Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implic...Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.展开更多
A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to t...A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.展开更多
The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcom...The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.展开更多
This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using prec...This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.展开更多
The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary diffe...The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.展开更多
An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise in...An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the展开更多
General purpose graphic processing unit (GPU) calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has ...General purpose graphic processing unit (GPU) calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method (PIM) for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.展开更多
In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the met...In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations(ODEs) are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.展开更多
This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matr...This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.展开更多
As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long...As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.展开更多
In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show...In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show that this model has a simple algorithm and high data utilization,avoids the negative influences caused by the correlation among the data acquired from the difference method and its accuracy is improved compared with the difference method.In addition,the strict weight of CPⅢprecise trigonometric leveling control network was also discussed in this paper.The results demonstrate that the ranging error of trigonometric leveling can be neglected when the vertical angle is less than 3 degrees.The accuracy of CPⅢprecise trigonometric leveling control network has not changed significantly before and after strict weight.展开更多
Droplet clusters levitating over the locally heated water surface are considered a very promising phe-nomenon of microfluidics for the potential use of the droplets as unique microreactors for microbio-logical experim...Droplet clusters levitating over the locally heated water surface are considered a very promising phe-nomenon of microfluidics for the potential use of the droplets as unique microreactors for microbio-logical experiments.A new optical method is suggested for precise measurements of the sub-micron levitation height of single droplets.The method is based on the analysis of variable colors of the inter-ference halo around the droplet.For the first time,it is possible to measure the extremely low downward velocity of droplets,which grow due to steam condensation.This velocity was found to be 5-8 nm/s.The height of the levitation of various droplets just before their coalescence with a layer of water was also determined.Such measurements might be used for the verification of sophisticated models for the droplet levitation to be developed for a very thin layer of humid air under the droplet when the Knudsen effect should be taken into account.展开更多
This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analys...This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analysis so that the parameter N, which has been takenas a constant and an independent pa- rameter without consideration ofthe problems in the original method, can be generated automaticallyby the algorithm itself.展开更多
Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix d...Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.展开更多
In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means t...In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.展开更多
With ongoing economic,scientific,and technological developments,the electronic devices used in daily lives are developing toward precision and miniaturization,and so the demand for high-precision manufacturing machine...With ongoing economic,scientific,and technological developments,the electronic devices used in daily lives are developing toward precision and miniaturization,and so the demand for high-precision manufacturing machinery is expanding.The most important piece of equipment in modern high-precision manufacturing is the macro-micro motion platform(M3P),which offers high speed,precision,and efficiency and has macro-micro motion coupling characteristics due to its mechanical design and composition of its driving components.Therefore,the design of the control system is crucial for the overall precision of the platform;conventional proportional–integral–derivative control cannot meet the system requirements,and so M3Ps are the subject of a growing range of modern control strategies.This paper begins by describing the development history of M3Ps,followed by their platform structure and motion control system components,and then in-depth assessments of the macro,micro,and macro-micro control systems.In addition to examining the advantages and disadvantages of current macro-micro motion control,recent technological breakthroughs are noted.Finally,based on existing problems,future directions for M3P control systems are given,and the present conclusions offer guidelines for future work on M3Ps.展开更多
The exact analytic method was given by [1] . It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high...The exact analytic method was given by [1] . It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams. It can have the fourth convergent precision without increasing computation work. The present computation method is not only simple but also fast. The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements. The correctness of the theory in this paper is confirmed.展开更多
A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative met...A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.展开更多
Moiré images that are generally termed as moiré fringes have been generated due to the interference of two repetitive gratings. These patterns can be applied to many uses in metrology such as the measurement...Moiré images that are generally termed as moiré fringes have been generated due to the interference of two repetitive gratings. These patterns can be applied to many uses in metrology such as the measurements of surface profilometry of aerofoil, stress-strain effects, thermal deformation and so on. Moreover, 3D surface reconstruction as well as movement characterization of linearly and rotary moving objects can be visualized and identified by the moiré imaging technique. Recently it is approached as an emerging tool in the fields of biotechnology-particularly in biomechanics, nanotechnology, broadband communication and optoelectronics as well. Conventional Moiré interferometry evaluates the interference of two light waves being reflected on a reference surface and the object to be profiled. However, satisfactions in the requirements for the current significant issues in obtaining accurate measurements regarding the information of the movements as well as the dimensional deformations of objects dealing with the online inspection in micro-level and nano-level are still challenging. Particularly, for the demand of the present real-time auto-inspection of different precise information of movements objects statistically and dynamically. In that case single light wave system makes the moiré sensing system easier and applicable in real-time imaging. Furthermore, avoiding the employment of expensive conventional imaging facilities in 3-D measurement in mechanical as well as bio-mechanical systems has become a critical problem to be tackled. Therefore, research has been conducted focusing on the objective of developing a simple but precise measuring tool based on a single wave moiré imaging technique for multidimensional motion sensing by employing simple image processing approaches. An experimental set-up with a small CMOS camera has been developed capable of measuring the motion of an object by using a simply ink-printed straight optical grating lines attached to the moving objects. Several model experiments have been conducted for getting the information of movements of an object by adopting several mouse click options only on the moiré image visible at the computer screen. After getting information of the moiré image by the proposed technique, the movements of the object have been accurately identified. The system has been found simple and faster compared to the other conventional methods as well.展开更多
With determination micro-Fe by 1, 10-phenanthroline spectrophotometry for example, they are systematically introduced the combinatorial measurement and regression analysis method application about metheodic principle,...With determination micro-Fe by 1, 10-phenanthroline spectrophotometry for example, they are systematically introduced the combinatorial measurement and regression analysis method application about metheodic principle, operation step and data processing in the instrumental analysis, including: calibration curve best linear equation is set up, measurand best linear equation is set up, and calculation of best value of a concentration. The results showed that mean of thrice determination , s = 0 μg/mL, RSD = 0. Results of preliminary application are simply introduced in the basic instrumental analysis for atomic absorption spectrophotometry, ion-selective electrodes, coulometry and polarographic analysis and are contrasted to results of normal measurements.展开更多
基金supported by ONR UMass Dartmouth Marine and UnderSea Technology(MUST)grant N00014-20-1-2849 under the project S31320000049160by DOE grant DE-SC0023164 sub-award RC114586-UMD+2 种基金by AFOSR grants FA9550-18-1-0383 and FA9550-23-1-0037supported by Michigan State University,by AFOSR grants FA9550-19-1-0281 and FA9550-18-1-0383by DOE grant DE-SC0023164.
文摘Additive Runge-Kutta methods designed for preserving highly accurate solutions in mixed-precision computation were previously proposed and analyzed.These specially designed methods use reduced precision for the implicit computations and full precision for the explicit computations.In this work,we analyze the stability properties of these methods and their sensitivity to the low-precision rounding errors,and demonstrate their performance in terms of accuracy and efficiency.We develop codes in FORTRAN and Julia to solve nonlinear systems of ODEs and PDEs using the mixed-precision additive Runge-Kutta(MP-ARK)methods.The convergence,accuracy,and runtime of these methods are explored.We show that for a given level of accuracy,suitably chosen MP-ARK methods may provide significant reductions in runtime.
基金supported by the National Natural Science Foundation of China (Nos. 10902020 and 10721062)
文摘A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.
文摘The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.
文摘This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.
文摘The quasi-Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations ( ODEs). And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge-Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases.
基金Project supported by the National Natural Science Foundation of China(Nos.10902020 and 10721062)
文摘An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the
基金supported by the National Natural Science Foundation of China (Nos 40974066 and 40821062)National Basic Research Program of China (No 2007CB209602)
文摘General purpose graphic processing unit (GPU) calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method (PIM) for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.
基金supported by the National Natural Science Foundation of China (11132004 and 51078145)the Natural Science Foundation of Guangdong Province (9251064101000016)
文摘In this paper we present a precise integration method based on high order multiple perturbation method and reduction method for solving a class of singular twopoint boundary value problems.Firstly,by employing the method of variable coefficient dimensional expanding,the non-homogeneous ordinary differential equations(ODEs) are transformed into homogeneous ODEs.Then the interval is divided evenly,and the transfer matrix in every subinterval is worked out using the high order multiple perturbation method,and a set of algebraic equations is given in the form of matrix by the precise integration relation for each segment,which is worked out by the reduction method.Finally numerical examples are elaboratedd to validate the present method.
基金Project supported by the National Natural Science Foundation of China(No.10672194)the China-Russia Cooperative Project(the National Natural Science Foundation of China and the Russian Foundation for Basic Research)(No.10811120012)
文摘This paper presents a precise method for solving singularly perturbed boundary-value problems with the boundary layer at one end. The method divides the interval evenly and gives a set of algebraic equations in a matrix form by the precise integration relationship of each segment. Substituting the boundary conditions into the algebraic equations, the coefficient matrix can be transformed to the block tridiagonal matrix. Considering the nature of the problem, an efficient reduction method is given for solving singular perturbation problems. Since the precise integration relationship introduces no discrete error in the discrete process, the present method has high precision. Numerical examples show the validity of the present method.
基金Supported by the National Natural Science Foundation of China(No.51575014,51505020)the Key Foundation Project of China Academy of Railway Sciences(No.2021YJ200).
文摘As a key transmission component in computer numerical control(CNC) machine tools,the ball screw mechanism(BSM) is usually investigated under working load conditions. Its accuracy degradation process is relatively long,which is not conducive to the design and development of new products. In this paper,the normal wear depth of the BSM nut raceway is calculated under the variable speed operation condition using the fractal wear analysis method and the BSM’s accelerated degradation proportional wear model. Parameters of the acceleration degradation model of the double-nut preloaded ball screw pair are calculated based on the physical simulation results. The accelerated degradation test platform of the BSM is designed and manufactured to calculate the raceway wear model when the lubrication condition is broken under the variable-speed inertial load and the boundary lubrication condition under the uniform speed state. Three load forces and two samples are selected for the accelerated degradation test of the BSM. The measured friction torque of the BSM is employed as the evaluation index of the accuracy degradation test. In addition,the life cycle of the accuracy retention is accurately calculated by employing the parameters of the physical simulation model of the BSM. The calculations mentioned above can be used to estimate BSM’s accuracy performance degradation law under normal operating conditions. The application of the proposed model provides a new research method for researching the precision retention of the BSM.
基金National Natural Science Foundation of China(No.41661091)。
文摘In view of the limitation of the difference method,the adjustment model of CPⅢprecise trigonometric leveling control network based on the parameter method was proposed in the present paper.The experiment results show that this model has a simple algorithm and high data utilization,avoids the negative influences caused by the correlation among the data acquired from the difference method and its accuracy is improved compared with the difference method.In addition,the strict weight of CPⅢprecise trigonometric leveling control network was also discussed in this paper.The results demonstrate that the ranging error of trigonometric leveling can be neglected when the vertical angle is less than 3 degrees.The accuracy of CPⅢprecise trigonometric leveling control network has not changed significantly before and after strict weight.
基金support by the Ministry of Science and Higher Education of the Russian Federation (project No.FEWZ-2023-0002).
文摘Droplet clusters levitating over the locally heated water surface are considered a very promising phe-nomenon of microfluidics for the potential use of the droplets as unique microreactors for microbio-logical experiments.A new optical method is suggested for precise measurements of the sub-micron levitation height of single droplets.The method is based on the analysis of variable colors of the inter-ference halo around the droplet.For the first time,it is possible to measure the extremely low downward velocity of droplets,which grow due to steam condensation.This velocity was found to be 5-8 nm/s.The height of the levitation of various droplets just before their coalescence with a layer of water was also determined.Such measurements might be used for the verification of sophisticated models for the droplet levitation to be developed for a very thin layer of humid air under the droplet when the Knudsen effect should be taken into account.
基金the National Natural Science Foundation of China (No.19872016,19872017)the National Key Basic Research Special Foundation (G1999032805)the Foundation for University Key Teachers by the Ministry of Education of China
文摘This paper presents an improved precise integration algorithm fortransient analysis of heat transfer and some other problems. Theoriginal precise integration method is improved by means of the inve-rse accuracy analysis so that the parameter N, which has been takenas a constant and an independent pa- rameter without consideration ofthe problems in the original method, can be generated automaticallyby the algorithm itself.
基金Project supported by the National Natural Science Foundation of China(Nos.60273048and60174023).
文摘Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.
基金supported by the National Key Technology R&D Program (Grant 2011BAJ02B01-02)the National Natural Science Foundation of China (Grant 11602065)
文摘In this paper, the spectral element method(SEM)is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem.In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases.Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
基金This research was supported financially by the China Postdoctoral Science Foundation,the National Natural Science Foundation of China(Grant No.51705132)the Young Backbone Teacher Training Program in Henan University of Technology,the Education Department of Henan Province Natural Science Project(Grant No.21A460006)the Natural Science Project of Henan Provincial Department of Science and Technology(Grant No.222102220088).
文摘With ongoing economic,scientific,and technological developments,the electronic devices used in daily lives are developing toward precision and miniaturization,and so the demand for high-precision manufacturing machinery is expanding.The most important piece of equipment in modern high-precision manufacturing is the macro-micro motion platform(M3P),which offers high speed,precision,and efficiency and has macro-micro motion coupling characteristics due to its mechanical design and composition of its driving components.Therefore,the design of the control system is crucial for the overall precision of the platform;conventional proportional–integral–derivative control cannot meet the system requirements,and so M3Ps are the subject of a growing range of modern control strategies.This paper begins by describing the development history of M3Ps,followed by their platform structure and motion control system components,and then in-depth assessments of the macro,micro,and macro-micro control systems.In addition to examining the advantages and disadvantages of current macro-micro motion control,recent technological breakthroughs are noted.Finally,based on existing problems,future directions for M3P control systems are given,and the present conclusions offer guidelines for future work on M3Ps.
文摘The exact analytic method was given by [1] . It can be used for arbitrary variable coefficient differential equations and the solution obtained can have the second order convergent precision. In this paper, a new high precision algorithm is given based on [1], through a bending problem of variable cross-section beams. It can have the fourth convergent precision without increasing computation work. The present computation method is not only simple but also fast. The numerical examples are given at the end of this paper which indicate that the high convergent precision can be obtained using only a few elements. The correctness of the theory in this paper is confirmed.
文摘A matrix equation solved in an eddy current analysis,??-??method based on a domain decomposition method becomes a complex symmetric system.In general,iterative method is used as the solver.Convergence of iterative method in an interface problem is improved by increasing an accuracy of a solution of an iterative method of a subdomain problem.However,it is difficult to improve the convergence by using a small convergence criterion in the subdomain problem.Therefore,authors propose a method to introduce double-double precision into the interface problem and the subdomain problem.This proposed method improves the convergence of the interface problem.In this paper,first,we describe proposed method.Second,we confirm validity of the method by using Team Workshop Problem 7,standard model for eddy current analysis.Finally,we show effectiveness of the method from two numerical results.
文摘Moiré images that are generally termed as moiré fringes have been generated due to the interference of two repetitive gratings. These patterns can be applied to many uses in metrology such as the measurements of surface profilometry of aerofoil, stress-strain effects, thermal deformation and so on. Moreover, 3D surface reconstruction as well as movement characterization of linearly and rotary moving objects can be visualized and identified by the moiré imaging technique. Recently it is approached as an emerging tool in the fields of biotechnology-particularly in biomechanics, nanotechnology, broadband communication and optoelectronics as well. Conventional Moiré interferometry evaluates the interference of two light waves being reflected on a reference surface and the object to be profiled. However, satisfactions in the requirements for the current significant issues in obtaining accurate measurements regarding the information of the movements as well as the dimensional deformations of objects dealing with the online inspection in micro-level and nano-level are still challenging. Particularly, for the demand of the present real-time auto-inspection of different precise information of movements objects statistically and dynamically. In that case single light wave system makes the moiré sensing system easier and applicable in real-time imaging. Furthermore, avoiding the employment of expensive conventional imaging facilities in 3-D measurement in mechanical as well as bio-mechanical systems has become a critical problem to be tackled. Therefore, research has been conducted focusing on the objective of developing a simple but precise measuring tool based on a single wave moiré imaging technique for multidimensional motion sensing by employing simple image processing approaches. An experimental set-up with a small CMOS camera has been developed capable of measuring the motion of an object by using a simply ink-printed straight optical grating lines attached to the moving objects. Several model experiments have been conducted for getting the information of movements of an object by adopting several mouse click options only on the moiré image visible at the computer screen. After getting information of the moiré image by the proposed technique, the movements of the object have been accurately identified. The system has been found simple and faster compared to the other conventional methods as well.
文摘With determination micro-Fe by 1, 10-phenanthroline spectrophotometry for example, they are systematically introduced the combinatorial measurement and regression analysis method application about metheodic principle, operation step and data processing in the instrumental analysis, including: calibration curve best linear equation is set up, measurand best linear equation is set up, and calculation of best value of a concentration. The results showed that mean of thrice determination , s = 0 μg/mL, RSD = 0. Results of preliminary application are simply introduced in the basic instrumental analysis for atomic absorption spectrophotometry, ion-selective electrodes, coulometry and polarographic analysis and are contrasted to results of normal measurements.