Data hiding methods involve embedding secret messages into cover objects to enable covert communication in a way that is difficult to detect.In data hiding methods based on image interpolation,the image size is reduce...Data hiding methods involve embedding secret messages into cover objects to enable covert communication in a way that is difficult to detect.In data hiding methods based on image interpolation,the image size is reduced and then enlarged through interpolation,followed by the embedding of secret data into the newly generated pixels.A general improving approach for embedding secret messages is proposed.The approach may be regarded a general model for enhancing the data embedding capacity of various existing image interpolation-based data hiding methods.This enhancement is achieved by expanding the range of pixel values available for embedding secret messages,removing the limitations of many existing methods,where the range is restricted to powers of two to facilitate the direct embedding of bit-based messages.This improvement is accomplished through the application of multiple-based number conversion to the secret message data.The method converts the message bits into a multiple-based number and uses an algorithm to embed each digit of this number into an individual pixel,thereby enhancing the message embedding efficiency,as proved by a theorem derived in this study.The proposed improvement method has been tested through experiments on three well-known image interpolation-based data hiding methods.The results show that the proposed method can enhance the three data embedding rates by approximately 14%,13%,and 10%,respectively,create stego-images with good quality,and resist RS steganalysis attacks.These experimental results indicate that the use of the multiple-based number conversion technique to improve the three interpolation-based methods for embedding secret messages increases the number of message bits embedded in the images.For many image interpolation-based data hiding methods,which use power-of-two pixel-value ranges for message embedding,other than the three tested ones,the proposed improvement method is also expected to be effective for enhancing their data embedding capabilities.展开更多
A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inne...A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.展开更多
The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; a...The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.展开更多
With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） meth...With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.展开更多
In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model f...In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.展开更多
In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the II...In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square （MLS） approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin （IIEFG） method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin （EFG） method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.展开更多
The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The r...The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the eff ects of the Winkler coeffi cient, Pasternak coeffi cient and damping coeffi cient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary diff erential equations with variable coeffi cients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verifi ed through two numerical examples. The infl uences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with diff erent taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.展开更多
Spatial interpolation is a common tool used in the study of fishery ecology, especially for the construction of ecosystem models. To develop an appropriate interpolation method of determining fishery resources density...Spatial interpolation is a common tool used in the study of fishery ecology, especially for the construction of ecosystem models. To develop an appropriate interpolation method of determining fishery resources density in the Yellow Sea, we tested four frequently used methods, including inverse distance weighted interpolation(IDW), global polynomial interpolation(GPI), local polynomial interpolation(LPI) and ordinary kriging(OK).A cross-validation diagnostic was used to analyze the efficacy of interpolation, and a visual examination was conducted to evaluate the spatial performance of the different methods. The results showed that the original data were not normally distributed. A log transformation was then used to make the data fit a normal distribution. During four survey periods, an exponential model was shown to be the best semivariogram model in August and October 2014, while data from January and May 2015 exhibited the pure nugget effect.Using a paired-samples t test, no significant differences(P>0.05) between predicted and observed data were found in all four of the interpolation methods during the four survey periods. Results of the cross-validation diagnostic demonstrated that OK performed the best in August 2014, while IDW performed better during the other three survey periods. The GPI and LPI methods had relatively poor interpolation results compared to IDW and OK. With respect to the spatial distribution, OK was balanced and was not as disconnected as IDW nor as overly smooth as GPI and LPI, although OK still produced a few 'bull's-eye' patterns in some areas.However, the degree of autocorrelation sometimes limits the application of OK. Thus, OK is highly recommended if data are spatially autocorrelated. With respect to feasibility and accuracy, we recommend IDW to be used as a routine interpolation method. IDW is more accurate than GPI and LPI and has a combination of desirable properties, such as easy accessibility and rapid processing.展开更多
In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using ...In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.展开更多
In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This st...In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.展开更多
Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the movi...Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.展开更多
Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the lo...Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method（FEM）.The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.展开更多
An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in th...An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.展开更多
Spatial interpolation methods are frequently used to estimate values of meteorological data in locations where they are not measured. However, very little research has been investigated the relative performance of dif...Spatial interpolation methods are frequently used to estimate values of meteorological data in locations where they are not measured. However, very little research has been investigated the relative performance of different interpolation methods in meteorological data of Xinjiang Uygur Autonomous Region (Xinjiang). Actually, it has importantly practical significance to as far as possibly improve the accuracy of interpolation results for meteorological data, especially in mountainous Xinjiang. There- fore, this paper focuses on the performance of different spatial interpolation methods for monthly temperature data in Xinjiang. The daily observed data of temperature are collected from 38 meteorological stations for the period 1960- 2004. Inverse distance weighting (IDW), ordinary kriging (OK), temperature lapse rate method (TLR) and multiple linear regressions (MLR) are selected as interpolated methods. Two rasterized methods, multiple regression plus space residual error and directly interpolated observed temperature (DIOT) data, are used to analyze and compare the performance of these interpolation methods respectively. Moreover, cross-validation is used to evaluate the performance of different spatial interpolation methods. The results are as follows: 1) The method of DIOT is unsuitable for the study area in this paper. 2) It is important to process the observed data by local regression model before the spatial interpolation. 3) The MLR-IDW is the optimum spatial interpolation method for the monthly mean temperature based on cross-validation. For the authors, the reliability of results and the influence of measurement accuracy, density, distribution and spatial variability on the accuracy of the interpolation methods will be tested and analyzed in the future.展开更多
A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(F...A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.展开更多
Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity proble...Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.展开更多
Regional estimates of evapotranspiration （ET） are critical for a wide range of applications. Satellite remote sensing is a promising tool for obtaining reasonable ET spatial distribution data. However, there are at ...Regional estimates of evapotranspiration （ET） are critical for a wide range of applications. Satellite remote sensing is a promising tool for obtaining reasonable ET spatial distribution data. However, there are at least two major problems that exist in the regional estimation of ET from remote sensing data. One is the conflicting requirements of simple data over a wide region, and accuracy of those data. The second is the lack of regional ET products that cover the entire region of northern China. In this study, we first retrieved the evaporative fraction （EF） by interpolating from the difference of day/night land surface temperature （AT） and the normalized difference vegetation index （NDVI） triangular-shaped scatter space. Then, ET was generated from EF and land surface meteorological data. The estimated eight-day EF and ET results were validated with 14 eddy covariance （EC） flux measurements in the growing season （July September） for the year 2008 over the study area. The estimated values agreed well with flux tower measurements, and this agreement was highly statistically significant for both EF and ET （p 〈0.01）, with the correlation coefficient for EF （R2=0.64） being relatively higher than for ET （R2---0.57）. Validation with EC-measured ET showed the mean RMSE and bias were 0.78 mm d-1 （22.03 W m-2） and 0.31 mm d-1 （8.86 W m-2）, respectively. The ET over the study area increased along a clear longitudinal gradient, which was probably controlled by the gradient of precipitation, green vegetation fractions, and the intensity of human activities. The satellite-based estimates adequately captured the spatial and seasonal structure of ET. Overall, our results demonstrate the potential of this simple but practical method for monitoring ET over regions with heterogeneous surface areas.展开更多
In this paper, using the interpolation perturbation method. the author seeks tosolve several nonlinear problems. Numerical examples show that the method Df thispaper has good accuracy.
This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit m...This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.展开更多
Interpolation methods in ArcGIS_ESRI Geostatistical Analyst tool allow obtaining unknown values at unsampled points from observed data and generating continuous surfaces. In this paper, forest data variables as tree h...Interpolation methods in ArcGIS_ESRI Geostatistical Analyst tool allow obtaining unknown values at unsampled points from observed data and generating continuous surfaces. In this paper, forest data variables as tree height and diameter measured in two plots in Central Mountains in Spain. These data were georeferenced to obtain maps that can visualize the spatial variability of these forest variables. In order to evaluate the best interpolation method that could adequately explain the spatial variability of those variables, two interpolation methods were studied： inverse results was made by means of statistical methods to analyze distance weighted （IDW） and Ordinary Kriging （OK）. A comparison of residuals. Results with the kriging method were slightly better.展开更多
文摘Data hiding methods involve embedding secret messages into cover objects to enable covert communication in a way that is difficult to detect.In data hiding methods based on image interpolation,the image size is reduced and then enlarged through interpolation,followed by the embedding of secret data into the newly generated pixels.A general improving approach for embedding secret messages is proposed.The approach may be regarded a general model for enhancing the data embedding capacity of various existing image interpolation-based data hiding methods.This enhancement is achieved by expanding the range of pixel values available for embedding secret messages,removing the limitations of many existing methods,where the range is restricted to powers of two to facilitate the direct embedding of bit-based messages.This improvement is accomplished through the application of multiple-based number conversion to the secret message data.The method converts the message bits into a multiple-based number and uses an algorithm to embed each digit of this number into an individual pixel,thereby enhancing the message embedding efficiency,as proved by a theorem derived in this study.The proposed improvement method has been tested through experiments on three well-known image interpolation-based data hiding methods.The results show that the proposed method can enhance the three data embedding rates by approximately 14%,13%,and 10%,respectively,create stego-images with good quality,and resist RS steganalysis attacks.These experimental results indicate that the use of the multiple-based number conversion technique to improve the three interpolation-based methods for embedding secret messages increases the number of message bits embedded in the images.For many image interpolation-based data hiding methods,which use power-of-two pixel-value ranges for message embedding,other than the three tested ones,the proposed improvement method is also expected to be effective for enhancing their data embedding capabilities.
基金The National Natural Science Foundation of China (No.61362001,61102043,61262084,20132BAB211030,20122BAB211015)the Basic Research Program of Shenzhen(No.JC201104220219A)
文摘A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.
文摘The operator splitting method is used to deal with the Navier-Stokes equation, in which the physical process described by the equation is decomposed into two processes： a diffusion process and a convection process; and the finite element equation is established. The velocity field in the element is described by the shape function of the isoparametric element with nine nodes and the pressure field is described by the interpolation function of the four nodes at the vertex of the isoparametric element with nine nodes. The subroutine of the element and the integrated finite element code are generated by the Finite Element Program Generator （FEPG） successfully. The numerical simulation about the incompressible viscous liquid flowing over a cylinder is carded out. The solution agrees with the experimental results very well.
基金The National Natural Science Foundation of China(No.60702027)the Free Research Fund of the National Mobile Communications Research Laboratory of Southeast University (No.2008B07)the National Basic Research Program of China(973 Program)(No.2007CB310603)
文摘With the linear interpolation method, an improved absorbing boundary condition（ABC）is introduced and derived, which is suitable for the alternating-direction-implicit finite- difference time-domain （ADI-FDTD） method. The reflection of the ABC caused by both the truncated error and the phase velocity error is analyzed. Based on the phase velocity estimation and the nonuniform cell, two methods are studied and then adopted to improve the performance of the ABC. A calculation case of a rectangular waveguide which is a typical dispersive transmission line is carried out using the ADI-FDTD method with the improved ABC for evaluation. According to the calculated case, the comparison is given between the reflection coefficients of the ABC with and without the velocity estimation and also the comparison between the reflection coefficients of the ABC with and without the nonuniform processing. The reflection variation of the ABC under different time steps is also analyzed and the acceptable worsening will not obscure the improvement on the absorption. Numerical results obviously show that efficient improvement on the absorbing performance of the ABC is achieved based on these methods for the ADI-FDTD.
基金This work was supported by the National Natural Science Foundation of China(10071037)
文摘In this paper, a new derivative free trust region method is developed based on the conic interpolation model for the unconstrained optimization. The conic interpolation model is built by means of the quadratic model function, the collinear scaling formula, quadratic approximation and interpolation. All the parameters in this model are determined by objective function interpolation condition. A new derivative free method is developed based upon this model and the global convergence of this new method is proved without any information on gradient.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Shanghai Leading Academic Discipline Project, China (Grant No. S30106)
文摘In this paper, an improved interpolating moving least-square （IIMLS） method is presented. The shape function of the IIMLS method satisfies the property of the Kronecker 5 function. The weight function used in the IIMLS method is nonsingular. Then the IIMLS method can overcome the difficulties caused by the singularity of the weight function in the IMLS method. The number of unknown coefficients in the trial function of the IIMLS method is less than that of the moving least-square （MLS） approximation. Then by combining the IIMLS method with the Galerkin weak form of the potential problem, the improved interpolating element-free Galerkin （IIEFG） method for two-dimensional potential problems is presented. Compared with the conventional element-free Galerkin （EFG） method, the IIEFG method can directly use the essential boundary conditions. Then the IIEFG method has higher accuracy. For demonstration, three numerical examples are solved using the IIEFG method.
基金AHKJT of China under Grant Nos.1708085QE121 and 1808085ME147AHEDU of China under Grant No.TSKJ2017B13
文摘The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the eff ects of the Winkler coeffi cient, Pasternak coeffi cient and damping coeffi cient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary diff erential equations with variable coeffi cients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verifi ed through two numerical examples. The infl uences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with diff erent taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.
基金The National Basic Research Program of China under contract No.2015CB453303the National Natural Science Foundation of China under contract No.U1405234+1 种基金the Aoshan Science&Technology Innovation Program under contract No.2015ASKJ02-05the Special Fund of the Taishan Scholar Project
文摘Spatial interpolation is a common tool used in the study of fishery ecology, especially for the construction of ecosystem models. To develop an appropriate interpolation method of determining fishery resources density in the Yellow Sea, we tested four frequently used methods, including inverse distance weighted interpolation(IDW), global polynomial interpolation(GPI), local polynomial interpolation(LPI) and ordinary kriging(OK).A cross-validation diagnostic was used to analyze the efficacy of interpolation, and a visual examination was conducted to evaluate the spatial performance of the different methods. The results showed that the original data were not normally distributed. A log transformation was then used to make the data fit a normal distribution. During four survey periods, an exponential model was shown to be the best semivariogram model in August and October 2014, while data from January and May 2015 exhibited the pure nugget effect.Using a paired-samples t test, no significant differences(P>0.05) between predicted and observed data were found in all four of the interpolation methods during the four survey periods. Results of the cross-validation diagnostic demonstrated that OK performed the best in August 2014, while IDW performed better during the other three survey periods. The GPI and LPI methods had relatively poor interpolation results compared to IDW and OK. With respect to the spatial distribution, OK was balanced and was not as disconnected as IDW nor as overly smooth as GPI and LPI, although OK still produced a few 'bull's-eye' patterns in some areas.However, the degree of autocorrelation sometimes limits the application of OK. Thus, OK is highly recommended if data are spatially autocorrelated. With respect to feasibility and accuracy, we recommend IDW to be used as a routine interpolation method. IDW is more accurate than GPI and LPI and has a combination of desirable properties, such as easy accessibility and rapid processing.
基金supported by the State Key Development Program for Basic Research of China (Grant No 2006CB303102)Science and Technology Commission of Shanghai Municipality,China (Grant No 09DZ2272900)
文摘In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.
基金Project supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.10902076)the Natural Science Foundation of Shanxi Province of China(Grant No.2007011009)+1 种基金the Scientific Research and Development Program of the Shanxi Higher Education Institutions(Grant No.20091131)the Doctoral Startup Foundation of Taiyuan University of Science and Technology(Grant No.200708)
文摘In this paper, a meshfree boundary integral equation （BIE） method, called the moving Kriging interpolation- based boundary node method （MKIBNM）, is developed for solving two-dimensional potential problems. This study combines the DIE method with the moving Kriging interpolation to present a boundary-type meshfree method, and the corresponding formulae of the MKIBNM are derived. In the present method, the moving Kriging interpolation is applied instead of the traditional moving least-square approximation to overcome Kronecker＇s delta property, then the boundary conditions can be imposed directly and easily. To verify the accuracy and stability of the present formulation, three selected numerical examples are presented to demonstrate the efficiency of MKIBNM numerically.
基金Project supported by the National Natural Science Foundation of China(Grant No.11072117)the Natural Science Foundation of Ningbo City,China(GrantNo.2013A610103)+2 种基金the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6090131)the Disciplinary Project of Ningbo City,China(GrantNo.SZXL1067)the K.C.Wong Magna Fund in Ningbo University,China
文摘Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging inter- polation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.
基金Supported by the Aviation Science Foundationof China(2009ZB5052)the Specialized Research Foundation for the Doctor Program of Higher Education(20070287039)~~
文摘Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method（FEM）.The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.
基金supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Shanxi Province,China(Grant No.2013011022-6)
文摘An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.
文摘Spatial interpolation methods are frequently used to estimate values of meteorological data in locations where they are not measured. However, very little research has been investigated the relative performance of different interpolation methods in meteorological data of Xinjiang Uygur Autonomous Region (Xinjiang). Actually, it has importantly practical significance to as far as possibly improve the accuracy of interpolation results for meteorological data, especially in mountainous Xinjiang. There- fore, this paper focuses on the performance of different spatial interpolation methods for monthly temperature data in Xinjiang. The daily observed data of temperature are collected from 38 meteorological stations for the period 1960- 2004. Inverse distance weighting (IDW), ordinary kriging (OK), temperature lapse rate method (TLR) and multiple linear regressions (MLR) are selected as interpolated methods. Two rasterized methods, multiple regression plus space residual error and directly interpolated observed temperature (DIOT) data, are used to analyze and compare the performance of these interpolation methods respectively. Moreover, cross-validation is used to evaluate the performance of different spatial interpolation methods. The results are as follows: 1) The method of DIOT is unsuitable for the study area in this paper. 2) It is important to process the observed data by local regression model before the spatial interpolation. 3) The MLR-IDW is the optimum spatial interpolation method for the monthly mean temperature based on cross-validation. For the authors, the reliability of results and the influence of measurement accuracy, density, distribution and spatial variability on the accuracy of the interpolation methods will be tested and analyzed in the future.
基金co-supported by the National Key R&D Program of China(Nos.2018YFF01012401-05)the National Natural Science Foundation of China(No.51975243)+2 种基金Jilin Provincial Department of Education(No.JJKH20180084KJ),Chinathe Fundamental Research Funds for the Central Universities and Jilin Provincial Department of Science&Technology Fund Project,China(Nos.20170101043JC and 20180520072JH)Graduate Innovation Fund of Jilin University,China(No.101832018C184).
文摘A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)
文摘Based on the improved interpolating moving least-squares （ⅡMLS） method and the Galerkin weak form, an improved interpolating element-free Galerkin （ⅡEFG） method is presented for two-dimensional elasticity problems in this paper. Compared with the interpolating moving least-squares （IMLS） method presented by Lancaster, the ⅡMLS method uses the nonsingular weight function. The number of unknown coefficients in the trial function of the ⅡMLS method is less than that of the MLS approximation and the shape function of the ⅡMLS method satisfies the property of Kronecker δ function. Thus in the ⅡEFG method, the essential boundary conditions can be applied directly and easily, then the numerical solutions can be obtained with higher precision than those obtained by the interpolating element-free Galerkin （IEFG） method. For the purposes of demonstration, four numerical examples are solved using the ⅡEFG method.
基金supported by the National Basic Research Program of China (No. 2012CB956202)the National Natural Science Foundation of China (Grant No. 41105076)+1 种基金the National Special Scientific Research Project for Public Interest (Forestry) (Grant No. GYHY201204105)the National Key Technology R & D Program (Grant No. 2012BAC22B04)
文摘Regional estimates of evapotranspiration （ET） are critical for a wide range of applications. Satellite remote sensing is a promising tool for obtaining reasonable ET spatial distribution data. However, there are at least two major problems that exist in the regional estimation of ET from remote sensing data. One is the conflicting requirements of simple data over a wide region, and accuracy of those data. The second is the lack of regional ET products that cover the entire region of northern China. In this study, we first retrieved the evaporative fraction （EF） by interpolating from the difference of day/night land surface temperature （AT） and the normalized difference vegetation index （NDVI） triangular-shaped scatter space. Then, ET was generated from EF and land surface meteorological data. The estimated eight-day EF and ET results were validated with 14 eddy covariance （EC） flux measurements in the growing season （July September） for the year 2008 over the study area. The estimated values agreed well with flux tower measurements, and this agreement was highly statistically significant for both EF and ET （p 〈0.01）, with the correlation coefficient for EF （R2=0.64） being relatively higher than for ET （R2---0.57）. Validation with EC-measured ET showed the mean RMSE and bias were 0.78 mm d-1 （22.03 W m-2） and 0.31 mm d-1 （8.86 W m-2）, respectively. The ET over the study area increased along a clear longitudinal gradient, which was probably controlled by the gradient of precipitation, green vegetation fractions, and the intensity of human activities. The satellite-based estimates adequately captured the spatial and seasonal structure of ET. Overall, our results demonstrate the potential of this simple but practical method for monitoring ET over regions with heterogeneous surface areas.
文摘In this paper, using the interpolation perturbation method. the author seeks tosolve several nonlinear problems. Numerical examples show that the method Df thispaper has good accuracy.
基金the National Natural Science Foundation of China(Nos.41807223 and 51908175)the Fundamental Research Funds for the Central Universities(No.B210202096)+1 种基金the Natural Science Foundation of Guangdong Province(No.2018A030310346)the Water Conservancy Science and Technology Innovation Project of Guangdong Province(No.2020-11),China。
文摘This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.
文摘Interpolation methods in ArcGIS_ESRI Geostatistical Analyst tool allow obtaining unknown values at unsampled points from observed data and generating continuous surfaces. In this paper, forest data variables as tree height and diameter measured in two plots in Central Mountains in Spain. These data were georeferenced to obtain maps that can visualize the spatial variability of these forest variables. In order to evaluate the best interpolation method that could adequately explain the spatial variability of those variables, two interpolation methods were studied： inverse results was made by means of statistical methods to analyze distance weighted （IDW） and Ordinary Kriging （OK）. A comparison of residuals. Results with the kriging method were slightly better.
