With the advancement of structural health monitoring technology, the increasing precision in modeling, scalability of model parameters, and complexity of external environments have introduced significant challenges to...
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With the advancement of structural health monitoring technology, the increasing precision in modeling, scalability of model parameters, and complexity of external environments have introduced significant challenges to damage identification. Notably, the ill-posed nature of largescale parameter identification from refined models has become a critical technical challenge. regularization methods are widely employed to mitigate ill-posedness and control the complexity of identification problems. Traditional regularization methods often penalize imbalances in damage parameters, leading to errors and suboptimal convergence, failing to accurately reflect actual damage conditions. To address these challenges, an information entropy regularization term is introduced to capture the distribution of structural damage location and severity. By integrating regularization term with an adjoint sensitivity optimization algorithm, a refined iterative approach is developed to manage large-scale damage parameter identification from detailed finite element models. Numerical analyses on a 2D stress plate and a 3D wing, along with experimental validation on impact damage of clamped plates, demonstrate the accuracy and effectiveness of the proposed method.
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.
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.
Nedelec vector finite elements are used for the numerical solution of a regularized version of the quasi-stationary Maxwell equations written in terms of a scalar and a vector magnetic potential with special calibrati...
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Nedelec vector finite elements are used for the numerical solution of a regularized version of the quasi-stationary Maxwell equations written in terms of a scalar and a vector magnetic potential with special calibration taking into account the conductivity of the medium. An optimal energy estimate for the error of the approximate solution in Lipschitz polyhedral domains is established. Numerical results are presented that demonstrate the stability of the method. DOI: 10.1134/S0965542512030116
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...
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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.
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...
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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.
Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector *** derive sufficient conditions on the well-posedness of the new regularization,and design an iter...
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Motivated by the study of regularization for sparse problems,we propose a new regularization method for sparse vector *** 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 *** convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at ***,we present numerical examples to illustrate the features of the new regularization and algorithm.
The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier-Stokes equations from the viewpoint of regularization of differential-a...
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The objective of the paper is to present a method, called the sequential regularization method (SRM), for the nonstationary incompressible Navier-Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs), and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is O(epsilon(m)), where m is the number of the SRM iterations and a is the regularisation parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit-difference scheme is analyzed and its stability is proved under the usual step-size condition of explicit schemes. It appears that the SRM formulation is new in the Navier-Stokes context. Unlike other regularizations or pseudocompressibility methods in the Navier-Stokes context, the regularization parameter epsilon in the SRM need not be very small and the regularized problem in the sequence may be essentially nonstiff in time direction for any epsilon. Hence the stability condition is independent of epsilon even for explicit time discretization. Numerical experiments are given to verify our theoretical results.
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...
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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.
The purpose of this work is to create an identical approximate regularization method for solving a Cauchy problem of two-dimensional heat conduction equation. The problem is severely ill-posed. The convergence rates a...
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The purpose of this work is to create an identical approximate regularization method for solving a Cauchy problem of two-dimensional heat conduction equation. The problem is severely ill-posed. The convergence rates are obtained under a priori regularization parameter choice rule. Numerical results are presented for two examples with smooth and continuous but not smooth boundaries and compared the identical approximate regularization solutions which are displayed in text. The numerical results show that our method is effective, accurate, and stable to solve the ill-posed Cauchy problems.
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