共查询到20条相似文献，搜索用时 125 毫秒
1.
2.
地球物理反演是指根据一组观测结果来估计假设的地下模型的参数。因为模型所伴隋的响应可能是模型参数的非线性函数,因此在反演中非线性最小二乘方法是有用的。反演的一种普通类型是利用马奎特—列文伯格法实现迭代的阻尼最小二乘。通常,这种方法是通过常规的方法解有关的法方程来实现的。然而对于同样的法方程采用奇异值分解法(SVD)在计算精度上就会有明显的提高。迭代的最小二乘模拟在地球物理的多种问题中得到了应用,用两个实例来说明:(1)地震子波的反褶积;(2)根据地表重力资料推断一个隐伏台阶的位置。再广而言之,非线性最小二乘反演可以用于估计任意一组能得出适当数学描述的地球物理观测结果所对应的地下模型。 相似文献
3.
对于一般增长曲线模型,当设计阵和协方差阵满足一定的条件时,均值矩阵(XBZ)的最小二乘估计(LSE)与最佳线性无偏估计(BLUE)相等,可用LSE代替BLUE。当这些条件不满足时,用LSE代替BLUE就要蒙受一些损失,有时这种损失很大,因而研究这种损失的大小显得相当重要,通常用它们协方差阵的差异来度量,从不同的准则出发,可以定义不同的相对效率,利用广义行列式定义了一种新的相对效率,并给出了它们的下界。 相似文献
4.
最小二乘直线拟合方法及其在同位素地质年代学中的应用研究 总被引：2，自引：0，他引：2
最小二乘法(least squares method)是直线拟合常用的方法,在自然科学和社会科学内被广泛应用,尤其在同位素地质年代学领域更是必不可少。仅考虑x或y误差的普通最小二乘法(normal/ordinary least squares)广为人知,但事实上最小二乘法并非如此简单,尤其是在同时考虑x、y误差(乃至误差相关)并采用加权处理时,其数学处理方法会变得十分复杂,而此时普通最小二乘法显得极不合理。本文在前人研究的基础上,结合同位素地质年龄计算的需要,对直线拟合的最小二乘法进行了系统地总结研究,详细介绍了普通最小二乘法、加权普通最小二乘法(normal/ordinary weighting least squares)、标准加权最小二乘法(standard weighting model)、标准独立加权最小二乘法(standard independent weighting model)、独立加权最小二乘法(independent weighting model)及误差相关最小二乘法(error correlated independent weighting model)的数学原理及相关变量的计算过程。在此基础上,进一步阐述了MSWD(mean squared weighted deviation)这个同位素地质年代学中经常使用的参数的数学意义,以及MSWD对计算结果的评判意义。准确理解这些数学方法,对于我们合理选择同位素地质年龄相关参数的计算方法,科学评价直线拟合结果并探讨其地质意义至关重要。我们的研究同时有助于拓展和完善数学领域最小二乘法的基本理论,并可用于其他领域相似的研究之中。 相似文献
5.
针对黏介质成像存在的问题及最小二乘逆时偏移方法的优势,通过广义标准线性固体(GSLS)的三维黏声波动方程,基于三维黏声波动方程的伴随算子及最小二乘逆时偏移框架,实现了三维黏声最小二乘逆时偏移方法。采用极性编码技术大幅度降低黏声最小二乘逆时偏移算法的计算量与内存,使三维黏声最小二乘逆时偏移算法的实用化成为可能。在模型试算部分,首先通过Marmousi模型验证了该方法对传统声波最小二乘逆时偏移方法的优势,最后对三维含Q平层模型及盐丘模型进行试算,证明了三维黏声最小二乘逆时偏移算法的正确性。 相似文献
6.
进化-最小二乘支持向量机的边坡稳定性估计 总被引：1，自引：0，他引：1
针对最小二乘支持向量机的参数选择问题,用遗传算法来搜索最小二乘支持向量机的相关参数,避免了人工搜索参数的盲目性,提高了模型的推广性能。根据大量的实际边坡工程数据,建立了基于进化-最小二乘支持向量机的边坡稳定性模型,并将其应用于估计丁家河磷矿自然边坡稳定状况。计算结果与工程实际情况一致,表明了该方法的有效性和合理性。 相似文献
7.
8.
9.
本文针对阵列式天线探地雷达系统的目标成像问题,理论模拟分析了最小二乘(LS)估计、Capon估计、幅度相位估计(APES)三种波束形成算法在目标回波到达角(direction of arrival,DOA)估计上的效果和精度,提出了基于DOA估计的阵列式探地雷达逆向投影目标成像方法。该方法综合利用多输入多输出(MIMO)阵列信号估计得到的目标回波信号DOA和阵列空间观测信息对目标体进行成像,通过成像点空间扫描对各测点估计DOA幅度值在成像点的加权积分进行目标定位及反射强度估计。该方法实现简单高效,可以广泛应用于地下简单目标体的快速成像。 相似文献
10.
变形监测在工程项目中是一项非常重要且必不可少的环节,因此,获得原始监测数据并进行有效的处理和预测对项目的安全实施具有关键作用。本文以长春某段地铁监测数据为例,分别用丹麦法稳健估计法和最小二乘法进行数据处理,得出丹麦法稳健估计在单一状态抗拒粗差方面优于最小二乘法的结论。 相似文献
11.
Yong Ge Tianjun Wu Jianghao Wang Jianghong Ma Yunyan Du 《Earth Science Informatics》2012,5(3-4):137-152
In optical image registration, the reference control points (RCPs) used as explanatory variables in the polynomial regression model are generally assumed to be error free. However, this most frequently used assumption is often invalid in practice because RCPs always contain errors. In this situation, the extensively applied estimator, the ordinary least squares (LS) estimator, is biased and incapable of handling the errors in RCPs. Therefore, it is necessary to develop new feasible methods to address such a problem. This paper discusses the scaled total least squares (STLS) estimator, which is a generalization of the LS estimator in optical remote sensing image registration. The basic principle and the computational method of the STLS estimator and the relationship among the LS, total least squares (TLS) and STLS estimators are presented. Simulation experiments and real remotely sensed image experiments are carried out to compare LS and STLS approaches and systematically analyze the effect of the number and accuracy of RCPs on the performances in registration. The results show that the STLS estimator is more effective in estimating the model parameters than the LS estimator. Using this estimator based on the error-in-variables model, more accurate registration results can be obtained. Furthermore, the STLS estimator has superior overall performance in the estimation and correction of measurement errors in RCPs, which is beneficial to the study of error propagation in remote sensing data. The larger the RCP number and error, the more obvious are these advantages of the presented estimator. 相似文献
12.
13.
Application of expert rules in indirect approaches for landslide susceptibility assessment 总被引：3，自引：2，他引：1
Landslide susceptibility (LS) assessment by indirect approaches presents some limitations due to (1) the tendency to simplify the environmental factors (i.e., variables) and (2) the assumptions that landslides occur under the same combination of variables for a study site. Recently, some authors have discussed the interest to introduce expert knowledge in the indirect approaches in order to improve the quality of indirect LS maps. However, if the results are reliable, the procedures used seem fastidious and a very good knowledge of the study site is essential. The objectives of this paper are to discuss a methodology to introduce the expert knowledge in the indirect mapping process. After the definition of the expert rules associated to three landslide types, several indirect LS maps are produced by two indirect exploratory approaches, based on fuzzy set theory and on a modification of a bivariate method called expert weight of evidence. Then, the indirect LS maps are confronted to a landslide inventory and a LS map produced by a direct approach. The analyses indicate that the methodology used to introduce the expert rules in the mapping process increases the predictive power of indirect LS map. Finally, some indications about advantages and drawbacks of each approach are given to help the geoscientist to introduce his expert knowledge in the landslide susceptibility mapping process. 相似文献
14.
固定配比的钠化膨润土与土壤在不同pH条件下对重金属离子的吸附效果研究 总被引：1，自引：0，他引：1
研究了固定配比的钠化膨润土与土壤在不同pH条件下对重金属离子的吸附效果。钠化膨润土与污染土壤按质量比1∶10和1∶20的比例混合,用碳酸氢铵-二乙三胺五乙酸(AB-DTPA)法提取土壤中有效态重金属。结果表明,在钠化膨润土与土壤质量比为1∶20的条件下,取得了最佳的修复效果;在pH=9.14时该混合土壤对重金属的总体吸附效果最佳。在实际土壤修复中,针对不同重金属污染,应灵活调整修复材料与污染土壤的配比和土壤的pH条件。 相似文献
15.
悬索缆道测流,往往使流速仪形成垂直偏角,对流速有一定影响.分别率定了LS25-1型旋桨流速仪和LS68-1型旋杯流速仪在不同下倾角时与流速的关系流速仪的垂直偏角对流速有明显影响,并随偏角的加大而增加,偏角在10°以内影响不大;同时也率定了LS68-1型旋杯流速仪自动调整垂直下倾角时与流速的关系,下倾角在10°～30°以内对流速无明显变化,超过30°时,流速系统偏小.解决办法是(1)流速小有偏角时用LS68-1型旋杯流速仪,流速大时用LS25-3型旋桨流速仪,二者均有自动调平的功能;(2)合理选择铅鱼的型式和重量,本文提供了数据. 相似文献
16.
In an open pit mine, the selection of blocks for mill feed necessitates the use of a conditionally unbiased estimator not only to maximize profits, but also to predict precisely the grades at the mill. Estimation of blocks usually is done using a series of blasthole assays on a regular grid. In many instances, the blasthole grades show a lognormal-like distribution. This study examines an estimator based on the hypothesis of bilognormality between the true block grade and the estimate obtained using the blastholes. The properties of the estimator are established and the estimator is proven to be conditionally unbiased. It is almost as precise as the lognormal kriging estimator when the points are multilognormal. However, it is more precise than lognormal krigings when only univariate lognormality is present or when the distribution is not exactly lognormal. The estimator also is shown to be robust to errors in the specifications of the variogram model or of the expectation of Z. Contrary to lognormal krigings, the estimator does only a slight correction to the original estimate obtained using the blastholes assays. 相似文献
17.
In the predicting of geological variables, artificial neural networks (ANNs) have some drawbacks including possibility of getting trapped in local minima, over training, subjectivity in the determining of model parameters and the components of its complex structure. Recently, support vector machines (SVM) has been found to be popular in prediction studies due to its some advantages over ANNs. Because the least squares SVM (LS‐SVM) provides a computational advantage over SVM by converting quadratic optimization problem into a system of linear equations, LS‐SVM method is also tried in study. The main purpose of this study is to examine the capability of these two SVM algorithms for the prediction of tensile strength of rock materials and to compare its performance with ANN and linear regression (MLR) models. Total porosity, sonic velocity, slake durability index and aggregate impact value were used as input in modeling applications. Favorite performance evaluation measures were employed to assess developed models. The results determined in study indicate that the SVM, LS‐SVM and ANN methods are successful tools for prediction of tensile strength variable and can give good prediction performances than MLR model. Although these three methods are powerful artificial intelligence techniques, LS‐SVM makes the running time considerably faster with the higher accuracy. In terms of accuracy, the LS‐SVM model resulted in error reductions relative to that of the other models. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
18.
Highly Robust Variogram Estimation 总被引：5，自引：0，他引：5
Marc G. Genton 《Mathematical Geology》1998,30(2):213-221
The classical variogram estimator proposed by Matheron is not robust against outliers in the data, nor is it enough to make simple modifications such as the ones proposed by Cressie and Hawkins in order to achieve robustness. This paper proposes and studies a variogram estimator based on a highly robust estimator of scale. The robustness properties of these three estimators are analyzed and compared. Simulations with various amounts of outliers in the data are carried out. The results show that the highly robust variogram estimator improves the estimation significantly. 相似文献
19.
BLU Estimators and Compositional Data 总被引：5，自引：0，他引：5
One of the principal objections to the logratio approach for the statistical analysis of compositional data has been the absence of unbiasedness and minimum variance properties of some estimators: they seem not to be BLU estimator. Using a geometric approach, we introduce the concept of metric variance and of a compositional unbiased estimator, and we show that the closed geometric mean is a c-BLU estimator (compositional best linear unbiased estimator with respect to the geometry of the simplex) of the center of the distribution of a random composition. Thus, it satisfies analogous properties to the arithmetic mean as a BLU estimator of the expected value in real space. The geometric approach used gives real meaning to the concepts of measure of central tendency and measure of dispersion and opens up a new way of understanding the statistical analysis of compositional data. 相似文献
20.
Estimating Mean Fracture Trace Length and Density from Observations in Convex Windows 总被引：19，自引：3，他引：16
M. Mauldon 《Rock Mechanics and Rock Engineering》1998,31(4):201-216
Summary Although window samples of fracture traces are widely recognized to be length-biased and censored, they are often the best
source of data for inferring statistical parameters of fracture sets. This paper presents new estimators for mean fracture
trace length and density that correct for the effects of bias and censoring. A stereological estimator of mean trace length
is derived for parallel traces in a rectangular sampling window, an end-point estimator of mean trace length is derived for
windows with arbitrary convex boundaries and for arbitrary trace length distributions, and an end-point estimator of trace
density is derived for windows with arbitrary convex boundaries and for arbitrary trace length and trace orientation distributions.
Results for rectangular and circular windows are obtained as special cases of the general solutions for arbitrary convex windows.
When applied to circular windows, the end-point estimator of mean trace length is, in addition, independent of the trace orientation
distribution. The estimators are easily determined from field data. The end-point estimator of trace density requires knowing
only the area of the window and the number of end-points inside the window. The end-point estimator of mean trace length,
when applied to circular windows, requires, in addition, the number of end-points outside the window (of those traces that
intersect the window) and the stereological estimator of mean trace length requires only the apparent mean trace length and
the height of the window. 相似文献