In order to solve the lack of relevant evaluation research on the accuracy of HMP155A humidity sensor calibration results in the past, this paper designs the corresponding experimental scheme, and obtains the correspo...In order to solve the lack of relevant evaluation research on the accuracy of HMP155A humidity sensor calibration results in the past, this paper designs the corresponding experimental scheme, and obtains the corresponding calibration results according to the experimental scheme;Then the measurement uncertainty of the indication error in the calibration results is evaluated by GUM, and the corresponding extended uncertainty </span><i><span style="font-family:Verdana;">U</span></i><sub><span style="font-family:Verdana;">95</span></sub><span style="font-family:Verdana;"> is obtained. Finally, according to the requirements of JJF1094-2016 characteristic evaluation of measuring instruments, combined with the calibration results and the actual situation of </span><i><span style="font-family:Verdana;">U</span></i><sub><span style="font-family:Verdana;">95</span></sub><span style="font-family:Verdana;">, the conformity of the indication error of calibration is determined. The result is that each calibration point of the sensor meets the requirements of conformity determination and is within the qualified range. This research effectively makes up for the blank of the previous research on the conformity determination of the indication error of the calibration results and has strong theoretical and practical significance.展开更多
As a kind of compulsory verification of the metering equipment, fuel tanker throughout the country, its accuracy is related to People's Daily life consumption. It is very important to introduce measurement uncerta...As a kind of compulsory verification of the metering equipment, fuel tanker throughout the country, its accuracy is related to People's Daily life consumption. It is very important to introduce measurement uncertainty into conformity assessment in order to better judge the indication error of the tanker and ensure the accuracy and fairness of the tanker. This paper analyzes the measurement uncertainty of the calibration of indicator value error of the tanker, determines the application basis of the measurement uncertainty, and summarizes the application of the measurement uncertainty in the calibration of indicator value error of the tanker according to the uncertainty requirements of ISO/IEC 17025:2017, so as to help the verifier to make more accurate qualification judgment and avoid risks.展开更多
In this article,we discuss the approach to solving a nonlinear PDE equation,specifically the p-Laplacian equation,with a general(nonlinear)boundary condition.We establish the existence and uniqueness of the solution,s...In this article,we discuss the approach to solving a nonlinear PDE equation,specifically the p-Laplacian equation,with a general(nonlinear)boundary condition.We establish the existence and uniqueness of the solution,subject to certain assumptions outlined in this paper.To solve our nonlinear problem using the Finite Element Method(FEM),we derive an appropriate variational formulation.Additionally,we introduce a study of the residual a posteriori-error indicator,establishing both upper and lower bounds to control the error.The upper bound is determined using averaging interpolators in some quasi-norms defined by Barrett and Liu.Furthermore,we prove the equivalence between the residual error and the true error e=u−u_(h).Lastly,we perform a simulation of the p-Laplacian problem in the L-shape domain using a Matlab program in two-dimensional space.展开更多
In this work,we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials(FGMs).A recovery type error indicator combined with quadtree decomposition is emp...In this work,we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials(FGMs).A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement.The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations.The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle.The study is then extended to the analysis of orthotropic FGMs.It is observed that,if the gradation in fracture properties is neglected,the material gradient plays a secondary role,with the fracture behaviour being dominated by the orthotropy of the material.However,when the toughness increases along the crack propagation path,a substantial gain in fracture resistance is observed.展开更多
This paper examines the forecasting performance of different kinds of GARCH model （GRACH, EGARCH, TARCH and APARCH） under the Normal, Student-t and Generalized error distributional assumption. We compare the effect ...This paper examines the forecasting performance of different kinds of GARCH model （GRACH, EGARCH, TARCH and APARCH） under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze are the daily stocks indexes for Shenzhen Stock Exchange （SSE） in China from April 3^rd, 1991 to April 14^th, 2005. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that TARCH and GARCH models give better forecasting performance than EGARCH and APARCH models. In forecasting performance, the model under normal distribution gives more accurate forecasting performance than non-normal densities and generalized error distributions clearly outperform the student-t densities in case of SSE.展开更多
This paper focuses on constructing the adaptive analysis model based on the Finite Element Method(FEM)with an unstructured mesh,which includes taking full advantage of the two-dimensional triangle’s ability to discre...This paper focuses on constructing the adaptive analysis model based on the Finite Element Method(FEM)with an unstructured mesh,which includes taking full advantage of the two-dimensional triangle’s ability to discretize any complex model.The error indicator and h-type refinement scheme for FEM has been presented by providing a simple error indicator based on the difference value of nodal fundamental physical variables.It provides an effective measure of the error in the numerical solution,which can lead to an adaptive refinement scheme,determining the optimal location of new inserted nodes that are mainly distributed in the local high stress gradient domain.A numerical experiment is presented to demonstrate that the proposed error indicator reasonably tracks the distribution of the true error,and the effectiveness of the proposed adaptive analysis procedure,which achieves significantly higher convergence rates compared to the uniform mesh.展开更多
Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive r...Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms.An adaptive strategy based on theℜ-parameter is proposed for continuous flows,while a hybrid adaptive algorithm employing a combination of error indicators and theℜ-parameter is developed for discontinuous flows.Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.展开更多
In this paper,the Chebyshev-Galerkin spectral approximations are em-ployed to investigate Poisson equations and the fourth order equations in one dimen-sion.Meanwhile,p-version finite element methods with Chebyshev po...In this paper,the Chebyshev-Galerkin spectral approximations are em-ployed to investigate Poisson equations and the fourth order equations in one dimen-sion.Meanwhile,p-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations.The efficient and reliable a posteriori error esti-mators are given for different models.Furthermore,the a priori error estimators are derived independently.Some numerical experiments are performed to verify the the-oretical analysis for the a posteriori error indicators and a priori error estimations.展开更多
This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indica...This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.展开更多
A boundary collocation method based on the least-square technique and a corresponding adaptive computation process have been developed for the plate bending problem. The trial functions are constructed using a series ...A boundary collocation method based on the least-square technique and a corresponding adaptive computation process have been developed for the plate bending problem. The trial functions are constructed using a series of the biharmonic polynomials, and the local error indicators are given by the residuals of the energy density on the boundary. In comparison with the conventional collocation methods, the solution accuracy in the present method can be improved in an economical and efficient way. In order to demonstrate the efficiency and advantages of the adaptive boundary collocation method proposed in this paper, two numerical examples are presented for circular plates subjected to uniform loads and restrained by mixed boundary conditions. The numerical results for the examples show good agreement with ones presented in the literature.展开更多
文摘In order to solve the lack of relevant evaluation research on the accuracy of HMP155A humidity sensor calibration results in the past, this paper designs the corresponding experimental scheme, and obtains the corresponding calibration results according to the experimental scheme;Then the measurement uncertainty of the indication error in the calibration results is evaluated by GUM, and the corresponding extended uncertainty </span><i><span style="font-family:Verdana;">U</span></i><sub><span style="font-family:Verdana;">95</span></sub><span style="font-family:Verdana;"> is obtained. Finally, according to the requirements of JJF1094-2016 characteristic evaluation of measuring instruments, combined with the calibration results and the actual situation of </span><i><span style="font-family:Verdana;">U</span></i><sub><span style="font-family:Verdana;">95</span></sub><span style="font-family:Verdana;">, the conformity of the indication error of calibration is determined. The result is that each calibration point of the sensor meets the requirements of conformity determination and is within the qualified range. This research effectively makes up for the blank of the previous research on the conformity determination of the indication error of the calibration results and has strong theoretical and practical significance.
文摘As a kind of compulsory verification of the metering equipment, fuel tanker throughout the country, its accuracy is related to People's Daily life consumption. It is very important to introduce measurement uncertainty into conformity assessment in order to better judge the indication error of the tanker and ensure the accuracy and fairness of the tanker. This paper analyzes the measurement uncertainty of the calibration of indicator value error of the tanker, determines the application basis of the measurement uncertainty, and summarizes the application of the measurement uncertainty in the calibration of indicator value error of the tanker according to the uncertainty requirements of ISO/IEC 17025:2017, so as to help the verifier to make more accurate qualification judgment and avoid risks.
文摘In this article,we discuss the approach to solving a nonlinear PDE equation,specifically the p-Laplacian equation,with a general(nonlinear)boundary condition.We establish the existence and uniqueness of the solution,subject to certain assumptions outlined in this paper.To solve our nonlinear problem using the Finite Element Method(FEM),we derive an appropriate variational formulation.Additionally,we introduce a study of the residual a posteriori-error indicator,establishing both upper and lower bounds to control the error.The upper bound is determined using averaging interpolators in some quasi-norms defined by Barrett and Liu.Furthermore,we prove the equivalence between the residual error and the true error e=u−u_(h).Lastly,we perform a simulation of the p-Laplacian problem in the L-shape domain using a Matlab program in two-dimensional space.
基金E.Martínez-Paneda acknowledges financial support from the Royal Commission for the 1851 Exhibition through their Research Fellowship programme(RF496/2018).
文摘In this work,we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials(FGMs).A recovery type error indicator combined with quadtree decomposition is employed for adaptive mesh refinement.The proposed approach is capable of capturing the fracture process with a localized mesh refinement that provides notable gains in computational efficiency.The implementation is validated against experimental data and other numerical experiments on orthotropic materials with different material orientations.The results reveal an increase in the stiffness and the maximum force with increasing material orientation angle.The study is then extended to the analysis of orthotropic FGMs.It is observed that,if the gradation in fracture properties is neglected,the material gradient plays a secondary role,with the fracture behaviour being dominated by the orthotropy of the material.However,when the toughness increases along the crack propagation path,a substantial gain in fracture resistance is observed.
文摘This paper examines the forecasting performance of different kinds of GARCH model （GRACH, EGARCH, TARCH and APARCH） under the Normal, Student-t and Generalized error distributional assumption. We compare the effect of different distributional assumption on the GARCH models. The data we analyze are the daily stocks indexes for Shenzhen Stock Exchange （SSE） in China from April 3^rd, 1991 to April 14^th, 2005. We find that improvements of the overall estimation are achieved when asymmetric GARCH models are used with student-t distribution and generalized error distribution. Moreover, it is found that TARCH and GARCH models give better forecasting performance than EGARCH and APARCH models. In forecasting performance, the model under normal distribution gives more accurate forecasting performance than non-normal densities and generalized error distributions clearly outperform the student-t densities in case of SSE.
基金supported by the Hunan Provincial Natural Science Foundation of China.(Grant No.2023JJ50222).
文摘This paper focuses on constructing the adaptive analysis model based on the Finite Element Method(FEM)with an unstructured mesh,which includes taking full advantage of the two-dimensional triangle’s ability to discretize any complex model.The error indicator and h-type refinement scheme for FEM has been presented by providing a simple error indicator based on the difference value of nodal fundamental physical variables.It provides an effective measure of the error in the numerical solution,which can lead to an adaptive refinement scheme,determining the optimal location of new inserted nodes that are mainly distributed in the local high stress gradient domain.A numerical experiment is presented to demonstrate that the proposed error indicator reasonably tracks the distribution of the true error,and the effectiveness of the proposed adaptive analysis procedure,which achieves significantly higher convergence rates compared to the uniform mesh.
文摘Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms.An adaptive strategy based on theℜ-parameter is proposed for continuous flows,while a hybrid adaptive algorithm employing a combination of error indicators and theℜ-parameter is developed for discontinuous flows.Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.
基金This work was supported by National Natural Science Foun-dation of China(Grant No.11201212 and 11301252),CSC(No.201408380045)Promotive Research Fund for Excellent Young and Middle-Aged Scientists of Shandong Province(No.BS2012DX004)and AMEP of Linyi University.
文摘In this paper,the Chebyshev-Galerkin spectral approximations are em-ployed to investigate Poisson equations and the fourth order equations in one dimen-sion.Meanwhile,p-version finite element methods with Chebyshev polynomials are utilized to solve Poisson equations.The efficient and reliable a posteriori error esti-mators are given for different models.Furthermore,the a priori error estimators are derived independently.Some numerical experiments are performed to verify the the-oretical analysis for the a posteriori error indicators and a priori error estimations.
基金supported by the NSF of China(No.10971166)the National Basic Research Program(No.2005CB321703).
文摘This paper is concerned with a stabilized approach to low-order mixed finite element methods for the Stokes equations.We will provide a posteriori error analysis for the method.We present two a posteriori error indicators which will be demonstrated to be globally upper and locally lower bounds for the error of the finite element discretization.Finally two numerical experiments will be carried out to show the efficiency on constructing adaptive meshes.
基金the National Natural Science Foundation of China (No. 10472051)
文摘A boundary collocation method based on the least-square technique and a corresponding adaptive computation process have been developed for the plate bending problem. The trial functions are constructed using a series of the biharmonic polynomials, and the local error indicators are given by the residuals of the energy density on the boundary. In comparison with the conventional collocation methods, the solution accuracy in the present method can be improved in an economical and efficient way. In order to demonstrate the efficiency and advantages of the adaptive boundary collocation method proposed in this paper, two numerical examples are presented for circular plates subjected to uniform loads and restrained by mixed boundary conditions. The numerical results for the examples show good agreement with ones presented in the literature.
