基于高斯过程回归的地下水模型结构不确定性分析与控制

目前针对模型结构不确定性的研究方法主要为贝叶斯模型平均方法,而该方法受到模型权重计算困难等影响,应用受限。基于数据驱动的模型结构误差统计学习方法最近得到关注。研究采用高斯过程回归方法对地下水模型结构误差进行统计模拟,并将DREAMzs算法与高斯过程回归相结合,对地下水模型和统计模型的参数同时进行识别。基于此方法,分别以理想岩溶裂隙海水入侵过程和溶质运移柱体实验为例,进行地下水数值模拟及预测结果的不确定性分析。相对于不考虑模型结构误差条件的不确定性分析,结果表明,考虑结构误差之后,能够明显减少参数识别过程中的参数补偿影响,且能显著提高模型的预测性能。因此,基于高斯过程回归的模型结构不确定性分析可以一定程度控制地下水数值模拟的不确定性,提高模型预测可靠性。     

边坡失效概率估计的高斯过程动态响应面法

针对传统响应面法在求解具有高度非线性隐式功能函数边坡可靠性问题上的局限性,采用适用于处理高维度、小样本、非线性回归问题的高斯过程回归模型构建隐式功能函数的响应面,将高斯过程响应面与蒙特卡罗模拟法相结合,通过构造合理的迭代方式,在利用高斯过程回归模型的不确定性评价功能获取最优采样点的基础上,实现了高斯过程响应面动态更新,由此提出了边坡失效概率快速估计的高斯过程动态响应面法。利用数值算例验证了该方法的有效性,在此基础上对3个边坡算例进行了可靠性分析。结果表明,与传统响应面法相比较,该方法计算精度与计算效率明显较高,易于与既有的边坡分析软件相结合,且实现容易,适用于边坡可靠性的快速分析。     

A structured analysis of uncertainty surrounding modeled impacts of groundwater-extraction rules

Integrating economic and groundwater models for groundwater-management can help improve understanding of trade-offs involved between conflicting socioeconomic and biophysical objectives. However, there is significant uncertainty in most strategic decision-making situations, including in the models constructed to represent them. If not addressed, this uncertainty may be used to challenge the legitimacy of the models and decisions made using them. In this context, a preliminary uncertainty analysis was conducted of a dynamic coupled economic-groundwater model aimed at assessing groundwater extraction rules. The analysis demonstrates how a variety of uncertainties in such a model can be addressed. A number of methods are used including propagation of scenarios and bounds on parameters, multiple models, block bootstrap time-series sampling and robust linear regression for model calibration. These methods are described within the context of a theoretical uncertainty management framework, using a set of fundamental uncertainty management tasks and an uncertainty typology.     

A multidimensional fuzzy least-squares regression approach for estimating hydraulic gradients in unconfined aquifer formations and its application to the Gulf Coast aquifer in Goliad County,Texas

Epistemic uncertainties arise during the estimation of hydraulic gradients in unconfined aquifers due to planar approximation of the water table as well as data gaps arising from factors such as instrument failures and site inaccessibility. A multidimensional fuzzy least-squares regression approach is proposed here to estimate hydraulic gradients in situations where epistemic uncertainty is present in the observed water table measurements. The hydraulic head at a well is treated as a normal (Gaussian) fuzzy variable characterized by a most likely value and a spread. This treatment results in hydraulic gradients being characterized as normal fuzzy numbers as well. The multidimensional fuzzy least-squares regression has an exact analytical form and as such can be implemented easily using matrix algebra methods. However, the method was noted to be sensitive to round-off and truncation errors when the epistemic uncertainties are small. A closeness index based on the cardinality of a fuzzy number is used to evaluate how well the regression model fits the fuzzy hydraulic head observations. A fuzzy Euclidian distance measure is used to compare two fuzzy numbers and to evaluate how fuzziness in the observed hydraulic heads affects the fuzziness in the estimated hydraulic gradients. The Euclidian distance measure is also used to ascertain the influence of each well on the fuzzy hydraulic gradient estimation. The fuzzy regression framework is illustrated by applying it to evaluate hydraulic gradients in the unconfined portion of the Gulf Coast aquifer in Goliad County, TX. The results from the case-study indicate that there is greater uncertainty associated with the estimation of the hydraulic gradients in the vertical (Z-axis) direction. The epistemic uncertainties in the hydraulic head data at the wells have a significant impact on the gradient estimates when they are of the same order of magnitude as the most likely values of the observed heads. The influence analysis indicated that 5 of the 13 wells in the network had a critical influence on at least one of the hydraulic gradients. Three wells along the northeastern section of the study area and bordering the Victoria County were noted to have the least influence on the regression estimates. The fuzzy regression framework along with the associated goodness-of-fit and influence measures provides a useful set of tools to characterize the uncertainties in the hydraulic heads and gradients arising from data gaps and planar water table approximation.     

Reliability Analysis of Quick Sand Condition

First order reliability method (FORM) is generally used for reliability analysis in geotechnical engineering. This article adopts generalized regression neural network (GRNN) based FORM, Gaussian process regression (GPR) based FORM and multivariate adaptive regression spline (MARS) based FORM for reliability analysis of quick sand condition. GRNN is related to the radial basis function (RBF) network. GPR is developed based on probabilistic framework. MARS is a nonparametric regression technique. A comparative study has been carried out between the developed models. The performance of GPR based FORM and MARS based FORM match well with the FORM. This article gives the alternative methods for reliability analysis of quick sand condition.     

基于不确定性的地下水污染风险评价研究进展

地下水污染风险研究在工程决策中具有重要意义。但地下水系统本身具有各种不确定性,基于这些不确定性的地下水污染风险评价也因此具有不确定性,而且贯穿整个地下水污染风险评价过程。所以,进行不确定性分析是对地下水污染风险进行评价时的必要步骤。一般来讲,基于不确定性分析的地下水污染风险评价结果更可靠,因此也更具有实用价值。本文在对不确定性进行分类（随机不确定性和模糊不确定性）的基础上,通过大量文献调研和分析,对目前国内外用于地下水污染风险评价分析的不确定性分析方法（包括随机理论方法、模糊理论方法、随机-模糊耦合方法等）进行了归纳总结,并基于各种方法目前的研究现状,分析了不确定性理论在地下水污染风险评价研究中的发展前景。     

高放废物深地质处置地下水数值模拟应用综述

开展地下水数值模拟研究是高放废物处置场地安全评价的重要组成部分,然而深地质处置介质类型的复杂性、基岩深部资料的相对匮乏性导致模拟结果存在不确定性,如何刻画深部地下水动力场并评估可能引起的风险已成为高放废物处置安全评价中重点关注的问题。在大量文献调研的基础上,综述了世界典型国家高放废物深地质处置场地的地下水数值模拟与不确定性分析应用,并归纳总结该领域研究经验,得到以下认识:（1）深地质处置场深部构造、裂隙的发育与展布决定了地下水循环条件,探究适用于基岩裂隙地区新的水文地质试验方法是提高地下水数值模型仿真性的基础;（2）不同尺度模型融合是解决深地质处置地下水模拟的有效技术方法,区域尺度多采用等效连续介质法,场地尺度使用等效连续多孔介质和离散裂隙网络耦合模型,处置库尺度使用离散裂隙网络方法,其次需重点关注未来大时间尺度下放射性核素在地质体中的迁移转化规律,模拟预测场址区域地下水环境长期循环演变对核素迁移的潜在影响;（3）考虑到不同的处置层主岩岩性以及在多介质中发生的THMC（温度场—渗流场—应力场—化学场）过程,目前国内外常用的地下水模拟软件有:Porflow、Modflow、GMS及MT3DMS等用于模拟孔隙或等效连续介质,Connectflow、Feflow及FracMan等用于模拟地下水和核素在结晶岩、花岗岩等裂隙中的迁移,TOUGH系列软件主要应用于双重介质的水流、溶质及热运移模拟;（4）指导开展有针对性的模型和参数的不确定性分析工作,减少投入工作量,提高模型精度,并可针对处置库长期演变、废物罐失效、极端降雨等多情景预测模拟,为处置库安全评价及设计提供基础数据支撑;（5）针对我国深地质处置地下水数值模拟研究现状,下一步应加强区域地质、水文地质、裂隙测量以及现场试验等相关的调查及监测工作,多介质耦合、多场耦合模拟及不确定性分析研究将会是未来的研究重点。     

复信号分析技术在地质雷达预报岩溶裂隙水中的应用研究

对岩溶裂隙水进行及时准确的预报,是当前岩溶隧道设计和施工中亟待研究和解决的关键问题。复信号分析技术能够提取多个参数进行综合判断,基于此优点,尝试将复信号分析技术引入到地质雷达探查水体的研究中。对雷达数据中的水体异常分别从振幅、频率和相位等方面进行综合判断,克服了以往判断依据单一的缺点,为利用地质雷达进行岩溶裂隙水预报提供了一种切实可行的方法。首先,介绍了复信号分析技术的原理,阐述了在地质雷达信号处理中引入复信号分析技术的必要性;然后探讨了基于复信号分析技术的地质雷达预报岩溶裂隙水的可行性,得出了判断水体的依据。最后结合工程实例,对地质雷达数据进行了复信号处理,并对岩溶裂隙水进行了综合判断。与开挖结果对比显示,复信号分析技术的运用较大的提高了岩溶裂隙水预报的准确性和可信性。     

Uncertainty analysis of groundwater model based on data assimilation北大核心CSCD

黑河流域中下游地下水系统受上游冰冻圈融水和降雨的补给,由气候变暖导致的冰冻圈萎缩致使中下游地下水系统的稳定性面临更多的风险。地下水模型是地下水系统稳定性评估的有效手段,但是地下水模型参数往往存在较大的不确定性。为此,本文提出了基于数据同化算法的不确定性分析方法,通过包含观测资料信息减小模型不确定性。采用所提方法分析了(基于MODFLOW构建)黑河流域中游地下水模型中13个参数的不确定性,讨论了算法超参数的影响及其最优取值,分析了地下水模型参数的不确定性。实验结果证明数据同化算法可有效减小地下水模型参数的不确定性,观测资料的种类与数量对参数不确定性的减小起到重要作用;不同地下水模型参数的不确定性不同,地表水与地下水相互作用频繁的区域参数不确定性较大;含水层渗透系数、含水层给水度以及灌溉回流系数对模型输出的地下水位输出影响显著,河床水力传导系数对模型输出的河流流量影响较大。本研究将为地下水研究提供更加可靠的模型方法,为西北内流区地下水哺育的绿洲生态系统稳定可持续研究提供重要支撑。     

开采量不确定条件下数值模拟结果的可靠性分析

地下水数值模拟过程中,人工开采量大都被当作确定项处理。但实际情况是开采量往往缺乏准确的统计数据,尤其是农业灌溉开采量,在计算中具有更大的不确定性。传统的处理方法是将这些人工开采量概化为抽水量确定的开采井,显然不能反映实际情况。采用概率论及数理统计的方法,分析了概化后开采量的不确定性,得出开采量服从正态分布。以此为基础,运用蒙特卡罗方法,对开采量不确定条件下数值模拟的结果进行可靠性分析。结果表明：传统处理方法不能反映开采量不确定条件下数值模拟结果可靠性的变化情况,而采用随机模拟的方法,可以计算出不同的给定允许降深条件下,模拟结果的可靠性。     

An intelligent response surface method for analyzing slope reliability based on Gaussian process regression

Problems in geotechnical engineering inevitably involve many uncertainties in the analysis. Reliability methods are important for evaluating slope stability and can take the uncertainties into consideration. In this paper, a novel intelligent response surface method is proposed in which a machine learning algorithm, namely Gaussian process regression, is used to approximate the high-dimensional and highly nonlinear response hypersurface. An iterative algorithm is also proposed for updating the response surface dynamically by adding the new training point nearest to the limit state surface to the initial training database at each step. The proposed Gaussian process response surface method is used to analyze three different case studies to assess its validity and efficiency. Direct Monte Carlo simulation is also carried out in each case to serve as the benchmark. Comparing with other methods confirms the accuracy and efficiency of the novel intelligent response surface method, which requires fewer performance function calls and avoids the need to normalize the correlative non-normal variables.     

Uncertainty propagation in geochemical calculations: non-linearity in solubility equilibria

Uncertainty in the results of geochemical equilibrium calculations may be estimated from input uncertainties using either derivative approximations or Monte Carlo simulations. While derivative methods are fast and convenient for many equilibria, inherently non-linear aspects of solubility equilibria may lead to a failure of the linear approximation and thus to asymmetric and/or bimodal uncertainty in calculated concentrations. In these cases, the use of derivative methods and the assumption of Gaussian uncertainty in the calculated concentrations misrepresent the propagated uncertainty. Equilibria with gibbsite, calcite, and the chromate analog of jarosite are examined.     

基于统计方法的干旱区地下水最大可开采量的确定

为克服地下水可开采量确定过程中确定性模型的局限性、失真和参数确定困难等弊端,合理的确定地下水可开采量,基于研究区不同区域地下水水位与开采量监测资料,采用多元线性回归和非线性多元回归统计方法对不同情况下地下水最大开采量进行探讨。结果表明：1964—1990年期间百口泉水源地地下水开采量在持续增加,并以1976年前增加较明显,且地下水水位均表现为下降趋势;非线性多元回归分析法对降深与开采量拟合的结果和误差精度均优于多元线性回归分析法;基于拟合的非线性多元回归方程,可确定水源地正常运行条件下的开采量为1 391万m3、极限开采条件下的开采量1 856万m3、疏干开采条件下的开采量1 992万m3。     

Towards a hierarchical parametrization to address prior uncertainty in ensemble-based data assimilation

Ensemble-based methods are becoming popular assisted history matching techniques with a growing number of field applications. These methods use an ensemble of model realizations, typically constructed by means of geostatistics, to represent the prior uncertainty. The performance of the history matching is very dependent on the quality of the initial ensemble. However, there is a significant level of uncertainty in the parameters used to define the geostatistical model. From a Bayesian viewpoint, the uncertainty in the geostatistical modeling can be represented by a hyper-prior in a hierarchical formulation. This paper presents the first steps towards a general parametrization to address the problem of uncertainty in the prior modeling. The proposed parametrization is inspired in Gaussian mixtures, where the uncertainty in the prior mean and prior covariance is accounted by defining weights for combining multiple Gaussian ensembles, which are estimated during the data assimilation. The parametrization was successfully tested in a simple reservoir problem where the orientation of the major anisotropic direction of the permeability field was unknown.     

地下水数值模拟不确定性分析研究进展

地下水数值模拟不确定性分析旨在提高研究区域地下水流的模拟精度。学者们将地下水数值模拟不确定性分析分为:模型的不确定性、参数的不确定性以及资料的不确定性三类,其中参数的不确定性分析在研究中是最为重要的。同时,对模型、参数、资料不确定性分析的研究进展和成果进行归纳总结,补充关于参数不确定性分析过程中的替代模型的一些研究成果以及模型不确定性分析的多模型分析;强调在地下水数值模拟的过程中,重视模型、资料的不确定性分析;展望未来,随着地下水数值模拟不确定性分析研究的深入,方法和应用会更加多样化。     

异烟酸-吡唑啉酮分光光度法测定地下水中氰化物的不确定度评定

采用不确定度连续传递模型,对异烟酸-吡唑啉酮分光光度法测定地下水中氰化物的不确定度进行评定。分析了不确定度的重要来源,包括样品制备、标准溶液配制、标准曲线拟合和仪器测量过程等引入的不确定度分量。采用x、y双误差回归方式对标准曲线进行拟合,通过分析得知,样品中氰化物浓度越低,其相对不确定度越大。     

基岩岛屿地下水流场数值模拟研究

岛屿是我国领土的重要组成部分,对国家安全和国防军事意义非凡。岛屿的地下水资源尤为珍贵,地下水流场模拟是研究地下水分布规律的重要手段。水文地质条件复杂、可利用的观测井较少等原因,造成了基岩岛屿水文地质模型概化精度不高、初始条件难以获取等问题。为克服基岩岛屿地下水流场模拟的诸多困难,将珠海外伶仃岛作为研究区,利用数字高程模型数据开展地质地貌建模; 利用探地雷达法、直流电法与地质分析对岛屿进行探测,获取了地层数据; 采用地下水遥感评估法,利用实测井位数据,确定了地下水的初始水位,进而对基岩岛屿地下水流场进行建模; 最终,通过对外伶仃岛地下水流场的数值模拟得出地下水模拟流场图。岛上多个测点的探测水位值与模拟水位相关性较好,其拟合优度R²为0.872 2。由此可见,综合遥感、物探、水文地质手段等技术方法获取的数据,采用地下水模拟软件或程序实现基岩岛屿地下水流场的数值模拟,是基岩岛屿地下水资源研究的一个有效方法。     

基于NSMC方法的某核工程场地裂隙地下水数值模拟不确定分析

裂隙介质渗透结构表现为高度的非均质性与各项异性。为了科学有效地预测某核工程场地裂隙地下水的流动规律,揭示裂隙岩体地下水的渗流特性,笔者等采用Pilot Point调参方法与null space Monte Carlo方法（NSMC）,开展了裂隙岩体渗透结构的不确定性分析研究,构建了符合实际水文地质条件的多个渗流数值模型集合。结果表明：该方法获得的各个实现地下水位模拟结果能够与实际观测数据较好吻合,可反映工程场地裂隙地下水动力特征与流动趋势;各个实现的参数化渗透结构在空间上存在一定的差异性,但整体变化趋势是保持一致的,渗透参数的不确定性表现为在实测数据分布区域相对较低,钻孔空白区域相对较高;该方法可以弥补单一、确定性模拟结果在表征裂隙介质渗透结构方面的局限性,有效地降低模型参数的不确定性与随机性。此方法对进一步提升裂隙岩体渗流模拟精度与预测能力,深化裂隙地下水迁移规律的认识具有重要的意义。     

Groundwater head uncertainty analysis in unsteady-state water flow models using the interval and perturbation methods

In the numerical simulation of groundwater flow, uncertainties often affect the precision of the simulation results. Stochastic and statistical approaches such as the Monte Carlo method, the Neumann expansion method and the Taylor series expansion, are commonly employed to estimate uncertainty in the final output. Based on the first-order interval perturbation method, a combination of the interval and perturbation methods is proposed as a viable alternative and compared to the well-known equal interval continuous sampling method (EICSM). The approach was realized using the GFModel (an unsaturated-saturated groundwater flow simulation model) program. This study exemplifies scenarios of three distinct interval parameters, namely, the hydraulic conductivities of six equal parts of the aquifer, their boundary head conditions, and several hydrogeological parameters (e.g. specific storativity and extraction rate of wells). The results show that the relative errors of deviation of the groundwater head extremums (RDGE) in the late stage of simulation are controlled within approximately ±5% when the changing rate of the hydrogeological parameter is no more than 0.2. From the viewpoint of the groundwater head extremums, the relative errors can be controlled within ±1.5%. The relative errors of the groundwater head variation are within approximately ±5% when the changing rate is no more than 0.2. The proposed method of this study is applicable to unsteady-state confined water flow systems.

     

Hydrogeochemical characteristics prediction using multiple linear regression: case study on unconfined aquifer in northeastern Tunisia

The main factors and mechanisms controlling the groundwater chemistry and mineralization are recognized through hydrochemical data. However, water quality prediction remains a key parameter for groundwater resources management and planning. The geochemical study of groundwater of a multilayered aquifer system in Tunisia is recognized by measurements of the pH, EC, total dissolved solids (TDS), major ion concentration and nitrates of 36 samples from pumping wells covering the aquifer extension and analyzed using standard laboratory and field methods. The calcite precipitation, gypsum, anhydrite and halite dissolution, and direct and reverse ion exchange are the principal process of chemical evolution in the Nadhour-Saouaf aquifer system. Using stepwise regression, the concentration groups of (Ca, Cl, and NO₃), (Cl, SO₄, and Mg), and (Ca and Na) exhibit significant prediction of TDS in Plio-Quaternary, Miocene, and Oligocene aquifer levels, respectively. The highest values of R ² and adjusted R ² close to 1 revealed the accuracy of the developed models which is confirmed by the weak difference between the measured and estimated values varying between ?12 and 8%. The important uncertainty parameters that affected the estimated TDS are assessed by the sensitivity analysis method. The concentration of (Cl), (Ca and Cl), and (Na) are the major parameters affecting the TDS sensitivity of the Plio-Quaternary, Miocene, and Oligocene aquifer levels, respectively. Hence, the developed TDS models provide a more simple and easy alternative to other methods used for groundwater quality estimation and prediction as proven from external validation on groundwater samples unconsidered in the model construction.