Interpolation Procedure Research Articles

Modified recurrent equation-based cubic spline interpolation for missing data recovery in phasor measurement unit (PMU).

Smart grid systems require high-quality Phasor Measurement Unit (PMU) data for proper operation, control, and decision-making. Missing PMU data may lead to improper actions or even blackouts. While the conventional cubic interpolation methods based on the solution of a set of linear equations to solve for the cubic spline coefficients have been applied by many researchers for interpolation of missing data, the computational complexity increases non-linearly with increasing data size. In this work, a modified recurrent equation-based cubic spline interpolation procedure for recovering missing PMU data is proposed. The recurrent equation-based method makes the computations of spline constants simpler. Using PMU data from the State Load Despatch Center (SLDC) in Madhya Pradesh, India, a comparison of the root mean square error (RMSE) values and time of calculation (ToC) is calculated for both methods. The modified recurrent relation method could retrieve missing values 10 times faster when compared to the conventional cubic interpolation method based on the solution of a set of linear equations. The RMSE values have shown the proposed method is effective even for special cases of missing values (edges, continuous missing values). The proposed method can retrieve any number of missing values at any location using observed data with a minimal number of calculations.

NREL-5MW Wind Turbine Noise Prediction by FWH-LES

This paper deals with large onshore wind turbine aeroacoustics. Noise from the NREL 5 MW device is predicted by the permeable-surface Ffowcs Williams–Hawkings equation (FWH-P), starting from the postprocessing of LES data on different acoustic surfaces S. Their size and placement is aimed at embedding most of the aerodynamic sources of sound surrounding rotor and nacelle. Due to the presence of eddies that inevitably cross S, this paper compares results from open and closed acoustic surfaces, and the outflow disk averaging technique. The issues related to the interpolation process of LES data on S is discussed as well. In order to assess the LES/FWH-P aeroacoustic platform, LES and FWH-P pressures are compared in the very-near field. It is shown that, within the limits of the discretization settings imposed by the interpolation procedure and for the Reynolds number working condition investigated herein, the lack of quadrupole sources outside the permeable surface(s) deeply affect the quality of FWH-P acoustic pressures with respect to direct LES signals.

A New Ridgely-Nevitt Regression-Based Computational Tool for Resistance and Power Predictions for Trawlers

This paper aims to present the architecture and the prediction accuracy of a new computational procedure of the “Ship Power V 1.0” software based on the Ridgely–Nevitt regression, applied to hull resistance predictions for Ridgely-Nevitt series trawlers. The Ridgely-Nevitt series is an important series of trawlers developed by and tested at the Webb Institute. Experimental resistance data have also been presented in the form of a regression model used to develop a new procedure of the “Ship Power V 1.0” software. Furthermore, this new procedure was completely harmonized with other software procedures based on the Holtrop and Van Oortmerssen evaluation methods. Although the mathematical formulation of the Ridgely-Nevitt regression model allows the assessment of the residual resistance coefficient of only nine values from the speed-length ratio, the implementation of an interpolation procedure made possible resistance predictions for any speeds from the acceptable speed-length ratio range. Resistance prediction accuracy improvement introduced by the new procedure was proven by the validation of calculation results not only against experimental data but also against the prediction results of other software procedures for three hulls from the Ridgely-Nevitt fishing vessel series. MAPE (mean absolute percentage error) values calculated against experimental data for the analyzed models were 3.26, 1.71, and 3.36, respectively. Prediction result comparisons of the Ridgely-Nevitt regression-based “Ship Power V 1.0” computational procedure and the experimental data and predictions of other computational procedures performed on three hulls from the Ridgely-Nevitt series have shown a substantial improvement in prediction accuracy.

Structure‐preserving invariant interpolation schemes for invertible second‐order tensors

AbstractTensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, that is, symmetric or non‐symmetric, invertible square tensors are proposed. Critically, the proposed schemes rely on a combined polar and spectral decomposition of the tensor data , followed by an individual interpolation of the two rotation tensors and and the positive definite diagonal eigenvalue tensor resulting from this decomposition. Two different schemes are considered for a consistent rotation interpolation within the special orthogonal group , either based on relative rotation vectors or quaternions. For eigenvalue interpolation, three different schemes, either based on the logarithmic weighted average, moving least squares or logarithmic moving least squares, are considered. It is demonstrated that the proposed interpolation procedure preserves the structure of a tensor, that is, and remain orthogonal tensors and remains a positive definite diagonal tensor during interpolation, as well as scaling and rotational invariance (objectivity). Based on selected numerical examples considering the interpolation of either symmetric or non‐symmetric tensors, the proposed schemes are compared to existing approaches such as Euclidean, Log‐Euclidean, Cholesky and Log‐Cholesky interpolation. In contrast to these existing methods, the proposed interpolation schemes result in smooth and monotonic evolutions of tensor invariants such as determinant, trace, fractional anisotropy (FA), and Hilbert's anisotropy (HA). Moreover, a consistent spatial convergence behavior is confirmed for first‐ and second‐order realizations of the proposed schemes. The present work is mainly motivated by the frequently occurring necessity for remeshing or mesh adaptivity when applying the finite element method to complex problems of nonlinear continuum mechanics with inelastic constitutive behavior, which requires the consistent interpolation of tensor‐valued history data for the transfer between different meshes. However, the proposed schemes are very general in nature and suitable for the interpolation of general invertible second‐order square tensors independent of the specific application.

On Form, Cyclicity and Temporality in Leoš Janáček’s String Quartet No. 1

Objectives: The study aimed is to identify the underlying temporal structures, procedures and devices employed by Janáček in the composition of his First-String Quartet, by way of a thorough analysis of musical forms, relations and cyclicities of recurring themes and motifs, and an examination of referential semantic structures.
 Methods: The study applied a descriptive-analytical method in the framework of a textual approach to the composition under consideration. This includes identifying procedures of contrast, juxtaposition, interpolation, temporal intercutting, and superimposition described by T. Clifton, often employed together with a montage-style technique.
 Results: The results of the study of our analysis clearly show Janáčeck’s preference for the palindrome arch form and rondo-like forms, combined with features of ternarity. In their recurrences themes are mostly varied, occasionally transposed, and often curtailed, sometimes to the duration of a mere referential reminder. This form entails a specific temporality related in the palindrome form to a retrograde temporal directionality. The superimposition of themes and accompaniment textures also entails a superimposition of their temporal strata. Another poignant feature of this quartet’s temporality is the use of referential-semantic devices. This includes the multiplicity of inter-sectional and inter-movement citations of themes, motifs, and intonations.
 Conclusions: In the light of the results, the study recommends further empirical experimental research of the perception of temporal categories outlined in this paper, and to explore the relation of semantic referential structures and elements of speech in the melodic of Janáček.

Фотограмметрическая оценка деформационных процессов на оползневых склонах при обеспечении устойчивого развития территорий Кавказа

Introduction. Sustainable development of geo-resources in modern realities is a priority for ensuring sustainable development of the territories of the Russian Federation. In the absence of real mechanisms for its implementation, the territories most sensitive to climate change (the subtropical zone of the Caucasus) will be exposed to increased risks of an increase in dangerous hydro meteorological phenomena. At the same time, the issues of improving methods for assessing deformation processes on landslide slopes become particularly relevant. Materials and methods. The object of the study was a slope located near the “Winter Theater” (Sochi) on the road surface of the descent to the sea where a system of cracks was observed. The area under study was photographed point by point with a Nikon D3100 camera, after which the photographs were depixelized to obtain PNG ASCII files. After this file, standard smoothing processed the containing data arrays and three-dimensional interpolation procedures to obtain regression models that were presented in the software «gnuplot». Results. As a result of completed stage of research, a methodology for determining the deformation processes of slope systems using the photometric method, which is based on the processing of a high-precision raster image (photo) by analytical methods, was adapted and formed. In our case, there would be a series of values only for the line of sites (n = 9) for all pickets (N from 11 to 23). When analyzing only this series, we could conclude that ε varies nonlinearly from 12 (N= 23 m) to the first local maximum of 20 mm (N= 21 to 22 m). Afterwards there is a decline to 17 mm (N = 20 m) and so on, but in general, they do not exceed 23 mm. While when using the photometric method, we can observe in certain areas (segments) that the amount of deformation of the asphalt road reaches up to 40 mm. Discussion. Compared to most similar studies (geo-statistical methods for processing satellite images, classical geodetic methods, methods of geophysics, the photometric method for identifying fractured structures, as well as assessing their development, is more accurate and less labor-intensive in conducting field experiments. Conclusion. To ensure sustainable development of the Caucasus territories, it is necessary to significantly improve the quality of monitoring of road surfaces located in foothill and mountain areas (especially in the presence of serpentine roads). As a result of the completed stage of research, a methodology for determining the deformation processes of slope systems using the photometric method, which is based on the processing of a high-precision raster image (photo) by analytical methods, was adapted and formed. Future research should focus on the methodology for transitioning to displacement rates and considering the response spaces of crack profile dynamics. Resume. The article presents the results of studies of deformation processes of slope systems in a dangerous landslide zone (Winter Theater of Sochi) of the Eastern Black Sea region. It has been established that the width of the walls of crack No. 2 on the road section under study in 2022 increases nonlinearly according to a polynomial law, while the absolute values of deformations can vary from 3 to 40 mm. In addition, a methodology for using the photometric method to assess the degree of cracking in slope systems is presented. The results of the study can be used in the development of a methodology for geoecological monitoring of the condition of road surfaces of highways in mountainous areas. The proposed methodological approaches to processing raster data sets can be used to develop algorithms for managing natural and technical systems in the mining industry.

Numerical Method for Solving the Nonlinear Superdiffusion Equation with Functional Delay

For a space-fractional diffusion equation with a nonlinear superdiffusion coefficient and with the presence of a delay effect, the grid numerical method is constructed. Interpolation and extrapolation procedures are used to account for the functional delay. At each time step, the algorithm reduces to solving a linear system with a main matrix that has diagonal dominance. The convergence of the method in the maximum norm is proved. The results of numerical experiments with constant and variable delays are presented.

Framing the Residential Patterns of Asian Communities in Three Italian Cities: Evidence from Milan, Rome, and Naples

Today, the interplay between economic inequality, international migration, and urban transformation has raised awareness about segregation and its social implications on a global and European scale. As cities become home to diverse populations with various backgrounds including social, racial, ethnic, and cultural, the proximity of these groups becomes more pronounced. This article explores the residential segregation of four Asian immigrant groups in three major Italian cities: Milan, Rome, and Naples. Using data from the 2011 Italian General Population Census and employing an areal weighted interpolation procedure, the study measures segregation using both traditional two-group indices and multi-group indices that account for the complexities of contemporary societies. The results indicate a north–south disparity, with Naples exhibiting the highest levels of residential segregation. Among the analysed immigrant groups, Bangladeshis and Chinese tended to be more self-segregated, while Filipinos and Sri Lankans were relatively more dispersed. This research underscores the necessity for a nuanced understanding of segregation dynamics and the adoption of appropriate approaches to address the challenges and opportunities presented by the coexistence of diverse groups in urban areas. By contributing to the existing literature on residential segregation in Southern Europe, this study sheds light on the spatial patterns and social dynamics of different ethnic groups in Italian cities.

A new index to evaluate renewable energy potential: A case study on solar, wind and hybrid generation in Northeast Brazil

Human activities imply a high and increasing consumption of electricity. In this context, renewable sources, such as solar and wind energy, stand out due to the ecological and economic advantages associated with their use, but bring with them the need for monitoring and analyzing climatic variables such as solar irradiation and wind speed, in order to determine the potential of solar, wind or hybrid (solar and wind) generation of a region. The main objective of the present study was to develop a method to rank the top locations or regions for wind, solar and hybrid electricity generation potential. In addition, two databases were created using spatial interpolation techniques to define values related to solar and wind energy sources in a case study for the state of Paraíba, Northeast Brazil. Thus, using public data from ground stations and satellites, two interpolation procedures were evaluated, Inverse Distance Weighted (IDW) and Kriging. Next, the best evaluated method (Kriging) was used to develop a database with exclusive resolution of 0.05° (latitude and longitude) for analysis of the wind, solar and hybrid potential of the Paraíba state, Brazil, used as case study. Finally, an index was created to determine the municipalities in the state that stand out with the best indicators for hybrid generation. From the index created, it was observed that the municipalities belonging to the intermediate geographical regions of Sousa-Cajazeiras and Patos have the best indicators for solar generation, while the regions of Campina Grande and João Pessoa stand out with greatest potential for wind energy production. The region of Campina Grande also had the best results for hybrid generation potential. The IP-PB index was the main contribution of this work, since the method can be applied to different regions of the world for the same purpose and other indexes for estimating renewable production potential were not found in the literature.

Deformation-Induced Surface Roughening of an Aluminum-Magnesium Alloy: Experimental Characterization and Crystal Plasticity Modeling.

The deformation-induced surface roughening of an Al-Mg alloy is analyzed using a combination of experiments and modeling. A mesoscale oligocrystal of AA5052-O, obtained by recrystallization annealing and subsequent thickness reduction by machining, that contains approx. 40 grains is subjected to uniaxial tension. The specimen contains one layer of grains through the thickness. A laser confocal microscope is used to measure the surface topography of the deformed specimen. A finite element model with realistic (non-columnar) shapes of the grains based on a pair of Electron Back-Scatter Diffraction (EBSD) scans of a given specimen is constructed using a custom-developed shape interpolation procedure. A Crystal Plasticity Finite Element (CPFE) framework is then applied to the voxel model of the tension test of the oligocrystal. The unknown material parameters are determined inversely using an efficient, custom-built optimizer. Predictions of the deformed shape of the specimen, surface topography, evolution of the average roughness with straining and texture evolution are compared to experiments. The model reproduces the averaged features of the problem, while missing some local details. As an additional verification of the CPFE model, the statistics of surface roughening are analyzed by simulating uniaxial tension of an AA5052-O polycrystal and comparing it to experiments. The averaged predictions are found to be in good agreement with the experimentally observed trends. Finally, using the same polycrystalline specimen, texture-morphology relations are discovered, using a symbolic Monte Carlo approach. Simple relations between the Schmid factor and roughness can be inferred purely from the experiments. Novelties of this work include: realistic 3D shapes of the grains; efficient and accurate identification of material parameters instead of manual tuning; a fully analytical Jacobian for the crystal plasticity model with quadratic convergence; novel texture-morphology relations for polycrystal.

Deep Neural Networks are Utilized in Energy Management Systems for identifying Theft of Electricity

The installation of connected systems is essential for the identification of renewable energy thieves because it generate enormous volumes of the information, include information about customer behavior, that could potentially be identify electricity theft using machine learning and deep learning techniques. This project describes a method for detecting theft that employs extensive information in the time and frequency domains in a deep neural network-based classification approach. Through data interpolation and synthetic data generation procedures, we solve dataset flaws such as missing data and class imbalance issues. We evaluate and analyze the contribution of features from both the temporal and frequency domains, execute experiments in combined and reduced feature space using principal component analysis, and lastly add a minimal redundancy-based strategy to maximizing significance for determining what's most pertinent features. We increase the detection performance of power theft by optimizing hyper parameters with a Bayesian optimizer and using an adaptive moment estimation optimizer to run tests with varying values of critical parameters to identify the ideal settings that produce the greatest accuracy. Since we train the model with over and under sampling datasets, it provides the equal representation while training the model. Key Words: Cyberbullying, Neural Networks Machine learning, social media. Deep Neural Network, Natural language processing, Artificial Neural Network.

A shape-preserving spline interpolation for sampling designs from inverse distributions

Given a strictly monotone cumulative function F:[a,b]⟶[c,d], with a,b,c,d∈R, a<b and c<d, such that F[a,b]=[c,d]. The possibility of using the spline interpolation procedure, to approximate the inverse of F, is a natural way in some applications, and it leads to schemes that are stable and feasible to implement. We prove that, with a shape-preserving quadratic Hermite interpolation scheme based on quadratic B-splines, we can preserve the monotonicity of the inverse of F while maintaining a third-order estimate of the interpolation error. To illustrate the effectiveness of this approach, we provide some examples of application, such as the inversion of cumulative distribution functions (arc-length and normal cumulative distributions) and the computation of the Lambert W-function.

METHOD OF DATA IDENTIFICATION IN THE SYSTEM OF INFORMATION SUPPORT OF ANTI-AIRCRAFT MISSILE UNITS BASED ON THE INTERPOLATION METHOD

The issue of making timely decisions in the control system of anti-aircraft missile units in order to ensure the rapid detection of air targets and their timely firing at long distances requires constant attention from military specialists of the leading countries of the world. The article presents the results of developing a methodology for identifying data in the information support system of anti-aircraft missile units based on the interpolation method. The object of research is the process of data identification in the information support system of anti-aircraft missile units. The subject of research is data interpolation methods. The purpose of the research is to develop a methodology for identifying data in the information support system of anti-aircraft missile units based on the interpolation method. Conclusions. An algorithm has been developed that implements a methodology for identifying the targeting data of the air defense missile control center, obtained from data from radio engineering troops, with the data of the unit's own or attached reconnaissance and targeting station and allows to increase the accuracy of combat information. To determine that the marks from the target received from the reconnaissance and targeting station and from the control center of the air defense missile unit are marks of the same target, an interpolation procedure is performed, provided that the data received from both sources is secondary information of the target observation vector. The interpolation procedure itself involves the formation of a spatial identification strobe and a comparison of the target trajectory obtained from the trace data of the own (supporting) reconnaissance and targeting station and the interpolated data of the target's movement relative to the latest external targeting data in the opposite direction. This algorithm can be used to implement the relevant tasks in the complex of automation tools for the control center of military units of air defense missile forces, automated workstations of commanders of air defense missile forces, which will reduce the time for searching and detecting air targets by the missile guidance station of the air defense missile system and directly increase the firepower of these units.

Use of XTFEM based on the consecutive interpolation procedure of quadrilateral element to calculate J-integral and SIFs of an FGM plate

An extended twice - interpolation finite element method (XTFEM) based on the consecutive interpolation procedure (CIP) of quadrilateral element in two-dimensional (2D) with continuous nodal stress for stress fields near material interface and geometry boundary such as inclusion and hole is presented. In contrast to the traditional approaches, the approximation shape functions constructed based on the CIP involve both nodal values and averaged nodal gradients as interpolation conditions. The CIP for quadrilateral element is developed recently by Tinh Quoc Bui, et al., 2014.In this research, we exhibit a pioneering extension of CIP – based consecutive-interpolation quadrilateral element enhanced by enrichment in terms of local partition of unity method to precisely model of a functionally graded material (FGM) plate had a single-edge crack a, and the influence of holes and inclusions near the crack was investigated in 2D structure to calculate the stress intensity factors (SIFs), an important parameter in predicting the direction of the crack even when the crack is no longer growing, taking advantages of the strengths and making use all the desirable features of both techniques, the CIP and the local enriched partition of unity method. Using MATLAB codes combined with XTFEM based on CIP of quadrilateral element. The accuracy and performance of the proposed XTFEM are compared to standard finite element method (FEM) (ANSYS). The comparison revealed the following analytical results: SIFs of the FGM isotropic plate had a crack a with an average error of 2.55% and the J-integral of 2.86%. The XTFEM gave better errors than FEM compared to the Exact and Experimental methods.

Home-to-school pedestrian mobility GPS data from a citizen science experiment in the Barcelona area

The analysis of pedestrian GPS datasets is fundamental to further advance on the study and the design of walkable cities. The highest resolution GPS data can characterize micro-mobility patterns and pedestrians’ micro-motives in relation to a small-scale urban context. Purposed-based recurrent mobility data inside people’s neighbourhoods is an important source in these sorts of studies. However, micro-mobility around people’s homes is generally unavailable, and if data exists, it is generally not shareable often due to privacy issues. Citizen science and its public involvement practices in scientific research are valid options to circumvent these challenges and provide meaningful datasets for walkable cities. The study presents GPS records from single-day home-to-school pedestrian mobility of 10 schools in the Barcelona Metropolitan area (Spain). The research provides pedestrian mobility from an age-homogeneous group of people. The study shares processed records with specific filtering, cleaning, and interpolation procedures that can facilitate and accelerate data usage. Citizen science practices during the whole research process are reported to offer a complete perspective of the data collected.

Metamaterial lenses for monostatic and bistatic 77 GHz radar systems

AbstractMetamaterial lenses are appealing thin alternatives to conventional dielectric lenses. In this contribution we describe their design and application in two exemplary 77 GHz automotive radar sensors operating in monostatic and bistatic modes. The frontends are built around commercially available MMICs and small feed antennas are used in coordination with the six-layer printed circuit board-based realizations of metamaterial lenses. The design follows the principles of dielectric lenses, while the required local phase shift is obtained from a set of metasurface bandpasses. Their design uses a novel interpolation procedure to extract layout parameters for a given phase shift. Despite the small structural sizes due to the high frequency, the fabricated frequency-selective surfaces show very good performance in the required frequency range. Verification measurements were conducted on single bandpasses as well as on metamaterial lenses mounted on the radar frontend. The results agree very well with the simulation and confirm the applicability of thin lenses operating at mm-wave frequencies for automotive radar applications.

Use of falling weight deflectometer data to determine the effective structural number of full-depth asphalt pavements for structural condition assessment

The effective structural number (SNeff) determined from the falling weight deflectometer (FWD) has been widely used for pavement structural evaluations. In Indiana, the AASHTO 1993 method is currently used to determine SNeff, but it was found to be inaccurate for full-depth asphalt pavements. Thus, this study developed an enhanced model to more accurately estimate SNeff of full-depth asphalt pavements. The AASHTO 1993 method and the Rohde model tend to overestimate the SNeff, and the Rohde model was calibrated using the FWD deflection thresholds. Since the calibrated Rohde model requires an interpolation procedure sometimes resulting in negative deflections, a more practical method was developed using an FWD database generated by finite element analyses. New model provides SNeff values nearly identical to the calibrated Rohde model without the problem of negative deflections. Therefore, this enhanced SNeff prediction model is recommended for evaluating the structural conditions of full-depth asphalt pavements.

On quantitative off-axis Scanning Transmission Ion Microscopy (STIM)

Spurred by a need to determine major (C, H, N and O) contents in biological tissue sections, a formalism for quantitative off-axis Scanning Transmission Ion Microscopy (OA-STIM) has been established. This can be used with, or without, simultaneous Elastic Backscattering Spectroscopy (EBS) to provide quantitative major element composition and thickness information. As part of the work, an empirical predictor with one free parameter for the proton–proton differential scattering cross section was implemented. The predictor values were in extremely close agreement with high accuracy literature data. For 2 MeV p–12C elastic scattering at forward angles ≤45°an interpolation procedure was used to determine the relative deviations from the Rutherford cross sections were determined to be ≤6.4%. The interpolation was based on a Coulomb field, angular momentum quantum number and nuclear structure dependent nuclear penetration factor. Finally, the quantitative combination of simultaneous OA-STIM and EBS data is discussed.

On the Simulations of Second-Order Oscillatory Problems with Applications to Physical Systems

Second-order oscillatory problems have been found to be applicable in studying various phenomena in science and engineering; this is because these problems have the capabilities of replicating different aspects of the real world. In this research, a new hybrid method shall be formulated for the simulations of second-order oscillatory problems with applications to physical systems. The proposed method shall be formulated using the procedure of interpolation and collocation by adopting power series as basis function. In formulating the method, off-step points were introduced within the interval of integration in order to bypass the Dahlquist barrier, improve the accuracy of the method and also upgrade the order of consistence of the method. The paper further validated the some properties of the hybrid method derived and from the results obtained; the new method was found to be consistent, convergent and stable. The simulation results generated as a result of the application of the new method on some second-order oscillatory differential equations also showed that the new hybrid method is computationally reliable.

Numerical solution of second-order nonlinear partial differential equations originating from physical phenomena using Hermite based block methods

A Hermite based block method (HBBM) is proposed for the numerical solution of second-order non-linear elliptic partial differential equations (PDEs). The development of the method was accomplished through the methodology of interpolation and collocation procedures. The method’s analysis reveals that it satisfied the requirements for a numerical technique to be convergent. The implementation of the method is extensively discussed. Five numerical examples originating from physical phenomena are presented, and the applicability and accuracy of the HBBM are established by comparing them with the existing methods; the haar wavelet collocation method, the modified cubic B-spline collocation method, and the modified decomposition method. The proposed methods of HBBM are more accurate, stable, and convergent