. The results showed that the pressure and temperature interpolate errors could be decreased by 5.18 % and 14.5 %, respectively, with only an additional 115 s, at the fillet and film hole area where the local gradient was high. When the strength analysis was implemented, the maximum stress error reduction was 25.04 MPa at the stress concentration region.

Applied the Cokriging interpolation method to survey Air Quality Index (AQI) for dust TSP in Da Nang city

Mapping to forecast the air pollution concentration in Da Nang city is an urgent issue for management agencies and researchers of environmental pollution. Although the simulation of spatial location has become popular, it uses the classical interpolation methods with low reliability. Based on the distribution of air quality monitoring stations located in industrial parks, residential areas, transport axes... and sources of air pollution, the application of geostatistical theories, this study presents the results of the Cokriging's interpolation selection which provides forecast results of air pollution distribution in Da Nang city with high reliability. In this article, we use the recorded TSP concentrations (one of major air pollution causes at large metropolis) at several observational stations in Da Nang city, employ the Cokriging interpolation method to find suitable models, then predict TSP dust concentrations at some unmeasured stations in the city. Our key contribution is finding good statistical models by several criteria, then fitting those models with high precision.

Screening and optimization of interpolation methods for mapping soil-borne polychlorinated biphenyls

There is yet no scientific consensus, and for now, on how to choose the optimal interpolation method and its parameters for mapping soil-borne organic pollutants. Take the polychlorinated biphenyls (PCBs) for instance, we present the comparison of some classic interpolation methods using a high-resolution soil monitoring database. The results showed that empirical Bayesian kriging (EBK) has the highest accuracy for predicting the total PCB concentration, while root mean squared error (RMSE) in inverse distance weighting (IDW) is among the highest in these interpolation methods. The logarithmic transformation of non-normally distributed data contributed to enhance considerably the semivariogram for modeling in kriging interpolation. The increasing of search neighborhood reduced IDW's RMSE, but slightly affected in ordinary kriging (OK), while both of them resulted in over smooth of prediction map. The existence of outliers made the difference between two points increase sharply, and thereby weakening spatial autocorrelation and decreasing the accuracy. As predicted error increased continuously, the prediction accuracy of different interpolation methods reached unanimity gradually. The attempt of the assisted interpolation algorithm did not significantly improve the prediction accuracy of the IDW method. This study constructed a standardized workflow for interpolation, which could reduce human error to reach higher interpolation accuracy for mapping soil-borne PCBs.

Improving Rainfall Fields in Data-Scarce Basins: Influence of the Kernel Bandwidth Value of Merging on Hydrometeorological Modeling

Accurate rainfall fields are important for several hydrological and meteorological applications. In poorly instrumented basins, the lack of rain gauges heavily affects the spatial rainfall estimation, yet neither remote sensed nor climate model estimates are good enough for management applications. To tackle this problem, we investigate the impacts of combining both sources of information by varying the kernel bandwidth value of the double smoothing merging algorithm and analyzing the error of the rainfall fields. We explored the correlation between rain gauge density and bandwidth and compared the results against classical geostatistical interpolation methods based solely on in-situ measurements. Propagation of rainfall error into hydrological modelling is usual, and therefore we evaluated the influence of the bandwidth in streamflow simulations implementing two hydrological models. The hydrological evaluation considered the analysis of hydrological signatures rather than just performance metrics. We found that there is a clear correlation between kernel bandwidth and monitoring network density and that the bandwidth also affects hydrological performance. Simple bilinear downscaling did not produce a significant difference in meteorological or hydrological errors, and rain gauge network configuration also impacts the error of the field. We conclude that merging outperforms the results of classical interpolation methods, in some cases by 20% or 50%, suggesting the suitability of the method for being applied in data-scarce domains.

Monte Carlo simulations of electron interactions with the DNA molecule: A complete set of physics models for Geant4-DNA simulation toolkit

In this study we are introducing an update of the Geant4-DNA physics constructor “option 6” including electron interactions with all constituents of the DNA molecule in addition to those already publicly available for liquid water. The new implementation is based on the interaction cross sections of electrons with the four DNA nucleobases, deoxyribose and phosphoric acid for elastic scattering, electronic excitation and ionisation in the 11 eV – 1 MeV energy range. An additional sampling method to estimate the transferred secondary electron energy produced by ionisation is also introduced and can be optionally activated instead of the classical interpolation method based on the differential cross section tables, thus eliminating the need to upload large data files. The implementation in Geant4-DNA was verified by calculating range and electronic stopping power in the various materials. Good agreement is observed with the data available in the literature, and calculations with the interpolation method and the sampling method showed less than 4% difference. No differences were observed in terms of computational cost.

Learning-based super-resolution interpolation for sub-Nyquist sampled laser speckles

Information retrieval from visually random optical speckle patterns is desired in many scenarios yet considered challenging. It requires accurate understanding or mapping of the multiple scattering process, or reliable capability to reverse or compensate for the scattering-induced phase distortions. In whatever situation, effective resolving and digitization of speckle patterns are necessary. Nevertheless, on some occasions, to increase the acquisition speed and/or signal-to-noise ratio (SNR), speckles captured by cameras are inevitably sampled in the sub-Nyquist domain via pixel binning (one camera pixel contains multiple speckle grains) due to finite size or limited bandwidth of photosensors. Such a down-sampling process is irreversible; it undermines the fine structures of speckle grains and hence the encoded information, preventing successful information extraction. To retrace the lost information, super-resolution interpolation for such sub-Nyquist sampled speckles is needed. In this work, a deep neural network, namely SpkSRNet, is proposed to effectively up sample speckles that are sampled below 1/10 of the Nyquist criterion to well-resolved ones that not only resemble the comprehensive morphology of original speckles (decompose multiple speckle grains from one camera pixel) but also recover the lost complex information (human face in this study) with high fidelity under normal- and low-light conditions, which is impossible with classic interpolation methods. These successful speckle super-resolution interpolation demonstrations are essentially enabled by the strong implicit correlation among speckle grains, which is non-quantifiable but could be discovered by the well-trained network. With further engineering, the proposed learning platform may benefit many scenarios that are physically inaccessible, enabling fast acquisition of speckles with sufficient SNR and opening up new avenues for seeing big and seeing clearly simultaneously in complex scenarios.

Effect of interpolation methods on quantifying terrain surface roughness under different data densities

Terrain surface roughness (TSR) is an important parameter in various geoscience applications. TSR can be easily estimated from digital elevation models (DEMs), which are generally derived from the interpolation of Light Detection and Ranging (LiDAR) point clouds. Thus, the quality of TSR is inevitably influenced by data density and interpolation method. However, to what extent the data density can be reduced and which method is more accurate than the others for quantifying TSR are still ambiguous. Thus, this paper evaluated the performance of five classical interpolation methods (ordinary kriging (OK), thin plate spline (TPS), natural neighbor (NN), Delaunay with linear interpolation (TIN) and inverse distance weighting (IDW)) for quantifying TSR under different airborne LiDAR data densities (90 %, 70 %, 50 %, 30 % and 10 % of the original data) in three study sites (samp1, samp2 and samp3) with different terrain characteristics. Results demonstrate that regardless of data density and study sites, TPS is consistently more accurate than the other methods for DEM production in terms of root mean square error (RMSE) and normalized median absolute deviation (NMAD), while IDW produces the worst results. Moreover, the reduction of data density to 50 % of the original data results in no obvious accuracy loss of DEMs for all the interpolation methods. For quantifying TSRs from DEMs, IDW shows the highest accuracy when data density is larger than 50 % in samp1 and samp2, and larger than 70 % in samp3, while TPS obtains the best results in the other densities; however, the surfaces of IDW are very coarse, which makes terrain details unrecognizable. Additionally, the DEM-based TSRs of all the interpolation methods can endure the reduction of LiDAR data to 50 % of the original samples without considerable accuracy decreases, especially for TPS. Overall, TPS can be considered as a promising method for LiDAR DEM production and TSR quantification.

A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids

The classical radial point interpolation method (RPIM) is a powerful meshfree numerical technique for engineering computation. In the original RPIM, the moving support domain for the quadrature point is usually employed for the field function approximation, but the local supports of the nodal shape functions are always not in alignment with the integration cells constructed for numerical integration. This misalignment can result in additional numerical integration error and lead to a loss in computation accuracy. In this work, a modified RPIM (M-RPIM) is proposed to address this issue. In the present M-RPIM, the misalignment between the constructed integration cells and the nodal shape function supports is successfully overcome by using a fixed support domain that can be easily constructed by the geometrical center of the integration cell. Several numerical examples of free vibration analysis are conducted to evaluate the abilities of the present M-RPIM and it is found that the computation accuracy of the original RPIM can be markedly improved by the present M-RPIM.

Parametric Curves Metamodelling Based on Data Clustering, Data Alignment, POD-Based Modes Extraction and PGD-Based Nonlinear Regressions

In the context of parametric surrogates, several nontrivial issues arise when a whole curve shall be predicted from given input features. For instance, different sampling or ending points lead to non-aligned curves. This also happens when the curves exhibit a common pattern characterized by critical points at shifted locations (e.g., in mechanics, the elastic-plastic transition or the rupture point for a material). In such cases, classical interpolation methods fail in giving physics-consistent results and appropriate pre-processing steps are required. Moreover, when bifurcations occur into the parametric space, to enhance the accuracy of the surrogate, a coupling with clustering and classification algorithms is needed. In this work we present several methodologies to overcome these issues. We also exploit such surrogates to quantify and propagate uncertainty, furnishing parametric stastistical bounds for the predicted curves. The procedures are exemplified over two problems in Computational Mechanics.

Optical flow driven interpolation for isotropic FIB-SEM reconstructions

Background and Objective: Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM) allows three-dimensional ultrastructural analysis of cells and tissues at the nanoscale. The technique iteratively removes a section of the sample with a FIB and takes an SEM image from the exposed surface. The section thickness is usually higher than the image pixel size to reduce acquisition time, thus resulting in anisotropic resolution. In this work, we explore novel interpolation methods along the sectioning direction to produce isotropic resolution and facilitate proper interpretation of the FIB-SEM 3D volumes.Methods: Classical interpolation methods are usually applied in this context under the assumption that the changes through successive images are relatively smooth. However, the actual 3D arrangement of the structures in the sample may cause significant changes in the biological features between consecutive images of the FIB-SEM stacks. We have developed a novel interpolation strategy that accounts for this variation by using the Optical Flow (OF) to estimate it. As an intermediate stage, OF-compensated images are produced by aligning the spatial regions of the biological structures. Interpolated images are then generated from these OF-compensated images. The final isotropic stack is assembled by interleaving the interpolated images with the original images of the anisotropic stack.Results: OF-driven and classical interpolation methods were compared using an objective assessment based on Pearson Correlation Coefficient (PCC) and a qualitative evaluation based on visual results, using public datasets and representative anisotropy conditions. The objective assessment demonstrated that the OF-driven interpolation always yields higher PCC values, with interpolated images closer to the ground truth. The qualitative evaluation corroborated those results and confirmed that classical interpolation may blur areas with substantial changes between consecutive images whereas OF-driven interpolation provides sharpness.Conclusions: We have developed an OF-driven interpolation approach to generating FIB-SEM stacks with isotropic resolution from experimental anisotropic data. It adapts to the rapid variation of the biological structures observed through the images of the FIB-SEM stack. Our approach outperforms classical interpolation and manages to produce sharp interpolated views in cases where there are significant changes between consecutive experimental images.

Prediction of geoid undulations: Random forest versus classic interpolation techniques

AbstractLocal geoid determination studies are commonly carried out today to establish the relationship between the ellipsoidal height determined by satellite geodesy methods and the orthometric height found using geoid undulation . The aim of this study was to determine a local geoid using the kriging, local polynomial (LP), and inverse distance to a power (IDP) interpolation methods along with the random forest (RF) regression method and to compare the performance. For the application, 193 Global Navigation Satellite System (GNSS)/leveling points homogeneously distributed over the study area were selected as reference data, and 70 GNSS/leveling points were selected as test data. The results were compared in terms of accuracy using well‐known performance metrics, namely, the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R2) values. According to the results, the highest R2 and the lowest RMSE and MAE values were obtained with the RF regression method. These findings demonstrated the superiority of the RF regression over the classic interpolation methods applied in the local geoid determination for the study area.

Using elements of machine learning to solve the inverse problem of reconstructing the hydraulic conductivity field for a filtration problem

In the modern world, machine learning methods are widely used. In the oil industry, there is also a noticeable trend to use these methods in the context of digitalization and intellectualization of the entire production process. The present work is devoted to the development of a technique for solving the inverse problem of restoring the permeability field of an oil reservoir with the combined use of machine learning elements and a filtration model. A computational algorithm has been implemented, which implies close mutual integration of the filtration part and the machine learning block, the results of which are used to parameterize the physically meaningful model. A network of radial basis functions is used as a machine learning model. The proposed solution search procedure includes the numerical solution of the direct and adjoint problems for the filtration model. Solving the adjoint problem allows one to apply gradient optimization methods widely used in machine learning methods. The paper presents the results of a numerical experiment. On the example of a symmetrical two-dimensional development element, a solution was obtained for the problem of restoring the permeability field for a set of zonal-heterogeneous oil reservoirs. For the reconstructed fields, the characteristic sizes of inhomogeneities coincide with the initial ones with sufficient accuracy. The fundamental possibility of a qualitative restoration of the porosity-permeability characteristics of the interwell space is shown, which is impossible when using classical interpolation methods without involving additional data. The paper studies the influence of the choice of the type of control parameter on the behavior of the objective function and its derivative, which affects the process of solving the inverse problem. As a result of the study, the use of hydrodynamic resistance as an adaptable parameter in solving the inverse problem is proposed.

Ice volume and basal topography estimation using geostatistical methods and ground-penetrating radar measurements: application to the Tsanfleuron and Scex Rouge glaciers, Swiss Alps

Abstract. Ground-penetrating radar (GPR) is widely used for determining mountain glacier thickness. However, this method provides thickness data only along the acquisition lines, and therefore interpolation has to be made between them. Depending on the interpolation strategy, calculated ice volumes can differ and can lack an accurate error estimation. Furthermore, glacial basal topography is often characterized by complex geomorphological features, which can be hard to reproduce using classical interpolation methods, especially when the field data are sparse or when the morphological features are too complex. This study investigates the applicability of multiple-point statistics (MPS) simulations to interpolate glacier bedrock topography using GPR measurements. In 2018, a dense GPR data set was acquired on the Tsanfleuron Glacier (Switzerland). These data were used as the source for a bedrock interpolation. The results obtained with the direct-sampling MPS method are compared against those obtained with kriging and sequential Gaussian simulations (SGSs) on both a synthetic data set – with known reference volume and bedrock topography – and the real data underlying the Tsanfleuron Glacier. Using the MPS modeled bedrock, the ice volume for the Scex Rouge and Tsanfleuron glaciers is estimated to be 113.9 ± 1.6 million cubic meters. The direct-sampling approach, unlike the SGS and kriging, allowed not only an accurate volume estimation but also the generation of a set of realistic bedrock simulations. The complex karstic geomorphological features are reproduced and can be used to significantly improve for example the precision of subglacial flow estimation.

A new strategy combined HASM and classical interpolation methods for DEM construction in areas without sufficient terrain data

A new strategy combined HASM and classical interpolation methods for DEM construction in areas without sufficient terrain data

Sparse Hardy function model of regional velocity field from GNSS data

Classical Hardy function interpolation method is often necessary in establishment of regional velocity field. In this work, a regularization method, namely the L1-norm regularization, also called the least absolute shrinkage selection operator (Lasso), is employed to improve the traditional method. With the new method, a sparse model can be obtained with many zero elements in the parameter vector. Compared to L2-norm regularization, which is also called the Tikhonov regularization, the L1-norm regularization will select the best model automatically by making the coefficient of the unnecessary kernels zero, through solving a convex optimization problem. In this paper, the velocity field dataset derived from global navigation satellite system data is used to establish models in different directions. By comparing the interpolation accuracy of velocity at the same unknown points of Hardy function improved by Lasso and Tikhonov regularizations respectively, the feasibility of the former is verified. The results show that L1-norm regularization method has a slightly worse interpolation accuracy than Tikhonov regularization method in North and Up directions, but in East direction, the interpolation effect is much better and all directions can get great sparse performance. More specifically, the prediction accuracy of the proposed method in the East direction is improved by 17.3%, but in North and Up directions is decreased by 5.4% and 6.3% respectively in comparison with that of Tikhonov regularization method, though the sparse rates of them are over 60%. In addition, besides selecting the root mean square error as the evaluation standard for model selection, we can also select the sparse rate as the evaluation criteria to make the model much sparser if necessary. A sparse model would be beneficial in terms of better interpretability and improved variable assigning efficiency. To summarize, L1-norm regularization can be viewed as a potential alternative in velocity field modelling.

Structure tensor-based interpolation for the derivation of accurate digital elevation models

For many geoscience applications, the quality of digital elevation models (DEMs) is the first and foremost requirement. DEM quality generally depends on the interpolation procedure, especially in forested areas with complex terrain. However, classical interpolation methods do not always preserve terrain features, owing to their isotropic and local estimation nature. Therefore, this paper presents a feature-preserving interpolation method, where a structure tensor is integrated into the radial basis function to ensure its anisotropy. This method alleviates the influence of points located on different surface patches. The performance of the proposed method was compared with those of classical interpolation methods, including the inverse distance weighting (IDW), ordinary kriging (OK), topo to raster (ANUDEM), and natural neighbour (NN) methods. The performance of these methods was tested on benchmark data provided by the International Society for Photogrammetry and Remote Sensing (ISPRS) Commission, and on one private dataset. Both datasets were collected via the airborne light detection and ranging (LiDAR) technique. The results from both datasets demonstrate that from a quantitative perspective, the proposed method produces more accurate DEMs than the classical interpolation methods. Specifically, in terms of root mean square error (RMSE), the proposed method is at least 15.8% and 7.6% more accurate when applied to the ISPRS and private data, respectively. Moreover, the proposed method produces more visually appealing surfaces with a good trade-off between terrain feature retention and noise removal.