A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality.

基于Power Extrapolation和Adaptive Method的网页评估新算法

Google的PageRank算法通过对超链接结构的分析,有效地提高了搜索结果的排序质量。PowerExtrapolation算法通过特征值直接求解马尔可夫超链接矩阵的主特征向量,但该算法的迭代次数与参数d的选择密切相关,而参数d的确定目前无明显规律可寻。另一方面,AdaptiveMethod通过将马尔可夫超链接矩阵稀疏化以达到节省迭代时间的目的。文章在PowerExtrapolation算法的基础上引入AdaptiveMethod,实验结果初步证明了新算法可以减少迭代运算的时间。

SnO_2-based solid solutions for CH_4 deep oxidation: Quantifying the lattice capacity of SnO_2 using an X-ray diffraction extrapolation method

A series of SnO2‐based catalysts modified by Mn, Zr, Ti and Pb oxides with a Sn/M （M=Mn, Zr, Ti and Pb） molar ratio of 9/1 were prepared by a co‐precipitation method and used for CH4 and CO oxidation. The Mn3＋, Zr4＋, Ti4＋and Pb4＋cations are incorporated into the lattice of tetragonal rutile SnO2 to form a solid solution structure. As a consequence, the surface area and thermal stability of the catalysts are improved. Moreover, the oxygen species of the modified catalysts become easier to be reduced. Therefore, the oxidation activity over the catalysts was improved, except for the one modified by Pb oxide. Manganese oxide demonstrates the best promotional effects for SnO2. Using an X‐ray diffraction extrapolation method, the lattice capacity of SnO2 for Mn2O3 was 0.135 g Mn2O3/g SnO2, which indicates that to form stable solid solution, only 21%Sn4＋cations in the lattice can be maximally replaced by Mn3＋. If the amount of Mn3＋cations is over the capacity, Mn2O3 will be formed, which is not favorable for the activity of the catalysts. The Sn rich samples with only Sn‐Mn solid solution phase show higher activity than the ones with excess Mn2O3 species.

A SIMPLE PROOF OF STABILITY AND CONVERGENCE IN L＿2 FOR SOME DIFFERENCE SCHEMES AND THEIR EXTRAPOLATION METHOD FOR PARABOLIC EQUATIONS

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Fatigue life evaluation of girth butt weld within welded cast steel joints based on the extrapolation notch stress method

The fatigue life evaluation of the girth butt weld within the welded cast steel joint was studied based on the extrapolation notch stress method.Firstly,the mesh sensitivity of the finite element model of the welded cast steel joint was analyzed to determine the optimal mesh size.Based on the stress field analysis of the finite element model of the welded cast steel joint at the weld toe and weld root,the sharp model of the extrapolation notch stress method was applied to derive the effective notch stress of the rounded model belonging to the effective notch stress method,in which the key problem is to calculate the extrapolation point C,and the extrapolation point C has an exponential function relationship with the geometric parameters of the welded cast steel joint.By setting different values of geometric parameters,the corresponding value of parameter C is calculated,and then the functional relationship between the extrapolation point C and the geometric parameters can be obtained by the multiple linear regression analysis.Meanwhile,the fatigue life evaluation of the girth butt weld within welded cast steel joints based on the effective notch stress was performed according to the guideline recommended by the IIW(International Institute of Welding).The results indicate that the extrapolation notch stress method can effectively simplify the process of calculating the effective notch stress and accurately evaluate the fatigue life of the girth butt weld within welded cast steel joints.

Extrapolation Method for Cauchy Principal Value Integral with Classical Rectangle Rule on Interval

In this paper,the classical composite middle rectangle rule for the computation of Cauchy principal value integral(the singular kernel 1=(x-s))is discussed.With the density function approximated only while the singular kernel is calculated analysis,then the error functional of asymptotic expansion is obtained.We construct a series to approach the singular point.An extrapolation algorithm is presented and the convergence rate of extrapolation algorithm is proved.At last,some numerical results are presented to confirm the theoretical results and show the efficiency of the algorithms.

SVD-MPE: An SVD-Based Vector Extrapolation Method of Polynomial Type

An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors , where , N being very large. Such sequences arise, for example, in the solution of systems of linear or nonlinear equations by fixed-point iterative methods, and are simply the required solutions. In most cases of interest, however, these sequences converge to their limits extremely slowly. One practical way to make the sequences converge more quickly is to apply to them vector extrapolation methods. Two types of methods exist in the literature: polynomial type methods and epsilon algorithms. In most applications, the polynomial type methods have proved to be superior convergence accelerators. Three polynomial type methods are known, and these are the minimal polynomial extrapolation (MPE), the reduced rank extrapolation (RRE), and the modified minimal polynomial extrapolation (MMPE). In this work, we develop yet another polynomial type method, which is based on the singular value decomposition, as well as the ideas that lead to MPE. We denote this new method by SVD-MPE. We also design a numerically stable algorithm for its implementation, whose computational cost and storage requirements are minimal. Finally, we illustrate the use of SVD-MPE with numerical examples.

GENERALIZED INVERSE RATIONAL EXTRAPOLATION METHODS FOR MATRIX SEQUENCES

Assume that a convergent matrix sequence{An}:An→A（n→∞）, An,A∈C3×3.We want to form a new matrix sequence {Hn}, derived from {An}, which has also A aslimit and whose convergence is faster than the of {An}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {An} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is

EXTRAPOLATION FOR COLLOCATION METHOD OF THE FIRST KIND VOLTERRA INTEGRAL EQUATIONS

1. Introduction It is known that the following Cauchy problem for a parabolic partial differential equation (where the values at the right boundary, u.(1, t)=v(t) are unknown and sought for) is ill-posed: the solution (v) does not depend continuously on the data (g). In order to treat the ill-posedness and develop the numerical method, one reformulates the problem as a Volterra integral equation of the first kind wish a convolution type kernel (see Sneddon [1], Carslaw and Jaeger [2])

Submarine Magnetic Field Extrapolation Based on Boundary Element Method

In order to master the magnetic field distribution of submarines in the air completely and exactly and study the magnetic stealthy performance of submarine,a mathematic model of submarine magnetic field extrapolation is built based on the boundary element method(BEM).An experiment is designed to measure three components of magnetic field on the envelope surface surrounding a model submarine.The data in different heights above the model submarine are obtained by use of tri-axial magnetometers.The results show that this extrapolation model has good stabilities and high accuracies compared the measured data with the extrapolated data.Moreover,the model can reflect the submarine magnetic field distribution in the air exactly,and is valuable in practical engineering.

LeaderRank的外推加速方法

复杂网络中的节点排序在网络结构和传播动力学等研究中占据重要地位.LeaderRank作为一种重要的节点排序算法,已得到了广泛应用.在幂法计算LeaderRank的基础上,提出3种计算LeaderRank的外推方法,分别为Aitken外推法、幂外推法和改进幂外推法.为了对比各方法的优劣,在4个真实网络上进行数值实验,结果表明:Aitken外推法的计算速度优于幂外推法,而精度略差于幂外推法;改进幂外推法则在计算速度和精度上均有优良表现.

山洪灾害雨量预警指标分析方法评述与展望

山洪灾害预警指标是山洪灾害预报预警的核心,我国现阶段主要采用经验法和水位流量反推法确定雨量预警指标,并逐步推广应用复合预警指标法和动态临界雨量法。在系统阐述国内外常用雨量预警指标分析方法及其特点基础上,针对山洪灾害预警指标分析中需考虑的降雨时空分布变化、高含砂水流、泥石流及其他不确定因素影响问题,提出今后雨量预警指标研究方向。

光伏电站理论发电功率的优化计算模型与方法

光伏电站理论发电功率计算结果的准确性直接影响弃光电量的统计,对电网调度及光伏发展规划影响重大。理论发电功率的传统计算方法有样板逆变器法和气象数据外推法,当样板逆变器的出力受到限制时,样板逆变器法计算结果不准确,而气象数据外推法参数众多且难以确定。针对上述问题,提出了一种光伏电站理论发电功率优化计算方法。首先,介绍了样板逆变器法和气象数据外推法的计算原理,并分析了两种方法的特点和不足。然后,基于光伏电站历史出力及气象信息,提出了改进样板逆变器法和改进气象数据外推法。在实际应用中,当弃光未发生或者在弃光初始阶段采用计算精度更高的改进样板逆变器法开展计算,当样板逆变器出力受到限制时,切换至改进气象数据外推法进行求解。最后,对国内某光伏电站在不同气象条件下开展仿真计算,验证了所提方法的合理性和有效性。

71℃试验法寿命外推结果的影响因素分析

目的研究71℃试验法用于火工品贮存寿命外推结果的准确性。方法采用对比分析的方法,对美军标和国军标中71℃试验法的寿命影响因素进行分析。结果加速模型、试验条件和外推温度取值对火工品的寿命外推结果均有影响。结论71℃试验法评估结果的准确性取决于使用场景是否正确,试验条件设置是否合理,贮存环境温度取值是否准确,并提出了71℃试验法的使用建议。

基于自注意力和门控循环神经网络的雷达回波外推算法研究

为提升现有神经网络对雷达回波序列的时、空特征提取能力,建立外推性能更优的时、空序列预测模型,开展雷达回波外推算法改进研究。基于深圳市气象局与中国香港天文台共同建立的雷达回波数据集,在数据处理层面,通过改进对雷达回波图像序列归一化的方法,提升了常用的5种时、空序列预测模型对强回波的预测水平;在模型算法层面,将两个联立的自注意力结构引入ST-LSTM结构,组成新的循环门控单元,并将这些循环门控单元进行堆叠,建立ST-SARNN模型。选用CSI和POD作为精度评价指标,进行模型对比分析得到:(1)改进的归一化方法提升了近几年内常用的5种时、空序列预测模型对强回波的预测水平。(2)加入自注意力的ST-SARNN模型对雷达回波的预测性能显著优于ConvLSTM、PredRNN和MIM等模型。改进的归一化方法能改变样本数据分布,并在一定程度上提升模型外推性能;自注意力结构能够有效挖掘雷达回波序列的时、空特征,进而改进神经网络的外推表现。

动车组空心车轴应力强度因子研究

为研究动车组空心车轴应力强度因子,首先分析了车轴应力强度因子的影响因素,建立了含裂纹车轴有限元模型,并使用叠加法求解不同载荷下的应力强度因子。然后采用应力外推法和位移外推法计算了应力强度因子,并将计算结果与文献形状因子公式法进行对比。最后根据应力强度因子的一般解析式和位移外推法的计算结果,使用五次多项式对形状因子函数进行拟合,通过设置不同的裂纹深度和载荷验证了形状因子函数和解析式的适用性。结果表明该方法对于求解同一载荷模式下的车轴应力强度因子具有一定的参考价值。

光流法雷达外推产品在突发强降水预报中的应用

地形条件复杂的山丘区中小河流洪水突发性强、汇流时间短,高准确率和长时效性降水短时临近预报产品对提高突发洪水预报精度尤为关键。以2021年9月河南省鸭河口水库出现的千年一遇特大洪水为例,利用国家气象信息中心提供的三源融合格点实况降水资料,检验基于改进光流法的雷达外推降水预报产品在本次洪水过程中0~1 h和0~3 h降水预报的TS评分和预报偏差。结果表明:(1)改进光流法在0~1 h的逐小时降水预报上较为精准,累计雨量在50 mm以下时,TS评分在0.45~0.85之间;雨量在50~70 mm之间时,TS评分在0.35~0.70之间;雨量在70 mm以上时,TS评分在0.25~0.35之间。50 mm以上雨量有较高TS评分表现出改进光流法在极端强降水预报中的优势性。(2)改进光流法在0~3 h的降水预报上,累计雨量在50 mm以下时,TS评分在0.55~0.85之间;在50 mm以上时,TS评分在0.35~0.75之间。该降水预报产品不仅对极端性降水预报效果较好,且预报时效长达3 h,可为防洪调度提供更长的决策时间。(3)改进光流法在0~3 h的降水预报产品与融合实况格点降水相比,雨量在20 mm以下的预报结果比较接近,平均绝对误差在10 mm以内;雨量在20 mm以上时,随雨量增大,平均误差、平均绝对误差、均方根误差均逐渐增大。(4)改进光流法在0~3 h的降水预报产品对影响范围小、降水强度大、维持时间长、累计雨量大的极端强降水有较好的预报表现。研究成果可为洪水预报模型提供一种较为可靠的降水输入预报。

基于Extrapolation Tikhonov正则化算法的重力数据三维约束反演

通过研究重力数据三维反演解的病态性,利用基于拉格朗日插值方法的Extrapolation Tikhonov正则化方法来解决反演中解的不唯一性和不稳定性问题,该方法最大限度的减少了因正则化参数的引入而在反演结果中介入的误差,同时详细讨论了基于三种选择原则的正则化双参数的具体选择方法,模型试算结果表明,与原Tikhonov方法相比,该方法提高了反演的拟合精度.其次,为了消除核函数随深度增加而快速衰减对反演结果的影响,本文改进了前人的重力数据三维反演深度加权函数,改进后的加权函数与原函数相比能更好的识别异常体底部密度分布特征,对于埋深较深的异常体具有较好的识别效果,更好的解决了由近地面趋肤效应作用引起的密度分布不均的问题.同时,利用上下限约束函数限制每一个立方体的密度差范围,并应用于多组人工合成模型.结果表明:该反演方法能准确地获得正演模型的预设参数范围和位置.

基于频次与极值外推综合的载荷外推总体方法

载荷外推作为载荷谱编制的重要技术手段,当前研究缺乏对于载荷外推总体方法的全面梳理、马尔可夫稳态分布的求解方法适应性不够、缺乏不同非参频次外推方法的比较与选用原则,导致不便生成高精度载荷谱以支撑装备性能设计。围绕坦克在高机动和极限工况下的载荷谱编制问题,基于某坦克行进间身管位移数据样本,分别使用基于雨流矩阵及核密度估计的非参数外推法、基于马尔可夫链蒙特卡洛(Markov Chain Monte Carlo,MCMC)的信号重构法以及Metropolis-Hastings(简称MH)直接采样法进行了载荷频次外推,并针对MCMC的信号重构法提出了一种改良马尔可夫稳态分布的求解方法。应用所提出的频次-极值相结合的载荷外推总体方法对坦克身管位移进行了频次扩充与极值预测,并结合实车试验结果验证了方法的准确性。研究结果表明:改良的马尔可夫稳态分布求解方法是有效的;在样本长度足够、外推精度要求不甚高的情况下,MH直接采样法可作为一种新的频次外推方法;运用频次-极值相结合的载荷外推总体方法所得结果精度较高;形成的频次外推法选用原则对于载荷谱编制过程中的方法选择具有一定的指导意义。研究工作为装备载荷谱的高质量编制提供了成熟的技术路线和参考。

复合材料胶接用发泡胶的工艺验证与固化动力学

通过动态差示扫描量热分析(DSC)研究了一种中温固化的发泡胶的固化工艺和固化动力学。为证实DSC峰值温度T_(p)与升温速率β的自然对数存在线性关系,在DSC测试中除采用β为5、10、15和20 K/min的升温速率组合外,还特意设定升温速率β为1、2.718、7.389和20 K/min,则lnβ等于或近似为0、1、2、3以便于计算,由此可确定固化工艺参数并快速地估算活化能E_(a)。结合其他关于热固化、热分解甚至一些高分子材料结晶的文献数据,进一步证实了T_(p)与lnβ往往存在线性关系。利用上述线性关系所获得的特性温度参数T_(1)和ΔT值,可以解释活化能的大小并快速求解动力学数据。研究结果建立并证实了区别于Kissinger和Ozawa方法的另一种简易而且可靠的反应动力学求解方法,并用数学极限的方法进行推导给出了活化能的解析解。上述简易方法求解热致反应或结晶变化的动力学参数是合理有效的。