某水电站地下洞室群初始地应力场反演回归分析

采用三维弹塑性有限元法对某水电站地下洞室群三维初始地应力场进行了反演回归分析。计算结果表明,厂区初始地应力场分布规律合理,实测点处地应力计算值与实测值吻合较好,可以作为后续数值分析和地质力学模型试验的依据。     

大型水电站厂区三维地应力场回归反演分析

岩体初始地应力场是地下洞室围岩稳定与支护结构设计所需要的基本因素之一,初始地应力场是否可靠将直接影响到工程设计与施工的可靠性与安全性。结合某水电站厂区的地质条件及地应力实测资料,引入灰色控制系统理论,采用三维有限元法和采用静态的三因素灰色计算模型GM(0, 3)对厂区岩体初始应力场进行回归反演分析。计算结果表明,厂区存在较大的水平向地质构造作用,岩体的地应力由自重和构造应力叠加而成。实测点的计算应力值与实测值在量值上和方向上都较为接近,表明经过回归得到的地应力场是合理的,从而获得地下厂房厂区初始应力场较为合理的分布规律,为地下厂房的开挖模拟及稳定性分析提供了合理的初始应力场。     

基于侧压力系数的岩爆区初始地应力场二次反演分析

为准确获得桑珠岭隧址区初始地应力场分布规律,提出在岩爆区初始地应力场的二次反演方法。采用最小二乘法寻优准则对隧址区初始地应力场进行多元线性回归分析,利用叠加原理得到在一次反演下的初始地应力场;采用表面应力解除法测量隧道开挖后的洞壁二次应力,记录发生岩爆的部位并据此判断侧压力系数的大小,与在一次反演下相应位置的侧压力系数进行对比,如果两者都大于或者等于或者小于1,则以在一次反演下计算得到的侧压力系数为基准,以其大小不变作为约束条件对初始地应力进行修正,当采用修正后的初始地应力作为应力边界条件,计算得到隧道开挖后的洞壁二次应力与实测洞壁二次应力最接近时,以此时修正后的初始地应力和原位地应力进行回归得到在二次反演下的地应力场。结果表明：当测量原位地应力的钻孔较少且计算区域较大时,一次反演回归得到离钻孔较远位置的应力计算值与实测值存在一定的误差;二次反演在原位地应力的基础上增加实测洞壁二次应力进行修正,得到离钻孔较远位置的应力计算值与实测值吻合更好,所提出的二次反演方法可为类似工程的研究提供参考。     

锦屏二级水电站引水隧洞区域三维初始地应力场反演回归分析

本文采用三维有限元法对锦屏二级水电站引水隧洞区域的三维初始地应力场进行了反演回归分析,实测点处地应力计算值与实测值吻合较好,表明经过回归得到的地应力场是合理的,可为隧洞设计、稳定性分析和确定合理的施工方案提供基础性资料和科学依据。     

大岗山水电站坝区初始地应力场反演分析

针对大岗山水电站坝区V型河谷地形地貌特征,根据地应力实测资料及地质构造条件,考虑边坡浅表全风化、强风化地层以及断层破碎带对坝区初始地应力场的影响,建立了坝区初始地应力场三维回归计算分析模型。通过多元回归三维数值计算,求得地应力最优回归系数,较为准确地反演了大岗山坝区的初始地应力场。计算结果表明,大岗山坝区初始地应力场是一个在浅部以构造应力为主、在深部以自重应力为主、由构造应力和自重应力联合组成的中等偏高的地应力场,研究结果为坝区边坡开挖及长期稳定性分析提供了重要依据。     

小湾水电站坝址区三维初始地应力场反演回归分析

基于小湾水电站坝址区工程地质地形条件,研究分析了影响工程考察域初始地应力场的基本因素及其空间分布,建立了坝址区三维有限元计算模型和初始地应力场参数空间分布模型;利用大型通用有限元软件MSC.Marc和地应力实测资料,借助最小二乘法原理,以回归精度为目标函数,优化了构造挤压荷载的模拟和作用组合,实现了初始应力场空间分布模型的参数估计。计算结果表明,改进后的方法较传统方法回归精度有了较大提高,能较为合理地模拟小湾坝址区三维初始地应力场。     

岭回归在岩体初始地应力场反演中的应用

为使反演得到的岩体初始地应力场更加符合实际,提出岩体初始地应力场应采用压缩应力场进行叠加,反演得到边界构造荷载的大小不应过大,反演得到应力场的组成应与实测原位地应力的组成一致。依据多元线性回归相关理论,在岩体初始地应力场反演中,首先揭示了负回归系数、过大回归系数以及不显著回归系数的原因,即若采用最小二乘法求解回归系数,自变量之间的多重共线性可能会导致负的、过大的以及不显著的回归系数;然后给出了出现多重共线性的来源,即测得原位地应力的范围过窄会导致自变量之间存在多重共线性,以及采用多元多方程表示岩体初始地应力场易导致自变量之间接近完全多重共线性;最后给出了检验以及避免多重共线性的一些方法,并通过斑竹林隧道岩体初始地应力场的反演进行应用,发现在岩体初始地应力场的反演过程中,若自变量之间存在多重共线性,则岭回归可有效替代最小二乘法求解回归系数。     

蒲石河抽水蓄能电站地下厂房三维初始应力场反演分析

采用三维非线性有限元反演回归分析计算方法,提出侧压力系数函数拟合方法,考虑了地质构造,地形地貌以及实测应力对初始应力场的影响。对蒲石河抽水蓄能电站地下厂房区域初始地应力场进行反演回归分析研究,实测点处附近应力分布的局部特性证明反演计算方法是合理的。     

基于复杂地质体的地应力场智能识别方法研究

初始地应力是地下开采及施工所需要考虑的重要影响因素,地应力值的准确获得通常采用现场测量与反演计算结合实现。针对某铜镍矿复杂地质体,在已有监测数据的基础上建立三维正交数值模型,获得监测点的地应力计算值。利用遗传规划程序,回归地应力监测点的地应力与各自变量的函数关系。建立地应力实测值和计算值之差的平方和最小的目标优化函数,使用遗传算法智能算法对目标函数进行优化,最终获得了矿区的原岩应力场。检测样本验证结果显示,计算值与实测值的误差控制在10%以内,一定程度上证明了该地应力场智能识别方法的可靠性,可为以后复杂地质体矿区地应力场的计算提供较为可行的研究方法。     

三维初始地应力场反分析的径向基函数法

通过对初始地应力场计算方法的回顾,提出了基于径向基函数的人工神经网络初始地应力场的三维反分析方法。径向基网络的可以避免在反分析过程中出现过拟合现象,从而保证反分析结果更加可靠.此外,该方法综合了目前各种初始地应力场模拟方法的优点,并考虑了多种因素对地应力场分布的影响。实例证明,由作者提出方法所模拟的初始地应力场是合理的,精确度也较高。此外,由于考虑了断层的作用对初始地应力场的影响,可以较好地解释实测地应力值分散的原因。     

水文相关中的最小二乘回归问题探讨

在研究了水文相关中利用最小二乘原理进行回归分析方法的基础上，指出了传统水文回归分析方法的使用条件、局限性和存在的问题。提出了不同性质的变量在回归分析时应区别对待的概念。结合水文观测的实际情况，研究了相关变量观测值均存在误差情况下，以变量的观测误差作权进行回归分析的概念，提出了建立基于最小二乘原理基础上的双加权回归模型，并研究了该模型的解算方法。同时推导了估计参数和预测值的误差估计公式，通过估计参数和模型误差的研究，有助于提高水文变量回归的精度和误差估计水平。     

Landslide susceptibility zonation mapping and its validation in part of Garhwal Lesser Himalaya, India, using binary logistic regression analysis and receiver operating characteristic curve method

A landslide susceptibility zonation (LSZ) map helps to understand the spatial distribution of slope failure probability in an area and hence it is useful for effective landslide hazard mitigation measures. Such maps can be generated using qualitative or quantitative approaches. The present study is an attempt to utilise a multivariate statistical method called binary logistic regression (BLR) analysis for LSZ mapping in part of the Garhwal Lesser Himalaya, India, lying close to the Main Boundary Thrust (MBT). This method gives the freedom to use categorical and continuous predictor variables together in a regression analysis. Geographic Information System has been used for preparing the database on causal factors of slope instability and landslide locations as well as for carrying out the spatial modelling of landslide susceptibility. A forward stepwise logistic regression analysis using maximum likelihood estimation method has been used in the regression. The constant and the coefficients of the predictor variables retained by the regression model have been used to calculate the probability of slope failure for the entire study area. The predictive logistic regression model has been validated by receiver operating characteristic curve analysis, which has given 91.7% accuracy for the developed BLR model.     

Comparison of approaches to spatial estimation in a bivariate context

The problem of estimating a regionalized variable in the presence of other secondary variables is encountered in spatial investigations. Given a context in which the secondary variable is known everywhere (or can be estimated with great precision), different estimation methods are compared: regression, regression with residual simple kriging, kriging, simple kriging with a mean obtained by regression, kriging with an external drift, and cokriging. The study focuses on 19 pairs of regionalized variables from five different datasets representing different domains (geochemical, environmental, geotechnical). The methods are compared by cross-validation using the mean absolute error as criterion. For correlations between the principal and secondary variable under 0.4, similar results are obtained using kriging and cokriging, and these methods are superior slightly to the other approaches in terms of minimizing estimation error. For correlations greater than 0.4, cokriging generally performs better than other methods, with a reduction in mean absolute errors that can reach 46% when there is a high degree of correlation between the variables. Kriging with an external drift or kriging the residuals of a regression (SKR) are almost as precise as cokriging.     

Nonlinear regression for dependent variables

Nonlinear regression methods can be used to fit functions for two related variables where both variables are subject to error. A computer program for nonlinear estimation described previously has been modified to fit such functions for a given set of data. A numerical example is provided for a second-degree equation in xand y.A closer fit to an observed set of data is possible if the error structure for the variables is specified.     

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.     

回归模型在辐射环境监测中的应用

提出了回归分析前作变量变换的依据，并认为变量的概率分布相同时可不作变量变换；应用江苏省土壤中镭和钍的数据建立的数学模型，对该省污染预测、重复调查本底具有现实意义。     

Excel回归分析及其在矿井瓦斯涌出量预测中的应用

回归分析方法是处理变量之间相关关系的有利工具,在很多领域都有应用。介绍了多元线性回归分析的数学原理,以及用MicrosoftExcel工作表进行多元回归分析的多种方法。在应用实例中用常村矿井的钻孔实测数据,演示了Excel多元线性回归各种方法的分析过程。     

Application of logistic regression for landslide susceptibility zoning of Cekmece Area, Istanbul, Turkey

As a result of industrialization, throughout the world, cities have been growing rapidly for the last century. One typical example of these growing cities is Istanbul, the population of which is over 10 million. Due to rapid urbanization, new areas suitable for settlement and engineering structures are necessary. The Cekmece area located west of the Istanbul metropolitan area is studied, because the landslide activity is extensive in this area. The purpose of this study is to develop a model that can be used to characterize landslide susceptibility in map form using logistic regression analysis of an extensive landslide database. A database of landslide activity was constructed using both aerial-photography and field studies. About 19.2% of the selected study area is covered by deep-seated landslides. The landslides that occur in the area are primarily located in sandstones with interbedded permeable and impermeable layers such as claystone, siltstone and mudstone. About 31.95% of the total landslide area is located at this unit. To apply logistic regression analyses, a data matrix including 37 variables was constructed. The variables used in the forwards stepwise analyses are different measures of slope, aspect, elevation, stream power index (SPI), plan curvature, profile curvature, geology, geomorphology and relative permeability of lithological units. A total of 25 variables were identified as exerting strong influence on landslide occurrence, and included by the logistic regression equation. Wald statistics values indicate that lithology, SPI and slope are more important than the other parameters in the equation. Beta coefficients of the 25 variables included the logistic regression equation provide a model for landslide susceptibility in the Cekmece area. This model is used to generate a landslide susceptibility map that correctly classified 83.8% of the landslide-prone areas.     

线性回归与最小一乘法

论述了用最小一乘法估计两变数线性回归模型中的参数。计算方法为：通过定点的解法，一般解法，两点法和单纯形法。对于最小一乘解，在实际分析时会出现一些问题，如解的不灵敏性、解的多重性以及突出点的多少对回归线有不同影响等。     

主成分-逐步回归在滑坡稳定性分析中的应用

多元回归分析是概率统计理论滑坡稳定性研究中的一种重要应用。然而,一般多元回归方法存在局限性,本文引入主成分-逐步回归模型,既尽可能全面考虑到各影响因素,又能解决因素之间多重相关性可能带来的误差。在理论探讨的基础上,本文结合巴东县赵树岭滑坡研究进行了工程实例分析。