In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under...In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under the a priori bound assumption for the exact solution.Secondly,a modified Tikhonov regularization method is used to solve this ill-posed problem.Under the a priori and the a posteriori regularization parameter choice rule,the error estimates between the regularization solutions and the exact solution are obtained.Finally,some numerical examples are presented to verify that our method is effective.展开更多
In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional...In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.展开更多
The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized funct...The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized functional was established, and the functional was solved by the sensitivity coefficient and Newtonaphson iteration method. Moreover, the orthogonal experimental design was used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and efficiency. It illustrated a detailed case of AlSiTMg sand mold casting and the temperature measurement experiment was done. The physical properties of sand mold and the interracial heat transfer coefficient were identified at the meantime. The results indicated that the new regularization method was efficient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.展开更多
The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inv...The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.展开更多
In this paper, the Tikhonov regularization method was used to solve the nondegenerate compact hnear operator equation, which is a well-known ill-posed problem. Apart from the usual error level, the noise data were sup...In this paper, the Tikhonov regularization method was used to solve the nondegenerate compact hnear operator equation, which is a well-known ill-posed problem. Apart from the usual error level, the noise data were supposed to satisfy some additional monotonic condition. Moreover, with the assumption that the singular values of operator have power form, the improved convergence rates of the regularized solution were worked out.展开更多
The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matri...The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.展开更多
Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design...Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.展开更多
Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed ...Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed to realize effective continuation. According to the Poisson integral plane approximate relationship between observation and continuation data, the computation formulae combined with the fast Fourier transform（FFT）algorithm are transformed to a frequency domain for accelerating the computational speed. The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results. The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data, and the continuation results show good precision.展开更多
Scatterometer is an instrument which provides all-day and large-scale wind field information, and its application especially to wind retrieval always attracts meteorologists. Certain reasons cause large direction erro...Scatterometer is an instrument which provides all-day and large-scale wind field information, and its application especially to wind retrieval always attracts meteorologists. Certain reasons cause large direction error, so it is important to find where the error mainly comes. Does it mainly result from the background field, the normalized radar cross-section （NRCS） or the method of wind retrieval？ It is valuable to research. First, depending on SDP2.0, the simulated ＇true＇ NRCS is calculated from the simulated ＇true＇ wind through the geophysical mode] function NSCAT2. The simulated background field is configured by adding a noise to the simulated ＇true＇ wind with the non-divergence constraint. Also, the simulated ＇measured＇ NRCS is formed by adding a noise to the simulated ＇true＇ NRCS. Then, the sensitivity experiments are taken, and the new method of regularization is used to improve the ambiguity removal with simulation experiments. The results show that the accuracy of wind retrieval is more sensitive to the noise in the background than in the measured NRCS; compared with the two-dimensional variational （2DVAR） ambiguity removal method, the accuracy of wind retrieval can be improved with the new method of Tikhonov regularization through choosing an appropriate regularization parameter, especially for the case of large error in the background. The work will provide important information and a new method for the wind retrieval with real data.展开更多
Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced...Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.展开更多
Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image ...Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.展开更多
Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water va...Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water vapor from 1300 nm to 1350 nm,the temperature probability distribution of nonuniform temperature distribution,for which a parabolic temperature profile is selected as an example in this paper,was retrieved by making the use of regularization methods.To examine the effectiveness of regularization methods,truncated singular value decomposition(TSVD),Tikhonov regularization and a revised Tikhonov regularization method were implemented to retrieve the temperature probability distribution.The results derived by using the three regularization methods were compared with that by using constrained linear least-square fitting.The results show that regularization methods not only generate closer temperature probability distributions to the original,but also are less sensitive to measurement noise.Particularly,the revised Tikhonov regularization method generate solutions in better agreement with the original ones than those obtained by using TSVD and Tikhonov regularization methods.The results obtained in this work can enrich the temperature distribution information,which is expected to play a more important role in combustion diagnosis.展开更多
Crosswell seismic tomography can be used to study the lateral variation of reservoirs, reservoir properties and the dynamic movement of fluids. In view of the instability of crosswell seismic tomography, the gradient ...Crosswell seismic tomography can be used to study the lateral variation of reservoirs, reservoir properties and the dynamic movement of fluids. In view of the instability of crosswell seismic tomography, the gradient method was improved by introducing regularization, and a gradient regularization method is presented in this paper. This method was verified by processing numerical simulation data and physical model data.展开更多
The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance...The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance,are detected and located in a contactless manner.However,the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed problem.In this work,we present an inverse multiquadric(IMQ)regularization method based on the level set function for reconstructing buried pipelines.In the case of locating underwater objects,the unknown inversion area is split into two parts,the background and the pipeline with known conductivity.The geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion image.To obtain a binary image,the IMQ is used as the regularization term,which‘pushes’the level set function away from 0.We also provide an appropriate method to select the bandwidth and regularization parameters for the IMQ regularization term,resulting in reconstructed images with sharp edges.The simulation results and analysis show that the proposed method performs better than classical inversion methods.展开更多
Ship maneuverability, in the field of ship engineering, is often predicted by maneuvering motion group （MMG） mathematical model. Then it is necessary to determine hydrodynamic coefficients and interaction force coef...Ship maneuverability, in the field of ship engineering, is often predicted by maneuvering motion group （MMG） mathematical model. Then it is necessary to determine hydrodynamic coefficients and interaction force coefficients of the model. Based on the data of free running model test, the problem for obtaining these coefficients is called inverse one. For the inverse problem, ill-posedness is inherent, nonlinearity and great computation happen, and the computation is also insensitive, unstable and time-consuming. In the paper, a regularization method is introduced to solve ill-posed problem and genetic algorithm is used for nonlinear motion of ship maneuvering. In addition, the immunity is applied to solve the prematurity, to promote the global searching ability and to increase the converging speed. The combination of regularization method and immune genetic algorithm（RIGA） applied in MMG mathematical model, showed rapid converging speed and good stability.展开更多
The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate reg...The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.展开更多
In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul...In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.展开更多
This paper presents anew regularization method for solving operator equations of the first kind; the convergence rate of the regularized solution is improved, as compared with the ordinary Tikhonov regularization.
A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Four...A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum展开更多
In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strateg...In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a priori bound of exact solution are not needed for the a posteriori choice rule. Numerical results are presented to show the stability and effectiveness of the method.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11961044)。
文摘In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under the a priori bound assumption for the exact solution.Secondly,a modified Tikhonov regularization method is used to solve this ill-posed problem.Under the a priori and the a posteriori regularization parameter choice rule,the error estimates between the regularization solutions and the exact solution are obtained.Finally,some numerical examples are presented to verify that our method is effective.
基金supported by the National Natural Science Foundation of China(11961044)the Doctor Fund of Lan Zhou University of Technologythe Natural Science Foundation of Gansu Provice(21JR7RA214)。
文摘In this paper,we consider the inverse problem for identifying the source term of the time-fractional equation with a hyper-Bessel operator.First,we prove that this inverse problem is ill-posed,and give the conditional stability.Then,we give the optimal error bound for this inverse problem.Next,we use the fractional Tikhonov regularization method and the fractional Landweber iterative regularization method to restore the stability of the ill-posed problem,and give corresponding error estimates under different regularization parameter selection rules.Finally,we verify the effectiveness of the method through numerical examples.
文摘The inverse heat conduction method is one of methods to identify the casting simulation parameters. A new inverse method was presented according to the Tikhonov regularization theory. One appropriate regularized functional was established, and the functional was solved by the sensitivity coefficient and Newtonaphson iteration method. Moreover, the orthogonal experimental design was used to estimate the appropriate initial value and variation domain of each variable to decrease the number of iteration and improve the identification accuracy and efficiency. It illustrated a detailed case of AlSiTMg sand mold casting and the temperature measurement experiment was done. The physical properties of sand mold and the interracial heat transfer coefficient were identified at the meantime. The results indicated that the new regularization method was efficient in overcoming the ill-posedness of the inverse heat conduction problem and improving the stability and accuracy of the solutions.
基金Project supported by the National Natural Science Foundation of China(Grant No.41175025)
文摘The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.
文摘In this paper, the Tikhonov regularization method was used to solve the nondegenerate compact hnear operator equation, which is a well-known ill-posed problem. Apart from the usual error level, the noise data were supposed to satisfy some additional monotonic condition. Moreover, with the assumption that the singular values of operator have power form, the improved convergence rates of the regularized solution were worked out.
基金supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019)the National 973 Project of China (No.2013CB733302)+2 种基金the China Postdoctoral Science Foundation (No.2016M602301)the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08)the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)
文摘The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.
基金Project supported by the National Natural Science Foundation of China(No.61603322)the Research Foundation of Education Bureau of Hunan Province of China(No.16C1542)
文摘Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector recovery.We derive sufficient conditions on the well-posedness of the new regularization,and design an iterative algorithm,namely the iteratively reweighted algorithm(IR-algorithm),for efficiently computing the sparse solutions to the proposed regularization model.The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length.Finally,we present numerical examples to illustrate the features of the new regularization and algorithm.
基金supported by the National Natural Science Foundation of China(41304022,41174026,41104047)the National 973 Foundation(61322201,2013CB733303)+1 种基金the Key laboratory Foundation of Geo-space Environment and Geodesy of the Ministry of Education(13-01-08)the Youth Innovation Foundation of High Resolution Earth Observation(GFZX04060103-5-12)
文摘Downward continuation is a key step in processing airborne geomagnetic data. However,downward continuation is a typically ill-posed problem because its computation is unstable; thus, regularization methods are needed to realize effective continuation. According to the Poisson integral plane approximate relationship between observation and continuation data, the computation formulae combined with the fast Fourier transform（FFT）algorithm are transformed to a frequency domain for accelerating the computational speed. The iterative Tikhonov regularization method and the iterative Landweber regularization method are used in this paper to overcome instability and improve the precision of the results. The availability of these two iterative regularization methods in the frequency domain is validated by simulated geomagnetic data, and the continuation results show good precision.
基金supported by the National Natural Science Foundation of China (Grant No. 40775023)
文摘Scatterometer is an instrument which provides all-day and large-scale wind field information, and its application especially to wind retrieval always attracts meteorologists. Certain reasons cause large direction error, so it is important to find where the error mainly comes. Does it mainly result from the background field, the normalized radar cross-section （NRCS） or the method of wind retrieval？ It is valuable to research. First, depending on SDP2.0, the simulated ＇true＇ NRCS is calculated from the simulated ＇true＇ wind through the geophysical mode] function NSCAT2. The simulated background field is configured by adding a noise to the simulated ＇true＇ wind with the non-divergence constraint. Also, the simulated ＇measured＇ NRCS is formed by adding a noise to the simulated ＇true＇ NRCS. Then, the sensitivity experiments are taken, and the new method of regularization is used to improve the ambiguity removal with simulation experiments. The results show that the accuracy of wind retrieval is more sensitive to the noise in the background than in the measured NRCS; compared with the two-dimensional variational （2DVAR） ambiguity removal method, the accuracy of wind retrieval can be improved with the new method of Tikhonov regularization through choosing an appropriate regularization parameter, especially for the case of large error in the background. The work will provide important information and a new method for the wind retrieval with real data.
基金supported by the Natural Science Foundation of China (Nos. 11971230, 12071215)the Fundamental Research Funds for the Central Universities(No. NS2018047)the 2019 Graduate Innovation Base(Laboratory)Open Fund of Jiangsu Province(No. Kfjj20190804)
文摘Recently,inverse problems have attracted more and more attention in computational mathematics and become increasingly important in engineering applications.After the discretization,many of inverse problems are reduced to linear systems.Due to the typical ill-posedness of inverse problems,the reduced linear systems are often illposed,especially when their scales are large.This brings great computational difficulty.Particularly,a small perturbation in the right side of an ill-posed linear system may cause a dramatical change in the solution.Therefore,regularization methods should be adopted for stable solutions.In this paper,a new class of accelerated iterative regularization methods is applied to solve this kind of large-scale ill-posed linear systems.An iterative scheme becomes a regularization method only when the iteration is early terminated.And a Morozov’s discrepancy principle is applied for the stop criterion.Compared with the conventional Landweber iteration,the new methods have acceleration effect,and can be compared to the well-known acceleratedν-method and Nesterov method.From the numerical results,it is observed that using appropriate discretization schemes,the proposed methods even have better behavior when comparing withν-method and Nesterov method.
基金This work is supported by the National Natural Science Foundation of China nos.11971215 and 11571156,MOE-LCSMSchool of Mathematics and Statistics,Hunan Normal University,Changsha,Hunan 410081,China.
文摘Regularization methods have been substantially applied in image restoration due to the ill-posedness of the image restoration problem.Different assumptions or priors on images are applied in the construction of image regularization methods.In recent years,matrix low-rank approximation has been successfully introduced in the image denoising problem and significant denoising effects have been achieved.Low-rank matrix minimization is an NP-hard problem and it is often replaced with the matrix’s weighted nuclear norm minimization(WNNM).The assumption that an image contains an extensive amount of self-similarity is the basis for the construction of the matrix low-rank approximation-based image denoising method.In this paper,we develop a model for image restoration using the sum of block matching matrices’weighted nuclear norm to be the regularization term in the cost function.An alternating iterative algorithm is designed to solve the proposed model and the convergence analyses of the algorithm are also presented.Numerical experiments show that the proposed method can recover the images much better than the existing regularization methods in terms of both recovered quantities and visual qualities.
基金support by the National Science Foundation for Distinguished Youth Scholars of China(Grant No.61225006)National Natural Science Foundation of China(Grant No.60972087)Natural Science Foundation of Beijing,China(Grant No.3112018).
文摘Regularization methods were combined with line-of-sight tunable diode laser absorption spectroscopy(TDLAS)to measure nonuniform temperature distribution.Relying on measurements of 12 absorption transitions of water vapor from 1300 nm to 1350 nm,the temperature probability distribution of nonuniform temperature distribution,for which a parabolic temperature profile is selected as an example in this paper,was retrieved by making the use of regularization methods.To examine the effectiveness of regularization methods,truncated singular value decomposition(TSVD),Tikhonov regularization and a revised Tikhonov regularization method were implemented to retrieve the temperature probability distribution.The results derived by using the three regularization methods were compared with that by using constrained linear least-square fitting.The results show that regularization methods not only generate closer temperature probability distributions to the original,but also are less sensitive to measurement noise.Particularly,the revised Tikhonov regularization method generate solutions in better agreement with the original ones than those obtained by using TSVD and Tikhonov regularization methods.The results obtained in this work can enrich the temperature distribution information,which is expected to play a more important role in combustion diagnosis.
文摘Crosswell seismic tomography can be used to study the lateral variation of reservoirs, reservoir properties and the dynamic movement of fluids. In view of the instability of crosswell seismic tomography, the gradient method was improved by introducing regularization, and a gradient regularization method is presented in this paper. This method was verified by processing numerical simulation data and physical model data.
基金supported by the National Natural Sci-ence Foundation of China(No.52101383)the Fundamen-tal Research Funds for the Central Universities(No.3072021CF0802)+3 种基金the Key Laboratory of Advanced Marine Communication and Information Technology,Ministry of Industry and Information Technology(No.AMCIT2101-02)the Sino-Russian Cooperation Fund of Harbin Engi-neering University(No.2021HEUCRF006)the Ministry of Science and Higher Education of the Russian Federation(No.075-15-2020-934)the International Science&Technology Cooperation Program of China(No.2014DF R10240).
文摘The electric inversion technique reconstructs the subsurface medium distribution from acquired data.On the basis of electric inversion,objects buried under the earth or seabed,such as pipelines and unexploded ordnance,are detected and located in a contactless manner.However,the process of accurately reconstructing the shape of the target object is challenging because electric inversion is a nonlinear and ill-posed problem.In this work,we present an inverse multiquadric(IMQ)regularization method based on the level set function for reconstructing buried pipelines.In the case of locating underwater objects,the unknown inversion area is split into two parts,the background and the pipeline with known conductivity.The geometry of the pipeline is represented based on the level set function for achieving a noiseless inversion image.To obtain a binary image,the IMQ is used as the regularization term,which‘pushes’the level set function away from 0.We also provide an appropriate method to select the bandwidth and regularization parameters for the IMQ regularization term,resulting in reconstructed images with sharp edges.The simulation results and analysis show that the proposed method performs better than classical inversion methods.
文摘Ship maneuverability, in the field of ship engineering, is often predicted by maneuvering motion group （MMG） mathematical model. Then it is necessary to determine hydrodynamic coefficients and interaction force coefficients of the model. Based on the data of free running model test, the problem for obtaining these coefficients is called inverse one. For the inverse problem, ill-posedness is inherent, nonlinearity and great computation happen, and the computation is also insensitive, unstable and time-consuming. In the paper, a regularization method is introduced to solve ill-posed problem and genetic algorithm is used for nonlinear motion of ship maneuvering. In addition, the immunity is applied to solve the prematurity, to promote the global searching ability and to increase the converging speed. The combination of regularization method and immune genetic algorithm（RIGA） applied in MMG mathematical model, showed rapid converging speed and good stability.
文摘The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.
文摘In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.
文摘This paper presents anew regularization method for solving operator equations of the first kind; the convergence rate of the regularized solution is improved, as compared with the ordinary Tikhonov regularization.
文摘A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum
文摘In this paper, we consider an unknown source problem for the modified Helmholtz equation. The Tikhonov regularization method in Hilbert scales is extended to deal with ill-posedness of the problem. An a priori strategy and an a posteriori choice rule have been present to obtain the regularization parameter and corresponding error estimates have been obtained. The smoothness parameter and the a priori bound of exact solution are not needed for the a posteriori choice rule. Numerical results are presented to show the stability and effectiveness of the method.
