NLS问题的不适定性及正则化解算方法     

唐利民 《测绘科学》2010,35(6):103-104,235

本文进一步完善定义了NLS问题的两种不适定性,对产生这两种不适定问题的现象进行了分析。借助于正则化理论,通过添加稳定泛函,结合高斯-牛顿法,构造了不适定NLS问题的正则化高斯-牛顿法求解公式;解决了普通高斯-牛顿法在迭代过程中其Jacobian矩阵是秩亏或者严重病态导致的不能收敛的问题;给出了非线性秩亏自由网平差的正则化高斯-牛顿法步骤;以几个经典NLS问题为例进行了数值实验,说明了本文所提方法的适用性。  相似文献   

贝叶斯正则化的Elman神经网络电离层TEC预报模型   总被引：1，自引：0，他引：1  

汤俊  高鑫 《大地测量与地球动力学》2020,40(8):799-805

利用2017年中低纬电离层总电子含量、地磁活动指数、年积日等参数,首次建立基于贝叶斯正则化(Bayesian regularization)的Elman回归神经网络(BR-Elman)的电离层TEC预报模型。同时,根据地磁活动指数的变化特征,分别进行平静电离层和扰动电离层预报建模。实验结果表明,该方法在平静期5 d预测值的均方根误差为1.19 TECu,残差为1.03 TECu,相关系数为0.93;在扰动期5 d预测值均方根误差为1.34 TECu,残差为1.01 TECu,相关系数为0.91。贝叶斯正则化的BP神经网络模型以及传统BP神经网络模型在平静期与扰动期5 d的预测上,均方根误差最小为1.87 TECu,残差最小为1.50 TECu,相关系数最优为0.87。通过对比分析,该模型较其他2个模型的预报效果有明显改善。  相似文献   

INTEGRAL REPRESENTATIONS AND REGULARIZATIONS FOR A DIVERGENT SERIES SOLUTION OF A BEAM SUBJECTED TO SUPPORT MOTIONS     

J. T. CHEN  H.-K. HONG  C. S. YEH  S. W. CHYUAN 《地震工程与结构动力学》1996,25(9):909-925

Derived herein is the integral representation solution of a Rayleigh-damped Bernoulli–Euler beam subjected to multi-support motion, which is free from calculation of a quasi-static solution, and in which the modal participation factor for support motion is formulated as a boundary modal reaction, thus making efficient calculation feasible. Three analytical methods, including (1) the quasi-static decomposition method, (2) the integral representation with the Cesàro sum technique, and (3) the integral representation in conjunction with Stokes' transformation, are presented. Two additional numerical methods of (4) the large mass FEM simulation technique and (5) large stiffness FEM simulation technique are easily incorporated into a commercial program to solve the problem. It is found that the results obtained by using these five methods are in good agreement, and that both the Cesàro sum and Stokes' transformation regularization techniques can extract the finite part of the divergent series of the integral representation. In comparison with the Mindlin method and Cesàro sum technique, Stokes' transformation is the best way because it is not only free of calculation of the quasi-static solution, but also because it can obtain the convergence rate as rapidly as the mode acceleration method can.  相似文献   

一种基于Helmert方差分量估计的岭参数确定方法   总被引：5，自引：2，他引：3  

戴吾蛟  冯光财  朱建军 《大地测量与地球动力学》2006,26(4):30-33

为了使岭参数具有一个明确的含义,提出了一种基于Helm ert方差分量估计的岭参数确定方法。该方法把约束条件作为一类参数之间互相独立的虚拟观测,从而把岭参数转变为两类观测值的权比,然后用Helm ert方差分量估计的方法确定岭参数。通过算例,比较了该方法与岭迹法、L曲线法的效果。结果表明,该方法不仅计算过程简单、直接,而且精度也优于其他几种方法。  相似文献   

Undersea Buried Pipeline Reconstruction Based on the Level Set and Inverse Multiquadric Regularization Method     

SHANG Wenjing  XUE Wei  XU Yidong  MAKAROV Sergey B.  LI Yingsong 《中国海洋大学学报(英文版)》2022,21(1):101-112

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 pa-rameters 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.  相似文献