Linear Spline Interpolation Research Articles

Determination of emissivity profiles using a Bayesian data-driven approach

In this paper, we explore the determination of a spectral emissivity profile that closely matches real data, intended for use as an initial guess and/or a priori information in a retrieval code. Our approach employs a Bayesian method that integrates the CAMEL (Combined ASTER MODIS Emissivity over Land) emissivity database with the MODIS/Terra＋Aqua Yearly Land Cover Type database. The solution is derived as a convex combination of high-resolution Huang profiles using the Bayesian framework. We test our method on IASI (Infrared Atmospheric Sounding Interferometer) data and find that it outperforms the linear spline interpolation of the CAMEL data and the Huang emissivity database itself.

Automated Maximum Torque per Ampere Identification for Synchronous Reluctance Machines with Limited Flux Linkage Information

The synchronous reluctance machine is well-known for its highly nonlinear magnetic saturation and cross-saturation characteristics. For high performance and high-efficiency control, the flux-linkage maps and maximum torque per ampere table are of paramount importance. This study proposes a novel automated online searching method for obtaining accurate flux-linkage and maximum torque per ampere Identification. A limited 6 × 2 dq-axis flux-linkage look-up table is acquired by applying symmetric triangle pulses during the self-commissioning stage. Then, three three-dimensional modified linear cubic spline interpolation methods are applied to extend the flux-linkage map. The proposed golden section searching method can be easily implemented to realize higher maximum torque per ampere accuracy after 11 iterations with a standard drive, which is a proven faster solution with reduced memory sources occupied. The proposed algorithm is verified and tested on a 15-kW SynRM drive. Furthermore, the iterative and execution times are evaluated.

Correlation of satellite-based LAI and actual crop yield

The main objective of this article was to investigate the correlation between actual crop yield and Sentinel-2 Leaf Area Index (LAI) for the further possibility of predict model creating. To do so, the following steps have been done. Step 1 – the dataset of actual crop yield was collected for 2364 fields in Ukraine represented with maize, soy, sunflower, winter wheat, winter rapeseed and winter barley. Step 2 – the dataset of Sentinel-2 LAI was collected for 2016-2018 period according to the actual crop yield available. Step 3 – LAI preprocessing (spatial averaging, temporal interpolation/extrapolation to fill the time series gaps, smoothing time series dynamics, temporal averaging). In order to accomplish the process of filling the gaps for the LAI time series, the regular time series dynamics of LAI with a 1-day interval were created using 4 methods: linear interpolation, spline interpolation, LOCF (Last Observation Carried Forward) and ARIMA (AutoRegressive Integrated Moving Average). The time series smoothing process have been accomplish using the local polynomial regression (LOESS) function with different degrees of smoothing. The LAI dynamics preprocessing step did not strongly affect the improvement of the correlation coefficients. Thus, the smoothing process for the time series LAI dynamics at the 0.1 degree of smoothing according to the LOCF and ARIMA gap-filling methods of improved correlation coefficients by 0.01 on average. Step 4 – actual yield values were related to preprocessed satellite-based LAI (correlation of actual yields and LAI). A strong relationship was not indicated (with averaged by vegetation periods correlation coefficient of 0.4 for maize, 0.52 – soy, 0.39 – sunflower, 0.86 – winter barley, 0.54 – winter rapeseed and 0.5 – winter wheat). Since the reliability of obtained correlation coefficients also depends on how many observed data points were in the sample, the hypothesis test of the "significance of the correlation coefficient" has been performed and shows the significance level of p < 0.05 for all crops except winter barley (there is insufficient evidence to conclude that high correlation coefficient of 0.86 for this crop is significant). The average correlation coefficient for all crops is about 0.5 (p < 0.05) which is considered low/moderate. Thus, an attempt to create a linear crop yield prediction model using only Leaf Area Index (LAI) derived from Sentinel-2 will not be effective (based on the cases considered).

Stochastic integrodifferential models of fractional orders and Leffler nonsingular kernels: well-posedness theoretical results and Legendre Gauss spectral collocation approximations

Stochastic fractional integrodifferential models are widely employed to model several natural phenomena these days. This current work focuses on the well-posedness results and numerical solutions of a specific form of these models considering the Leffler nonsingular kernels operator wherein the stochastic term is driven by the standard Brownian motion. Accordingly, a combination of sufficient conditions, topological theorems, and Banach space theory are utilized to construct the well-posedness proof. For treating the numerical issue, a familiar spectral collocation technique relying upon shifted Legendre series expansion theory is proposed. The basic properties of Brownian motion and a linear spline interpolation method are used to simulate the standard Brownian motion at a fixed time value. In addition, the idea of the Gauss-Legendre numerical integration rule is implemented to approximate the finite integral. We also devote our attention to the concept of convergence of the proposed method and demonstrate its analysis. Ultimately, the obtained theoretical results and the presented method are examined with five numerous applications. The obtained results indicate the high accuracy and efficiency of applying this method in solving stochastic models of the above-mentioned form.

Missing Data Imputation for Solar Radiatıon by Deep Neural Network

The quality of observations is fundamental issue in natural sciences. Here, the accurate and complete data is required to accomplish satisfactory estimations. There are several factors impairing the quality of measurements, such as a broken or mis-calibrated device and error in reading the measurements. Thus, this study primarily aims the imputation of the missing values in measurement of solar radiation data. Deep Neural Network (DNN) method was used to handle the missing data, and benchmarked with the classical approaches, i.e., Mean Imputation (MI), which one of the most frequently adopted data imputation method in the pertinent literature, the Linear Interpolation (LI) and Spline Interpolation (SI). The overall results highlighted that the DNN method outperformed its counterparts in terms of missing value handling through providing a greater accuracy according to the various performance metrics compared to the classical methods. It is believed that the proposed approach could make valuable contribution to the body of knowledge as well as providing significant overview to the interested researchers by filling the important gap exists in the pertinent literature.

Methodological approaches for imputing missing data into monthly flows series

Missing data is one of the main difficulties in working with fluviometric records. Database gaps may result from fluviometric stations components problems, monitoring interruptions and lack of observers. Incomplete series analysis generates uncertain results, negatively impacting water resources management. Thus, proper missing data consideration is very important to ensure better information quality. This work aims to analyze, comparatively, missing data imputation methodologies in monthly river-flow time series, considering, as a case study, the Doce River, located in Southeast Brazil. Missing data were simulated in 5%, 10%, 15%, 25% and 40% proportions following a random distribution pattern, ignoring the missing data generation mechanisms. Ten missing data imputation methodologies were used: arithmetic mean, median, simple and multiple linear regression, regional weighting, spline and Stineman interpolation, Kalman smoothing, multiple imputation and maximum likelihood. Their performances were compared through bias, root mean square error, absolute mean percentage error, determination coefficient and concordance index. Results indicate that for 5% missing data, any methodology for imputing can be considered, recommending caution for arithmetic mean method application. However, as the missing data proportion increases, it is recommended to use multiple imputation and maximum likelihood methodologies when there are support stations for imputation, and the Stineman interpolation and Kalman Smoothing methods when only the studied series is available.
 Keywords: Doce river, imputation, missing data.

Features of a real-time s-shaped acceleration/deceleration curve constructing with piecewise linear interpolation of complex-shaped surfaces

In this paper we considered the problem of an s-shaped acceleration/deceleration curve constructing in real time with linear-spline interpolation, taking into account given constraints on the contour acceleration, jerk, and feed rate. The input data for the s-curve were defined in the lookahead algorithm and the geometric smoothing module. The choice of a particular acceleration/deceleration strategy depends on the segment length, the allowable feed rates at the segment junction, and the given kinematic constraints. Each trajectory segment can have a maximum of seven time intervals and their rounding will produce inaccuracies when forming the velocity profile. Therefore, to compensate for rounding errors, the method of half division was applied, which made it possible to remove gaps in the velocity contour. The experimental data obtained indicate the correctness of the chosen approach for its implementation as part of the CNC for high-speed machining of surfaces with complex shapes. Key words Feed-rate planning algorithm, s-shaped acceleration/deceleration, trajectory smoothing, numerical control system, real-time, frame preview algorithm. Acknowledgements The research was carried out with financial support of Ministry of Science and Higher Education of Russian Federation in the frame of state assignment (project no.FSFS-2020-0031).

On the use of flyash-lime-gypsum (FaLG) bricks in the storage facilities for low level nuclear waste

In the present study, radiation shielding and protection ability of prepared Flyash-lime-Gypsum (FaLG) bricks has been studied in terms of energy exposure build up factors and dose parameters. The energy exposure build up factors of Flyash-lime-Gypsum (FaLG) bricks have been calculated for the energy range of 0.015 MeV–15 MeV and for penetration depth upto 40 mfp directly using a new and simplified Piecewise Linear Spline Interpolation Method (PLSIM). In this new method, the calculations of G.P fitting parameters are not required. The verification and accuracy of this new method has been checked by comparing the results of exposure build up factor for NBS concrete calculated using present method with the results obtained by using G.P fitting method. Further, the relative dose distribution and reduced exposure dose rate for various radioactive isotopes without any shielding material and with Flyash-lime-Gypsum (FaLG) bricks have been calculated in the energy range of 59.59–1332 keV. On the basis of the obtained results, it has been reported that the prepared Flyash-lime-Gypsum (FaLG) bricks possess satisfactory radiation shielding properties and can be used as environmentally safe storage facilities for low level nuclear waste.

Frequency Interpolation of LOFAR Embedded Element Patterns Using Spherical Wave Expansion

This paper describes the use of spherical wave expansion (SWE) to model the embedded element patterns of the LOFAR low-band array. The goal is to reduce the amount of data needed to store the embedded element patterns. The coefficients are calculated using the Moore–Penrose pseudoinverse. The Fast Fourier Transform (FFT) is used to interpolate the coefficients in the frequency domain. It turned out that the embedded element patterns can be described by only 41.8% of the data needed to describe them directly if sampled at the Nyquist rate. The presented results show that a frequency resolution of 1 MHz is needed for proper interpolation of the spherical wave coefficients over the 80 MHz operating frequency band of the LOFAR low-band array. It is also shown that the error due to interpolation using the FFT is less than the error due to linear interpolation or cubic spline interpolation.

선형 스플라인 보간법을 활용한 교류철도 고장점표정 보정기법에 대한 고찰

In this paper, we compare and analyze the characteristics of the boosting current ratio, which occurs differently depending on the ground configuration of the traction line, to derive the main causes of the fault location error. To this end, the Power system analysis program (PSCAD/EMTDC) is utilized to derive the characteristics of the boosting current ratio due to the other-line absorption phenomenon through modeling and simulation. Furthermore, to derive problems from existing calibration methods, we analyze facial expression errors by classifying single linear interpolation calibrations into multiple cases. We present a correction technique using linear spline interpolation to improve the accuracy of the fault point representation even under the nonlinear boost current ratio characteristic conditions due to integrated ground and other line absorption phenomena.

Fluid-Structure Interaction for the Classroom: Interpolation, Hearts, and Swimming!

While students may find spline interpolation quite digestible, based on their familiarity with continuity of a function and its derivatives, some of its inherent value may be missed when students only see it applied to standard data interpolation exercises. In this paper, we offer alternatives where students can qualitatively and quantitatively witness the resulting dynamical differences when objects are driven through a fluid using different spline interpolation methods. They say, seeing is believing; here we showcase the differences between linear and cubic spline interpolation using examples from fluid pumping and aquatic locomotion. Moreover, students can define their own interpolation functions and visualize the dynamics that unfold. To solve the fluid-structure interaction system, the open-source fluid dynamics software IB2d is used. In that vein, all simulation codes, analysis scripts, and movies are provided for streamlined use.

Alat Bantu Prediksi Kecepatan pada Gerak Lurus Berubah Beraturan Menggunakan Metode Interpolasi Berdimensi Satu

The purpose of this study is to create a speed prediction tool in a uniformly accelerated linear motion using a single-dimensional interpolation method consisting of linear, cubic, cubic spline, and nearest neighbor interpolation methods. This tool is packaged in the form of Graphic User Interface (GUI) using Matlab programming language. This tool can be used as a medium of the analysis of the object speed experiencing a uniformly accelerated linear motion and a combination of several uniformly accelerated linear motions. Speed prediction results using linear, cubic, and cubic spline interpolation methods do not differ much from the results of analytical calculations, while speed prediction results using nearest neighbor interpolation method are less in line with the results of analytical calculations because nearest neighbor interpolation method will generate constant values around the data point. This tool can also be used as a learning medium to make it easier for students to learn the concept of uniformly accelerated linear motion in order to reduce the misconceptions in the material.

Numerical integrators for Lagrangian oceanography

Abstract. A common task in Lagrangian oceanography is to calculate a large number of drifter trajectories from a velocity field precalculated with an ocean model. Mathematically, this is simply numerical integration of an ordinary differential equation (ODE), for which a wide range of different methods exist. However, the discrete nature of the modelled ocean currents requires interpolation of the velocity field in both space and time, and the choice of interpolation scheme has implications for the accuracy and efficiency of the different numerical ODE methods. We investigate trajectory calculation in modelled ocean currents with 800 m, 4 km, and 20 km horizontal resolution, in combination with linear, cubic and quintic spline interpolation. We use fixed-step Runge–Kutta integrators of orders 1–4, as well as three variable-step Runge–Kutta methods (Bogacki–Shampine 3(2), Dormand–Prince 5(4) and 8(7)). Additionally, we design and test modified special-purpose variants of the three variable-step integrators, which are better able to handle discontinuous derivatives in an interpolated velocity field. Our results show that the optimal choice of ODE integrator depends on the resolution of the ocean model, the degree of interpolation, and the desired accuracy. For cubic interpolation, the commonly used Dormand–Prince 5(4) is rarely the most efficient choice. We find that in many cases, our special-purpose integrators can improve accuracy by many orders of magnitude over their standard counterparts, with no increase in computational effort. Equivalently, the special-purpose integrators can provide the same accuracy as standard methods at a reduced computational cost. The best results are seen for coarser resolutions (4 and 20 km), thus the special-purpose integrators are particularly advantageous for research using regional to global ocean models to compute large numbers of trajectories. Our results are also applicable to trajectory computations on data from atmospheric models.

Convergence analysis of an iterative algorithm to solve system of nonlinear stochastic Itô‐Volterra integral equations

In this paper, an efficient and accurate numerical iterative algorithm based on the linear spline interpolation for solving the system of nonlinear stochastic Itô‐Volterra integral equations is presented. The most important merit of this method is that it does not need to solve any system of nonlinear algebraic equations. An upper bound for the linear spline approximation of the stochastic function is provided. Using this upper bound and under the Lipschitz and linear growth conditions, the convergence analysis of the suggested method is studied. Finally, to verify the efficiency of the proposed scheme, some problems in the finance, physics, and biology are investigated, and the obtained results are compared with the stochastic ‐method.

A meshfree method for the BGK model for rarefied gas dynamics

In this paper, we have applied semi-Lagrangian schemes with meshfree interpolation, based on a moving least squares method, to solve the BGK model for rarefied gas dynamics. Sod’s shock tube problems are presented for a large range of mean free paths in one-dimensional physical space and three-dimensional velocity space. In order to validate the solutions obtained from the meshfree method, we have used the piecewise linear spline interpolation. Furthermore, we have compared the solutions of the BGK model with the solutions obtained from direct simulation Monte Carlo method. In the case of a very small mean free path, the numerical solutions are compared with the exact solutions of the compressible Euler equations. Overall, we found that the meshfree interpolation gives better approximation than the piecewise linear spline interpolation.

Wireless channel estimation in OFDM systems based on collaborative filtering techniques

Abstract In this paper, a new channel estimation algorithm in Orthogonal Frequency Division Multiplexing (OFDM) systems is proposed. The proposed algorithm is suitable for cases with low density of pilot sub-carriers, where standard interpolation methods (linear, second order and cubic spline interpolation) are inaccurate. The algorithm improves the interpolation methods by employing memory based collaborative filtering (CF) techniques which are less sensitive to the number and location of the pilot subcarriers. CF algorithms are usually used in the context of recommender systems (e-commerce) for predictions of the unknown user-item ratings based on known values of similar users. The advantage of CF is the ability to e ciently produce quality predictions with highly sparse data. Computer simulations are used to verify the proposed channel estimation algorithm and demonstrate that the proposed algorithm improves predictive accuracy metrics, such as Root Mean Squared Error (RMSE), compared to usual estimation methods.

Modeling the Impact of Foreign Equity, Foreign Debt and FDI on Indian Economic Growth Through VECM Approach

Foreign portfolio investment and foreign direct investment are the backbone of any economy as well as contributing to the growth of all developing economies. Herein, it motivated to do the study by investigating the causality between foreign investment and economic growth in India. To find out the exact causation effectively, we have employed a vector error correction model method of causality. The testing time series data period is from 1993 to 2017. Here, in this study, we converted annual gross domestic product and foreign direct investment data into monthly figures. For this we used econometric disaggregation techniques know as linear spline interpolation method for monthly data conversion. ADF unit root test confirms the presence of unit root at level and stationary at first difference. Johansen co-integration test is done after achieving the stationarity and it shows those variables are co-integrated. Whereas Granger causality test results show no-causality exists between (i) FDI and GDP (ii) GDP and FDI (iii) FE and GDP (iv) FD and GDP (v) FE and FDI (vi) FD and FDI (vii) FE and FD and uni-directional causality exist between GDP and FE (ii) GDP and FD (ii) FDI and FE (iv) FDI and FD (v) FD and FE. The results advocates that FDI, FE, FD boost the economic growth of India.

A comparison of linear interpolation and spline interpolation for turbine efficiency curves in short-term hydropower scheduling problems

The purpose of short-term hydropower scheduling (STHS) in a competitive electricity market is to maximize the profit in the near future while adapting to the mid-term strategies for system operation. To ensure a realistic and feasible operation for STHS, it is crucial to accurately represent the hydropower production function (HPF). The turbine efficiency can be represented by a two-dimensional table provided by the turbine manufacturers or measured by the hydropower producers on-site with some given efficiency values for a set of net water head and discharge values. In literature, the actual efficiency value for any working point is usually linearly interpolated from the given efficiency values. To the best of authors’ knowledge, no study has been done so far to investigate how a nonlinear interpolation for the turbine efficiency, i.e. spline interpolation, may contribute to the application of STHS. In this paper, we compare the performance of linear interpolation and spline interpolation for turbine efficiency curves in the STHS problem and the bidding strategy in intraday market. The interpolation methods are tested on an operational hydro-power scheduling model, Short-term Hydro Optimization Program (SHOP), which is used by most large hydropower producers in the Nordic countries. Numerical tests demonstrate superior behavior of spline interpolation for the estimation of turbine efficiency between measured points. Compared to linear interpolation, spline interpolation for turbine efficiency curves gives smoother discharge transitions in day-ahead scheduling and is vital for obtaining continuous marginal cost curves in intraday trading. Based on the results in this paper, spline interpolation is a promising alternative to linear interpolation for turbine efficiency curves in STHS.

APPLICATION OF MACHINE LEARNING TO FILL IN THE MISSING MONITORING DATA OF AIR QUALITY

In this paper, three machine learning models have been applied to predict and fill in the missing monitoring data of air quality for Gia Lam and Nha Trang stations in Hanoi and Khanh Hoa respectively, including Autoregressive Moving Average (ARMA), Artificial Neural Network (ANN), and Support Vector Regression (SVR). Two air pollutants being NO2 and PM10 were selected for this study. The experimental results showed that the performance of all three studied models is better than that of some traditional approaches, including Multiple Linear Regression (LR) and Spline interpolation. Besides that, ARMA, ANN and SVR can capture the fluctuation of concentrations of the selected pollutants. These results indicated that the machine learning is a feasible approach to deal with the missing of data which is one of the biggest problems of air quality monitoring stations in Viet Nam.

Missing data management and statistical measurement of socio-economic status: application of big data

Socio-economic status measurement is an ongoing problem where different suggested measurements are given by researchers. This work investigates a socio-economic status measurement derived from natural correlations of variables which can better and meaningfully cluster African countries for the level of status. The researcher used 48 African countries socio-economic yearly time series data from 1993 to 2013 of IMF 2013 data set for data management (i.e, 2737 variables for 21 years), however, the analysis is reasonably done based on recent 14 years time series data. In data management, missing values are treated (imputed) by using regression estimates, Lagrange interpolation, linear interpolation and linear spline interpolation based on the appropriate method which best fits for the trend of data with minimum error at each time level. From principal component and factor analysis of average time series data, 7 principal factors contributed by 84 variables which explain 70% of the variation in the data set are suggested as a socio-economic status measuring components and as a result the considered clustering methods (K-mean Method, Average linkage method, Ward’s method and Bootstrap Ward’s method) are agreed on six clusters of countries, those are statistically significant at 95%, where as three countries each where suggested as outlier-countries made an individual cluster.