In this article,we study the empirical likelihood(EL)method for autoregressive models with spatial errors.The EL ratio statistics are constructed for the parameters of the models.It is shown that the limiting distribu...In this article,we study the empirical likelihood(EL)method for autoregressive models with spatial errors.The EL ratio statistics are constructed for the parameters of the models.It is shown that the limiting distributions of the EL ratio statistics are chi-square distributions,which are used to construct confidence intervals for the parameters of the models.A simulation study is conducted to compare the performances of the EL based and the normal approximation(NA)based confidence intervals.Simulation results show that the confidence intervals based on EL are superior to the NA based confidence intervals.展开更多
To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However...To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However,we prove that the spatial simulation error of the finite difference method is associated with the dot product of the spatial dispersion relation of the finite-difference weights and the spectrum of the seismic wavefield.Based on the dot product relation,we construct a L_(2) norm cost function to minimize spatial simulation error.For solving this optimization problem,the seismic wavefield infor-mation in wavenumber region is necessary.Nevertheless,the seismic wavefield is generally obtained by costly forward modeling techniques.To reduce the computational cost,we substitute the spectrum of the seismic wavelet for the spectrum of the seismic wavefield,as the seismic wavelet plays a key role in determining the seismic wavefield.In solving the optimization problem,we design an exhaustive search method to obtain the solution of the L_(2) norm optimization problem.After solving the optimization problem,we are able to achieve the finite-difference weights that minimize spatial simulation error.In theoretical error analyses,the finite-difference weights from the proposed method can output more accurate simulation results compared to those from previous optimization algorithms.Furthermore,we validate our method through numerical tests with synthetic models,which encompass homogenous/inhomogeneous media as well as isotropic and anisotropic media.展开更多
The study aims to investigate county-level variations of the COVID-19 disease and vaccination rate. The COVID-19 data was acquired from usafact.org, and the vaccination records were acquired from the Ohio vaccination ...The study aims to investigate county-level variations of the COVID-19 disease and vaccination rate. The COVID-19 data was acquired from usafact.org, and the vaccination records were acquired from the Ohio vaccination tracker dashboard. GIS-based exploratory analysis was conducted to select four variables (poverty, black race, population density, and vaccination) to explain COVID-19 occurrence during the study period. Consequently, spatial statistical techniques such as Moran’s I, Hot Spot Analysis, Spatial Lag Model (SLM), and Spatial Error Model (SEM) were used to explain the COVID-19 occurrence and vaccination rate across the 88 counties in Ohio. The result of the Local Moran’s I analysis reveals that the epicenters of COVID-19 and vaccination followed the same patterns. Indeed, counties like Summit, Franklin, Fairfield, Hamilton, and Medina were categorized as epicenters for both COVID-19 occurrence and vaccination rate. The SEM seems to be the best model for both COVID-19 and vaccination rates, with R2 values of 0.68 and 0.70, respectively. The GWR analysis proves to be better than Ordinary Least Squares (OLS), and the distribution of R2 in the GWR is uneven throughout the study area for both COVID-19 cases and vaccinations. Some counties have a high R2 of up to 0.70 for both COVID-19 cases and vaccinations. The outcomes of the regression analyses show that the SEM models can explain 68% - 70% of COVID-19 cases and vaccination across the entire counties within the study period. COVID-19 cases and vaccination rates exhibited significant positive associations with black race and poverty throughout the study area.展开更多
Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the resul...Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.展开更多
The stochastic models of the usual joints are first established through intro-ducing the concepts of“clearance characteristic element”and“clearance space”.After de-riving the probability density function of the jo...The stochastic models of the usual joints are first established through intro-ducing the concepts of“clearance characteristic element”and“clearance space”.After de-riving the probability density function of the joint clearance and making the probabilisticanalysis of the resulted kinematic errors,the sampling formulas of the independent varia-bles of the joint clearances are further deduced.Through Monte Carlo simulation,the sta-tistical characteristics and frequency histograms of the kinematic errors are then analysedon computer.展开更多
Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to t...Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to the minimum condition principle of form error evaluation, the mathematic model and optimization objective of the GASA are given. The algorithm avoids the optimization and linearization, and can be fulfilled in three steps. First construct two parallel quadrates based on the preset two reference points of the spatial line respectively;second construct centerlines by connecting one quadrate each vertices to another quadrate each vertices;after that, calculate the distances between measured points and the constructed centerlines. The minimum zone straightness error is obtained by repeating comparing and reconstructing quadrates. The principle and steps of the algorithm to evaluate spatial straightness error is described in detail, and the mathematical formula and program flowchart are given also. Results show that this algorithm can evaluate spatial straightness error more effectively and exactly.展开更多
Taking the CNC machining for the spatial barrel-cam with rectilinear translating and a conical roller follower as an example, the calculation method and the law of the profile error influenced by the tool error is given.
In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differen...In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.展开更多
This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the propertie...This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.展开更多
Cold storage is the vital infrastructure of cold chain logistics. In this study, we analyzed the spatial pattern evolution characteristics, spatial autocorrelation and influencing factors of cold storage in China by u...Cold storage is the vital infrastructure of cold chain logistics. In this study, we analyzed the spatial pattern evolution characteristics, spatial autocorrelation and influencing factors of cold storage in China by using kernel density estimation(KDE), spatial autocorrelation analysis(SAA), and spatial error model(SEM). Results showed that: 1) the spatial distribution of cold storage in China is unbalanced, and has evolved from ‘one core’ to ‘one core and many spots’, that is, ‘one core’ refers to the Bohai Rim region mainly including Beijing, Tianjin, Hebei, Shandong and Liaoning regions, and ‘many spots’ mainly include the high-density areas such as Shanghai, Fuzhou, Guangzhou, Zhengzhou, Hefei, Wuhan, ürümqi. 2) The distribution of cold storage has significant global spatial autocorrelation and local spatial autocorrelation, and the ‘High-High’ cluster area is the most stable, mainly concentrated in the Bohai Rim;the ‘Low-Low’ cluster area is grouped in the southern China. 3) Economic development level, population density, traffic accessibility, temperature and land price, all affect the location choice of cold storage in varying degrees, while the impact of market demand on it is not explicit.展开更多
提出一种切片Gibbs抽样的马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)算法来计算空间误差模型未知参数的联合贝叶斯估计,通过2个模拟仿真说明提出的贝叶斯估计方法的有效性与切片Gibbs抽样算法的优势,实证分析说明模型和提出的...提出一种切片Gibbs抽样的马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)算法来计算空间误差模型未知参数的联合贝叶斯估计,通过2个模拟仿真说明提出的贝叶斯估计方法的有效性与切片Gibbs抽样算法的优势,实证分析说明模型和提出的贝叶斯估计方法的有效性。展开更多
基金supported by the Natural Science Foundation of Guangxi(2022GXNSFAA035556)the National Natural Science Foundation of China(12161009,12061017)+1 种基金Center for Applied Mathematics of Guangxi(Guangxi Normal University)Key Laboratory of Interdisciplinary Research for Data Science,Education Department of Guangxi Zhuang Autonomous Region.
文摘In this article,we study the empirical likelihood(EL)method for autoregressive models with spatial errors.The EL ratio statistics are constructed for the parameters of the models.It is shown that the limiting distributions of the EL ratio statistics are chi-square distributions,which are used to construct confidence intervals for the parameters of the models.A simulation study is conducted to compare the performances of the EL based and the normal approximation(NA)based confidence intervals.Simulation results show that the confidence intervals based on EL are superior to the NA based confidence intervals.
基金supported by the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(No.2021QNLM020001)the Major Scientific and Technological Projects of Shandong Energy Group(No.SNKJ2022A06-R23)+1 种基金the Funds of Creative Research Groups of China(No.41821002)the Major Scientific and Technological Projects of CNPC(No.ZD2019-183-003).
文摘To reduce the spatial simulation error generated by the finite difference method,previous researchers compute the optimal finite-difference weights always by minimizing the error of spatial dispersion relation.However,we prove that the spatial simulation error of the finite difference method is associated with the dot product of the spatial dispersion relation of the finite-difference weights and the spectrum of the seismic wavefield.Based on the dot product relation,we construct a L_(2) norm cost function to minimize spatial simulation error.For solving this optimization problem,the seismic wavefield infor-mation in wavenumber region is necessary.Nevertheless,the seismic wavefield is generally obtained by costly forward modeling techniques.To reduce the computational cost,we substitute the spectrum of the seismic wavelet for the spectrum of the seismic wavefield,as the seismic wavelet plays a key role in determining the seismic wavefield.In solving the optimization problem,we design an exhaustive search method to obtain the solution of the L_(2) norm optimization problem.After solving the optimization problem,we are able to achieve the finite-difference weights that minimize spatial simulation error.In theoretical error analyses,the finite-difference weights from the proposed method can output more accurate simulation results compared to those from previous optimization algorithms.Furthermore,we validate our method through numerical tests with synthetic models,which encompass homogenous/inhomogeneous media as well as isotropic and anisotropic media.
文摘The study aims to investigate county-level variations of the COVID-19 disease and vaccination rate. The COVID-19 data was acquired from usafact.org, and the vaccination records were acquired from the Ohio vaccination tracker dashboard. GIS-based exploratory analysis was conducted to select four variables (poverty, black race, population density, and vaccination) to explain COVID-19 occurrence during the study period. Consequently, spatial statistical techniques such as Moran’s I, Hot Spot Analysis, Spatial Lag Model (SLM), and Spatial Error Model (SEM) were used to explain the COVID-19 occurrence and vaccination rate across the 88 counties in Ohio. The result of the Local Moran’s I analysis reveals that the epicenters of COVID-19 and vaccination followed the same patterns. Indeed, counties like Summit, Franklin, Fairfield, Hamilton, and Medina were categorized as epicenters for both COVID-19 occurrence and vaccination rate. The SEM seems to be the best model for both COVID-19 and vaccination rates, with R2 values of 0.68 and 0.70, respectively. The GWR analysis proves to be better than Ordinary Least Squares (OLS), and the distribution of R2 in the GWR is uneven throughout the study area for both COVID-19 cases and vaccinations. Some counties have a high R2 of up to 0.70 for both COVID-19 cases and vaccinations. The outcomes of the regression analyses show that the SEM models can explain 68% - 70% of COVID-19 cases and vaccination across the entire counties within the study period. COVID-19 cases and vaccination rates exhibited significant positive associations with black race and poverty throughout the study area.
基金supported by National Natural Science Foundation of China (Grant No. 51075198)Jiangsu Provincial Natural Science Foundation of China (Grant No. BK2010479)+2 种基金Innovation Research of Nanjing Institute of Technology, China (Grant No. CKJ20100008)Jiangsu Provincial Foundation of 333 Talents Engineering of ChinaJiangsu Provincial Foundation of Six Talented Peak of China
文摘Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on ＂The Guide to the Expression of Uncertainty in Measurement（GUM）＂. In order to compute spatial straightness error（SSE） accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization（QPSO） is proposed to solve the minimum zone SSE and Monte Carlo Method（MCM） is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function（PDF） for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine（CMM） is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.
文摘The stochastic models of the usual joints are first established through intro-ducing the concepts of“clearance characteristic element”and“clearance space”.After de-riving the probability density function of the joint clearance and making the probabilisticanalysis of the resulted kinematic errors,the sampling formulas of the independent varia-bles of the joint clearances are further deduced.Through Monte Carlo simulation,the sta-tistical characteristics and frequency histograms of the kinematic errors are then analysedon computer.
文摘Considering the characteristics of spatial straightness error, this paper puts forward a kind of evaluation method of spatial straightness error using Geometric Approximation Searching Algorithm (GASA). According to the minimum condition principle of form error evaluation, the mathematic model and optimization objective of the GASA are given. The algorithm avoids the optimization and linearization, and can be fulfilled in three steps. First construct two parallel quadrates based on the preset two reference points of the spatial line respectively;second construct centerlines by connecting one quadrate each vertices to another quadrate each vertices;after that, calculate the distances between measured points and the constructed centerlines. The minimum zone straightness error is obtained by repeating comparing and reconstructing quadrates. The principle and steps of the algorithm to evaluate spatial straightness error is described in detail, and the mathematical formula and program flowchart are given also. Results show that this algorithm can evaluate spatial straightness error more effectively and exactly.
文摘Taking the CNC machining for the spatial barrel-cam with rectilinear translating and a conical roller follower as an example, the calculation method and the law of the profile error influenced by the tool error is given.
文摘In this paper, error-correction coding (ECC) in Gray codes is considered and its performance in the protecting of spatial image watermarks against lossy data compression is demonstrated. For this purpose, the differences between bit patterns of two Gray codewords are analyzed in detail. On the basis of the properties, a method for encoding watermark bits in the Gray codewords that represent signal levels by a single-error-correcting (SEC) code is developed, which is referred to as the Gray-ECC method in this paper. The two codewords of the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of distortion caused by the watermark embedding. The stochastic analyses show that an error-correcting capacity of the Gray-ECC method is superior to that of the ECC in natural binary codes for changes in signal codewords. Experiments of the Gray-ECC method were conducted on 8-bit monochrome images to evaluate both the features of watermarked images and the performance of robustness for image distortion resulting from the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional averaging-based method, the Gray-ECC method yields watermarked images with less amount of signal distortion and also makes the watermark comparably robust for lossy data compression.
文摘This paper demonstrates how channel coding can improve the robustness of spatial image watermarks against signal distortion caused by lossy data compression such as the JPEG scheme by taking advantage of the properties of Gray code. Two error-correction coding (ECC) schemes are used here: One scheme, referred to as the vertical ECC (VECC), is to encode information bits in a pixel by error-correction coding where the Gray code is used to improve the performance. The other scheme, referred to as the horizontal ECC (HECC), is to encode information bits in an image plane. In watermarking, HECC generates a codeword representing watermark bits, and each bit of the codeword is encoded by VECC. Simple single-error-correcting block codes are used in VECC and HECC. Several experiments of these schemes were conducted on test images. The result demonstrates that the error-correcting performance of HECC just depends on that of VECC, and accordingly, HECC enhances the capability of VECC. Consequently, HECC with appropriate codes can achieve stronger robustness to JPEG—caused distortions than non-channel-coding watermarking schemes.
基金Under the auspices of the National Social Science Fund of China(No.15BGL185,19XJL004)General Project of Humanities and Social Sciences Research and Planning Fund of Ministry of Education(No.19YJA790097)+1 种基金Social Science Fund of Fujian Province(No.FJ2017C080)A Key Discipline of Henan University of Animal Husbandry and Economy‘Business Enterprise Management’(No.MXK2016201)。
文摘Cold storage is the vital infrastructure of cold chain logistics. In this study, we analyzed the spatial pattern evolution characteristics, spatial autocorrelation and influencing factors of cold storage in China by using kernel density estimation(KDE), spatial autocorrelation analysis(SAA), and spatial error model(SEM). Results showed that: 1) the spatial distribution of cold storage in China is unbalanced, and has evolved from ‘one core’ to ‘one core and many spots’, that is, ‘one core’ refers to the Bohai Rim region mainly including Beijing, Tianjin, Hebei, Shandong and Liaoning regions, and ‘many spots’ mainly include the high-density areas such as Shanghai, Fuzhou, Guangzhou, Zhengzhou, Hefei, Wuhan, ürümqi. 2) The distribution of cold storage has significant global spatial autocorrelation and local spatial autocorrelation, and the ‘High-High’ cluster area is the most stable, mainly concentrated in the Bohai Rim;the ‘Low-Low’ cluster area is grouped in the southern China. 3) Economic development level, population density, traffic accessibility, temperature and land price, all affect the location choice of cold storage in varying degrees, while the impact of market demand on it is not explicit.
