Accurate Interpolation Research Articles

High-Resolution Precipitation Modeling in Complex Terrains Using Hybrid Interpolation Techniques: Incorporating Physiographic and MODIS Cloud Cover Influences

The inclusion of physiographic and atmospheric influences is critical for spatial modeling of orographic precipitation in complex terrains. However, attempts to incorporate cloud cover frequency (CCF) data when interpolating precipitation are limited. CCF considers the rain shadow effect during interpolation to avoid an overly strong relationship between elevation and precipitation in areas at equivalent altitudes across rain shadows. Conventional multivariate regression or geostatistical methods assume the precipitation–explanatory variable relationship to be steady, even though this relation is often non-stationarity in complex terrains. This study proposed a novel spatial mapping approach for precipitation that combines regression-kriging (RK) to leverage its advantages over conventional multivariate regression and the spatial autocorrelation structure of residuals via kriging. The proposed hybrid model, RK (GT + CCF), utilized CCF and other physiographic factors to enhance the accuracy of precipitation interpolation. The implementation of this approach was examined in a mountainous region of southern Syria using in situ monthly precipitation data from 57 rain gauges. The RK model’s performance was compared with conventional multivariate regression models (CMRMs) that used geographical and topographical (GT) factors and CCF as predictors. The results indicated that the RK model outperformed the CMRMs with a root mean square error of <8 mm, a mean absolute percentage error range of 5–15%, and an R2 range of 0.75–0.96. The findings of this study showed that the incorporation of MODIS–CCF with physiographic variables as covariates significantly improved the interpolation accuracy by 5–20%, with the largest improvement in modeling precipitation in March.

Study of groundwater temperature spatio-temporal variation in the city of Wroclaw. Preliminary results.

In Wrocław over the past 20 years, the recorded increase in the average ambient air temperature is approx. 0.5 °C. In addition, urbanisation has created a phenomenon called the Urban Heat Island (UHI). The combined effect of the UHI and climate change can influence groundwater temperature by penetrating underground. The phenomenon of elevated groundwater temperatures in urban areas is called the Subsurface Urban Heat Island (SSUHI). This study focuses on the spatial distribution of temperature in shallow aquifers in the city of Wroclaw. The spatial distribution was analysed based on groundwater temperature maps developed with various interpolation techniques. The results of measurements in a network of 65 piezometers conducted in the 2004-2005 hydrological year have been used in this study. The temperatures recorded show seasonal variation with the lowest recorded in February (1.3 °C) and the highest in August (24.5 °C) with the annual average of 13.2 °C. The data has been processed with the Inverse Distance Weighted (IDW), Radial Basis Function (RBF) and Kriging interpolation methods. Furthermore, the cokriging method based on multivariate linear regression models has been used to assess if variable such as distance from the city centre improve the interpolation performance expressed as the lowest RMS error value. It has been established that the Kriging univariate regression model based interpolation method produced the best results (RMS error equal to 1.33 °C) and that the distance from the city centre has improved the accuracy of interpolation.

High-Accuracy and High-Tolerance Laser Encoder With a Grating-Pyramid Configuration

Laser encoders is promising positioning sensors for nanometer measurement. It is a key challenge for laser encoders to offer high accuracy while ensuring high tolerance in service. In this paper, we present a laser encoder employing a grating-pyramid configuration. This configuration realizes double diffraction via a single retro-reflector, which offers the following two advantages: (i) providing high-resolution output signals due to optical quadruple frequency; (ii) improving alignment tolerance due to retro-reflection of the single pyramid. Its operating principle is described in detail, and the performance are evaluated. Simulation result presents that stand-off error and pitch error are the critical head-to-scale tolerance for the developed laser encoder. Experiment result shows that the laser encoder offers a stand-off tolerance of ±0.68 mm and a pitch tolerance of ±1.67°. Furthermore, an interpolation accuracy of 3 nm is achieved, which indicates that the laser encoder would achieve nanometer-level resolution. Both simulation and experimental results demonstrate its high-accuracy and high-tolerance.

Model for Choosing the Shape Parameter in the Multiquadratic Radial Basis Function Interpolation of an Arbitrary Sine Wave and Its Application

In multiquadratic radial basis function (MQ-RBF) interpolation, shape parameters have a direct effect on the interpolation accuracy. The paper presents an MQ-RBF interpolation technique with optimized shape parameters for estimating the parameters of sine wave signals. At first, we assessed the impact of basic sinusoidal parameters on the MQ-RBF interpolation outcomes through numerical experiments. The results indicated that the angular frequency of a sine wave is a crucial determinant of the corresponding MQ-RBF interpolation shape parameters. A linear regression method was then used to establish the optimal parameter selection formula for a single-frequency sine wave, based on a large volume of experimental data. For multi-frequency sinusoidal signals, appropriate interpolation shape parameters were selected using the random walk algorithm to create datasets. These datasets were subsequently used to train several regression models, which were then evaluated and compared. Based on its operational cost and prediction accuracy, the random forest algorithm was chosen to establish the shape parameter selection model for multi-frequency sinusoidal signals. The inclusion of the Bayesian optimizer resulted in a highly accurate model. The establishment of this model enabled the adaptive selection of the corresponding shape parameters for any sine wave signal, providing a convenient means of selecting MQ-RBF interpolation shape parameters. Furthermore, the paper proposes an MQ-RBF interpolation subdivision least squares method that significantly improves the estimation accuracy of sine wave parameters. The practicality of the method was validated by successfully applying it in the calibration of the clock delay mismatch of a time-interleaved analog-to-digital converter system.

Spectral methods for solving elliptic PDEs on unknown manifolds

In this paper, we propose a mesh-free numerical method for solving elliptic PDEs on unknown manifolds, identified with randomly sampled point cloud data. The PDE solver is formulated as a spectral method where the test function space is the span of the leading eigenfunctions of the Laplacian operator, which are approximated from the point cloud data. While the framework is flexible for any test functional space, we will consider the eigensolutions of a weighted Laplacian obtained from a symmetric Radial Basis Function (RBF) method induced by a weak approximation of a weighted Laplacian on an appropriate Hilbert space. In this paper, we consider a test function space that encodes the geometry of the data yet does not require us to identify and use the sampling density of the point cloud. To attain a more accurate approximation of the expansion coefficients, we adopt a second-order tangent space estimation method to improve the RBF interpolation accuracy in estimating the tangential derivatives. This spectral framework allows us to efficiently solve the PDE many times subjected to different parameters, which reduces the computational cost in the related inverse problem applications. In a well-posed elliptic PDE setting with randomly sampled point cloud data, we provide a theoretical analysis to demonstrate the convergence of the proposed solver as the sample size increases. We also report some numerical studies that show the convergence of the spectral solver on simple manifolds and unknown, rough surfaces. Our numerical results suggest that the proposed method is more accurate than a graph Laplacian-based solver on smooth manifolds. On rough manifolds, these two approaches are comparable. Due to the flexibility of the framework, we empirically found improved accuracies in both smoothed and unsmoothed Stanford bunny domains by blending the graph Laplacian eigensolutions and RBF interpolator.

GNSS rapid precise point positioning enhanced by low Earth orbit satellites

The Low Earth Orbit (LEO) satellites can be used to effectively speed up Precise Point Positioning (PPP) convergence. In this study, 180 LEO satellites with a global distribution are simulated to evaluate their contribution to the PPP convergence. LEO satellites can give more redundant observations and improve satellite geometric distributions, particularly for a single Global Navigation Satellite System (GNSS). The convergence speed of the PPP float solution using the Global Positioning System (GPS, G) or BeiDou Navigation Satellite System (BDS, C) single system as well as the G/C/Galileo navigation satellite system (Galileo, E)/GLObal NAvigation Satellite System (GLONASS, R) combined system with LEO satellites added is improved by 90.0%, 91.0%, and 90.7%, respectively, with respect to the system without LEO satellites added. We introduced LEO observations to assist GNSS in PPP-AR (Ambiguity Resolution) and PPP-RTK (Real Time Kinematic). The success fix rate of a single system is significantly improved, and the Time-To-First-Fix (TTFF) of G and G/C/E is reduced by 86.4% and 82.8%, respectively, for the PPP-AR solution. We analyzed the positioning performance of LEO satellite assisted G/C/E PPP-RTK in the reference networks of different scales, namely different atmospheric delay interpolation accuracies. The success fix rate of the G/C/E combined system is improved from 86.8 to 94.9%, and the TTFF is reduced by 36.8%, with the addition of LEO satellites in the 57 km reference network. In the 110 km reference network, the success fix rate of the G/C/E combined system is improved from 64.0 to 88.6%, and the TTFF is reduced by 32.1%. GNSS PPP-RTK with adding the LEO satellites in the reference networks of different scales shows obvious improvement because the atmospheric correlation decreases with increasing distance from the reference networks.

Towards texture accurate slice interpolation of medical images using PixelMiner

Quantitative image analysis models are used for medical imaging tasks such as registration, classification, object detection, and segmentation. For these models to be capable of making accurate predictions, they need valid and precise information. We propose PixelMiner, a convolution-based deep-learning model for interpolating computed tomography (CT) imaging slices.PixelMiner was designed to produce texture-accurate slice interpolations by trading off pixel accuracy for texture accuracy. PixelMiner was trained on a dataset of 7829 CT scans and validated using an external dataset. We demonstrated the model's effectiveness by using the structural similarity index (SSIM), peak signal to noise ratio (PSNR), and the root mean squared error (RMSE) of extracted texture features. Additionally, we developed and used a new metric, the mean squared mapped feature error (MSMFE). The performance of PixelMiner was compared to four other interpolation methods: (tri-)linear, (tri-)cubic, windowed sinc (WS), and nearest neighbor (NN).PixelMiner produced texture with a significantly lowest average texture error compared to all other methods with a normalized root mean squared error (NRMSE) of 0.11 (p < .01), and the significantly highest reproducibility with a concordance correlation coefficient (CCC) ≥ 0.85 (p < .01).PixelMiner was not only shown to better preserve features but was also validated using an ablation study by removing auto-regression from the model and was shown to improve segmentations on interpolated slices.

Spatial distribution and reserve estimation of sand and gravel deposits using geostatistical methods in west Basrah, southern Iraq

Sand and gravel are among the most common natural materials. They are generally used as a raw material in concrete, road construction, mixing with asphalt and filling material, among other uses. Sand and gravel deposits are widespread within the southern and central regions of Iraq. Among these deposits are the alluvial sand and gravel that form the upper part of the Dibdibba Formation in the Al-Rafiya, Al-Tuba, Chwaibda and Safwan blocks in west Basrah, southern Iraq. In this research, grain size distribution for channel samples collected from each block was determined. Thickness of overburden and industrial beds was measured and the stripping ratio (SR) was calculated. Geostatistical interpolation approaches including inverse distance weighting (IDW) and ordinary kriging (OK) were utilised to predict the spatial distribution of sand and gravel deposits and their reserves from borehole data. Data validation using the mean error (ME) and root-mean-square error (RMSE) were applied. The deposits can be characterised as gravelly sand (gS) in the Al-Tuba, Al-Rafiya and Chwaibda blocks, while it is a sandy gravel (sG) in the Safwan block. The overburden gypcrete beds varied between 1 and 3 ​m thick, while the industrial sand and gravel beds which appear as planar and sometimes lenticular deposits ranging between 3 and 8 ​m thick. The SR is generally low, considering the easily removed lightweight material of the overburden bed and the easily extractable fairly flat and near-surface friable sand and gravel deposits. Reserves are estimated as 376.63 Million m3 and 385.97 Million m3 using the IDW and OK approaches, respectively. Based on the least error values of ME and RMSE, we conclude that the OK method is the more accurate spatial interpolation approach for sand and gravel reserve estimation in all blocks compared to the IDW method.

THE EFFECT OF THE NUMBER OF INPUTS ON THE SPATIAL INTERPOLATION OF ELEVATION DATA USING IDW AND ANNS

Spatial interpolation is a required method to generate a continuous surface such as Digital Elevation Model (DEM) because field investigation for most of the surface’s part is time-consuming with a high demand in both human resources and monetory cost. One of the most used deterministic interpolation models is Inverse Distance Weighting (IDW) model. The model takes several neighbors’ information, and the weights are constructed based on the distance between the interpolated point and the neighbors’ points. From the machine learning model, Artificial Neural Networks (ANNs) model has also been used for spatial interpolation. The input of ANNs model is also one of the parameters that need to be defined when building the model. This paper evaluated the effect of the number of inputs (neighbors) on the elevation interpolation accuracy. We applied IDW and ANNs to interpolate the elevation of Balikpapan City, Indonesia. The results show that the accuracy increases significantly when the number of inputs is between one and three. However, after three inputs, additional input would not change the accuracy significantly. ANNs performed better than IDW. For three or more inputs, the MAE of ANNs and IDW interpolations are below 1.1 and around 2 meters, respectively.

Moving least squares approximation using variably scaled discontinuous weight function

Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable piecewise Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically.

Improvement of the multi-source weighted-ensemble precipitation dataset and application in the arid area of Tianshan Mountains, central Asia

With high resolution and wide coverage, satellite precipitation products like the Multi-Source Weighted Ensemble Precipitation (MSWEP) could support hydrological research in arid regions, where the spatial heterogeneity of precipitation is high, but rain gauges are sparse, but these products are inevitably subject to errors. In this study, we integrated measured precipitation and topographic data, and improved MSWEP by interpolation and an optimal regression model. The Tianshan Mountain area was taken as a typical arid area, and spatial stratified heterogeneity of precipitation was analyzed. The results show that: (1) The optimal regression model combined the advantages of site interpolation and MSWEP and improved the underestimation of precipitation in mountainous areas; (2) The precipitation decreased from West to East, and from North to South, and the precipitation in West and East subregions increased linearly with the elevation. The maximum precipitation height zone in the North is located at 4300 m. There are two maximum precipitation height zones in the South; (3) The accuracy of spatial interpolation of station data was limited by the uneven distribution of the stations in the East subregion, and the inaccuracy of MSWEP was due to the land cover and topography of the North and South subregions. The improved MSWEP (IMMSWEP) not only resolved the problem of lack of rainfall stations in arid area, but also resulted in an inversion of regional spatial precipitation differentiation with high resolution and high precision, providing a reference for meteorological researchers.

Gap Filling Method and Estimation of Net Ecosystem CO2 Exchange in Alpine Wetland of Qinghai–Tibet Plateau

The net ecosystem CO2 exchange (NEE) and water and energy fluxes at the alpine ecosystem level were obtained through the eddy covariance technique in an alpine wetland of the Longbao Region, Qinghai–Tibet Plateau. Our research used the NEE as the research object combined with meteorological factors. The NEE prediction model was constructed using Reddyproc and machine learning. Moreover, the effects of the data and features on the models and the selection of the model parameters were discussed. The results revealed the following information: (1) After removing the NEE outliers according to the friction wind speed thresholds of the different seasons, the NEE interpolation accuracy (R2) reached 0.65. Additionally, the NEE data dispersion decreased after removing the outliers, and the data quality improved effectively. (2) The decision coefficients (R2) of the eight kinds of combined machine learning algorithm models varied from 0.22 to 0.62, and the root mean square error (RMSE) ranged from 2.10 to 2.99 μmol s−1 m−2. Additionally, the multilayer perceptron (MLP) model had the best stability and the best interpolation effect. (3) There was a seasonal difference between the estimated values of Reddyproc and the estimated values of MLP. The monthly mean values of January, February, March, and October were lower than the monthly mean values of the latter, while the monthly mean values from April to September were higher than the monthly mean values of the latter, indicating that the prediction of the machine learning algorithm tends towards the carbon source in the cold season (nongrowing season) and tends towards the carbon sink in the warm season (growing season). (4) Reddyproc detected the outliers through the relationship between the night NEE and frictional wind speed, which made it possible to accurately estimate the nighttime flux under the condition of determining the threshold of the night frictional wind speed, thus obtaining a better NEE estimate with fewer input parameters. Before the training and prediction of the MLP model, the NEE was detected for the time series outliers, and the prediction accuracy was significantly improved, indicating that the elimination of the time series outliers is essential for NEE model training and further indicating that the understanding of the potential mechanism of the NEE is of great significance for the prediction model.

Comparative Analysis of Methods for Hourly Electricity Demand Forecasting in the Absence of Data – A Case Study

Abstract Scope and purpose of work This paper examines the impact of the number of gaps in data, the analytical form, and the model type selection criterion on the accuracy of interpolation and extrapolation forecasts for hourly data. Materials and methods Forecasts were developed on the basis of predictors that are based on: classical time series forecasting models and regression time series forecasting models, hybrid time series forecasting models and hybrid regression forecasting models for uncleared series, and exponential smoothing models for cleared series of two or three types of seasonal fluctuations, with minimum estimates of errors in interpolation or extrapolation forecasts. Results Adaptive and hybrid regression models have proved to have the most favorable predictive properties. Most hybrid time series models for systematic and non-systematic gaps and for both analytical forms are single models that generally describe fluctuations within a 24-hour cycle. Conclusions The lowest estimators of prediction errors involving interpolation were obtained for exponential smoothing models, followed by hybrid regression models. A reverse sequence was obtained for extrapolative forecasting.

The effects of station density in geostatistical prediction of air temperatures in Sweden: A comparison of two interpolation techniques

High fidelity gridded temperature datasets are difficult to obtain for areas with sparse coverage of meteorological stations given that sparsity of stations is known to introduce uncertainty in the interpolation of climatic variables generally. Inspired by their potential for optimal results especially for small sample datasets, the accuracy of interpolation results of Empirical Bayesian Kriging (EBK) and EBK-Regression Prediction (EBKRP) spatial prediction techniques were assessed and compared under varying sampling density scenarios, using monthly maximum temperature normals (1991–2020) for the entire area of Sweden. The objective of the was to understand how EBK and EBKRP interpolation techniques perform in different sampling density scenarios and in a sparse data setting, and the possible difference in the prediction accuracy between the two techniques. The 708 sampled stations obtained from the historical climatology database of the Swedish Meteorological and Hydrological Institute (SMHI) were split into seven sampling density subsets, ranging from 1 sample per 63,614 km 2 to 1 sample per 634,350 km 2 and representing both low and high sampling density scenarios. EBK interpolation technique was implemented using temperature data while land use land cover (LULC) and digital elevation model (DEM) were used as temperature covariates for the EBKRP interpolation models. The prediction accuracy assessment was based on five robust prediction performance indicators - mean error, mean absolute error, mean square error, root mean square error and Pearson correlation (R) - obtained from independent validation/cross-validation operations. Prediction accuracy was found to be generally positively related to sampling density and sampling density accounted for 85%–87% of interpolation accuracy for both EBK and EBKRP techniques. Although sampling density increased linearly, the rate of change in accuracy from one sampling density step to the next was not particularly proportional. A rapid increase in accuracy was observed when transiting from 40% to 60% sampling density scenario, but the rate of change in accuracy remained fairly stable before and after this (40% to 60%) sampling density scenario. For equivalent sampling density set-ups, EBKRP consistently performed better than EBK in all the accuracy metrics and EBKRP proved to be about 40% better than EBK. However, the two interpolation techniques produced generally very low prediction biases at all the sampling density scenarios investigated. Our study suggests that potential effects of low sampling density and non-stationarity of temperature data can be significantly reduced by applying EBK but especially EBKRP when coupled with relevant covariates. We also concluded that EBK and EBKRP can be applied to generate accurate prediction surfaces even in a widely varying sampling density setting including environments with moderately low sample density. This is especially true for continuous and slowly varying phenomena such as temperature and similar variables. • Station density is positively related to interpolation accuracy of air temperature but in non-linear fashion. • Univariate and multivariate Empirical Bayesian Kriging interpolation techniques can produce high prediction accuracy result even when data density is small or locally non-stationary. • Multivariate Empirical Bayesian Kriging technique performs better than the univariate technique in different sampling density settings when predicting air temperature. • Normally distributed data can generally improve prediction results even when data density is relatively small or sparse.

Improving seabed substrate mapping with high-resolution bottom trawl data

Accurate seabed substrate maps are essential for marine management, as substrate is an important component of the habitat type and used as a proxy for the prevailing benthic community. The provision of substrate maps, however, is hampered by the excessive costs of at-sea observations and, consequently, the uncertainty associated with spatial models used to interpolate these observations to full-coverage maps. Here, we tested whether high-resolution distributions of bottom trawling activity, readily collected under EU law, could improve the accuracy of substrate interpolations. Fishing distributions contain indirect information of the substrate type, as targeted species often show habitat preferences and gear types are designed for particular substrates. For two study areas in the Danish North Sea, we demonstrate that including spatial distributions of bottom trawl fisheries in substrate interpolation models results in more accurate substrate predictions. This potentially opens a novel source of previously unused information for improved seabed substrate interpolation.

Gaussian mixture model based radio environment mapping for an underlay Device‐to‐Device network

AbstractEfficient management of the scant radio resources in densely deployed Device‐to‐Device (D2D) and IoT networks in 5G+ and 6G wireless era would require continuous and reliable information feedback regarding the actual on‐ground resource utilization. Toward that goal, radio environment maps (REM) are becoming increasingly important as they provide critical information relevant for network management. REM essentially entails the estimation of the radio environment at unsampled locations using the values measured by a few dedicated REM sensors by interpolation. Hence, the accuracy of REM is dependent upon two major factors (1) the sensor deployment and (2) the interpolation scheme. So far, the ordinary Kriging (OK) with randomly deployed sensors is the most prevalent method of REM creation. However, the underlying assumption in OK is that the radio environment conforms to a Gaussian spatial random field (GSRF). In reality, the spatial random field generated by a D2D network displays non‐Gaussian characteristics. Hence, a variational Bayesian based Gaussian mixture model enabled Kriging (VK) method has been proposed in this work which achieves better interpolation accuracy than OK with a lower run‐time computational complexity. A comparison of various sensor deployment schemes on the basis of REM accuracy in fading channel conditions has also been conducted. Additionally, a spatial‐correlation based method has been proposed to estimate the minimum number of required REM sensors to ensure reliable REM performance. The simulation results indicate a superiority of hexagonal deployment of sensors over other schemes and establish VK as a more accurate interpolation algorithm than OK.

Point Cloud Data Processing Optimization in Spectral and Spatial Dimensions Based on Multispectral Lidar for Urban Single-Wood Extraction

Lidar can effectively obtain three-dimensional information on ground objects. In recent years, lidar has developed rapidly from single-wavelength to multispectral hyperspectral imaging. The multispectral airborne lidar Optech Titan is the first commercial system that can collect point cloud data on 1550, 1064, and 532 nm channels. This study proposes a method of point cloud segmentation in the preprocessed intensity interpolation process to solve the problem of inaccurate intensity at the boundary during point cloud interpolation. The entire experiment consists of three steps. First, a multispectral lidar point cloud is obtained using point cloud segmentation and intensity interpolation; the spatial dimension advantage of the multispectral point cloud is used to improve the accuracy of spectral information interpolation. Second, point clouds are divided into eight categories by constructing geometric information, spectral reflectance information, and spectral characteristics. Accuracy evaluation and contribution analysis are also conducted through point cloud truth value and classification results. Lastly, the spatial dimension information is enhanced by point cloud drop sampling, the method is used to solve the error caused by airborne scanning and single-tree extraction of urban trees. Classification results showed that point cloud segmentation before intensity interpolation can effectively improve the interpolation and classification accuracies. The total classification accuracy of the data is improved by 3.7%. Compared with the extraction result (377) of single wood without subsampling treatment, the result of the urban tree extraction proved the effectiveness of the proposed method with a subsampling algorithm in improving the accuracy. Accordingly, the problem of over-segmentation is solved, and the final single-wood extraction result (329) is markedly consistent with the real situation of the region.

Local structural health monitoring system in aircraft based on fiber Bragg grating array

In this study, a structural health monitoring system for aircraft wings based on a fiber-optic grating sensing network was designed, and a three-dimensional position correction algorithm based on fiber Bragg grating (FBG) array test data was developed. Solving the deformation parameters using mathematical models of strain-position offset introduces errors, leading to inaccurate measurements and affecting the preciseness of three-dimensional-reconstructed surfaces. Two fitting algorithms (bitone and spline with linear interpolations) are proposed to improve this method in analyzing errors at the measured points of the wing structure. The relative error of each measurement point of the reconstructed wing structure using the bitone and spline interpolation methods was lower than 4.96%. Furthermore, the absolute error was within 0.014 mm, the average relative error was lower than 3.47%, and the root-mean-square error was lower than 0.01 mm. Compared to linear interpolation, the average relative error decreased by up to 5.84%. The experimental results show that the measurement accuracy of bitone and spline interpolation was significantly higher than that of linear interpolation. FBG array measurements using bitone and spline interpolations for the local structural health monitoring system of aircraft improve the fitting reconstruction effect for the wing structure and stabilize the compensation effect.

Spatial wind speed interpolation using Isoparametric shape functions for structural loading

This study developed a spatial interpolation technique using Isoparametric finite element shape functions to derive wind speed records for all unsampled Kansas counties from actual data recorded at 17 city locations within and around Kansas. A computational method using the Kaimal spectrum is presented for generating artificial time histories of wind speeds. This is done to extract wind-cycle distribution using the Rainflow counting technique, which can be used as input for fatigue analysis procedures of highway sign structures. Comprehensive validation, verification and benchmarking has been performed in this paper at all spatial and time span levels to guarantee the accuracy and efficiency of the algorithm developed. The comparison of the validation measures strongly suggests a very accurate interpolation scheme that can be confidently used in further fatigue computations and analysis. A user-friendly software was designed using C# to extract wind-speed cycles for all Kansas counties related to different time spans. This software is expected to facilitate fatigue-life prediction because it generates a full range of wind-loading.

Whitney edge elements and the Runge phenomenon

It is well known that Lagrange interpolation based on equispaced nodes can yield poor results. Oscillations may appear when using high degree polynomials. For functions of one variable, the most celebrated example has been provided by Carl Runge in 1901, who showed that higher degrees do not always improve interpolation accuracy. His example was then extended to multivariate calculus and in this work we show that it is meaningful, in an appropriate sense, also for Whitney edge elements, namely for differential 1-forms.