Kriging Interpolation Algorithm Research Articles

Retracted] Interpolation Method for Visual Simulation of Engine Exhaust Flame

Propulsive force and exhaust fluid temperature are important indicators in the performance of an engine. An investigation of the effects of propellant composition, plane flight conditions, and engine operating environment on rocket thrust and the range of smoke plume temperature can provide references in the design of engine mechanics at the optimization of propellant composition, in monitoring of target identification and in the evolving of stealth of stealth technology. In order to understand the characteristics of the engine tail flame, a visual simulation of the engine tail flame was carried out by combining the engine operating conditions with the tail flame conditions. Based on the advantages of the bicubic spline interpolation algorithm and the Kriging interpolation algorithm, this paper proposes a hybrid interpolation algorithm, which performs color mapping and three‐dimensional space separation in the engine plume data set and model, and visualizes the engine and engine plume. The simulation realizes real‐time monitoring of the functions of various engine components through characteristic colors. The research results show that the hybrid interpolation method can effectively visualize the engine exhaust flame. The simulated plume has a relatively obvious temperature peak at 0.7 m, and the temperature of the plume flow field is significantly higher than that of the frozen plume flow field by about 200 ~1000 K. This shows that the algorithm in this paper helps to visualize the expression of engine tail flame information.

Improvement of Kriging interpolation with learning kernel in environmental variables study

ABSTRACT Kriging interpolation is a spatial interpolation method widely employed in the field of data analytics and prediction of environmental variables, which provides the best linear unbiased prediction of intermediate values. The core principle of Kriging interpolation is searching for data distribution regularity and predicting regionalised variable value, and it can be transferred into two descriptions of learning process: function fitting problem and coefficient optimisation problem. Although these two problems could be solved by many traditional algorithms like multiple linear regression method, the parameter estimation of variogram model becomes quite difficult when there are drifts or noises in the raw data. The purpose of this paper is to improve the Kriging interpolation algorithm with learning kernels based on Estimation of Distribution Algorithms (EDAs) and Least-Squares Support Vector Machine (LSSVM). The experiments have been carried out based on a real-world case with environmental variables. Compared with other machine learning methods, experimental results verify the effectiveness of the proposed algorithm.

Mapping Atmospheric Corrosivity in Shandong

Air pollution can significantly accelerate the process of material corrosion, which may cause significant economic losses and serious safety incidents. Atmospheric corrosion maps provide atmospheric corrosivity in a given geographic scope, which can guide the designers to select the most suitable anti-corrosion materials for outdoor projects, also provide useful information for maintenance. This article investigated mapping of atmospheric corrosivity in Shandong Province, China. In order to obtain atmospheric corrosivity data, 100 exposure corrosion test sites were established in Shandong according to International Standard Organization (ISO) 8565. Hot-dip galvanized steel samples were exposed for 1 year in the test sites. Taking the results of exposure corrosion test as the data, inverse distance weighting (IDW) and ordinary kriging (OK) interpolation algorithm were used to estimate the atmospheric corrosivity of Shandong Province according to ISO 9223. The validity of OK and IDW was compared in developing atmospheric corrosion maps of Shandong Province on a 1 × 1 km resolution. The cross-validation results showed that OK interpolation algorithm with Gaussian semivariogram model get the best result in the prediction of corrosion rate. When the corrosion category was used as the criterion, the IDW interpolation algorithm of power 4 performed best, predicted results of 74 sites (n = 100) were consistent with observed. However, high mean relative errors (MRE more than 37%) and relatively low correlation (R2 about 24%) indicated that the prediction results of the two interpolation algorithms had a large error, which was caused by the low data density and the complicated corrosive factors of the atmosphere.

Reconstruction and Nowcasting of Rainfall Field by Oblique Earth-Space Links Network: Preliminary Results from Numerical Simulation

High-precision rainfall field reconstruction and nowcasting play an important role in many aspects of social life. In recent years, the rain-induced signal attenuation of oblique earth-space links (OELs) has been presented to monitor regional rainfall. In this paper, we set up the first OEL in Nanjing, China, for the estimation of rain intensity. A year of observations from this link are also compared with the measurements from laser disdrometer OTT-Parsivel (OTT), between which the correlation is 0.86 and the determination coefficient is 0.73. Then, the simulation experiment is carried out: an OELs network is built, and the Kriging interpolation algorithm is employed to perform rainfall field reconstruction. The rainfall fields of plum rain season from 2016 to 2019 have been reconstructed by this network, which shows a good agreement with satellite remote sensing data. The resulting root-mean-square errors are lower than 3.46 mm/h and spatial correlations are higher than 0.80. Finally, we have achieved the nowcasting of rainfall field based on a machine-learning approach, especially deep learning. It can be seen from experiment results that the motion of rain cell and the position of peak rain intensity are predicted successfully, which is of great significant for taking concerted actions in case of emergency. Our experiment demonstrates that the densely distributed OELs are expected to become a futuristic rainfall monitoring system complementing existing weather radar and rain gauge observation networks.

Improved RSS Data Generation Method Based on Kriging Interpolation Algorithm

The traditional method of constructing RSS fingerprint database costs a large amount of time and human resource due to adopting the point-by-point method to sample RSS value, and consequently the positioning method based on RSS fingerprint model is difficult to be widely applied. In this paper, a RSS data generation method is proposed based on Kriging spatial interpolation algorithm. The proposed method firstly selects the model of variogram according to the properties of field, and subsequently solves the variogram by using the observation points with the restriction of unbiased estimation and minimum estimation variance, finally calculates RSS data for the estimation points. The experimental results show that the proposed method accurately acquires the RSS data of estimation points while the required reference points are much less than that of conventional point-by-point method.

An Improved Spatio-Temporal Kriging Interpolation Algorithm and Its Application in Slope

Slope stability analysis based on the deformation monitoring data has been commonly used to predict and warn slope disasters. However, due to breakdown of the monitoring equipment or restrictions and interferences of internal and external factors in the area, the loss of data is unavoidable during the process of the slope monitoring. This problem can be solved by the spatio-temporal Kriging interpolation algorithm. However, the subjective factors and theoretical semi-variogram of variogram models, and many parameters estimation may lead to low interpolation precision and poor calculation efficiency. In this paper, a hybrid spatio-temporal interpolation algorithm was presented by combining the improved adaptive genetic algorithm (IAGA) with the spatio-temporal Kriging interpolation method, and it was applied to monitor the deformation of HP1 slope in Yuebao open-pit mine. The results showed that the interpolation precision of the proposed method was about 1 times higher than that of the traditional spatio-temporal Kriging method and the spatio-temporal method of Gaussian process regression method. In addition, after the interpolation analysis of the missing part of the monitoring data, the maximum cumulative displacement of all monitoring points was around 35.8 mm, and the rate of the displacement deformation didn't exceed 2 mm/d for three consecutive days. The deformation trend was basically consistent with the actual slope. It shows that the improved spatio-temporal Kriging interpolation algorithm (ISTKIA) has certain feasibility and reliability, and could provide a new idea for the research of related problems in related fields.

Radio Environment Map Construction by Kriging Algorithm Based on Mobile Crowd Sensing

In the IoT era, 5G will enable various IoT services such as broadband access everywhere, high user and devices mobility, and connectivity of massive number of devices. Radio environment map (REM) can be applied to improve the utilization of radio resources for the access control of IoT devices by allocating them reasonable wireless spectrum resources. However, the primary problem of constructing REM is how to collect the large scale of data. Mobile crowd sensing (MCS), leveraging the smart devices carried by ordinary people to collect information, is an effective solution for collecting the radio environment information for building the REM. In this paper, we build a REM collecting prototype system based on MCS to collect the data required by the radio environment information. However, limited by the budget of the platform, it is hard to recruit enough participants to join the sensing task to collect the radio environment information. This will make the radio environment information of the sensing area incomplete, which cannot describe the radio information accuracy. Considering that the Kriging algorithm has been widely used in geostatistics principle for spatial interpolation for Kriging giving the best unbiased estimate with minimized variance, we utilize the Kriging interpolation algorithm to infer complete radio environment information from collected sample radio environment information data. The interpolation performance is analyzed based on the collected sample radio environment information data. We demonstrate experiments to analyze the Kriging interpolation algorithm interpolation results and error and compared them with the nearest neighbor (NN) and the inverse distance weighting (IDW) interpolation algorithms. Experiment results show that the Kriging algorithm can be applied to infer radio environment information data based on the collected sample data and the Kriging interpolation has the least interpolation error.

Comparing potential spatial access with self-reported travel times and cost analysis to haemodialysis facilities in North-eastern Iran

End-stage renal disease patients regularly need haemodialysis three times a week. Their poor access to haemodialysis facilities is significantly associated with a high mortality rate. The present cross-sectional study aimed to measure the potential spatial access to dialysis services at a small area level (census tract level) in North Khorasan Province, Iran. The patients were interviewed to obtain their travel information. The two-step floating catchment area (2SFCA) method was used to measure the spatial accessibility of patients to the dialysis centres. The capacity of the dialysis centre was defined as the number of active dialysis facilities in each centre and the haemodialysis patients in each area were considered as the users of dialysis services. The travel cost from each patient's residence to the haemodialysis facilities was visualized by the Kriging interpolation algorithm in the study area. Spatial accessibility to the dialysis centre was poor in the northern part of the study area. Fortunately, there were not many haemodialysis patients in that area. Patients' travel costs were high in the northern areas compared to the rest of study area. We observed a statistically significant reverse correlation between the self-reported travel time and computed spatial accessibility (-0.570, P value <0.01, two-tailed spearman test). This study supports the notion that the 2SFCA method could be associated with revealed access time to dialysis facilities, especially in low traffic and in flat areas such as northern Khorasan. The mapping of patients' distribution and interpolated travel cost to the haemodialysis facilities could help policymakers to allocate health resources to the areas where the need is greater.

High-density salt-and-pepper noise removal using adaptive weighted kriging interpolation filter

An adaptive weighted kriging interpolation filter for removal of high-density salt-and-pepper noise (SPN) in images is proposed. The proposed scheme introduces a method for computing the estimation value of a noisy pixel in the center of the processing window. Different from the existing adaptive decision based on kriging interpolation algorithm, the proposed kriging interpolation for different adaptive windows cares about the action of not only the Euclidean distance between nonnoisy pixels but also the size of the current processing window. Therefore, the corrupted pixel is replaced by the inverse filtering-radius weighted sum of kriging interpolations for different adaptive windows. The final processing window is required to include at least three noncorrupted pixels. The proposed algorithm is extensively evaluated on a variety of benchmark images and the experimental results show that it outperforms several standard and popular algorithms in terms of visual quality and quantitative results.

An adaptive decision based kriging interpolation algorithm for the removal of high density salt and pepper noise in images

An adaptive decision based kriging interpolation technique for the removal of high density salt and pepper noise in images is proposed. The algorithm isolates the non noisy pixels and process only noisy pixel. The corrupted pixel is replaced by a value that is interpolated using the weights calculated using semi-variance between the corrupted pixels and the non noisy pixels in a confined neighborhood. The proposed technique requires at least three non noisy pixels in a current processing window, failing which the window increases adaptively. The proposed technique was found to exhibit good of quantitative evaluation and visual quality. The proposed algorithm also preserves image information with accurate noise detection when compared to many standard and existing algorithms.

Dental implant customization using numerical optimization design and 3-dimensional printing fabrication of zirconia ceramic.

This study proposes a new methodology for dental implant customization consisting of numerical geometric optimization and 3-dimensional printing fabrication of zirconia ceramic. In the numerical modeling, exogenous factors for implant shape include the thread pitch, thread depth, maximal diameter of implant neck, and body size. Endogenous factors are bone density, cortical bone thickness, and non-osseointegration. An integration procedure, including uniform design method, Kriging interpolation and genetic algorithm, is applied to optimize the geometry of dental implants. The threshold of minimal micromotion for optimization evaluation was 100μm. The optimized model is imported to the 3-dimensional slurry printer to fabricate the zirconia green body (powder is bonded by polymer weakly) of the implant. The sintered implant is obtained using a 2-stage sintering process. Twelve models are constructed according to uniform design method and simulated the micromotion behavior using finite element modeling. The result of uniform design models yields a set of exogenous factors that can provide the minimal micromotion (30.61μm), as a suitable model. Kriging interpolation and genetic algorithm modified the exogenous factor of the suitable model, resulting in 27.11μm as an optimization model. Experimental results show that the 3-dimensional slurry printer successfully fabricated the green body of the optimization model, but the accuracy of sintered part still needs to be improved. In addition, the scanning electron microscopy morphology is a stabilized t-phase microstructure, and the average compressive strength of the sintered part is 632.1MPa.

Spatial statistical analysis for the design of indoor particle-filter-based localization mechanisms

The accurate localization of end-users and resources is seen as one of the main pillars toward the successful implementation of context-based applications. While current outdoor localization mechanisms fulfill most application requirements, the design of accurate indoor localization mechanisms is still an open issue. Most research efforts are focusing on the design of mechanisms making use of the receiver signal strength indications generated by WLAN (wireless local area network) devices. However, the accuracy and robustness of such mechanisms can be severely compromised due to the random and unpredictable nature of radio channels. In this article, we develop a methodology incorporating various algorithms capable of coping with the unpredictable nature of radio channels. Following a holistic approach, we start by identifying the wireless equipment parameter setting, better meeting the implementation requirements of a robust indoor localization mechanism. We then make use of RANdom SAmple Consensus paradigm: a robust model-fitting mechanism capable of smoothing the data captured during the space survey. Using an experimental setup, we evaluate the benefits of integrating the floor plan and an ordinary Kriging interpolation algorithm in the estimation process. Our main findings show that our proposal can greatly improve the quality of the information to be used in the development of particle-filter-based indoor localization mechanisms.

Stream Kriging: Incremental and recursive ordinary Kriging over spatiotemporal data streams

Ordinary Kriging is widely used for geospatial interpolation and estimation. Due to the O(n3) time complexity of solving the system of linear equations, ordinary Kriging for a large set of source points is computationally intensive. Conducting real-time Kriging interpolation over continuously varying spatiotemporal data streams can therefore be especially challenging. This paper develops and tests two new strategies for improving the performance of an ordinary Kriging interpolator adapted to a stream-processing environment. These strategies rely on the expectation that, over time, source data points will frequently refer to the same spatial locations (for example, where static sensor nodes are generating repeated observations of a dynamic field). First, an incremental strategy improves efficiency in cases where a relatively small proportion of previously processed spatial locations are absent from the source points at any given iteration. Second, a recursive strategy improves efficiency in cases where there is substantial set overlap between the sets of spatial locations of source points at the current and previous iterations. These two strategies are evaluated in terms of their computational efficiency in comparison to ordinary Kriging algorithm. The results show that these two strategies can reduce the time taken to perform the interpolation by up to 90%, and approach average-case time complexity of O(n2) when most but not all source points refer to the same locations over time. By combining the approaches developed in this paper with existing heuristic ordinary Kriging algorithms, the conclusions indicate how further efficiency gains could potentially be accrued. The work ultimately contributes to the development of online ordinary Kriging interpolation algorithms, capable of real-time spatial interpolation with large streaming data sets.

Research on Algorithm of Delaunay Triangulation Net Interpolating the Best Point

Aiming at the folds caused by the sparse data in the process of DTM (Digital Terrain Model), this article proposed a method of interpolating spatial control points based on Delaunay triangulation and Kriging interpolation algorithm. The terrain data of an area with complex terrain in Xianyang was used to construct terrain model according to the proposed algorithm. Experimental results show that the method can finish the interpolation of the terrain denser data quickly and accurately, and it provides an efficient technological tool for building a true three-dimensional terrain model.

The Method of dealing with Geomagnetic Anomaly caused by Movable Magnetic Objects in Drawing the Geomagnetic Chart

The local geomagnetic chart is an effective tool to describe the geomagnetic information in the region accurately and visually which is a reference in application for future. Precision of local geomagnetic chart directly affects its value. When the movable magnetic objects are in the region, the distribution of geomagnetic field will be changed. When the movable magnetic objects are out the region, the distribution of geomagnetic field will recover to normal situation. Thus, magnetic objects can bring the error to some measured data. As an result, precision of the geomagnetic chart will reduce. On the basis of analysis of the existing geomagnetic model, the method to eliminate the movable geomagnetic anomaly in drawing the chart is proposed which is based on Taylor polynomial model. In this method, affected regions by magnetic object are gotten, the geomagnetic model are built in these affected region by precise data, the measured data in these region is replayed with model data, finally, the geomagnetic chart is draw by combined data using Kriging interpolation algorithm. The experiment results show that the method can improve the precision of the local magnetic chart when the movable magnetic objects exist in the measurement region.

The Improved Kriging Interpolation Algorithm for Local Underwater Terrain Based on Fractal Compensation

The interpolation-reconstruction of local underwater terrain using the underwater digital terrain map (UDTM) is an important step for building an underwater terrain matching unit and directly affects the accuracy of underwater terrain matching navigation. The Kriging method is often used in terrain interpolation, but, with this method, the local terrain features are often lost. Therefore, the accuracy cannot meet the requirements of practical application. Analysis of the geographical features is performed on the basis of the randomness and self-similarity of underwater terrain. We extract the fractal features of local underwater terrain with the fractal Brownian motion model, compensating for the possible errors of the Kriging method with fractal theory. We then put forward an improved Kriging interpolation method based on this fractal compensation. Interpolation-reconstruction tests show that the method can simulate the real underwater terrain features well and that it has good usability.

Volume Rendering of 3D Borehole Data Based on GPU

Taking 3D borehole data for research object, an algorithm flow of volume rendering based GPU is given. According to the limited and discrete characteristics of 3D borehole data, Kriging interpolation algorithm is used to construct a regular grid data model. Ray-casting algorithm based on GPU is realized with the Visualization Toolkit (VTK). The results show that after the application of volume rendering technology, it is easy to practice the functions of arbitrary section displaying, volume clipping and volume data extracting which are practicalities.

Sensitivity Analysis of Parameters Affecting the Number of Data Points in Kriging Interpolation

The more data used in Kriging interpolation, the more reliable the results will be, but time consumption will increase exponentially. In order to ensure as much as data be involved in interpolation and maintaining reasonable time consuming, the number of data points must be properly selected. The number of conditional data points is determined by average weight coefficient based on the deep analysis of Kriging interpolation algorithm of Geostatistics. When the average weight coefficient is small enough, finding the balance point, then accuracy and time consumption can achieve a best result. Change dimensions, grid size and the range of Variogram to analyze the sensitivity the data points selected imposed on them. The most ideal number of data points is 40-60, and the main affecting factor is calculation dimension.

Optimization based simulation of self-expanding Nitinol stent

Self-expanding Nitinol (nickel–titanium alloy) stents are tubular, often mesh like structure, which are expanded inside a diseased (stenosed) artery segment to restore blood flow and keep the vessel open following angioplasty. The super-elastic and shape memory properties of Nitinol reduce the risk of damage to the stent both during delivery into the body and due to accidents while in operation. However, as Nitinol stents are subjected to a long-term cyclic pulsating load due to the heart beating (typically 4×107cycles/year) fatigue fracture may occur. One of the major design requirements in medical implants is the device lifetime or, in engineering terms, fatigue life. In order to improve the mechanical properties of Nitinol stents, at first, a reliable procedure of finite element analysis (FEA) is established to provide quantitative measures of the stent’s strain amplitude and mean strain which are generated by the cyclic pulsating load. This allows prediction of the device’s life and optimization of stent designs. Secondly, the objective is to optimize the stent design by reducing the strain amplitude and mean strain over the stent, which are generated by the cyclic pulsating load. An optimization based simulation methodology was developed in order to improve the fatigue endurance of the stent. The design optimization approach is based on the Response Surface Method (RSM), which is used in conjunction with Kriging interpolation and Sequential Quadratic Programming (SQP) algorithm.

Research on Constructing 3D Geological Model of the Construction Layers in Daxing New City Area of Beijing

The new city in Daxing district is the focus of future development in the southern of Beijing city, establishing 3D geological model of its engineering construction layer can provide a scientific basis for urban planning and construction as well as the land’s proper utilization. After collecting the geological drilling data, we establish the geological model based on a 3D geological modeling platform developed by Peking University. The 3D spatial modeling method based on sections is used to analyze two key technical problems about simulation process named high-precision modeling and rapid modeling respectively. In the modeling process, Delaunay triangulation and Kriging interpolation algorithms are used. Furthermore, the manual intervention is achieved through the use of flexible and convenient 3D interactive modeling tools. The application examples indicate that the 3D geological model constructed by this method can better reflect the actual situation, it also possesses the advantages of high precision and fast modeling.