On the misuse of regression in earth science

Simple least-squares regression analysis is applied to almost all empirical curve-fitting problems in earth science (and related fields). Its use, however, should be restricted to predictive situations. For comparisons with theory or among fitted lines, the related technique termed functional analysisshould be employed. To apply this method, the ratio of the random components of the variances of the variables must be estimated. Principles are illustrated with examples from geomorphometry, especially the stream frequency-drainage density relation.     

Multiple regression with correlated independent variables

Multiple linear regression analysis may be used to describe the relation of one geologic variable to a number of other (independent) variables, and also may be used to fit a trend surface to geographically distributed variables. The leastsquares estimates of the regression coefficients differ unpredictably from the true coefficients if the independent variables are correlated. The estimates can be too large in absolute value, and may have the wrong sign. Also, the least-squares solution may be unstable in that replicate samples can give widely differing values of the regression coefficients. Ridgeregression analysis is a technique for removing the effect of correlations from the regression analysis. The procedure involves addition of a small constant K to the diagonal elements of the standardized covariance matrix. The estimates obtained are biased but have smaller sums of squared deviations between the coefficients and their estimates. The ridge trace, a plot of the coefficients versus K, helps determine the value of K that stabilizes the estimates. Correlations between geologic variables are common, and regression coefficients based on these data may be suspect. In trendsurface analysis, correlations between the geographic coordinates may differ widely, and extreme correlations may be introduced if higher order terms are used in the trend. Ridgeregression analysis serves to guide the geologist to a more reliable interpretation of the results of multiple regression if the independent variables are correlated.     

非线性回归分析的PSO小波网络方法及应用

文章介绍了粒子群算法（PSO）和小波神经网络的基本原理，把基于粒子群小波网络的混合算法应用到非线性回归问题中，并对算法解决非线性回归问题进行了实践分析，最后建立了测井响应值和物性参数孔隙度之间的回归模型。从仿真结果可以看出，本方法的回归值和岩心分析值符合较好，表明粒子群小波网络进行非线性回归分析是一种有效的数据回归方法。     

Wind speed prediction using statistical regression and neural network

Prediction of wind speed in the atmospheric boundary layer is important for wind energy assessment, satellite launching and aviation, etc. There are a few techniques available for wind speed prediction, which require a minimum number of input parameters. Four different statistical techniques, viz., curve fitting, Auto Regressive Integrated Moving Average Model (ARIMA), extrapolation with periodic function and Artificial Neural Networks (ANN) are employed to predict wind speed. These methods require wind speeds of previous hours as input. It has been found that wind speed can be predicted with a reasonable degree of accuracy using two methods, viz., extrapolation using periodic curve fitting and ANN and the other two methods are not very useful.     

多元线性回归和逐步回归分析在白石泉Cu-Ni硫化物矿床研究中的应用

新疆东天山的白石泉Cu-Ni硫化物矿床一直受到众多构造学家、岩石学家和矿床学家的关注,但是数学地质在此地的研究尚属空白。文中在系统的野外地质调查基础上,进行了系统采样和岩石地球化学分析,应用多元线性回归和逐步回归分析相结合的方法,借助SPSS数学统计软件系统的研究Cu-Ni变量与造岩元素变量的关系,建立Cu-Ni变量与其他变量的回归方程,验证与解释白石泉Cu-Ni硫化物矿床的成因、岩浆来源等问题,对指导找矿勘探有重要作用,对应用数学地质方法有指引作用。     

不连续系列的计算机加权适线法新探

从含有历史洪水不连续系列的克－闵假定及数理统计中参数估计理论入手,给出了不连序系列的计算机枷权适线法,并通过模型分析,工程实例计算和试验等检验,结果表明,该法较现行计算机适线法有较大程度的改善 。     

一个关于空间曲线的拟合方法

由于空间曲线方程较平面曲线复杂，其形式具有不唯一性，在对空间一组点进行拟合时，其精确表达式难以获得，在一些常用数学软件如Matlab、Mathematica中均未给出这类曲线的拟合方法。因此，笔者设计了一个关于空间曲线的拟合方法，并通过实例验证了该方法对某些空间曲线的有效性。     

滑坡预报的多元回归分析方法

在回顾了滑坡预报的概念、类型及已有滑坡预报的几种主要模型的基础上，利用多元回归分析方法，根据最小二乘法原理，建立了非线性回归预报模型，提出滑坡破坏的时间为位移．时间曲线的拐点，此方法一般适合于临滑预报。结合实例，利用黄龙西村滑坡位移．时间监测资料，采用该模型进行滑坡时间预报，和其他滑坡预报模型预报的结果接近，说明该模型具有一定的合理性。     

密度计法颗粒分析曲线的拟合及其修正

提出了密度计法颗粒分析试验的一种曲线拟合及修正方法，经验证效果较好。     

建立磁化率快速预测白马钒钛磁铁矿含量模型

根据白马钒钛磁铁矿区试验钻孔井壁岩矿石磁化率与钒钛磁铁矿含量的关系,矿区岩矿石磁化率与钒钛磁铁矿含量的相关性,建立了磁化率与钒钛磁铁矿含量的回归方程。通过此方程的应用可以快速判断井壁岩矿体的钒钛磁铁矿含量,指导采样布设。     

Efficiency of regression techniques for ore valuation at Kolar Gold Fields, India

The Kolar Gold Fields are some of the best known gold deposits in India. An example of ore valuation utilizing 49 ore blocks of the Oriental lode of the West Reefs, explored and developed in the Nundydroog mines, is given. In this reef system, there are large ore reserves of sulfidebearing quartz reefs, and the gold distribution is erratic both along strike and downdip. Ore valuation at present is based on the arithmetic mean of samples taken at peripheral positions of the blocks. Samples taken from internal portions of the blocks give a totally different picture of the value. To correct this discrepancy, normal regression and lognormal regression of internal block and total block values, over peripheral block values have been used to evaluate the deposits. The valuation efficiency criterion shows the logarithmic variance for distribution of ratios of unregressed and regressed block values with the corresponding arithmetic mean of internal stope values as observed inside the blocks. The studies have shown that the logarithmic variance is minimum if the logarithmic regression is used, thereby indicating maximum efficiency. Further, the undervaluation and overvaluation of low- and high-grade blocks is less for the logarithmic example. With help of the logarithmic regression equation an effective pay limit of 177.8 in.-dwt has been found for selective mining, for peripheral block values corresponding to the official pay limit of 240 in.-dwt.NGRI contribution number 71-281.     

铬天青S光度法及非线性拟合测定高纯硅中微量铝

铬天青S光度法是硅中铝含量的测定方法之一,该方法的标准曲线大多采用不过零点的线性拟合,导致低铝含量测定误差大。为提高方法准确度并降低方法检出限,研究了铝标准曲线低浓度部分的拟合问题,探讨了不同拟合模型对检测结果准确度的影响。实验结果表明,不同浓度铝标准液的吸光度在0~0.3 μg/mL范围内并不满足一次函数线性关系,采用三次函数关系y=-17.45230x³+10.42883x²+1.04047x (y为扣空白的吸光度,x为铝的质量浓度)拟合能获得良好结果,其相关系数R²为0.99975。利用已知铝含量的硅试液检验该公式,其相对标准偏差(RSD)为2.55%。样品中铝的测定值与电感耦合等离子体发射光谱法测定值吻合。该法可以显著提高低浓度的铝测定的准确性,可用于测定高纯硅中含量在0.55 μg/g以上的铝杂质。     

Construction of variance-based metamodels for probabilistic seismic analysis and fragility assessment

Finite element models used in industrial studies for seismic structural reliability analysis are in general very complex and computationally intensive. This is due to the important number of degrees of freedom as well as due to advanced damage models and failure modes that have to be simulated. In consequence, reliability studies are feasible only by means of simpler surrogate models able to represent essential physics. Then the choice of an accurate surrogate or metamodel is crucial for uncertainty propagation and sensitivity analysis. The construction of a pertinent metamodel is however a not simple task when random uncertainties, not explained by the model parameters, have to be accounted for. This is the case for transient seismic analysis where the ground motion, an intrinsically random phenomena, is modelled by a stochastic process that cannot be entirely described by a set of parameters. In this paper, we construct a versatile metamodel based on analysis of variance (ANOVA) decomposition. The ANOVA decomposition provides a convenient framework allowing both for parametric uncertainties and for stochastic variability introduced by seismic load. We then compute fragility curves and perform sensitivity analysis.     

深基坑施工时地表沉降预测的时序-投影寻踪回归模型

为了保证施工的正常进行、实现信息化施工,必须对基坑实际监测数据进行分析与预测。现有的趋势时间序列分析方法很难满足实际施工中高度非线性问题的拟合,预测误差较大。基于这点考虑,以天津某工程基坑施工地表沉降观测序列为例,在对原始数据进行分析的基础上,提出既可以考虑趋势时间序列,又具有高度非线性拟合性能的时序-投影寻踪回归模型。首先,通过比较分析几种时间序列方法的逼近误差和预测误差,寻求出一种逼近较好的时间序列预测方法。然后,将预测得到的时间序列和观测数据相结合,采用投影寻踪回归方法拟合。应用结果表明,该模型逼近性能良好,预测误差小,可为深基坑位移沉降的动态预测提供一条较好的途径,对基坑动态设计与信息化施工等方面具有重要的参考价值。     

利用变参数回归方法反演泥质岩裂缝密度

本文利用变参数回归分析建立了多口井的泥质岩储层裂缝密度模型。该模型的平均相对误差为１３．５％,较常系数回归分析、ＢＰ网络模型进行裂缝预测的精度高（平均相对误差分别为３８．７％、１７．９％）。通过实际资料处理认为该油田在纵向上随时代变老,深度加深,裂缝密度降低。即从Ｎ２２、Ｎ１２到Ｎ１,平均裂缝密度从０．７８条／ｍ、０．５条／ｍ降低到０．３条／ｍ。在平面上,沿构造轴部裂缝最发育,平均裂缝密度Ｎ２２、Ｎ１２、Ｎ１层分别为０．５８条／ｍ、０．６条／ｍ、０．３条／ｍ。     

A sequential sparse polynomial chaos expansion using Bayesian regression for geotechnical reliability estimations

Polynomial chaos expansions (PCEs) have been widely employed to estimate failure probabilities in geotechnical engineering. However, PCEs suffer from two deficiencies: (a) PCE coefficients are solved by the least-square minimization method which easily causes overfitting issues; (b) building a high order PCE is often computationally expensive. In order to overcome the aforementioned drawbacks, the Bayesian regression technique is employed to evaluate PCE coefficients, which not only provides a sparse solution but also avoids overfitting. With the aid of the predictive means and variances given by Bayesian analysis, a learning function is proposed to sequentially select the most informative samples that are critical to build a PCE. This sequential learning scheme can highly enhance the computational efficiency of PCEs. Besides, importance sampling (IS) is incorporated into the sequential learning (SL)-PCEs to deal with geotechnical problems with small failure probabilities. The proposed method of SL-PCE-IS is applied to three illustrative examples, which shows that the improved PCE method is more effective and efficient than the common PCEs method, leading to accurate estimations of small failure probabilities using fewer training samples.     

浅水方程模拟中确定糙率的回归系数法

基于水流模拟本身就是模拟模型回归求真(即实体原型)过程的认识,从模拟模型和实体原型之间的相关关系出发,应用统计学中的线性回归分析方法,通过回归系数建立了模型与原型糙率系数之间的关系式,提出了二维浅水方程模拟中糙率确定的回归系数法。数值试验表明,该方法并不依赖于糙率系数的初值,具有稳定性好、收敛速度快的特点;对磨刀门水道水流的数值模拟应用显示,该方法能有效地改善模拟计算的精度,具有较好的适应能力,简便实用,为二维浅水流动模拟计算时率定糙率系数提供了一种有效途径。     

群居蜘蛛优化算法在水文频率分析中的应用

水文频率分析在参数估计过程中常采用智能优化适线法,如蚁群算法、遗传算法、粒子群算法、模拟退火算法等,但这些算法模型参数难以有效确定,导致寻优结果存在不稳定的不足。为了克服传统优化适线法的缺陷,在系统阐述群居蜘蛛优化算法基本原理的基础上,将群居蜘蛛优化算法用于水文频率曲线的参数确定中,并与传统的参数估计方法(矩法、权函数法、概率权重矩法、遗传算法)加以比较。实例结果表明,该方法搜索效率高,寻优结果稳定,能较好获得参数的最优解。     

基于指数平滑法与回归分析相结合的滑坡预测

滑坡时间预报研究是滑坡研究中的一个热门课题。以实际监测数据为基础,把指数平滑法与非线性回归分析法结合起来;以滑坡的变形值和变形速率为判据,对滑坡进行时间失稳的动态跟踪预报。根据某滑坡的实际情况,对部分监测点位移进行了建模和预测,预测结果表明,该方法具有较高的精度,可以应用于实际工程。     

柳林地区煤层渗透率逐步回归分析与预测

渗透率是制约煤层气商业化开发至关重要的因素之一。以柳林地区煤层气勘探阶段获取的试井有效渗透率为基础,分析渗透率与有效应力、储层压力、煤层埋深等影响因素之间的关系,利用多元逐步回归分析方法建立渗透率预测模型。结果显示：柳林地区煤层渗透率回归方程具有较高的拟合度;多元逐步回归分析方法预测渗透率具有一定合理性;有利于煤层气开发的高渗区位于柳林地区中北部。