最小一乘方松弛计算法

以加权最小二乘法为基础的最小一乘方松弛算法,能有效削弱异常数据的影响,获得更稳健的回归方程.该算法适用于多元线性回归模型的参数估计,并以实例验证了该算法的稳健性.     

基于丹麦法稳健估计在地铁变形监测中的应用

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。     

正交最小二乘法及其在分析化学中的应用

介绍了一种线性模型参数回归分析方法-正交最小二乘法，并以电子探针微区分析技术分析环境样品的数据为例，对正交最小二乘法和经典最小二乘法的结果进行了详细比较。数据处理结果表明，当变自量和因变量都同时存在测量误差时（或自变量的测量误差与因变量的测量误差相比不能忽略时），正交最小二乘法获得的回归系数优于经典最小二乘法。对正交最小二乘法中的线性模型能解释的方差与经典最小二乘法中的相关系数的关系也进行了讨论。     

回归预测模型的稳健性讨论--以润扬大桥工程为例

经典的LS估计法(least squares estimation,LS estimation)是对每个观测数据都给予相同的权重,由此带来了对于异常值的处理不当,从而影响了回归模型的有效性,本文采用迭代加权最小二乘法来进行稳健估计(RobustEstimation),并基于MATLAB软件结合润扬大桥工程实例说明了此法的有效性。     

岩石抗剪强度参数的稳健估计

提出了Ｍ－稳健估计计算岩体抗剪强度参数Ｃ,ｆ值的计算模型和方法。通过对白云鄂博主矿原位试验数据的稳健估计计算结果与最小二乘法的计算结果的对比分析表明：采用稳健估计的方法所估计出的参数更可靠。     

基于偏最小二乘回归的融雪型洪水预报模型

本文采用偏最小二乘回归法对新疆塔什库尔干河流的实测流量资料进行分析,建立了日平均流量的偏最小二乘回归模型,采用建立的模型对2001年日平均流量进行了预报。研究分析表明,结果比较合理,这为融雪型洪水预报提供了一种新的思路和研究方法。     

丹麦法稳健估计在隧道椭圆拟合中的应用

隧道断面在设计时为一标准圆形,受到施工及外部环境的影响变形为偏心率很小的椭圆。减小粗差影响、精确确定椭圆的几何参数是其研究的重点。通过对上海某一隧道断面的测量试验,得出用丹麦法稳健估计可以有效减小粗差的影响,而且拟合值可以很好地逼近无粗差情况下的最小二乘拟合值。采用Matlab 语言实现算法,并详细介绍了用二项式变换求解椭圆参数的方法。     

油气勘探风险评价的偏最小二乘-最大熵法模型及应用

油气勘探风险的定量评价一直是国内外研究的难点。作者在分析传统风险评价方法的优缺点、剖析偏最小二乘法和最大熵法优势的基础上,首次提出了偏最小二乘-最大熵（PLSME）风险分析模型。偏最小二乘法较好地实现了多元线性回归、主成分分析和典型相关分析的有效综合,通过自变量的PLS回归线性处理,不仅能消除粗差解决变量之间的相关性问题,而且能辨识每一个自变量对因变量的控制程度;最大熵法通过对偏最小二乘得出的风险因子与总经济效益净现值关系式的检验,利用最大值、最小值和最可能值的训练,能了解指标最终服从的概率分布,客观得出风险的大小。两者结合起来构建的PLSME模型,能使风险评价结果更加准确、合理和客观。通过对四川德阳新场气田的实例应用,表明偏最小二乘一最大熵评价方法科学可行,对同类研究具有借鉴作用。     

偏最小二乘回归模型的城市水资源承载能力研究

影响城市水资源承载力的各个因素中,经常存在多重相关性,采用传统最小二乘回归法建模,其估计参数存在较大误差,预测精度降低.运用偏最小二乘回归方法,借助主成分分析与典型相关分析,采用成分提取的方法,克服了自变量间的多重相关性,建立了城市水资源承载能力模型,并对模型进行了分析,得到较为满意的效果.     

改进的最小二乘法在水文分析计算中的应用

在水分析计算中，经常涉及到变量之间的线性或非线性拟合，而在拟合各种特性曲线时，通常应用以实测资料与拟合曲线间的误差平方和最小作为目标函数的方法——最小二乘法，但这种方法忽视了所有实测点应与拟合曲线间的相对误差尽量不超过某一百分比的原则，为了达到上述要求，提出了非线性的加权最小二乘法及线性相关方程的最小距离平方和法，探讨改进了传统的最小二乘法达到优化的效果。最小距离平方和法与常用的图解法相比，本法所得成果较为客观；与传统的单方向(x或y方向)最小二乘回归法相比，所求线性方程不会因坐标系的选取而改变。最后应用算例进行了初步讨论。     

土壤铅含量高光谱遥感反演中波段选择方法研究

利用高光谱遥感数据进行了南京郊外土壤重金属元素铅的含量反演,由于高光谱数据波段众多,波段选择或变换至关重要。比较了基于次贪婪的前向选择模型的最小角度拟合和基于遗传算法进行波段选择的最小二乘和偏最小二乘拟合,结果发现基于遗传算法的偏最小二乘反演结果优于全波段的偏最小二乘,表明波段选择在高光谱反演重金属中是有益的。尽管采取了波段选择后的各方法在反演时均能达到70%以上的训练精度,但因遗传算法搜索的解空间范围更宽广,使得基于遗传算法的偏最小二乘优于前向选择模型的最小角度拟合。最后还比较了基于遗传算法的普通最小二乘和偏最小二乘拟合,结果表明偏最小二乘更优,因此在高光谱反演重金属含量当中,偏最小二乘精度较高,而在波段选择方法中,遗传算法更优。     

Contaminants in sediments: Using robust regression for grain-size normalization

Sediment contaminant concentrations usually show an inverse correlation with grain size. This can cause difficulties in distinguishing real differences in contamination from artifacts caused by variations in sediment texture. To overcome this, regression analysis is frequently used to remove the dependency of concentrations on grain size. However, least squares regression lines can be affected markedly by the presence of a small number of unusual samples in the dataset. These outliers may represent samples which are more severely contaminated or which were derived from areas with different underlying geology. They can be removed semi-manually, but robust regression methods such as least absolute values provide a convenient and objective alternative. The methods are illustrated using an example dataset of metal contaminants in sediments from the Humber Estuary, United Kingdom. Least squares regression on the complete dataset yields a rather poor grain size normalization for several elements. By contrast, least absolute values regression produces results very similar to those obtained by least squares regression after careful manual removal of outliers, but it avoids the need for subjective judgments of which data points to omit from the analysis. The intercepts of several of the fitted regression lines were non-zero, indicating that regression-based normalization is preferable to methods based on ratios.     

Combining Robustness with Efficiency in?the?Estimation of the Variogram

In the present paper, we propose a new method for the estimation of the variogram, which combines robustness with efficiency under intrinsic stationary geostatistical processes. The method starts by using a robust estimator to obtain discrete estimates of the variogram and control atypical observations that may exist. When the number of points used in the fit of a model is the same as the number of parameters, ordinary least squares and generalized least squares are asymptotically equivalent. Therefore, the next step is to fit the variogram by ordinary least squares, using just a few discrete estimates. The procedure is then repeated several times with different subsets of points and this produces a sequence of variogram estimates. The final estimate is the median of the multiple estimates of the variogram parameters. The suggested estimator will be called multiple variograms estimator. This procedure assures a global robust estimator, which is more efficient than other robust proposals. Under the assumed dependence structure, we prove that the multiple variograms estimator is consistent and asymptotically normally distributed. A simulation study confirms that the new method has several advantages when compared with other current methods.     

Fast automatic solution of the inverse resistivity problem

The paper presents a fast automatic approach to solve the inverse resistivity problem, assisted by optimization, which is a non-linear model-fitting technique. The selected inverse problems are ill-posed and the inverse solution is defined by ‘best fit’ in the sense of least-squares. Formulations are presented in a systematic manner for Newton’s method, least squares method and Marquardt’s modification (ridge regression) method based on local linearization of non-linear problem. The convergence of least-squares method and Marquardt’s method, to provide a robust solution, are first tested on a theoretical model and effectiveness of Marquardt’s method is demonstrated, and then two-field apparent resistivity curves from Banda district, India are interpreted and discussed.     

Outlier-resistant errors-in-variables regression: anomaly recognition and grain-size correction in stream sediments

Regression analysis is a well-established method to correct for grain size differences in suites of sediments. However, distortion caused by the presence of outliers and imprecision in both variables can hinder many common regression models from performing adequately. Median sum of weighted residuals (MSWR) regression is strongly outlier-resistant and accounts for imprecision in both variables for each member of a dataset. In a case study of Ni and Pb normalisation for a suite of stream sediments in NE Estonia, the ability of MSWR regression to detect anomalies was compared to ordinary least squares, weighted least squares, least absolute deviation and least median of squares regression. MSWR regression not only revealed more anomalous samples than the other methods, but also was able to distinguish anomalies in samples at comparatively low heavy metal concentration. This feature is particularly significant when tracking heavy metal dispersion downstream from point sources.     

Regression diagnostics and robust regression in geothermometer/geobarometer calibration: the garnet-clinopyroxene geothermometer revisited

Abstract The calibration of geothermometers and geobarometers should involve not only the determination of the parameters in the equation used, but also the uncertainties on, and the correlations between, these parameters. This necessitates the use of a technique such as least squares. Given the poor performance of least squares in the presence of outliers in the data, techniques for identifying outliers for exclusion—regression diagnostics, and techniques for handling data which include outliers—robust regression and jackknifing, are essential. These techniques are summarized and their importance is emphasized, and they are applied to the calibration of the garnet-clinopyroxene Fe-Mg exchange geothermometer.
The experimental data of Raheim & Green (1974) and Ellis & Green (1979) are explored using regression diagnostics to discover outliers in the data. After exclusion of the two influential outliers found, a new geothermometer equation for garnet-clinopyroxene Fe-Mg exchange is derived using robust regression and based on all the data: thus, T (K) = 2790 + 10 P + 3140x_ca,g/1.735 + In K _D where T is in Kelvin and P is in kbar. This equation, as might be hoped, is essentially identical to that of Ellis & Green (1979). Equations for calculating the uncertainty in a calculated temperature, contributed by uncertainties in the calibration, are also derived.     

Fitting variogram models by weighted least squares

The method of weighted least squares is shown to be an appropriate way of fitting variogram models. The weighting scheme automatically gives most weight to early lags and down-weights those lags with a small number of pairs. Although weights are derived assuming the data are Gaussian (normal), they are shown to be still appropriate in the setting where data are a (smooth) transform of the Gaussian case. The method of (iterated) generalized least squares, which takes into account correlation between variogram estimators at different lags, offer more statistical efficiency at the price of more complexity. Weighted least squares for the robust estimator, based on square root differences, is less of a compromise.     

基于LSSVM与MCS的路基沉降可靠度分析

提出了一种计算路基沉降可靠度的新方法。基于FLAC中的修正剑桥模型,以最小二乘支持向量机为核心技术,结合蒙特卡罗法构建计算模型。由于修正剑桥模型参数较多,对模型参数进行了敏感性分析,将对沉降影响较大的参数确定为随机变量。选取训练样本对支持向量机进行训练,按照随机变量的概率分布进行抽样,馈送到最小二乘支持向量机得到相应的响应值,用Matlab编制程序完成可靠度计算,并进行了算例分析。计算结果表明,蒙特卡罗法结合支持向量机的沉降可靠度计算方法应用于公路软基沉降可靠度计算是可行的。     

An approximate dynamic programming approachto decision making in the presence of uncertainty for surfactant-polymer flooding

The least squares Monte Carlo method is a decision evaluation method that can capture the effect of uncertainty and the value of flexibility of a process. The method is a stochastic approximate dynamic programming approach to decision making. It is based on a forward simulation coupled with a recursive algorithm which produces the near-optimal policy. It relies on the Monte Carlo simulation to produce convergent results. This incurs a significant computational requirement when using this method to evaluate decisions for reservoir engineering problems because this requires running many reservoir simulations. The objective of this study was to enhance the performance of the least squares Monte Carlo method by improving the sampling method used to generate the technical uncertainties used in obtaining the production profiles. The probabilistic collocation method has been proven to be a robust and efficient uncertainty quantification method. By using the sampling methods of the probabilistic collocation method to approximate the sampling of the technical uncertainties, it is possible to significantly reduce the computational requirement of running the decision evaluation method. Thus, we introduce the least squares probabilistic collocation method. The decision evaluation considered a number of technical and economic uncertainties. Three reservoir case studies were used: a simple homogeneous model, the PUNQ-S3 model, and a modified portion of the SPE10 model. The results show that using the sampling techniques of the probabilistic collocation method produced relatively accurate responses compared with the original method. Different possible enhancements were discussed in order to practically adapt the least squares probabilistic collocation method to more realistic and complex reservoir models. Furthermore, it is desired to perform the method to evaluate high-dimensional decision scenarios for different chemical enhanced oil recovery processes using real reservoir data.