Papers by Keyword: Ill-Posed

Abstract: Regularization is a method for improving the solution of ill-posed problems with neural networks. In regularization, a penalty term, called regularizer or prior, is added to the performance function. The penalty term is weighted with a regularization parameter, , to balance the trade-off between model bias and model variance. We have compared the performances of different priors on several different time series data sets, to see if there is any consistent difference in performance between priors. The conclusions from our study on real world time series data has weight decay the best performance and the Bishop smoother is the worst choice.

Abstract: A regularization homotopy iterative method established for ill-posed nonlinear least squares problem. Two new regularization parameter selecting strategies are proposed, which are called direct search method and interval division method. The calculation results of nonlinear least squares problems show that the regularization homotopy iterative method and parameter selecting strategies proposed in this paper are correctly and applicable. And also calculation results of nonlinear adjustment of free networks with rank deficiency of Jianglong bridge pier displacement defor-mation monitoring control network show that the method not only decrease the iterative matrix con-dition number, but also make the condition number small fluctuation in full iterative process.

Abstract: The regularization which constructs with the first filter function is precisely the Tikhonov regularization. This article has proven the Tikhonov functional minimization problem is decides suitably, namely satisfies the solution the existence, the solution unique reconciliation to rely on continuously the data stability; and this minimization problem in solves the first class equation equally the normal equation. The numerical simulation experiment's result indicated that distinguishes the inverse with the regular reduction solution parameter to have the numerical precision to be high and the stability is good and convergence rate quick characteristic.

Abstract: It is difficult to solve the inverse problem because it always ill-posed. This paper introduced a new approach based on Genetic Algorithms (GA) for solve the parabolic equation inverse problem. The GA transforms the inverse problem into an optimization problem. The results of numerical simulation show that the method has high accuracy and quick convergent speed. And it is easy to program and calculate. It is worth of practical application.

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: In this paper we discuss properties of dense granular °ows and elaborate on some properties of a model which generalises the classical plastic potential model using elements of the double shearing model. It is shown how the model is embedded into a Cosserat continuum model. The proposed model recti¯es the ill-posedness of both the non-associated °ow rule and the double shearing model and may be used for both granular materials and also for metals which possess a micro-structure which is capable of rotation.