Strain estimation using ordinary Kriging interpolation

— Performance of pilot-aided channel estimation techniques such as the Least Squares (LS) method depends on not only on the signal-to-noise ratio (SNR), channel conditions and pilot ratio, but also on the choice of interpolation method for deriving channel estimates at non-pilot subcarriers. This paper investigates the bit-error-rate (BER) performance of linear, spline and Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) interpolation methods in LS channel estimation over the three extended ITU channel profiles defined for Long Term Evolution (LTE) testing. Simulation results show that applying the linear interpolation method produces the best BER performance over the fading channel with the smallest multipath delay spread. It is also shown that the choice of best interpolation method actually depends on the SNR in some of the fading channel profiles. Index Terms—ITU, LS, LTE, PCHIP, spline. I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) technology has been adopted in many of the next generation communication systems such as Long Term Evolution (LTE) and Worldwide Interoperability for Microwave Access (WiMAX) [1]. OFDM is preferred not only because it offers high data rate transmission but also because of its flexibility and robustness against multipath fading [1]. Multipath channel fading exists when multiple delayed copies of a transmitted signal are received at the receiver, thereby resulting in the distortion of the transmitted signal. These distortions are collectively termed „channel fading‟, causing reception errors and hence increased bit-error-rate (BER). Channel fading can be broadly classified as time-selective and/or frequency selective, depending on the relationship between the fading channel and the transmitted signal parameters [2]. To combat multipath fading and improve BER, some form of channel estimation method is required in order to estimate the channel distortion effect for each of the active subcarriers within an OFDM symbol [3].

Considering the influence of key parameters such as bore angle, azimuth and sounding of wellbore, based on the spatial five-time PH curve with continuous unit tangent and directional curvature, no need for iteration, using Bessel polynomial interpolation method, optimization the spatial model and the curve description can accurately deduct the spatial parameters of the fifth point according to the determined four points of the space, and then establish the wellbore trajectory analytical equation to generate the well trajectory curve. Taking a directional well as an example, the wellbore trajectories of the wells from 403.9 meters to 976 meters were fitted by PH, cubic spline and linear interpolation method respectively, and compared with the real measuring points. The results show that the wells fitted by PH method, the differences of the bevel angle and the measured point, the azimuth angle and the measured point are 0.910° and 5.7°. The differences of the cubic spline and the measured point, the straight line method and the measured point are 4.240°, 5.86° and 6.54°, 9.09°. For the PH method, the trajectory inclination and azimuth differences are the smallest, which are 3.51% and 3.17%.

The satellite clock bias (SCB) with high sampling rate is needed in precise point positioning, and the sampling interval of SCB provided by the analysis center is relatively large, so SCB with large interval must be interpolated and encrypted by interpolation methods. Three interpolation methods are used to interpolate SCB from 5-minute sampling intervals to 30-second sampling intervals, and the interpolated results are compared and analyzed with the published SCB for 30-second sampling intervals. The results show that the accuracy of linear interpolation method is the highest, followed by cubic spline interpolation method and then Lagrange interpolation method. In addition, the interpolation accuracy of the three interpolation methods is the highest for GPS IIF and IIIA satellites launched in recent years, followed by IIR-M satellites launched in the middle of the period, and then IIR satellites launched in the early period.

Spatial interpolation method is the basis of soil heavy metal pollution assessment and remediation. The existing evaluation index for interpolation accuracy did not combine with actual situation. The selection of interpolation methods needs to be based on specific research purposes and research object characteristics. In this paper, As pollution in soils of Beijing was taken as an example. The prediction accuracy of ordinary kriging (OK) and inverse distance weighted (IDW) were evaluated based on the cross validation results and spatial distribution characteristics of influencing factors. The results showed that, under the condition of specific spatial correlation, the cross validation results of OK and IDW for every soil point and the prediction accuracy of spatial distribution trend are similar. But the prediction accuracy of OK for the maximum and minimum is less than IDW, while the number of high pollution areas identified by OK are less than IDW. It is difficult to identify the high pollution areas fully by OK, which shows that the smoothing effect of OK is obvious. In addition, with increasing of the spatial correlation of As concentration, the cross validation error of OK and IDW decreases, and the high pollution area identified by OK is approaching the result of IDW, which can identify the high pollution areas more comprehensively. However, because the semivariogram constructed by OK interpolation method is more subjective and requires larger number of soil samples, IDW is more suitable for spatial prediction of heavy metal pollution in soils.

Arterial spin labeling (ASL) magnetic resonance imaging (MRI) is a powerful imaging technology that can measure cerebral blood flow (CBF) quantitatively. However, since only a small portion of blood is labeled compared to the whole tissue volume, conventional ASL suffers from low signal-to-noise ratio (SNR), poor spatial resolution, and long acquisition time. In this paper, we proposed a super-resolution method based on a multi-scale generative adversarial network (GAN) through unsupervised training. The network only needs the low-resolution (LR) ASL image itself for training and the T1-weighted image as the anatomical prior. No training pairs or pre-training are needed. A low-pass filter guided item was added as an additional loss to suppress the noise interference from the LR ASL image. After the network was trained, the super-resolution (SR) image was generated by supplying the upsampled LR ASL image and corresponding T1-weighted image to the generator of the last layer. Performance of the proposed method was evaluated by comparing the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) using normal-resolution (NR) ASL image (5.5 min acquisition) and high-resolution (HR) ASL image (44 min acquisition) as the ground truth. Compared to the nearest, linear, and spline interpolation methods, the proposed method recovers more detailed structure information, reduces the image noise visually, and achieves the highest PSNR and SSIM when using HR ASL image as the ground-truth.

Application and numerical error analysis of multiscale method for air flow, heat and pollutant transfer through different scale urban areas

Noise logging is a method to determine the natural noise in a well. In the actual production logging process, it is a common situation that the noise data is not continuous with depth, which can be solved by the cubic spline interpolation method. This method is a piecewise interpolation method, which fits with a three-time polynomial in each segment interval, and adds up the polynomials on all intervals to get the interpolation formula. The interpolated data points are a smooth transition with good stability. In this article, the original noise data is interpolated to continuous noise data by cubic spline interpolation method, and then evaluated by noise imaging logging, which presents good results. The cubic-spline interpolation method ensures the internal connection of noise data, and also realizes the fine description and recognition of the characteristics of the output layer. This method will provide a low-cost and effective logging evaluation method for production logging, which has a wide range of applications.

In this paper, we aim to achieve two specific objectives. The first one is to examine the applicability of wavelet neural network (WNN) technique in ore grade estimation, which is based on integration between wavelet theory and Artificial Neural Network (ANN). Different wavelets are applied as activation functions to estimate Cu grade of borehole data in the hypogene zone of porphyry ore deposit, Shahr-e-Babak district, SE Iran. WNN parameters such as dilation and translation are fixed and only the weights of the network are optimized during its learning process. The efficacy of this type of network in function learning and estimation is compared with Ordinary Kriging (OK). Secondly, we aim to delineate the potassic and phyllic alteration regions in the hypogene zone of Cu porphyry deposit based on the estimation obtained of WNN and OK methods, and utilize Concentration–Volume (C–V) fractal model. In this regard, at first C–V log–log plots are generated based on the results of OK and WNN. The plots then are used to determine the Cu threshold values of the alteration zones. To investigate the correlation between geological model and C-V fractal results, the log ratio matrix is applied. The results showed that, Cu values less than 1.1% from WNN have more overlapped voxels with phyllic alteration zone by overall accuracy (OA) of 0.74. Spatial correlation between the potassic alteration zones resulted from 3D geological modeling and high concentration zones in C-V fractal model showed that the alteration zone has Cu values between 1.1% and 2.2% with OA of 0.72 and finally have an appropriate overlap with Cu values greater than 2.2% with OA of 0.7. Generally, the results showed that the WNN (Morlet activation function) with OA greater than OK can be can be a suitable and robust tool for quantitative modeling of alteration zones, instead of qualitative methods.

In this paper, the stability and smoothness of trajectory planning and attitude control of the manipulator are studied. The DH motion model of Kinova Jaco Gen-2 manipulator was established to solve the forward and inverse kinematics equations. Firstly, the third-order Bezier curve is designed to plan the trajectory of manipulator, which has good continuity and smoothness, and can control the workspace. Secondly, an attitude interpolation method based on quaternion is proposed. And different attitude interpolation methods are compared and analyzed, and spherical linear interpolation method is used to solve the problem of uneven velocity of the linear interpolation method. Finally, MATLAB robot toolbox is used to simulate and verify that the angle of each joint changes smoothly, and the trajectory of manipulator has good smoothness and stability based on Bezier curve and quaternion interpolation. According to the experimental results, the path planning based on the third order Bezier curve and spherical linear interpolation has a continuous smooth joint trajectory curve and a continuous joint angular velocity curve. The manipulator can move smoothly to the target point under the constraint of the end posture. Therefore, the trajectory planning method can be used as an ideal planning method for manipulator.

The damage analysis based on the modal parameters usually need to compare the test data with the computed data by theoretical analysis. In bridge structure damage analysis, it is impossible that the sensors are set at every node. So the test data need to be extended to every node by using interpolation technology. In the paper, three interpolation methods, cubic interpolation method, cubic spline interpolation method and sinc interpolation method, are introduced. Their applications in bridge structure damage analysis are discussed. The experiment results show that the best interpolation method is cubic spline interpolation method. Using the data processed by interpolation technology can well obtain the damage location of bridge.

관측정밀도 보다 높은 강수량 공간상세화를 위해서는 공간 내삽법에 대한 체계적인 조사와 기본적인 특성 평가가 선행되어야, 향후 방법적인 면에서 논란의 여지를 줄이고 상세화된 자료에 대한 불확실성도 가늠할 수 있다. 따라서 본 연구에서는 공간내삽방법에 대한 평가를 수행하고자 한다. 본 연구에서는 특정 지역 혹은 특정 사상 선정으로 인한 결과의 임의성을 최대한 줄이기 위해 우리나라 전역의 10년(2001-2010년)치 기상청 AWS지점 일자료를 사용하였다. 그리고 역거리가중법(Inverse distance weighted method; IDW), 크리깅법(Ordinary kriging; KRG), 다중이차내삽법(Multi-quadric interpolation method; MQI)을 적용하여 <TEX>$5km{\times}5km$</TEX> 격자강수량을 재산정 하였다. 각 내삽 방법에 대한 정량적 평가를 위하여 기준 방법으로 본 연구에서는 티센면적가중법(Thiessen polygon method; TSN)을 사용하였다. 2001년부터 2010년까지 10년 동안의 일강수량 공간 상세화 결과를 중권역 단위로 비교하였을 때, 기상청 AWS 관측망을 사용하는 경우 전체 평균에 있어 방법 간 차이는 크지 않았다. 그러나 관측소가 희박한 지역과 개별호우사상의 경우는 지역특성별로 방법 간 유의한 차이가 나타났다. In order to estimate a reliable spatial precipitation which has high resolution sub-measuring scale, a systematical research for spatial interpolation methods and evaluation of characteristics of them are required. This will be able to reduce disputes on selection of methodologies and estimate uncertainties of downscaled data. Therefore, we assessed the spatial interpolation methods using automatic weather system (AWS)'s daily data of Korea Meteorological Administration (KMA) during past 10 years (2001-2010), so as to reduce arbitrary interpretations of the result by selecting particular regions or storm events. In addition, we adopted inverse distance weighted method (IDW), ordinary kriging method (KRG) and multi-quadric interpolation method (MQI) to produce <TEX>$5km{\times}5km$</TEX> grid precipitation. For quantitative evaluations of each interpolation method, thiessen polygon method (TSN) was used as a comparison method. When comparing the gridded daily precipitation for the past 10 years (2001-2010) by middle scale basins, differences of whole average for each methods were not significant when using KMA's AWS network. However, in case of regions where stations were sparse and each storm event, significant differences were founded caused by interpolation methods or characteristics of regions.

Global climate change could have important effects on various environmental variables in many countries around the world. Changes in precipitation regime directly affect water resources management. So that, it is important to analyze the changes in the spatial and temporal rainfall pattern in order to improve water resources management policies. For this reason, non-parametric Mann-Kendall rank correlation test is used in order to examine the existence of trends in annual and monthly rainfall distribution. To understand the regional differences of precipitation in Turkey, the detected trends are spatially interpolated using geostatistical techniques in a GIS environment. The main objective of this paper is to evaluate three interpolation methods, concerning their suitability for spatial prediction of temporal trends of Turkey’s monthly and annual rainfall data. The study used a dense and homogeneous monthly precipitation database comprising 120 rain-gauge stations over a 32 years testing period of 1975–2009. The results conclusively show that significant positive trends are both infrequent and found only in outlying stations during March, April and October. In order to estimate and characterize the magnitude of observed changes at unmeasured locations, Ordinary Kriging, Inverse Distance Weighted and Completely Regularized Spline interpolation methods were employed and compared. A comparative analysis of interpolation techniques shows that Ordinary Kriging with having RMSE of 0.148 is the best choice. This is followed by Inverse Distance Weighted (RMSE 0.151), and Splines (RMSE 0.152). Cross validation of the results shows the largest over prediction at Kars rainfall station and largest under prediction at Burdur station. Upon for the examination of the cross-validation and spatial error clustering results, the Ordinary Kriging method was concluded to be the best algorithm in the interpolation process.

Visualization of the spatial transport of nutrients and organic matter contents in sediments under hydrodynamic perturbation conditions.

A total of 21 gauges across the mountainous leeward portion of the island of Oʻahu, Hawaiʻi, were used to compare rainfall interpolation methods and assess rainfall spatial variability over a 34-month monitoring period from 2005 to 2008. Traditional and geostatistical interpolation methods, including Thiessen polygon, inverse distance weighting (IDW), linear regression, ordinary kriging (OK), and simple kriging with varying local means (SKlm), were used to estimate wet and dry season rainfall. The linear regression and SKlm methods were used to incorporate two types of exhaustive secondary information: (1) elevation extracted from a digital elevation model (DEM), and (2) distance to a regional rainfall maximum. The Thiessen method produced the highest error, whereas OK produced the lowest error in all but one period. The OK method produced more accurate predictions than linear regression of rainfall against elevation when the correlation between rainfall and elevation is moderate (R<0.82). The SKlm method produced lower error than linear regression and IDW methods in all periods. Comparison of the OK interpolation map with gridded isohyet data indicate that the areas of greatest rainfall deficit were confined to the mountainous region of west Oʻahu.

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