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An Effective Meshless Approach for Inverse Cauchy Problems in 2D and 3D Electroelastic Piezoelectric Structures
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作者 Ziqiang Bai Wenzhen Qu Guanghua Wu 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第3期2955-2972,共18页
In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within... In the past decade,notable progress has been achieved in the development of the generalized finite difference method(GFDM).The underlying principle of GFDM involves dividing the domain into multiple sub-domains.Within each sub-domain,explicit formulas for the necessary partial derivatives of the partial differential equations(PDEs)can be obtained through the application of Taylor series expansion and moving-least square approximation methods.Consequently,the method generates a sparse coefficient matrix,exhibiting a banded structure,making it highly advantageous for large-scale engineering computations.In this study,we present the application of the GFDM to numerically solve inverse Cauchy problems in two-and three-dimensional piezoelectric structures.Through our preliminary numerical experiments,we demonstrate that the proposed GFDMapproach shows great promise for accurately simulating coupled electroelastic equations in inverse problems,even with 3%errors added to the input data. 展开更多
关键词 Generalized finite difference method meshless method inverse Cauchy problems piezoelectric problems electroelastic analysis
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Efficient Inverse Analysis for Solving a Coupled Conduction,Convection and Radiation Problem Involving Non⁃gray Participating Media
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作者 HE Zheng CAO Zhenkun +2 位作者 CHENG Xiang CUI Miao LIU Kun 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2024年第5期621-631,共11页
The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving t... The presence of non-gray radiative properties in a reheating furnace’s medium that absorbs,emits,and involves non-gray creates more complex radiative heat transfer problems.Furthermore,it adds difficulty to solving the coupled conduction,convection,and radiation problem,leading to suboptimal efficiency that fails to meet real-time control demands.To overcome this difficulty,comparable gray radiative properties of non-gray media are proposed and estimated by solving an inverse problem.However,the required iteration numbers by using a least-squares method are too many and resulted in a very low inverse efficiency.It is necessary to present an efficient method for the equivalence.The Levenberg-Marquardt algorithm is utilized to solve the inverse problem of coupled heat transfer,and the gray-equivalent radiative characteristics are successfully recovered.It is our intention that the issue of low inverse efficiency,which has been observed when the least-squares method is employed,will be resolved.To enhance the performance of the Levenberg-Marquardt algorithm,a modification is implemented for determining the damping factor.Detailed investigations are also conducted to evaluate its accuracy,stability of convergence,efficiency,and robustness of the algorithm.Subsequently,a comparison is made between the results achieved using each method. 展开更多
关键词 inverse problem coupled heat transfer problem Levenberg-Marquardt algorithm
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A STRONG POSITIVITY PROPERTY AND A RELATED INVERSE SOURCE PROBLEM FOR MULTI-TERM TIME-FRACTIONAL DIFFUSION EQUATIONS
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作者 Li HU Zhiyuan LI Xiaona YANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期2019-2040,共22页
In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-... In this article,we consider the diffusion equation with multi-term time-fractional derivatives.We first derive,by a subordination principle for the solution,that the solution is positive when the initial value is non-negative.As an application,we prove the uniqueness of solution to an inverse problem of determination of the temporally varying source term by integral type information in a subdomain.Finally,several numerical experiments are presented to show the accuracy and efficiency of the algorithm. 展开更多
关键词 fractional diffusion equation inverse source problem nonlocal observation observation UNIQUENESS Tikhonov regularization
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Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter
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作者 Hui Zhao Jijun Ao 《Journal of Applied Mathematics and Physics》 2024年第3期982-996,共15页
In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem an... In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach. 展开更多
关键词 inverse problem Sturm-Liouville Operator Weyl Function Eigenparameter-Dependent Jump Conditions
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A Note on the Inverse Connected p-Median Problem on Block Graphs
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作者 Chunsong Bai Liqi Zhang Jianjie Zhou 《Advances in Pure Mathematics》 2023年第4期181-186,共6页
Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. Their contributions include finding a nece... Recently, the inverse connected p-median problem on block graphs G(V,E,w) under various cost functions, say rectilinear norm, Chebyshev norm, and bottleneck Hamming distance. Their contributions include finding a necessary and sufficient condition for the connected p-median problem on block graphs, developing algorithms and showing that these problems can be solved in O(n log n) time, where n is the number of vertices in the underlying block graph. Using similar technique, we show that some results are incorrect by a counter-example. Then we redefine some notations, reprove Theorem 1 and redescribe Theorem 2, Theorem 3 and Theorem 4. 展开更多
关键词 Location Theory Block Graphs inverse Optimization Connected p-median
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An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method 被引量:1
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作者 Qiuyu Wang Krishna Kumar 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期2077-2090,共14页
This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeabi... This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications. 展开更多
关键词 inverse problem Fluid flow Granular media Automatic differentiation(AD) Lattice Boltzmann method(LBM)
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Inverse Electromagnetic Scattering by a Penetrable Chiral Object
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作者 Sotiria Dimitroula Paraskevi Roupa +1 位作者 Spyridon C. Athanasiadis Georgios Halikias 《Journal of Applied Mathematics and Physics》 2024年第9期3081-3098,共18页
We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering pr... We consider the inverse electromagnetic scattering problem of determining the shape of a perfectly conducting core inside a penetrable chiral body. We prove the well-posedness of the corresponding direct scattering problem by the variational method. We focus on a uniqueness result for the inverse scattering problem that is under what conditions an obstacle can be identified by the knowledge of the electric far-field pattern corresponding to all time-harmonic incident planes waves with a fixed wave number. To this end, we establish a chiral mixed reciprocity relation that connects the electric far-field pattern of a spherical wave with the scattered field of a plane wave. 展开更多
关键词 Chiral Media inverse Scattering problem Chiral Mixed Reciprocity Relation
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PERTURBATION ANALYSIS OF A CLASS OF MATRIX INVERSE PROBLEMS
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作者 戴华 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2000年第2期194-198,共5页
A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A={A∈R n×m |‖AX-B‖ F=min} is considered. The perturbation analysis of the solution to these problems is carried out. Th... A class of matrix inverse problems minimizing ‖A-‖ F on the linear manifold l A={A∈R n×m |‖AX-B‖ F=min} is considered. The perturbation analysis of the solution to these problems is carried out. The perturbation upper bounds of the solution are given for both the consistent and inconsistent cases. The obtained preturbation upper bounds are with respect to the distance from the perturbed solution to the unperturbed manifold. 展开更多
关键词 MATRIX inverse problem best approximation perturbation analysis
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Relevance vector machine technique for the inverse scattering problem 被引量:5
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作者 王芳芳 张业荣 《Chinese Physics B》 SCIE EI CAS CSCD 2012年第5期19-24,共6页
A novel method based on the relevance vector machine(RVM) for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.T... A novel method based on the relevance vector machine(RVM) for the inverse scattering problem is presented in this paper.The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered.The nonlinearity is embodied in the relation between the scattered field and the target property,which can be obtained through the RVM training process.Besides,rather than utilizing regularization,the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output.Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy,convergence,robustness,generalization,and improved performance in terms of sparse property in comparison with the support vector machine(SVM) based approach. 展开更多
关键词 inverse scattering problem through-wall problem relevance vector machine finite-difference time-domain
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An approach to estimating and extrapolating model error based on inverse problem methods:towards accurate numerical weather prediction 被引量:4
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作者 胡淑娟 邱春雨 +3 位作者 张利云 黄启灿 于海鹏 丑纪范 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第8期669-677,共9页
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
关键词 numerical weather prediction model error past data inverse problem
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An inverse problem in analytical dynamics 被引量:3
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作者 李广成 梅凤翔 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第8期1669-1671,共3页
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
关键词 inverse problem analytical dynamics INTEGRAL LAGRANGIAN
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An Online Model Correction Method Based on an Inverse Problem:Part I—Model Error Estimation by Iteration 被引量:3
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作者 XUE Haile SHEN Xueshun CHOU Jifan 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2015年第10期1329-1340,共12页
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
关键词 model error past data inverse problem error estimation model correction GRAPES-GFS
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THE WAVE EQUATION APPROACH TO THE TWO-DIMENSIONAL INVERSE PROBLEM FOR A GENERAL BOUNDED DOMAIN WITH PIECEWISE SMOOTH MIXED BOUNDARY CONDITIONS 被引量:2
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作者 E.M.E.Zayed, I.H.Abdel-Halim Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt E-mail: emezayed@hotmail.com & ismhalim@hotmail.com 《Acta Mathematica Scientia》 SCIE CSCD 2001年第2期171-181,共11页
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
关键词 inverse problem spectral distribution wave equation EIGENVALUES
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Wavelet network solution for the inverse kinematics problem in robotic manipulator 被引量:5
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作者 CHEN Hua CHEN Wei-shan XIE Tao 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第4期525-529,共5页
Wavelet network, a class of neural network consisting of wavelets, is proposed to solve the inverse kinematics problem in robotic manipulator. A wavelet network suitable for dealing with multi-input and multi-output s... Wavelet network, a class of neural network consisting of wavelets, is proposed to solve the inverse kinematics problem in robotic manipulator. A wavelet network suitable for dealing with multi-input and multi-output system is constructed. The network is optimized by reducing the number of wavelets handling large dimension problem according to the sample data. The algorithms for sparseness analysis of input data and fitting wavelets to the output data with orthogonal method are introduced. Then Levenberg-Marquardt algorithm is used to train the network. Simulation results showed that this method is capable of solving the inverse kinematics problem for PUMA560. 展开更多
关键词 inverse kinematics problem Robotic manipulator Wavelet network
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Inverse Eigenvalue Problem for Generalized Arrow-Like Matrices 被引量:3
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作者 Zhibin Li Cong Bu Hui Wang 《Applied Mathematics》 2011年第12期1443-1445,共3页
This paper researches the following inverse eigenvalue problem for arrow-like matrices. Give two characteristic pairs, get a generalized arrow-like matrix, let the two characteristic pairs are the characteristic pairs... This paper researches the following inverse eigenvalue problem for arrow-like matrices. Give two characteristic pairs, get a generalized arrow-like matrix, let the two characteristic pairs are the characteristic pairs of this generalized arrow-like matrix. The expression and an algorithm of the solution of the problem is given, and a numerical example is provided. 展开更多
关键词 Generalized Arrow-Like MATRICES CHARACTERISTIC Value inverse problem UNIQUE
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Inverse problem of pulsed eddy current field of ferromagnetic plates 被引量:2
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作者 陈兴乐 雷银照 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第3期40-47,共8页
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
关键词 pulsed eddy current electromagnetic field inverse problem ferromagnetic plate wall thickness measurement
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The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrdinger Equations 被引量:2
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作者 LI YUAN MA FU-MING 《Communications in Mathematical Research》 CSCD 2010年第4期321-336,共16页
This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the sca... This paper is concerned with the inverse scattering problems for Schrdinger equations with compactly supported potentials.For purpose of reconstructing the support of the potential,we derive a factorization of the scattering amplitude operator A and prove that the ranges of (A* A) ^1/4 and G which maps more general incident fields than plane waves into the scattering amplitude coincide.As an application we characterize the support of the potential using only the spectral data of the operator A. 展开更多
关键词 factorization method inverse scattering Schrdinger equation interior transmission problem
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An inverse problem in film/substrate indentation:extracting both the Young's modulus and thickness of films 被引量:2
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作者 Yin Zhang Feifei Gao +1 位作者 Zhiyue Zheng Zhihai Cheng 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2018年第6期1061-1071,共11页
In an indentation test,the effective Young's modulus of a film/substrate bilayer heterostructure varies with the indentation depth,a phenomenon known as the substrate effect.In previous studies investigating this,... In an indentation test,the effective Young's modulus of a film/substrate bilayer heterostructure varies with the indentation depth,a phenomenon known as the substrate effect.In previous studies investigating this,only the Young's modulus of the film was unknown.Once the effective Young's modulus of a film/substrate structure is determined at a given contact depth,the Young's modulus of the film can be uniquely determined,i.e.,there is a one-to-one relation between the Young's modulus of the film and the film/substrate effective Young's modulus.However,at times it is extremely challenging or even impossible to measure the film thickness.Furthermore,the precise definition of the layer/film thickness for a two-dimensional material can be problematic.In the current study,therefore,the thickness of the film and its Young's modulus are treated as two unknowns that must be determined.Unlike the case with one unknown,there are infinite combinations of film thickness and Young's modulus which can yield the same effective Young's modulus for the film/substrate.An inverse problem is formulated and solved to extract the Young's modulus and thickness of the film from the indentation depth-load curve.The accuracy and robustness of the inverse problem-solving method are also demonstrated. 展开更多
关键词 INDENTATION test FILM SUBSTRATE inverse problem
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Inverse problem of elastica of a variable-arc-length beam subjected to a concentrated load 被引量:5
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作者 Xiaowei Zhang Jialing Yang 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2005年第5期444-450,共7页
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
关键词 inverse problem. Elastica. Variable-arc-length beam-. Quasi-Newton method
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A NEW METHOD FOR INVERSE BLACK BODY RADIATION PROBLEM 被引量:2
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作者 CHEN Nanxian 《Chinese Physics Letters》 SCIE CAS 1987年第8期337-340,共4页
A completely new method is presented to solve the inverse black body radiation problem.The solution makes use of the widely known and easily implemented Fourier transform,and the expression is very simple and clear.Th... A completely new method is presented to solve the inverse black body radiation problem.The solution makes use of the widely known and easily implemented Fourier transform,and the expression is very simple and clear.This method is of major significance with respect not only to the numerical computation,but also to uniqueness or existence of this problem.At the same time,this method is also very useful for many other fields. 展开更多
关键词 problem UNIQUENESS inverse
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