Interpolation Technique Research Articles

Fine-scale deep learning model for time series forecasting

Time series data, characterized by large volumes and wide-ranging applications, requires accurate predictions of future values based on historical data. Recent advancements in deep learning models, particularly in the field of time series forecasting, have shown promising results by leveraging neural networks to capture complex patterns and dependencies. However, existing models often overlook the influence of short-term cyclical patterns in the time series, leading to a lag in capturing changes and accurately tracking fluctuations in forecast data. To overcome this limitation, this paper introduces a new method that utilizes an interpolation technique to create a fine-scaled representation of the cyclical pattern, thereby alleviating the impact of the irregularity in the cyclical component and hence enhancing prediction accuracy. The proposed method is presented along with evaluation metrics and loss functions suitable for time series forecasting. Experiment results on benchmark datasets demonstrate the effectiveness of the proposed approach in effectively capturing cyclical patterns and improving prediction accuracy.

Nonpremixed and Premixed FPV Modeling of a Turbulent CH4-H2 Bluff-Body Flame

ABSTRACT In this study, modeling of nonpremixed CH4/H2 bluff-body (HM1) flame was performed using nonpremixed and premixed-based flamelet progress variable (FPV) models. The models were developed in an OpenFOAM flow solver, and the performance of the different variants of the FPV model was evaluated in the prediction of flame structure. The premixed FPV tables were constructed by employing two different interpolation techniques, i.e. linear and cubic spline, to retrieve the reactive scalars outside the flammability range. A generalized progress variable equation was introduced in the flow solver, which can be used for both tabulation approaches. Inside the flammable range, the profiles of the reactive scalars obtained from premixed FPV were found to be similar to those of the nonpremixed FPV. However, there exists disparity in the profiles outside the flammable range, particularly in the fuel-rich side between the nonpremixed and premixed approaches. A modified k-ε model was found to be suitable for modeling the turbulence compared to standard k-ε and k-ω shear stress transport models. The predictions of mean reactive scalars by the premixed FPV model, when combined with the linear interpolation, agree very well with experimental data and with the nonpremixed FPV predictions. However, deviations were observed in the predictions of the mean reactive scalar while using the cubic spline method in premixed FPV. All three approaches exhibit almost similar variations in the predictions of minor species. The results obtained from the present approach depict that the developed solver can be extended for modeling turbulent-chemistry interactions arising in partially premixed turbulent flames.

Explainable machine learning for high frequency trading dynamics discovery

High-frequency trading (HFT) plays an essential role in the financial market. However, discovering and revealing trading dynamics remains a challenge in Fintech. In this study, we propose a novel explainable machine learning approach: Feature-Interpolation-based Dimension Reduction SCAN (FIDR-SCAN) to address the challenge by creating a trading map. The trading map deciphers an HFT security’s trading dynamics by marking the status of each transaction, grouping transactions in clusters, and identifying the trading markers. The proposed method presents new feature interpolation techniques to build a more informative and explainable feature space, unveiling hidden trading behaviors. It mines HFT data in their low-dimensional embedding to seek exceptional trading markers and classify the statuses of transactions. We validate the meaningfulness and effectiveness of the trading markers discovered by FIDR-SCAN in trading as well as examining its special characteristics. Additionally, we apply the proposed algorithm to cryptocurrency data and achieve reliable performance. We design AI trading algorithms by reusing trading markers identified during explainable trading dynamics discovery, applying them to HFT stock and cryptocurrency markets, besides constructing trading machines using identified trading markers. To the best of our knowledge, this study is the first to use interpretable machine learning to reveal HFT trading dynamics.

Optimising shapes of multiple pin fins in a microchannel using deep reinforcement learning and mesh deformation techniques

The utilisation of advanced pin fin designs in microchannels is useful for enhancing cooling efficiency. Advancements in machine learning and processing power have sparked interest in shape optimisation techniques. This research employs a novel framework that integrates Deep Artificial Neural Networks and Reinforcement Learning with a Computational Fluid Dynamics (CFD) solver to optimise multiple pin fin shapes within a microchannel. By incorporating Radial Basis Function interpolation and Proximal Policy Optimisation alongside FLUENT, acting as the CFD environment, the reinforcement learning agent adeptly explores the design space to enhance the thermohydraulic performance factor (TPF), aiming to maximise Nusselt number while minimising pressure loss. Unlike previous heat transfer optimisation studies, which typically required mesh regeneration at each step, the proposed framework could bypass the meshing step and alter the geometry directly by relying on the RBF interpolation technique to deform the mesh directly. Three distinct scenarios investigated in this study are uniform deformation of all pin fins, deformation of all pin fins arranged in two rows, and individual deformation of each pin fin. Extensive simulations, exceeding 90,000 different cases, demonstrate that although the optimisation process for the individual deformation of each pin fin requires more iterations compared to others, it surpasses them in terms of TPF improvement. Notably, significant improvements are achieved, such as a 49 % enhancement in Nusselt number and a 33 % reduction in pressure drop, culminating in an impressive 63 % increase in TPF compared to the initial geometry.

Computational Study of Coupled Whitham Broer Kaup equations via Interpolation technique

The main purpose of this study is to investigate the numerical solution of coupled Whitham Broer Kaup (WBK) equation via Quintic B-Spline interpolation technique. This problem is of significant interest in the study of nonlinear wave phenomena because of its applications in various fields, such as fluid dynamics, plasma physics, and nonlinear optics and climate modeling. For the temporal derivative, the forward difference technique and a quadrature rule are utilized to deal the integer and fractional models, respectively, while spatial operators and the solutions are then obtained using Quintic B-spline. Furthermore, the non-linear terms are linearized using Quasi-linearization technique. Absolute error, L2 and L∞ error norms are computed to check the accuracy of the proposed method. The computed results are represented graphically and compared with the exact solution. It is found that our method is efficient due to less computational cost and proffer better accuracy. Stability of the proposed method is discussed using Von-Neumann stability which identifies that the scheme is conditionally stable.

Efficient Interpolation Technique for the Analysis of RCS Problems

Efficient Interpolation Technique for the Analysis of RCS Problems

A Geospatial Framework of Food Demand Mapping

Spatial mapping of food demand is essential for understanding and addressing disparities in food accessibility, which significantly impact public health and nutrition. This research presents an innovative geospatial framework designed to map food demand, integrating individual dietary behaviors with advanced spatial analysis techniques. This study analyzes the spatial distribution of eating habits across Lithuania using a geospatial approach. The methodology involves dividing Lithuania into 60,000 points and interpolating survey data with Shepard’s operator, which relies on a weighted average of values at data points. This flexible approach allows for adjusting the number of points based on spatial resolution and sample size, enhancing the reliability and applicability of the generated maps. The procedure includes generating a structured grid system, incorporating measurements into the grid, and applying Shepard’s operator for interpolation, resulting in precise representations of food demand. This framework provides a comprehensive understanding of dietary behaviors, informing targeted policy interventions to improve food accessibility and nutrition. Traditional food spatial mapping approaches are often limited to specific polygons and lack the flexibility to achieve high granular detail. By applying advanced interpolation techniques and ensuring respondent location data without breaching privacy concerns, this study creates high-resolution maps that accurately represent regional differences in eating habits. The methodology’s flexibility allows for adjustments in spatial resolution and sample size, enhancing the maps’ validity and applicability. This novel approach facilitates the creation of detailed food demand maps at any granular level, providing valuable insights for policymakers and stakeholders. These insights enable the development of targeted strategies to improve food accessibility and nutrition. Additionally, the obtained information can be used for computer simulations to further analyze and predict food demand scenarios. By leveraging spatial data integration, this study contributes to a deeper understanding of the complex dynamics of food demand, identifying critical areas such as food deserts and swamps, and paving the way for more effective public health interventions and policies aimed at achieving equitable food distribution and better nutritional outcomes.

Secure consensus for positive multi‐agent systems with bumpless transfer control under Denial‐of‐Service attacks

AbstractThis article investigates the secure consensus control problem of positive multi‐agent systems under multiple‐mode Denial‐of‐Service (DoS) attacks. A bumpless transfer (BT) control based secure mode strategy is proposed to improve the switching transient performance due to the system being actively switched to secure mode when attack is detected. Considering possible time delays for agents dealing with the issues of DoS attacks, an asynchronous switching model is established between system models and communication topology. With the stability theory of positive systems, sufficient and necessary conditions are established to guarantee the positivity of multi‐agent systems under the secure mode strategy. Because the switching law caused by external attacks is unknown in advance, the BT control is specifically implemented through the controller gain interpolation technique. By multiple Lyapunov functions (MLFs) approach, secure consensus is achieved with a trade‐off among controller performance, attack parameters, and switching delays. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

A percolation model for numerical simulations of 2D non-gravity impregnation in porous media

The aim of this work is to propose a new percolation model for numerical simulation of impregnation in porous media. Indeed, the impregnation phenomena concern many engineering fields, and could affect mechanical behavior of the medium, specifically when it is coupled with other physics such as heat or chemistry. The understanding of this phenomenon requires sophisticated numerical models that take into account the coupling between different physics. Classical numerical methods present known problems such as high computational costs, spurious oscillations and are not well adapted to such a complex coupling problem. To avoid these computational difficulties, Self-organized Gradient Percolation (SGP) model could be a good compromise. SGP is a numerical model based on a probabilistic approach, namely gradient percolation, already introduced in the 1D case, [1]. In this work we explore the non-reactive case. Instead of using finite element methods to solve Richards’ equation, we model the propagation of the saturation in the medium by the evolution of gradient percolation clusters. We hence delimitate the “wet” zone of the porous media to which we associate macroscopic saturation using interpolation techniques. The obtained results are free from spurious oscillation, and computational cost is drastically reduced compared with the classical approaches based on the finite element method. We believe that the 2D-SGP method can be enhanced by a futur 3D extension, but also to include the chemical and thermo-mechanical aspects.

Implementation of a high-resolution micro-grating accelerometer using a subdivision interpolation technique

This paper proposes a subdivision interpolation technique for an optical accelerometer based on diffraction grating interferometry. The diffraction light intensity curve presents a sine shape with the increase of the acceleration. To address the issues of linearization signal processing across the entire range, a subdivision interpolation circuit is employed, in conjunction with a 90° phase shift and high-precision DC bias-voltage techniques, converting an analog signal with sinusoidal characteristics from the photodetector into standard incremental digital signals that vary linearly over the full range. The novel methodology, to the best of our knowledge, ensures that its performance is least affected by the phase imbalance, offset error, and amplitude mismatch induced by fabrication and alignment errors of the grating, achieving high-resolution digital signal output. The experiment results reveal that the optical accelerometer based on grating interferometry achieved a sensitivity of 85.2 V/g, a resolution of 137.6 µg, as well as a subdivision interpolation factor of 45. This work provides a significant guide for the development of high-resolution MOEMS accelerometers in practical applications.

Evaluation of Two Ecosystem Services Provided by a Pistia stratiotes Population on the Pacific Coast of South America.

One of the most fascinating wetlands on Peru's central coast is the Santa Rosa wetland (Chancay, Lima), an ecosystem threatened by anthropogenic activities. Some of these impacts have led to the uncontrolled growth of Pistia stratiotes, an invasive aquatic plant. This study sought to quantify the regulation and provisioning of ecosystem services provided by P. stratiotes using carbon storage and the provision of biomass as indicators. To this end, the biomasses of 50 plots measuring 0.0625 m2 were weighed and georeferenced and the percentages of dry biomass (%DB) and total organic carbon in the biomass (%C) were quantified. The biomass and its coordinates were entered into ArcGIS and a Kriging interpolation technique was applied to determine the total amount of biomass (B). It was found that P. stratiotes stored 3942.57 tCO2 and that 2132.41 tons of biomass could be obtained for fodder. The total carbon stored by this aquatic plant represented 28.46% of the total carbon sequestered in the wetland ecosystem by vascular plants, suggesting that its contribution to the carbon cycle is significant. This is the first study to estimate the biomass of a floating aquatic plant population in a coastal Peruvian wetland and is a pioneering study addressing the in situ carbon estimation of Peruvian floating aquatic plants. The results and methods proposed in this research will serve in the evaluation of the potential of ecosystem services among similar populations of floating aquatic species. In addition, the data presented can be used to establish plans for the management and use of this biomass in the production of soil fertilizers and cattle forage.

A novel residual-pyramid-attention super resolution model for mesoscale meteorological forecasting spatial downscaling

ABSTRACT Developing a spatial downscaling method using machine learning techniques has emerged as a significant endeavor in meteorological forecasting. In this study, we propose a novel Residual-Pyramid-Attention Super Resolution (RPASR) model that effectively addresses the checkerboard artifacts issue prevalent in existing approaches, offering a unique perspective on spatial downscaling. Moreover, we propose a unique scaling technique during the data training to enhance the prediction performance. To validate and apply the proposed method, we utilize both low and high-resolution meteorological variables obtained from a numerical weather prediction model and observations in the Zhangbei region, China. The results demonstrate the exceptional performance of the RPASR model in spatial downscaling, exhibiting superior accuracy in meteorological prediction. Notably, the model outperforms interpolation techniques, significantly reducing deviations by 50% for variables such as 2 m temperature (T2), 2 m humidity (rh2), and 10 m wind speed (wspd10). In practical applications, our proposed model surpasses the DeepSD super-resolution model and low-resolution simulations as a whole, particularly for T2, where it enhances the T2 correlation coefficient by 1.2% compared to DeepSD. Additionally, it reduces the T2 root mean square error by 10.6% and the rh2 root mean square error by 8.6% compared to the low-resolution simulations. Overall, the RPASR model demonstrates robust validation and exhibits promising potential for advancing spatial downscaling methods in meteorological forecasting.

Benchmarking Time-Frequency Representations of Phonocardiogram Signals for Classification of Valvular Heart Diseases Using Deep Features and Machine Learning

Heart sounds and murmur provide crucial diagnosis information for valvular heart diseases (VHD). A phonocardiogram (PCG) combined with modern digital processing techniques provides a complementary tool for clinicians. This article proposes a benchmark different time–frequency representations, which are spectograms, mel-spectograms and cochleagrams for obtaining images, in addition to the use of two interpolation techniques to improve the quality of the images, which are bicubic and Lanczos. Deep features are extracted from a pretrained model called VGG16, and for feature reduction, the Boruta algorithm is applied. To evaluate the models and obtain more precise results, nested cross-validation is used. The best results achieved in this study were for the cochleagram with 99.2% accuracy and mel-spectogram representation with the bicubic interpolation technique, which reached 99.4% accuracy, both having a support vector machine (SVM) as a classifier algorithm. Overall, this study highlights the potential of time–frequency representations of PCG signals combined with modern digital processing techniques and machine learning algorithms for accurate diagnosis of VHD.

Analysis of COVID-19 epidemic with intervention impacts by a fractional operator

This study introduces an innovative fractional methodology for analyzing the dynamics of COVID-19 outbreak, examining the impact of intervention strategies like lockdown, quarantine, and isolation on disease transmission. The analysis incorporates the Caputo fractional derivative to grasp long-term memory effects and non-local behavior in the advancement of the infection. Emphasis is placed on assessing the boundedness and non-negativity of the solutions. Additionally, the Lipschitz and Banach contraction theorem are utilized to validate the existence and uniqueness of the solution. We determine the basic reproduction number associated with the model utilizing the next generation matrix technique. Subsequently, by employing the normalized sensitivity index, we perform a sensitivity analysis of the basic reproduction number to effectively identify the controlling parameters of the model. To validate our theoretical findings, numerical simulations are conducted for various fractional order values, utilizing a two-step Lagrange interpolation technique. Furthermore, the numerical algorithms of the model are represented graphically to illustrate the effectiveness of the proposed methodology and to analyze the effect of arbitrary order derivatives on disease dynamics.

Fertility and quality of arable soils in Poland: spatial–temporal analysis of long-term monitoring

Soil quality is a globally important issue from the point of view of food production, maintenance of appropriate environmental quality and ecological balance. Assessing its quality and fertility using indices is one of the methods that make it possible to formulate recommendations for good soil management. The aim of the study was, therefore, to determine the spatial and temporal distribution of soil properties in the context of soil quality assessment (SQI) and soil fertility assessment (SFI, SEF, NIV, and SSFI) using the example of a Central European country (Poland). The inverse distance-weighted spatial interpolation technique was used to estimate the spatial distribution of soil quality and fertility indicators. So far, no research has been carried out that would include a comprehensive analysis of soil fertility and quality indicators in such a large research area over many years. The results of 216 points of monitoring the chemistry of arable soils in Poland from the period 1995–2020 for 28 physicochemical soil parameters were considered. The analyses carried out showed significant variability in the properties of the described soils in Poland, as evidenced by the principal component analysis (PCA) and the coefficient of variation (exceptions: bulk density, pH). It was found that heavy metals (Zn, Cd, Cu) were responsible for the deterioration of soil properties. The results obtained for different indices were different (SFI – most soils with good fertility, SEF – high fertility, NIV – soils highly enriched with nutrients, SQI – average soil quality). It was found that the SSFI is the most appropriate indicator among the analyzed indicators for Polish conditions in relation to arable soils, as it is adapted and calibrated to the specifics of this area. The Spearman correlation matrix showed that the largest group of statistically highly significant parameter pairs belonged to heavy metals (Ni/Zn, Zn/Pb, Zn/Cu, Ni/Cu). In contrast, the strongest correlations were recorded for Ni (with effective cation exchange capacity (ECEC), Mn, Mgav, Zn, Cu). The assessment revealed limiting factors and temporal trends in the overall evaluation of the quality of the country’s agricultural soils, which are important from the point of view of both sustainable development and agricultural production.

Integrating Interpolation and Extrapolation: A Hybrid Predictive Framework for Supervised Learning

In the domain of supervised learning, interpolation and extrapolation serve as crucial methodologies for predicting data points within and beyond the confines of a given dataset, respectively. The efficacy of these methods is closely linked to the nature of the dataset, with increased challenges when multivariate feature vectors are handled. This paper introduces a novel prediction framework that integrates interpolation and extrapolation techniques. Central to this method are two main innovations: an optimization model that effectively classifies new multivariate data points as either interior or exterior to the known dataset, and a hybrid prediction system that combines k-nearest neighbor (kNN) and linear regression. Tested on the port state control (PSC) inspection dataset at the port of Hong Kong, our framework generally demonstrates superior precision in predictive outcomes than traditional kNN and linear regression models. This research enriches the literature by illustrating the enhanced capability of combining interpolation and extrapolation techniques in supervised learning.

Measuring prairie snow water equivalent with combined UAV-borne gamma spectrometry and lidar

Abstract. Despite decades of effort, there remains an inability to measure snow water equivalent (SWE) at high spatial resolutions using remote sensing. Passive gamma ray spectrometry is one of the only well-established methods to reliably remotely sense SWE, but airborne applications to date have been limited to observing kilometre-scale areal averages. Noting the increasing capabilities of unoccupied aerial vehicles (UAVs) and miniaturization of passive gamma ray spectrometers, this study tested the ability of a UAV-borne gamma spectrometer and concomitant UAV-borne lidar to quantify the spatial variability of SWE at high spatial resolutions. Gamma and lidar observations from a UAV (UAV-gamma and UAV-lidar) were collected over two seasons from shallow, wind-blown, prairie snowpacks in Saskatchewan, Canada, with validation data collected from manual snow depth and density observations. A fine-resolution (0.25 m) reference dataset of SWE, to test UAV-gamma methods, was developed from UAV-lidar snow depth and snow survey snow density observations. The ability of UAV-gamma to resolve the areal average and spatial variability of SWE was promising with appropriate flight characteristics. Survey flights flown at a velocity of 5 m s−1, altitude of 15 m, and line spacing of 15 m were unable to capture the average or spatial variability of SWE within the uncertainty of the reference dataset. Slower, lower, and denser flight lines at a velocity of 4 m s−1, altitude of 8 m, and line spacing of 8 m were able to successfully observe areal average SWE and its variability at spatial resolutions greater than 22.5 m. Using a combination of UAV-based gamma SWE and UAV-based lidar snow depth improved the spatial representation of SWE substantially and permitted estimation of SWE at a spatial resolution 0.25 m with a ± 14.3 mm error relative to the reference SWE dataset. UAV-borne gamma spectrometry to estimate SWE is a promising and novel technique that has the potential to improve the measurement of shallow prairie snowpacks, and when combined with UAV-borne lidar snow depths, can provide fine-resolution, high-accuracy estimates of prairie SWE. Research on optimal hardware, data processing, and interpolation techniques is called for to further improve this remote sensing product and explore its application in other environments.

Evaluation and comparison of infiltration models for estimating infiltration capacity of different textures of irrigated soils

Accurate estimation of infiltration rates is crucial for effective irrigation system design and evaluation by optimizing irrigation scheduling, preventing soil erosion, and enhancing water use efficiency. This study evaluates and compares selected infiltration models for estimating water infiltration rates in the Shillanat-iv irrigation scheme in northern Ethiopia. Soil samples were collected to determine textural classes using hydrometer soil texture analysis and the United States Department of Agriculture (USDA) textural triangle. The soil textural map of the study was created using the inverse distance weight interpolation technique in ArcGIS version 10.4. Infiltration rates were measured using the double-ring infiltrometer for five soil textures: clay loam, loam, sandy clay loam, clay, and sandy loam. Six infiltration models (Kostiakov, Modified Kostiakov, Revised Modified Kostiakov, Philip, Horton, and Novel) were employed and evaluated using statistical parameters. Model calibration and validation were conducted using data from 38 points within the study area. The parameter values of the infiltration models were optimized using SPSS statistical software using least-squares errors. The results showed that, Revised Modified Kostiakov, Modified Kostiakov, and Novel infiltration models demonstrated superior capability in estimating infiltration rates for clay loam, loam, and sandy loam soil textures, respectively. Horton's model outperformed other models in estimating infiltration rates for both sandy clay loam and clay soil textures. The appropriately fitted infiltration models can be utilized in designing the irrigation system to estimate the infiltration rate of soil textures within the selected irrigation scheme and at similar sites with comparable soil textures.

Automated high-precision alignment of geologic maps with well orientation

The 3D reflection seismic interpretation entails the creation of structure maps of subsurface horizons across extensive areas, often spanning tens of thousands of square kilometers within sedimentary basins. To be correlated with well measurements, maps made from 3D reflection seismic are routinely assigned the correct depth at well control points. However, integrating orientation information measured from wells remains a challenge due to the absence of upscaling guidelines. We address the scale-dependent nature of geologic structure and well orientation information in subsurface mapping, particularly focusing on integrating kilometer-scale seismic interpretation with centimeter-scale well-measured dip and azimuth data. Our pioneering methodology streamlines this integration process through three essential steps: first, transforming well dip and azimuth into a gradient representation; second, smoothly extending gradient differences between the map and well within a user-defined radius of influence; and third, constructing an updated horizon map by bicubic spline interpolation to ensure automated and high-precision alignment. In addition, a structure-oriented interpolation technique is introduced to preserve faults and local structures during orientation correction. Application of the methodology to a 3D reflection seismic horizon demonstrates its effectiveness in automating the complex task of tying subsurface maps to well orientation information. This not only reduces the need for manual interventions but also introduces a new perspective on subsurface mapping. It provides a robust framework that enhances the accuracy and reliability of geologic interpretation, offering significant advancements beyond previous efforts in the literature.

The Role of Spatial Distribution of Geotechnical Soil Parameters in Site Investigation

Abstract The correct investigation of the foundation soil is essential for the optimal and efficient design of any structure. The interaction of a structure with the foundation soil can only be evaluated through the physical and mechanical characteristics of the intercepted geotechnical layers on the entire zone of influence. For this reason, the role of technical documentation that includes and summarizes field investigations and laboratory tests is particularly important. An important and sometimes complicated component in providing useful design information is the division into geotechnical or computational layers. This can be done at different levels, starting from the physical characteristics such as color, grain size distribution, plasticity and consistency and can continue with the evaluation of the mechanical characteristics of compressibility and shear strength. The aim of the paper is to create a graphical representation of the geotechnical parameters using a spatial interpolation technique (Kriging method). The creation of 2D maps using SURFER software assists geotechnical engineers in the correct interpretation of the geotechnical parameters. This interpolation technique for division into layers is also useful in quarries and borrows pits, when soil is used as construction material.