Papers by Keyword: Regularization Method

Abstract: The continuation inverse problem for a solution to an elliptic equation in cylindrical layer for a model of stationary diffusion process is considered. Cauchy data are given on the outer boundary of the cylindrical layer; need to recover a field at the inner boundary of the cylinder. The problem is reduced to three different Cauchy problems for a second order ordinary differential equation. On the base of necessary minimization conditions of the residual functional analytical formulas for a regularized quasisolution to the inverse problem are derived.

Abstract: In a large number of measurement data processing, the ill-posed problem is widespread. For such problems, this paper introduces the solution of ill-posed problem of the unity of expression and Tikhonov regularization method, and then to re-collinearity diagnostics and metrics based on proposed based on complex collinearity diagnostics and the metric regularization method is given regularization matrix selection methods and regularization parameter determination formulas. Finally, it uses a simulation example to verify the effectiveness of the method.

Abstract: We considered the regularization method for a kind of complete singular integral equation with Hilbert kernel on open arcs lying in a period strip. And based on this, we obtained the solvable Noether theorem for this kind of complete singular integral equations.

Abstract: In measurement data processing, tiny disturbance of the design matrix can enlarge the deviation between least squares estimation solution and true value and the solution distortion arises. By choosing the reasonable parameters according to the regularization method, and Under the constraints of two indicators which are the mean square error and the estimating efficiency，disturb the observation data by varying degrees on the design matrix to determine the relationship between regularization method and ill-conditioned problem in measurement data processing.

Abstract: The ill-posedness of nonlinear identification equation in time domain of structural dynamics system is studied and a new calculating method to weaken the influence of ill-posedness is proposed. Damped least squares method is an algorithm of Jacobian matrix positive-definable, which can obtain the solution of ill-posed nonlinear identification equation. But the solution is sensitive to the test noise of response in time domain of the structure. To solve the problem of instability of the solution, a new calculating method is proposed which combines damped least squares method with Tikhonov regularization method. First, the estimate of structural parameters is introduced to Tikhonov regularization function, and a more stable identification equation in time domain can be obtained. Second, the identification equation is solved with damped least squares method, and the iterative result is an approximate solution of the former ill-posed problem. The numerical example shows that the new method in this paper is efficient to solve the ill-posed nonlinear identification equation in time domain.

Abstract: A new method is proposed to identify the bridge effective pre-stress from the dynamic responses induced by the vehicle moving on a simply-supported beam bridge with eccentric straight pre-stress, based on the sensitivity analysis. The bridge is modeled as Euler beam elements and the moving vehicle is modeled as a two-degree freedom system with five parameters. After calculating dynamic responses of the bridge by vehicle-bridge coupled vibration analysis, the dynamic responses sensitivity can be obtained by using the direct derivation method, and the regularization method is adopted to identify the effective pre-stress. The effects on the identified results from different responses, different measuring locations and different road surface roughness are considered in the numerical simulations. The simulation studies indicate that the proposed method can be used to identify the effective pre-stress accurately and effectively for a simply-supported PRC beam bridges.

Abstract: Resistance spot welding (RSW) is an important welding process in modern industrial production, and the quality of welding nugget determines the strength of products to a large extent. Limited by the level of RSW quality monitor, however, RSW has rarely been applied to the fields with high welding quality requirements. Associated with the inversion theory, in this paper, an electromagnetic inverse model of RSW was established, and the analysis of influence factors, such as the layout of the probes, the discrete program and the regularization method, was implemented as well. The result shows that the layout of the probe and the regularization method has great influence on the model. When the probe is located at the y direction of x-axis or the x direction of y-axis and Conjugate Gradient method is selected, a much better outcome can be achieved.

Abstract: The problem of noninvasive computing the epicardial surface potentials from torso surface potentials constitutes one form of the inverse problem of ECG, which can be acted as a regression problem with multi-input and multi-output. In this study, the SVR method is invoked to predict the inverse solutions, which compared with the common regularization methods. To build an effective SVR model, the hyper-parameters of SVR are set carefully by using the grid search optimization method. The experiment results shows that SVR method is an effective way for solving the inverse ECG problem, which can reconstruct more accurate epicardial surface potentials distribution than the common regularization method, such as Tikhonv method and LSQR method.