Traditional Interpolation Research Articles

Structure the Radiation Dose Curve of Continuous Slope

The traditional interpolation and fitting can not restore the radiation dose curve with the radiation source characteristic. Therefore, during the reduction the field of one dimensional radiation dose, the mathematical structure method was used to restore the curve with the dose value of the radioactive source is inversely proportional to the square of the distance from the radioactive source.

Concurrent topological design of composite structures and materials containing multiple phases of distinct Poisson’s ratios

ABSTRACTMost studies on composites assume that the constituent phases have different values of stiffness. Little attention has been paid to the effect of constituent phases having distinct Poisson’s ratios. This research focuses on a concurrent optimization method for simultaneously designing composite structures and materials with distinct Poisson’s ratios. The proposed method aims to minimize the mean compliance of the macrostructure with a given mass of base materials. In contrast to the traditional interpolation of the stiffness matrix through numerical results, an interpolation scheme of the Young’s modulus and Poisson’s ratio using different parameters is adopted. The numerical results demonstrate that the Poisson effect plays a key role in reducing the mean compliance of the final design. An important contribution of the present study is that the proposed concurrent optimization method can automatically distribute base materials with distinct Poisson’s ratios between the macrostructural and microstructural levels under a single constraint of the total mass.

A new method for reconstruction of cross-sections using Tucker decomposition

The full representation of a d-variate function requires exponentially storage size as a function of dimension d and high computational cost. In order to reduce these complexities, function approximation methods (called reconstruction in our context) are proposed, such as: interpolation, approximation, etc. The traditional interpolation model like the multilinear one, has this dimensionality problem. To deal with this problem, we propose a new model based on the Tucker format – a low-rank tensor approximation method, called here the Tucker decomposition. The Tucker decomposition is built as a tensor product of one-dimensional spaces where their one-variate basis functions are constructed by an extension of the Karhunen–Loève decomposition into high-dimensional space. Using this technique, we can acquire, direction by direction, the most important information of the function and convert it into a small number of basis functions. Hence, the approximation for a given function needs less data than that of the multilinear model. Results of a test case on the neutron cross-section reconstruction demonstrate that the Tucker decomposition achieves a better accuracy while using less data than the multilinear interpolation.

Structure the Nuclear Radiation Dose Function of One Dimensional

The traditional interpolation and fitting cannot restore the radiation dose curve with the radiation source characteristic. Therefore, during the reduction the field of one dimensional radiation dose, the mathematical structure method was used to restore the curve with the dose value of the radioactive source is inversely proportional to the square of the distance from the radioactive source.

A physically consistent FVM interpolation scheme based on the discretized convection–diffusion equation

ABSTRACTA physically consistent difference scheme is proposed to discretize the convection–diffusion equation in this paper. The interface variables of control volume are calculated by the interpolation of the discretized convection–diffusion equation rather than the direct interpolation with neighbor nodes in the direction perpendicular to the interface. In the new scheme, all the nodes of parallel and normal to the interface are involved, which means that the influence of cross-stream fluxes is considered. Obviously, the proposed interpolation scheme is full of physical meaning and better than the traditional convective interpolation schemes. Two simulations of typical benchmark problems, lid-driven cavity flow in square cavity and flow over a backward-facing step, are carried out with this scheme and some traditional schemes to prove the advantages of the proposed scheme.

A novel key frames matching approach for human locomotion interpolation

A novel key frames matching approach for human locomotion interpolation is proposed in this paper. Firstly, locomotion data is transformed from body coordinate system to world coordinate system based on recursive algorithm; secondly, features of two feet and step distance are extracted; thirdly, key frames are extracted based on feature curve and the locomotion sequence is segmented; fourthly, a new approach for key frames matching is put forward; finally, transition frames are interpolated between the matched key frames using quaternion Slerp (Spherical linear interpolation) algorithm and linear interpolation algorithm. The main contributions of this paper are: i) different locomotion sequences can be synthesized in a controllable manner with good effect; ii) to extract locomotion features conveniently, locomotion data in body coordinate system is transformed to world coordinate system; iii) to analyze locomotion sequences intuitively and accurately, key frames are extracted and locomotion sequences are segmented based on feature curve analysis; iv) to avoid illogical jump of traditional interpolation between key frames, a new key frames matching strategy is put forward and only the key frames between two continuous segments can be chosen as matching frames. Experimental results based on the CMU MoCap database show that the proposed method can confirm the logical correctness and naturalness in the junction of two locomotion sequences.

Математико-картографическое моделирование пространственно-временного распределения опасных явлений погоды

The article describes a method of mapping climatic parameters (i. e. frequency and intensity) of severe weather events, based on the interpolation of weather station data. We applied regression-based interpolation, using some geographical variables (altitude, slope angle and curvature) for modeling their spatial distribution. Statistically significant correlations between geographical and climatic variables were selected based on regression analysis. They have been used to create a maps of frequency, average and maximum intensity of severe weather events for Perm region (160 600 km2). The proposed method allows to create more accurate and detailed maps of spatial distribution of severe weather events than traditional deterministic and geostatistical interpolation methods. The reliability of the results confirmed by a weather station observations and comparisons with MODIS satellite images thematic products. Significant advantage of proposed method is also its applicability to the risk assessment of severe weather events in ungauged site, or in ungauged areas.

Remapping annual precipitation in mountainous areas based on vegetation patterns: a case study in the Nu River basin

Abstract. Accurate high-resolution estimates of precipitation are vital to improving the understanding of basin-scale hydrology in mountainous areas. The traditional interpolation methods or satellite-based remote sensing products are known to have limitations in capturing the spatial variability of precipitation in mountainous areas. In this study, we develop a fusion framework to improve the annual precipitation estimation in mountainous areas by jointly utilizing the satellite-based precipitation, gauge measured precipitation, and vegetation index. The development consists of vegetation data merging, vegetation response establishment, and precipitation remapping. The framework is then applied to the mountainous areas of the Nu River basin for precipitation estimation. The results demonstrate the reliability of the framework in reproducing the high-resolution precipitation regime and capturing its high spatial variability in the Nu River basin. In addition, the framework can significantly reduce the errors in precipitation estimates as compared with the inverse distance weighted (IDW) method and the TRMM (Tropical Rainfall Measuring Mission) precipitation product.

A Post-Processing Strategy of a 3-DOF Parallel Tool Head Based on Velocity Control and Coarse Interpolation

It is a trend to develop and use the parallel tool heads with two rotational degrees of freedom and one translational degree of freedom in the aviation industry. Postprocessing is one of the most important components of a numerical control machining process, especially for the parallel tool heads with a closed-loop structure. Due to the nonlinear kinematic transmission characteristics of a parallel tool head, there would exist an obvious velocity fluctuation problem in task space; in addition, the position accuracy of the tool-axis vector cannot be ensured well by the traditional linear interpolation method; these problems should be solved through an appropriate postprocessing strategy. In this paper, by taking a typical 3-DOF parallel tool head as an object of study, a postprocessing strategy based on velocity control and coarse interpolation is investigated. First, the nonlinear kinematic transmission characteristics are analyzed, and the velocity transmission coefficient and coupling velocity transmission coefficient are proposed to evaluate the parameter-varying and coupling velocity transmission characteristics. Next, the velocity control is achieved through feed-rate optimization; meanwhile, a coarse interpolation method is used to ensure the position accuracy of the tool-axis vector. Finally, some experiments are performed, including a model validation experiment, a velocity fluctuation experiment, and a comprehensive cutting experiment. The results show that the velocity transmission model is correct, the velocity fluctuation is almost eliminated, and four typical aircraft structural parts with thin walls are qualified, which prove the effectiveness of the proposed postprocessing strategy.

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large-scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited. Traditional interpolation methods would fail at high upsampling ratios (say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large-scale models, especially for 3D cases.

Spatio-Temporal Analysis of Water Quality Parameters in Machángara River with Nonuniform Interpolation Methods

Water quality measurements in rivers are usually performed at intervals of days or months in monitoring campaigns, but little attention has been paid to the spatial and temporal dynamics of those measurements. In this work, we propose scrutinizing the scope and limitations of state-of-the-art interpolation methods aiming to estimate the spatio-temporal dynamics (in terms of trends and structures) of relevant variables for water quality analysis usually taken in rivers. We used a database with several water quality measurements from the Machángara River between 2002 and 2007 provided by the Metropolitan Water Company of Quito, Ecuador. This database included flow rate, temperature, dissolved oxygen, and chemical oxygen demand, among other variables. For visualization purposes, the absence of measurements at intermediate points in an irregular spatio-temporal sampling grid was fixed by using deterministic and stochastic interpolation methods, namely, Delaunay and k-Nearest Neighbors (kNN). For data-driven model diagnosis, a study on model residuals was performed comparing the quality of both kinds of approaches. For most variables, a value of k = 15 yielded a reasonable fitting when Mahalanobis distance was used, and water quality variables were better estimated when using the kNN method. The use of kNN provided the best estimation capabilities in the presence of atypical samples in the spatio-temporal dynamics in terms of leave-one-out absolute error, and it was better for variables with slow-changing dynamics, though its performance degraded for variables with fast-changing dynamics. The proposed spatio-temporal analysis of water quality measurements provides relevant and useful information, hence complementing and extending the classical statistical analysis in this field, and our results encourage the search for new methods overcoming the limitations of the analyzed traditional interpolators.

Succinct and fast empirical mode decomposition

Empirical mode decomposition (EMD) has been extensively studied and widely utilized in various areas. In this paper, order-statistics filters are used to replace the traditional interpolation methods and estimate envelopes of the EMD method. Window size selection criteria are proposed to optimize the processing results. Both simulated and experimental signal are applied to investigate characteristics and effectiveness of the proposed method. The results demonstrate that the envelope estimation procedure provides a tremendous enhancement of the EMD method. In the proposed method, application of the order-statistics filter can simplify the process of estimating envelopes and minimize the end effect of the traditional EMD method. Moreover, sifting stop criterion and window width selection are optimized to improve the decomposition speed and processed results. Hence, the processed method is fast, time efficient and effective, and is named as succinct and fast EMD (SF-EMD) in this paper. An application of multiple fault diagnosis for a rotor test rig verifies its potential in practical engineering.

An improved gravity compensation method for high-precision free-INS based on MEC–BP–AdaBoost

In recent years, with the rapid improvement of inertial sensors (accelerometers and gyroscopes), gravity compensation has become more important for improving navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper proposes a mind evolutionary computation (MEC) back propagation (BP) AdaBoost algorithm neural-network-based gravity compensation method that estimates the gravity disturbance on the track based on measured gravity data. A MEC–BP–AdaBoost network-based gravity compensation algorithm used in the training process to establish the prediction model takes the carrier position (longitude and latitude) provided by INS as the input data and the gravity disturbance as the output data, and then compensates the obtained gravity disturbance into the INS’s error equations to restrain the position error propagation. The MEC–BP–AdaBoost algorithm can not only effectively avoid BP neural networks being trapped in local extrema, but also perfectly solve the nonlinearity between the input and output data that cannot be solved by traditional interpolation methods, such as least-square collocation (LSC) interpolation. The accuracy and feasibility of the proposed interpolation method are verified through numerical tests. A comparison of several other compensation methods applied in field experiments, including LSC interpolation and traditional BP interpolation, highlights the superior performance of the proposed method. The field experiment results show that the maximum value of the position error can reduce by 28% with the proposed gravity compensation method.

Combination of Language Models for Word Prediction: An Exponential Approach

This paper proposes an exponential interpolation to merge a part-of-speech-based language model and a word-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -gram language model to accomplish word prediction tasks. In order to find a set of mathematical equations to properly describe the language modeling, a model based on partial differential equations is proposed. With the appropriate initial conditions, it was found an interpolation model similar to the traditional maximum entropy language model. Improvements in keystroke saved and perplexity over the word-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> -gram language model and two other traditional interpolation models is obtained, considering three different languages. The proposed interpolation model also provides additional improvement in hit rate parameter.

Roto++

Rotoscoping (cutting out different characters/objects/layers in raw video footage) is a ubiquitous task in modern post-production and represents a significant investment in person-hours. In this work, we study the particular task of professional rotoscoping for high-end, live action movies and propose a new framework that works with roto-artists to accelerate the workflow and improve their productivity. Working with the existing keyframing paradigm, our first contribution is the development of a shape model that is updated as artists add successive keyframes. This model is used to improve the output of traditional interpolation and tracking techniques, reducing the number of keyframes that need to be specified by the artist. Our second contribution is to use the same shape model to provide a new interactive tool that allows an artist to reduce the time spent editing each keyframe. The more keyframes that are edited, the better the interactive tool becomes, accelerating the process and making the artist more efficient without compromising their control. Finally, we also provide a new, professionally rotoscoped dataset that enables truly representative, real-world evaluation of rotoscoping methods. We used this dataset to perform a number of experiments, including an expert study with professional roto-artists, to show, quantitatively, the advantages of our approach.

A neural network approach to efficient valuation of large portfolios of variable annuities

Managing and hedging the risks associated with Variable Annuity (VA) products require intraday valuation of key risk metrics for these products. The complex structure of VA products and computational complexity of their accurate evaluation have compelled insurance companies to adopt Monte Carlo (MC) simulations to value their large portfolios of VA products. Because the MC simulations are computationally demanding, especially for intraday valuations, insurance companies need more efficient valuation techniques. Recently, a framework based on traditional spatial interpolation techniques has been proposed that can significantly decrease the computational complexity of MC simulation (Gan and Lin, 2015). However, traditional interpolation techniques require the definition of a distance function that can significantly impact their accuracy. Moreover, none of the traditional spatial interpolation techniques provide all of the key properties of accuracy, efficiency, and granularity (Hejazi et al., 2015). In this paper, we present a neural network approach for the spatial interpolation framework that affords an efficient way to find an effective distance function. The proposed approach is accurate, efficient, and provides an accurate granular view of the input portfolio. Our numerical experiments illustrate the superiority of the performance of the proposed neural network approach compared to the traditional spatial interpolation schemes.

A Novel 4-D Artificial-Neural-Network-Based Hybrid Large-Signal Model of GaAs pHEMTs

A novel hybrid large-signal model of GaAs pseudomorphic HEMTs (pHEMTs) is proposed for monolithic microwave integrated circuit design. This new model is based upon accurate electromagnetic (EM) description and creative multi-path artificial neural network (ANN) optimization. To precisely describe the EM effect in the high-frequency range, the extrinsic part of this model includes both lumped and distributed components. In order to re-grid the discrete data, the bias-dependent intrinsic elements are determined by ANNs rather than traditional interpolations. The dispersion effect is represented by nonlinear sources with the multi-path-dependent integration technique, which is described by processed multi-bias S-parameters. This proposed approach can be applicable to different bias conditions, which is also verified by different types of GaAs pHEMTs with good agreement. In addition, a class-AB Ka-band power amplifier and a Ka-band switch using a 0.15- $\mu {\text {m}}$ GaAs pHEMT process were designed based on the novel hybrid model for further practical verification.

On the Use of Gaussian Random Processes for Probabilistic Interpolation of CubeSat Data in the Presence of Geolocation Error

With their greatly reduced sizes, low development cost, and rapid construction time, CubeSats have merged as a platform of considerable interest for a wide range of applications, including remote sensing. Many applications require the interpolation of sensor data into a regularly spaced grid for the development of downstream scientific products. This problem is complicated for CubeSat platforms due to potentially significant uncertainties associated with the spatial position of the satellite. In this paper, we present a probabilistic approach to the data interpolation problem in which we estimate both the platform location and data samples on a regular grid given observations corrupted by noise and location error. Our approach is based on a Gaussian process model to connect the measured data to the values on the grid. Two statistical models for positional uncertainties are considered, one based on an assumption of independent errors and another motivated by positional errors associated with a specific platform of interest, the MicroMAS radiometer. In each case, the maximum a posteriori estimate of the positions and the data is generated using an optimized Gaussian process regression (OGPR) method resulting in two algorithms: OGPR-IID and OGPR-PCA. The performance of this approach is tested on both simulated data and advanced technology microwave sounder data where significant improvements both qualitatively and quantitatively relative to traditional interpolation methods are observed.

Geostatistical Evaluation of Spatial Variation Related to Groundwater Quality Database: Case Study for Arak Plain Aquifer, Iran

Geostatistical methods are one of the advanced techniques to interpolate groundwater quality data. Geostatistical interpolation techniques employ both the mathematical and the statistical properties of the measured points. Compiling the data distribution on spatial and temporal domain is of crucial importance in order to evaluate its quality and safety. The main purpose of this paper is to assess groundwater quality of Arak plain, Iran, by an unbiased interpolated method so called Kriging. Therefore, seven quality variables of Arak plain aquifer including TDS, SAR, EC, Na+, TH, Cl−, and SO42− have been analyzed, studied, and interpreted statistically and geostatistically. Utilized data in this study were collected from 97 water well samples in Arak plain, in 2012. After normalizing data, variogram as a geostatistical tool for defining spatial regression was calculated and experimental variograms have been plotted by GS+ software, then the best theoretical model was fitted to each variogram based on minimum RSS error. Cross validation was used to determine the accuracy of the estimated data. The uncertainty of the method could be well assessed via this method since the method not only gave the average error (around 0 in this study) but also gave the standard deviation of the estimations. Therefore, more than 3800 points were estimated by ordinary Kriging algorithm in places which have not been sampled. Finally, estimation maps of groundwater quality were prepared and map of estimation variance, EV, has been presented to assess the quality of estimation in each estimated point. Results showed that the Kriging method is more accurate than the traditional interpolation algorithms not honoring the spatial properties of the database.

Geospatial Predictive Modelling for Climate Mapping of Selected Severe Weather Phenomena Over Poland: A Methodological Approach

The main purpose of the study is to introduce methods for mapping the spatial distribution of the occurrence of selected atmospheric phenomena (thunderstorms, fog, glaze and rime) over Poland from 1966 to 2010 (45 years). Limited in situ observations as well the discontinuous and location-dependent nature of these phenomena make traditional interpolation inappropriate. Spatially continuous maps were created with the use of geospatial predictive modelling techniques. For each given phenomenon, an algorithm identifying its favourable meteorological and environmental conditions was created on the basis of observations recorded at 61 weather stations in Poland. Annual frequency maps presenting the probability of a day with a thunderstorm, fog, glaze or rime were created with the use of a modelled, gridded dataset by implementing predefined algorithms. Relevant explanatory variables were derived from NCEP/NCAR reanalysis and downscaled with the use of a Regional Climate Model. The resulting maps of favourable meteorological conditions were found to be valuable and representative on the country scale but at different correlation (r) strength against in situ data (from r = 0.84 for thunderstorms to r = 0.15 for fog). A weak correlation between gridded estimates of fog occurrence and observations data indicated the very local nature of this phenomenon. For this reason, additional environmental predictors of fog occurrence were also examined. Topographic parameters derived from the SRTM elevation model and reclassified CORINE Land Cover data were used as the external, explanatory variables for the multiple linear regression kriging used to obtain the final map. The regression model explained 89 % of annual frequency of fog variability in the study area. Regression residuals were interpolated via simple kriging.