This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the...This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.展开更多
Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the pred...Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.展开更多
The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (...The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.展开更多
Model error is one of the key factors restricting the accuracy of numerical weather prediction (NWP). Considering the continuous evolution of the atmosphere, the observed data (ignoring the measurement error) can ...Model error is one of the key factors restricting the accuracy of numerical weather prediction (NWP). Considering the continuous evolution of the atmosphere, the observed data (ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers' equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.展开更多
In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current ...In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.展开更多
This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-conn...This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.展开更多
An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse probl...An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.展开更多
Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different ...Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass (3 kD,10 kD,40 kD,70 kD,2 000 kD) were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.展开更多
Fault diagnosis of liquid rocket propulsion systems (LRPSs) is a very important issue in space launch activities particularly when manned space missions are accompanied, since the safety and reliability can be signi...Fault diagnosis of liquid rocket propulsion systems (LRPSs) is a very important issue in space launch activities particularly when manned space missions are accompanied, since the safety and reliability can be significantly enhanced by exploiting an efficient fault diagnosis system. Currently, inverse problem-based diagnosis has attracted a great deal of research attention in fault diagnosis domain. This methodology provides a new strategy to model-based fault diagnosis for monitoring the health of propulsion systems. To solve the inverse problems arising from the fault diagnosis of LRPSs, GAs have been adopted in recent years as the first and effective choice of available numerical optimization tools. However, the GA has many control parameters to be chosen in advance and there still lack sound theoretical tools to analyze the effects of these parameters on diagnostic performance analytically. In this paper a comparative study of the influence of GA parameters on diagnostic results is conducted by performing a series of numerical experiments. The objective of this study is to investigate the contribution of individual algorithm parameter to final diagnostic result and provide reasonable estimates for choosing GA parameters in the inverse problem-based fault diagnosis of LRPSs. Some constructive remarks are made in conclusion and will be helpful for the implementation of GA to the fault diagnosis practice of LRPSs in the future.展开更多
A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique ...A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.展开更多
In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid.The implicit n...In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid.展开更多
To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy curre...To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.展开更多
An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors (MEs) in past intervals. Given t...An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors (MEs) in past intervals. Given the analyses, the ME in each interval (6 h) between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year (2001-2005) GRAPES- GFS (Global Forecast System of the Global and Regional Assimilation and Prediction System) error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.展开更多
A family of variational principles (VP) has been developed for the unsteady inverse problem of the second type I B. It opens new ways for the inverse shape design of unsteady airfoils and can serve as key basis of m...A family of variational principles (VP) has been developed for the unsteady inverse problem of the second type I B. It opens new ways for the inverse shape design of unsteady airfoils and can serve as key basis of multipoint inverse shape design of steady airfoils and cascades.展开更多
The tridiagonal coefficient matrix for the "fixed-fixed" spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring...The tridiagonal coefficient matrix for the "fixed-fixed" spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the "fixed-fixed" and "fixed-fres" spring-mass systems. An example was given to illustrate the results.展开更多
This paper presents a formulation and solution for the inverse problem of nonholonomic dynamics: to find the form of nonholonomic constraints when some integrals are given and to find the generalized reactive forces o...This paper presents a formulation and solution for the inverse problem of nonholonomic dynamics: to find the form of nonholonomic constraints when some integrals are given and to find the generalized reactive forces of constraint acting on the system when the expression of the kinetic energy is given. An example is given to illustrate the application of the result.展开更多
Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devot...Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.展开更多
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ...An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.展开更多
To determine a variation of pipe's inner geometric shape as due to etch, the three-layered feedforward artificial neural network is used in the inverse analysis through observing the elastoplastic strains of the o...To determine a variation of pipe's inner geometric shape as due to etch, the three-layered feedforward artificial neural network is used in the inverse analysis through observing the elastoplastic strains of the outer wall under the working inner pressure. Because of different kinds of inner wail radii and eccentricity. several groups of strains calculated with computational mechanics are used for the network to do learning. Numerical calculation demonstrates that this method is effective and the estimated inner wall geometric parameters have high precision.展开更多
The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equippi...The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10272021, 10572021) and the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022).
文摘This paper presents an inverse problem in analytical dynamics. The inverse problem is to construct the Lagrangian when the integrals of a system are given. Firstly, the differential equations are obtained by using the time derivative of the integrals. Secondly, the differential equations can be written in the Lagrange equations under certain conditions and the Lagrangian can be obtained. Finally, two examples are given to illustrate the application of the result.
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘Errors inevitably exist in numerical weather prediction (NWP) due to imperfect numeric and physical parameterizations. To eliminate these errors, by considering NWP as an inverse problem, an unknown term in the prediction equations can be estimated inversely by using the past data, which are presumed to represent the imperfection of the NWP model (model error, denoted as ME). In this first paper of a two-part series, an iteration method for obtaining the MEs in past intervals is presented, and the results from testing its convergence in idealized experiments are reported. Moreover, two batches of iteration tests were applied in the global forecast system of the Global and Regional Assimilation and Prediction System (GRAPES-GFS) for July-August 2009 and January-February 2010. The datasets associated with the initial conditions and sea surface temperature (SST) were both based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results showed that 6th h forecast errors were reduced to 10% of their original value after a 20-step iteration. Then, off-line forecast error corrections were estimated linearly based on the 2-month mean MEs and compared with forecast errors. The estimated error corrections agreed well with the forecast errors, but the linear growth rate of the estimation was steeper than the forecast error. The advantage of this iteration method is that the MEs can provide the foundation for online correction. A larger proportion of the forecast errors can be expected to be canceled out by properly introducing the model error correction into GRAPES-GFS.
文摘The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0.
基金Project supported by the Special Scientific Research Project for Public Interest(Grant No.GYHY201206009)the Fundamental Research Funds for the Central Universities,China(Grant Nos.lzujbky-2012-13 and lzujbky-2013-11)the National Basic Research Program of China(Grant Nos.2012CB955902 and 2013CB430204)
文摘Model error is one of the key factors restricting the accuracy of numerical weather prediction (NWP). Considering the continuous evolution of the atmosphere, the observed data (ignoring the measurement error) can be viewed as a series of solutions of an accurate model governing the actual atmosphere. Model error is represented as an unknown term in the accurate model, thus NWP can be considered as an inverse problem to uncover the unknown error term. The inverse problem models can absorb long periods of observed data to generate model error correction procedures. They thus resolve the deficiency and faultiness of the NWP schemes employing only the initial-time data. In this study we construct two inverse problem models to estimate and extrapolate the time-varying and spatial-varying model errors in both the historical and forecast periods by using recent observations and analogue phenomena of the atmosphere. Numerical experiment on Burgers' equation has illustrated the substantial forecast improvement using inverse problem algorithms. The proposed inverse problem methods of suppressing NWP errors will be useful in future high accuracy applications of NWP.
基金Supported by the National Natural Science Foundation of China(11971433)First Class Discipline of Zhe-jiang-A(Zhejiang Gongshang University-Statistics,1020JYN4120004G-091),Graduate Scientic Research and Innovation Foundation of Zhejiang Gongshang University.
文摘In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable.
文摘This paper studies the influence of a finite container on an ideal gas.The trace of the heat kernel (t) =exp, where are the eigenvalues of the negative Laplacian -in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum ft which is surrounded by simply connected bounded domains Ωi with smooth boundaries Ωi(i = 1,… ,m) where the Dirichlet, Neumann and Robin boundary conditions on Ωi(i = 1,…,m) are considered. Some geometrical properties of Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω are examined by using the asymptotic expansions of (t) for short-time t. It is shown that the ideal gas can not feel the shape of its container Ω, although it can feel some geometrical properties of it.
基金The project supported by the National Natural Science Foundation of China(10272011)
文摘An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.
基金supported by a grant from the National Natural Science Foundation of China (NSFC) No. 81070826/30872886/30400497Sponsored by Shanghai Rising-Star Program No. 09QA1403700+1 种基金funded by Shanghai Leading Academic Discipline Project (Project Number: S30206)the Science and Technology Commission of Shanghai (08DZ2271100)
文摘Aim The purpose of this study was to develop a mathe-matical model to quantitatively describe the passive trans-port of macromolecules within dental biofilms. Methodology Fluorescently labeled dextrans with different molecular mass (3 kD,10 kD,40 kD,70 kD,2 000 kD) were used as a series of diffusion probes. Streptococcus mutans,Streptococcus sanguinis,Actinomyces naeslundii and Fusobacterium nucleatum were used as inocula for biofilm formation. The diffusion processes of different probes through the in vitro biofilm were recorded with a confocal laser microscope. Results Mathematical function of biofilm penetration was constructed on the basis of the inverse problem method. Based on this function,not only the relationship between average concentration of steady-state and molecule weights can be analyzed,but also that between penetrative time and molecule weights. Conclusion This can be used to predict the effective concentration and the penetrative time of anti-biofilm medicines that can diffuse through oral biofilm. Further-more,an improved model for large molecule is proposed by considering the exchange time at the upper boundary of the dental biofilm.
基金This work was supported by the National Natural Science Foundation of China(No.50106005)
文摘Fault diagnosis of liquid rocket propulsion systems (LRPSs) is a very important issue in space launch activities particularly when manned space missions are accompanied, since the safety and reliability can be significantly enhanced by exploiting an efficient fault diagnosis system. Currently, inverse problem-based diagnosis has attracted a great deal of research attention in fault diagnosis domain. This methodology provides a new strategy to model-based fault diagnosis for monitoring the health of propulsion systems. To solve the inverse problems arising from the fault diagnosis of LRPSs, GAs have been adopted in recent years as the first and effective choice of available numerical optimization tools. However, the GA has many control parameters to be chosen in advance and there still lack sound theoretical tools to analyze the effects of these parameters on diagnostic performance analytically. In this paper a comparative study of the influence of GA parameters on diagnostic results is conducted by performing a series of numerical experiments. The objective of this study is to investigate the contribution of individual algorithm parameter to final diagnostic result and provide reasonable estimates for choosing GA parameters in the inverse problem-based fault diagnosis of LRPSs. Some constructive remarks are made in conclusion and will be helpful for the implementation of GA to the fault diagnosis practice of LRPSs in the future.
文摘A new widly convergent method for solving the problem of operator identification is illustrated. Numerical simulations are carried out to test the feasibility and to study the general characteristics of the technique without the real measurement data. This technique is a direct application of the continuation homo-topy method for solving nonlinear systems of equations. It is found that this method does give excellent results in solving the inverse problem of the elliptic differential equations.
基金supported by the National Natural Science Foundation of China(Grants 11472161,11102102,and 91130017)the Independent Innovation Foundation of Shandong University(Grant 2013ZRYQ002)the Natural Science Foundation of Shandong Province(Grant ZR2014AQ015)
文摘In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid.The implicit numerical method is employed to solve the direct problem.For the inverse problem,we first obtain the fractional sensitivity equation by means of the digamma function,and then we propose an efficient numerical method,that is,the Levenberg-Marquardt algorithm based on a fractional derivative,to estimate the unknown order of a Riemann-Liouville fractional derivative.In order to demonstrate the effectiveness of the proposed numerical method,two cases in which the measurement values contain random measurement error or not are considered.The computational results demonstrate that the proposed numerical method could efficiently obtain the optimal estimation of the unknown order of a RiemannLiouville fractional derivative for a fractional Stokes' first problem for a heated generalized second grade fluid.
基金supported by the National Defense Basic Technology Research Program of China(Grant No.Z132013T001)
文摘To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.
基金funded by the National Natural Science Foundation Science Fund for Youth (Grant No.41405095)the Key Projects in the National Science and Technology Pillar Program during the Twelfth Fiveyear Plan Period (Grant No.2012BAC22B02)the National Natural Science Foundation Science Fund for Creative Research Groups (Grant No.41221064)
文摘An online systematic error correction is presented and examined as a technique to improve the accuracy of real-time numerical weather prediction, based on the dataset of model errors (MEs) in past intervals. Given the analyses, the ME in each interval (6 h) between two analyses can be iteratively obtained by introducing an unknown tendency term into the prediction equation, shown in Part I of this two-paper series. In this part, after analyzing the 5-year (2001-2005) GRAPES- GFS (Global Forecast System of the Global and Regional Assimilation and Prediction System) error patterns and evolution, a systematic model error correction is given based on the least-squares approach by firstly using the past MEs. To test the correction, we applied the approach in GRAPES-GFS for July 2009 and January 2010. The datasets associated with the initial condition and SST used in this study were based on NCEP (National Centers for Environmental Prediction) FNL (final) data. The results indicated that the Northern Hemispheric systematically underestimated equator-to-pole geopotential gradient and westerly wind of GRAPES-GFS were largely enhanced, and the biases of temperature and wind in the tropics were strongly reduced. Therefore, the correction results in a more skillful forecast with lower mean bias and root-mean-square error and higher anomaly correlation coefficient.
文摘A family of variational principles (VP) has been developed for the unsteady inverse problem of the second type I B. It opens new ways for the inverse shape design of unsteady airfoils and can serve as key basis of multipoint inverse shape design of steady airfoils and cascades.
基金Project supported by the National Natural Science Foundation of China(Grant No.10271074)
文摘The tridiagonal coefficient matrix for the "fixed-fixed" spring-mass system was obtained by changing spring length. And then a new algorithm of the inverse problem was designed to construct the masses and the spring constants from the natural frequencies of the "fixed-fixed" and "fixed-fres" spring-mass systems. An example was given to illustrate the results.
文摘This paper presents a formulation and solution for the inverse problem of nonholonomic dynamics: to find the form of nonholonomic constraints when some integrals are given and to find the generalized reactive forces of constraint acting on the system when the expression of the kinetic energy is given. An example is given to illustrate the application of the result.
基金supported by National Natural Science Foundation of China (No.50977072)the key project of Chinese Ministry of Education (No.109141)
文摘Non-contact magnetic measurement method is an effective way to study the air arc behavior experimentally. One of the crucial techniques is to solve an inverse problem for the electromagnetic field. This study is devoted to investigating different algorithms for this kind of inverse problem preliminarily, including the preconditioned conjugate gradient method, penalty function method and genetic algorithm. The feasibility of each algorithm is analyzed. It is shown that the preconditioned conjugate gradient method is valid only for few arc segments, the estimation accuracy of the penalty function method is dependent on the initial conditions, and the convergence of genetic algorithm should be studied further for more segments in an arc current.
文摘An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.
文摘To determine a variation of pipe's inner geometric shape as due to etch, the three-layered feedforward artificial neural network is used in the inverse analysis through observing the elastoplastic strains of the outer wall under the working inner pressure. Because of different kinds of inner wail radii and eccentricity. several groups of strains calculated with computational mechanics are used for the network to do learning. Numerical calculation demonstrates that this method is effective and the estimated inner wall geometric parameters have high precision.
文摘The inverse problem for a class of nonlinear evolution equations of dispersive type type was reduced to Cauchy problem of nonlinear evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to the inverse problem discussed here. The existence and uniqueness theorem of global solution it,as given for this class of nonlinear evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence and uniqueness of local solution presented by YUAN Zhong-xin.