1D SNMR吉洪诺夫正则化反演方法研究

地面核磁共振(SNMR)技术是目前世界上直接用来寻找地下水的技术。本文在讨论反演基本问题的基础上,用共轭梯度法实现了核磁共振的一维正则化反演。通过反演理论数据、噪声数据和实测数据,说明该方法的可靠性。     

正则化Kaczmarz算法在页岩纳米CT重构中的应用

利用X射线计算机断层成像（CT）方法对页岩的扫描成像是一种无损的,对研究页岩微纳孔隙结构有重要意义的方法.传统的CT重构通常使用的是显式的滤波反投影（Filtered Back Projection,FBP）方法,该算法具有较快的成像速度,但常伴随有伪影或不稳定等情况.对于纳米CT而言,可以通过迭代优化的方法对投影数据进行成像,传统的迭代成像有收敛速度慢导致的计算时间长等缺点.Kaczmarz算法作为一种重要的代数重建技术（ART）,由于其几何意义明显,操作容易等优点,在CT重构中起着重要的作用,我们可以通过块状迭代或随机迭代的方式对其收敛速度进行改进.对于所求解问题的不适定性,代数重建过程中需要引入正则化的技巧来改善解的稳定性.本文根据实际问题的需要,使用页岩数值模型,验证了正则化Kaczmarz方法的有效性,并对重庆漆辽龙马溪组页岩样品的实际数据进行了处理,得到了较好的效果.

     

Retrieval Snow Depth by Artificial Neural Network Methodology from Integrated AMSR-E and In-situ Data —— A Case Study in Qinghai-Tibet Plateau

On the basis of artificial neural network （ANN） model, this paper presents an algorithm for inversing snow depth with use of AMSR-E （Advanced Microwave Scanning Radiometer-Earth Observing System （EOS）） dataset, i.e., brightness temperature at 18.7 and 36.5GHz in Qinghai-Tibet Plateau during the snow season of 2002-2003. In order to overcome the overfitting problem in ANN modeling, this methodology adopts a Bayesian regularization approach. The experiments are performed to compare the results obtained from the ANN-based algorithm with those obtained from other existing algorithms, i.e., Chang algorithm, spectral polarization difference （SPD） algorithm, and temperature gradient （TG） algorithm. The experimental results show that the presented algorithm has the highest accuracy in estimating snow depth. In addition, the effects of the noises in datasets on model fitting can be decreased due to adopting the Bayesian regularization approach.     

Spectral analysis of nonlocal regularization in two‐dimensional finite element models

Strain‐softening in geomaterials often leads to ill‐posed boundary‐valued problems (BVP), which cannot be solved with finite element methods without introducing some kind of regularization such as nonlocal plasticity. Hereafter we propose to apply spectral analysis for testing the performance of nonlocal plasticity in regularizing ill‐posed BVP and producing mesh‐independent solutions when local plasticity usually fails. The spectral analysis consists of examining the eigenvalues and eigenvectors of the global tangential stiffness matrix of the incremental equilibrium equations. Based on spectral analysis, we propose a criterion for passing or failing the test of constitutive regularization in the context of BVP. If the eigenvalues of the tangential operator are all positive then the regularization succeeds, otherwise it fails and may not prevent artificial mesh‐dependent solutions from appearing. The approach is illustrated in the particular case of a biaxial compression with strain‐softening plasticity. In this particular case, local softening plasticity is found to produce negative eigenvalues in the tangential stiffness matrix, which indicates ill‐posed BVP. In contrast, nonlocal softening plasticity always produces positive eigenvalues, which regularizes ill‐posed BVP. The dominant eigenvectors, which generate localized deformation patterns, have a bandwidth independent of mesh size, provided that the mesh is fine enough to capture localization. These mesh‐independent eigenmodes explain why nonlocal plasticity produces numerical solutions that are mesh‐independent. Copyright © 2011 John Wiley & Sons, Ltd.     

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半参数模型在平面坐标转换中的应用

坐标转换在测绘领域一直起着至关重要的作用,而模型的选取又直接制约着转换的精度,通常在坐标转换中采用相似变换（Hermert）的方法,在平面坐标转换过程中一般采用4参数模型。然而当系统误差不可忽略时,该模型处理得到的结果并不理想。本文将半参数模型应用到平面坐标转换中,分别采用4参数模型和半参数模型两种方法对实验数据进行了处理,并进行了对比与分析。实验结果表明：在处理带有系统误差的平面坐标数据时,半参数模型比传统的参数模型更加精确。     

基于非局部总变差的消除不规则采样遥感图像复原方法

提出一种消除不规则采样的遥感图像复原方法,该方法结合了ACT算法和总变差（TV）图像复原模型以达到同时去除多种图像退化因素的目的,并且结合非局部均值（NLM）算子给出了基于NLTV的消除不规则采样遥感图像复原模型,最后使用算子分裂与扩展的坎贝尔投影算法求解模型。实验结果表明,该方法能够有效减少复原图像的阶梯效应并提高复原图像的纹理细节信息。     

基于ALR的Hopfield神经网络在高程拟合中的应用

运用具有正规化项的增广拉格朗日函数作为神经网络的能量函数,辅助二次曲面拟合,进一步探索Hopfield神经网络在高程拟合中的应用。实际算例表明,该方法可以大大提高神经网络的计算效率和可靠性。     

退化抛物型方程的广义T—周期解

本文证明了退化抛物型方程的边值问题