In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and un...In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and unconditionally stable in energy.Subsequently,we provide a detailed implementation procedure for full decoupling.Thus,at each time step,only a series of linear differential equations with constant coefficients need to be solved.To validate the effectiveness of our approach,we conduct an error analysis for this first-order scheme.Finally,some numerical experiments are provided to verify the energy dissipation of the system and the convergence of the proposed approach.展开更多
Chinese non-English majors are a large group of English learners.In the process of English pronunciation acquisition,issues such as incomplete phonological knowledge,transfer of mother tongue,and overgeneralization,le...Chinese non-English majors are a large group of English learners.In the process of English pronunciation acquisition,issues such as incomplete phonological knowledge,transfer of mother tongue,and overgeneralization,lead to confusion of phonemes and stress,misunderstanding of syllable structure,and errors of assimilation,drop,and epenthesis.The accuracy of English pronunciation can only be improved by knowing both English and Chinese phonological systems,strengthening the teaching of English phonological knowledge,and adopting various phonological training activities.展开更多
Based on error analysis, the influence of error sources on strapdown inertial navigation systems is discussed. And the maximum permissible component tolerances are established. In order to achieve the desired accuracy...Based on error analysis, the influence of error sources on strapdown inertial navigation systems is discussed. And the maximum permissible component tolerances are established. In order to achieve the desired accuracy (defined by circular error probability), the types of appropriate sensors are chosen. The inertial measurement unit (IMU) is composed of those sensors. It is necessary to calibrate the sensors to obtain their error model coefficients of IMU. After calibration tests, the accuracy is calculated by uniform design method and it is proved that the accuracy of IMU is satisfied for the desired goal.展开更多
In order to monitor the working state of piston motor and measure its instantaneous rotation speed accurately, the measuring principle and method of instantaneous rotation speed based on industrial personal computer a...In order to monitor the working state of piston motor and measure its instantaneous rotation speed accurately, the measuring principle and method of instantaneous rotation speed based on industrial personal computer and data acquisition card are introduced, and the major error source, influence mechanism and processing method of data quantization error are dis- cussed. By means of hybrid programming approach of LabVIEW and MATLAB, the instantaneous rotation speed measurement system for the piston motor in variable speed hydraulic system is designed. The simulation and experimental results show that the designed instantaneous speed measurement system is feasible. Furthermore, the sampling frequency has an important influ- ence on the instantaneous rotation speed measurement of piston motor and higher sampling frequency can lower quantization er- ror and improve measurement accuracy.展开更多
As a field in applied linguistics, error analysis is not only an instrument for language acquisition research but also an auxiliary tool for language teaching. It plays a significant role both in exploring the learnin...As a field in applied linguistics, error analysis is not only an instrument for language acquisition research but also an auxiliary tool for language teaching. It plays a significant role both in exploring the learning rules and improving the teaching of foreign languages. With this information, teachers could adjust their teaching plan and make their teaching more effective. In this paper I present some common errors that my students make in their learning process. Based on these, a further elaboration on how to correct errors, including the attitudes to them, the integrative principles, the concrete methods and techniques for error correction is discussed as well.展开更多
A Chebyshev fitting way for a propeller atlas across four quadrants is discussed. As an example, Chebyshev polynomial fitting results and its error analysis are given. Because it’s difficult generally to get a propel...A Chebyshev fitting way for a propeller atlas across four quadrants is discussed. As an example, Chebyshev polynomial fitting results and its error analysis are given. Because it’s difficult generally to get a propeller atlas across four quadrants, a way is used to construct an alternative with higher accuracy based on the properties. As an application example, an alternative for the propeller property of a Deep Submergence Vehicle across four quadrants is given practically and a simulation model of the four quadrants propeller for dynamic condition is set up. The model lays a foundation for DSV full operating-condition movement simulation. A lot of simulation work shows that the results are very close to the practical data and, therefore, are effective.展开更多
Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network mode...Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.展开更多
High surface area activated carbons were produced by thermal activation of waste bamboo scaffolding with phosphoric acid.Single component equilibrium dye adsorption was conducted on the carbons produced and compared w...High surface area activated carbons were produced by thermal activation of waste bamboo scaffolding with phosphoric acid.Single component equilibrium dye adsorption was conducted on the carbons produced and compared with a commercially available carbon.Two acid dyes with different molecular sizes,namely Acid Yellow 117(AY117) and Acid Blue 25(AB25),were used to evaluate the adsorption capacity of the produced carbons.It was found that the dye with smaller molecular size,AB 25,was readily adsorbed onto the produced carbon,nearly three times higher than a commercially available carbon,while the larger size dye,AY117,showed little adsorption.The experimental data were analyzed using isotherm equations including Langmuir,Freundlich,Tempkin,Toth,Redlich-Peterson and Sips equations.The equilibrium data were then analyzed using five different non-linear error analysis methods.展开更多
A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Base...A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.展开更多
The deformation and residual stress generated by the welding process can seriously affect the use of components.As a result,it is very important to understand the evolution of stress and strain during the welding proc...The deformation and residual stress generated by the welding process can seriously affect the use of components.As a result,it is very important to understand the evolution of stress and strain during the welding process.The strain measurement method based on digital image correlation(DIC)is an excellent method to detect welding strain and residual stress.The out-of-plane translation and out-of-plane rotation introduce errors to the two-dimensional DIC.In this paper,the causes of errors are analyzed theoretically,and the formulas of errors caused by the out-of-plane displacement and the out-of-plane rotation are derived.The out-of-plane translation experiment and the out-of-plane rotation experiment were carried out to verify the theory,and the experimental results are consistent with the theoretical analysis results.The error caused by the out-of-plane translation can be reduced by increasing the object distance;the error caused by the out-of-plane rotation is greatly affected by the rotation angle.展开更多
Forming limit curves（FLCs） are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are no...Forming limit curves（FLCs） are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are non-negligible under warm/hot stamping conditions. To investigate the experimental errors, experiments for obtaining the FLCs of the AA5754 are conducted at 250℃. Then, FE models are created and validated on the basis of experimental results. A number of FE simulations are carried out for FLC test-pieces and punches with different geometry configurations and varying friction coefficients between the test-piece and the punch. The errors for all the test conditions are predicted and analyzed. Particular attention of error analysis is paid to two special cases, namely, the biaxial FLC test and the uniaxial FLC test. The failure location and the variation of the error with respect to the friction coefficient are studied as well. The results obtained from the FLC tests and the above analyses show that, for the biaxial tension state, the friction coefficient should be controlled within 0.15 to avoid significant shifting of the necking location away from the center of the punch; for the uniaxial tension state, the friction coefficient should be controlled within 0.1 to guarantee the validity of the data collected from FLC tests. The conclusions summarized are beneficial for obtaining accurate FLCs under warm/hot stamping conditions.展开更多
Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given ...Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem.展开更多
In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel fu...In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.展开更多
In this paper we bring up a Monte Carlo theory based method to measure the ground vegetation parameters,and make quantitative description of the error.The leaf area index is used as the example in the study.Its mean a...In this paper we bring up a Monte Carlo theory based method to measure the ground vegetation parameters,and make quantitative description of the error.The leaf area index is used as the example in the study.Its mean and variance stability at different scales or in different time is verified using both the computer simulation and the statistics of remotely sensed images.And the error of Monte Carlo sampling method is analyzed based on the normal distribution theory and the central-limit theorem.The results show that the variance of leaf area index in the same area is stable at certain scales or in the same time of different years.The difference between experimental results and theoretical ones is small.The sig-nificance of this study is to establish a measurement procedure of ground vegetation pa-rameters with an error control system.展开更多
Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the ...Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the geometric errors of the tracking mirror mechanism. Proper calibration of LTS is essential prior to the use of it for metrology. A kinematics model that describes not only the motion but also the geometric variations of LTS is developed. Through error analysis of the proposed model, it is claimed that gimbals axis misalignments and tracking mirror center off-set are the key contributors to measuring errors of LTS. A self-calibration method is presented of calibrating LTS with planar constraints. Various calibration strategies utilizing single-plane and multiple-plane constraints are proposed for different situations. For each calibration strategy, issues about the error parameter estimation of LTS are exploded to find out in which conditions these parameters can be uniquely estimated. Moreover, these conditions reveal the applicability of the planar constraints to LTS self-calibration. Intensive studies have been made to check validity of the theoretical results. The results show that the measuring accuracy of LTS has increased by 5 times since this technique for calibration is used.展开更多
Based on the theories of error and error analysis, the article is trying to explore the effect of error and error analysis on SLA. Thus give some advice to the language teachers and language learners.
This paper presents a non-smooth multibody dynamic formulation and error analysis of an antenna pointing mechanism including frictional spatial revolute joints(FSRJs)with small clearance in the framework of the specia...This paper presents a non-smooth multibody dynamic formulation and error analysis of an antenna pointing mechanism including frictional spatial revolute joints(FSRJs)with small clearance in the framework of the special Euclidian group SE(3).The formulation leads to an inertial frame-invariant,a compact and unified description for rigid bodies and spatial revolute joints(SRJs).The geometric constraint of the bearing is covered by four open semi-cylinders,which can be treated as bilateral constraints assuming that the impact effects are negligible.The frictional contact problem is formulated as a horizontal linear complementary problem(HLCP),which is embedded in the Lie-group integration scheme.Error of the antenna pointing mechanism is modeled by means of the adjoint transformation and POE-based formula.The evolution of errors is obtained through the solution of non-smooth dynamics.The obtained numerical results illustrate the influences of FSRJs in dynamics modeling and error analysis of the antenna pointing mechanism.展开更多
Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential eq...Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.展开更多
MEMS accelerometers are widely used in various fields due to their small size and low cost,and have good application prospects.However,the low accuracy limits its range of applications.To ensure data accuracy and safe...MEMS accelerometers are widely used in various fields due to their small size and low cost,and have good application prospects.However,the low accuracy limits its range of applications.To ensure data accuracy and safety we need to calibrate MEMS accelerometers.Many authors have improved accelerometer accuracy by calculating calibration parameters,and a large number of published calibration methods have been confusing.In this context,this paper introduces these techniques and methods,analyzes and summarizes the main error models and calibration procedures,and provides useful suggestions.Finally,the content of the accelerometer calibration method needs to be overcome.展开更多
Ebulliometric method based on the error analysis equation is presented for systems with the large phase equilibrium constant. Application is given for the determination and calculation of binary vapor-liquid equilibri...Ebulliometric method based on the error analysis equation is presented for systems with the large phase equilibrium constant. Application is given for the determination and calculation of binary vapor-liquid equilibrium data for the ethanol+n-hexane system. It is also given the comparison results between the ebulliometric method based on the error analysis equation and the quasi-static method.展开更多
基金Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘In this paper,we develop a multi-scalar auxiliary variables(MSAV)scheme for the Cahn-Hilliard Magnetohydrodynamics system by introducing two scalar auxiliary variables(SAV).This scheme is linear,fully decoupled and unconditionally stable in energy.Subsequently,we provide a detailed implementation procedure for full decoupling.Thus,at each time step,only a series of linear differential equations with constant coefficients need to be solved.To validate the effectiveness of our approach,we conduct an error analysis for this first-order scheme.Finally,some numerical experiments are provided to verify the energy dissipation of the system and the convergence of the proposed approach.
文摘Chinese non-English majors are a large group of English learners.In the process of English pronunciation acquisition,issues such as incomplete phonological knowledge,transfer of mother tongue,and overgeneralization,lead to confusion of phonemes and stress,misunderstanding of syllable structure,and errors of assimilation,drop,and epenthesis.The accuracy of English pronunciation can only be improved by knowing both English and Chinese phonological systems,strengthening the teaching of English phonological knowledge,and adopting various phonological training activities.
文摘Based on error analysis, the influence of error sources on strapdown inertial navigation systems is discussed. And the maximum permissible component tolerances are established. In order to achieve the desired accuracy (defined by circular error probability), the types of appropriate sensors are chosen. The inertial measurement unit (IMU) is composed of those sensors. It is necessary to calibrate the sensors to obtain their error model coefficients of IMU. After calibration tests, the accuracy is calculated by uniform design method and it is proved that the accuracy of IMU is satisfied for the desired goal.
基金National Natural Science Foundation of China(No.51275375,No.51509006)Shaanxi Provincial Natural Science Basic Research Plan(No.2014JQ7246)+1 种基金The Science and Technology of Hubei Province(No.B2015115)Doctoral Research Foundation of Hubei University of Automotive Technology(No.BK201403)
文摘In order to monitor the working state of piston motor and measure its instantaneous rotation speed accurately, the measuring principle and method of instantaneous rotation speed based on industrial personal computer and data acquisition card are introduced, and the major error source, influence mechanism and processing method of data quantization error are dis- cussed. By means of hybrid programming approach of LabVIEW and MATLAB, the instantaneous rotation speed measurement system for the piston motor in variable speed hydraulic system is designed. The simulation and experimental results show that the designed instantaneous speed measurement system is feasible. Furthermore, the sampling frequency has an important influ- ence on the instantaneous rotation speed measurement of piston motor and higher sampling frequency can lower quantization er- ror and improve measurement accuracy.
文摘As a field in applied linguistics, error analysis is not only an instrument for language acquisition research but also an auxiliary tool for language teaching. It plays a significant role both in exploring the learning rules and improving the teaching of foreign languages. With this information, teachers could adjust their teaching plan and make their teaching more effective. In this paper I present some common errors that my students make in their learning process. Based on these, a further elaboration on how to correct errors, including the attitudes to them, the integrative principles, the concrete methods and techniques for error correction is discussed as well.
文摘A Chebyshev fitting way for a propeller atlas across four quadrants is discussed. As an example, Chebyshev polynomial fitting results and its error analysis are given. Because it’s difficult generally to get a propeller atlas across four quadrants, a way is used to construct an alternative with higher accuracy based on the properties. As an application example, an alternative for the propeller property of a Deep Submergence Vehicle across four quadrants is given practically and a simulation model of the four quadrants propeller for dynamic condition is set up. The model lays a foundation for DSV full operating-condition movement simulation. A lot of simulation work shows that the results are very close to the practical data and, therefore, are effective.
基金Project(51321065)supported by the Innovative Research Groups of the National Natural Science Foundation of ChinaProject(2013CB035904)supported by the National Basic Research Program of China(973 Program)Project(51439005)supported by the National Natural Science Foundation of China
文摘Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.
基金the support of the Research Grant Council of Hong Kong SARthe Innovation and Technology Fund of Hong Kong SAR+1 种基金the Hong Kong University of Science and TechnologyGreen Island International
文摘High surface area activated carbons were produced by thermal activation of waste bamboo scaffolding with phosphoric acid.Single component equilibrium dye adsorption was conducted on the carbons produced and compared with a commercially available carbon.Two acid dyes with different molecular sizes,namely Acid Yellow 117(AY117) and Acid Blue 25(AB25),were used to evaluate the adsorption capacity of the produced carbons.It was found that the dye with smaller molecular size,AB 25,was readily adsorbed onto the produced carbon,nearly three times higher than a commercially available carbon,while the larger size dye,AY117,showed little adsorption.The experimental data were analyzed using isotherm equations including Langmuir,Freundlich,Tempkin,Toth,Redlich-Peterson and Sips equations.The equilibrium data were then analyzed using five different non-linear error analysis methods.
基金Preject 50225519 supported by the National Outstanding Youth Science Foundation of China
文摘A three degree-of-freedom (DOF) planar changeable parallel mechanism is designed by means of control of different drive parameters. This mechanism possesses the characteristics of two kinds of parallel mechanism. Based on its topologic structure, a coordinate system for position analysis is set-up and the forward kinematic solutions are analyzed. It was found that the parallel mechanism is partially decoupled. The relationship between original errors and position-stance error of moving platform is built according to the complete differential-coefficient theory. Then we present a special example with theory values and errors to evaluate the error model, and numerical error solutions are gained. The investigations concentrating on mechanism errors and actuator errors show that the mechanism errors have more influences on the position-stance of the moving platform. It is demonstrated that improving manufacturing and assembly techniques can greatly reduce the moving platform error. The small change in position-stance error in different kinematic positions proves that the error-compensation of software can improve considerably the precision of parallel mechanism.
文摘The deformation and residual stress generated by the welding process can seriously affect the use of components.As a result,it is very important to understand the evolution of stress and strain during the welding process.The strain measurement method based on digital image correlation(DIC)is an excellent method to detect welding strain and residual stress.The out-of-plane translation and out-of-plane rotation introduce errors to the two-dimensional DIC.In this paper,the causes of errors are analyzed theoretically,and the formulas of errors caused by the out-of-plane displacement and the out-of-plane rotation are derived.The out-of-plane translation experiment and the out-of-plane rotation experiment were carried out to verify the theory,and the experimental results are consistent with the theoretical analysis results.The error caused by the out-of-plane translation can be reduced by increasing the object distance;the error caused by the out-of-plane rotation is greatly affected by the rotation angle.
基金Supported by National Natural Science Foundation of China(Grant No.51375201)Jilin Province Science and Technology Development Plan(Grant No.20130101048JC)Open Research Fund of Shanghai Key Laboratory of Digital Manufacturer for Thin-walled Structure(Grant No.2013001)
文摘Forming limit curves（FLCs） are commonly used for evaluating the formability of sheet metals. However, it is difficult to obtain the FLCs with desirable accuracy by experiments due to that the friction effects are non-negligible under warm/hot stamping conditions. To investigate the experimental errors, experiments for obtaining the FLCs of the AA5754 are conducted at 250℃. Then, FE models are created and validated on the basis of experimental results. A number of FE simulations are carried out for FLC test-pieces and punches with different geometry configurations and varying friction coefficients between the test-piece and the punch. The errors for all the test conditions are predicted and analyzed. Particular attention of error analysis is paid to two special cases, namely, the biaxial FLC test and the uniaxial FLC test. The failure location and the variation of the error with respect to the friction coefficient are studied as well. The results obtained from the FLC tests and the above analyses show that, for the biaxial tension state, the friction coefficient should be controlled within 0.15 to avoid significant shifting of the necking location away from the center of the punch; for the uniaxial tension state, the friction coefficient should be controlled within 0.1 to guarantee the validity of the data collected from FLC tests. The conclusions summarized are beneficial for obtaining accurate FLCs under warm/hot stamping conditions.
基金Supported by the National Natural Science Foundation of China (10871178)the Natural Science Foundation(Y606154)the Foundation of the Eduction Department of Zhejiang Province of China (Y200804008)
文摘Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the convergence ball of Ostrowski-Traub＇s method is obtained. An error analysis is given which matches the convergence order of the method. Finally, two examples are provided to show applications of our theorem.
文摘In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.
基金National Natural Science Foundation of China,No.41171262
文摘In this paper we bring up a Monte Carlo theory based method to measure the ground vegetation parameters,and make quantitative description of the error.The leaf area index is used as the example in the study.Its mean and variance stability at different scales or in different time is verified using both the computer simulation and the statistics of remotely sensed images.And the error of Monte Carlo sampling method is analyzed based on the normal distribution theory and the central-limit theorem.The results show that the variance of leaf area index in the same area is stable at certain scales or in the same time of different years.The difference between experimental results and theoretical ones is small.The sig-nificance of this study is to establish a measurement procedure of ground vegetation pa-rameters with an error control system.
基金National Natural Science Foundation of China (No. 50475038).
文摘Laser tracking system （LTS） is an advanced device for large size 3D coordinates measuring with the advantages of broad range, high speed and high accuracy. However, its measuring accuracy is highly dominated by the geometric errors of the tracking mirror mechanism. Proper calibration of LTS is essential prior to the use of it for metrology. A kinematics model that describes not only the motion but also the geometric variations of LTS is developed. Through error analysis of the proposed model, it is claimed that gimbals axis misalignments and tracking mirror center off-set are the key contributors to measuring errors of LTS. A self-calibration method is presented of calibrating LTS with planar constraints. Various calibration strategies utilizing single-plane and multiple-plane constraints are proposed for different situations. For each calibration strategy, issues about the error parameter estimation of LTS are exploded to find out in which conditions these parameters can be uniquely estimated. Moreover, these conditions reveal the applicability of the planar constraints to LTS self-calibration. Intensive studies have been made to check validity of the theoretical results. The results show that the measuring accuracy of LTS has increased by 5 times since this technique for calibration is used.
文摘Based on the theories of error and error analysis, the article is trying to explore the effect of error and error analysis on SLA. Thus give some advice to the language teachers and language learners.
基金supported by the National Natural Science Foundation of China(No.51635002 Key Program,52075016,U20A20281)。
文摘This paper presents a non-smooth multibody dynamic formulation and error analysis of an antenna pointing mechanism including frictional spatial revolute joints(FSRJs)with small clearance in the framework of the special Euclidian group SE(3).The formulation leads to an inertial frame-invariant,a compact and unified description for rigid bodies and spatial revolute joints(SRJs).The geometric constraint of the bearing is covered by four open semi-cylinders,which can be treated as bilateral constraints assuming that the impact effects are negligible.The frictional contact problem is formulated as a horizontal linear complementary problem(HLCP),which is embedded in the Lie-group integration scheme.Error of the antenna pointing mechanism is modeled by means of the adjoint transformation and POE-based formula.The evolution of errors is obtained through the solution of non-smooth dynamics.The obtained numerical results illustrate the influences of FSRJs in dynamics modeling and error analysis of the antenna pointing mechanism.
基金This project was supported by the National Natural Science Foundation of China (No. 19871080).
文摘Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.
基金This work has received funding from 5150 Spring Specialists(05492018012)the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.701697,Major Program of the National Social Science Fund of China(Grant No.17ZDA092)+1 种基金Basic Research Programs(Natural Science Foundation)of Jiangsu Province(BK20180794)333 High-Level Talent Cultivation Project of Jiangsu Province(BRA2018332)and the PAPD fund.
文摘MEMS accelerometers are widely used in various fields due to their small size and low cost,and have good application prospects.However,the low accuracy limits its range of applications.To ensure data accuracy and safety we need to calibrate MEMS accelerometers.Many authors have improved accelerometer accuracy by calculating calibration parameters,and a large number of published calibration methods have been confusing.In this context,this paper introduces these techniques and methods,analyzes and summarizes the main error models and calibration procedures,and provides useful suggestions.Finally,the content of the accelerometer calibration method needs to be overcome.
基金Supported by the National Natural Science Foundation of China(No. 29976035) and the Natural Science Foundation of Zhejiang Province.
文摘Ebulliometric method based on the error analysis equation is presented for systems with the large phase equilibrium constant. Application is given for the determination and calculation of binary vapor-liquid equilibrium data for the ethanol+n-hexane system. It is also given the comparison results between the ebulliometric method based on the error analysis equation and the quasi-static method.
