MODFLOW不同算法及参数设定对计算精度的影响

为了提高MODFLOW中模型计算的精确度,减少不收敛情况的发生,通过建立数值模型算例,分析了不同解算器对计算精度的影响差异、主要参数值的设定对计算精度产生的影响以及收敛指标与迭代次数的定量关系。结果表明,PCG、SAMG和GMG计算精度较高,WHS和SOR计算精度较低。PCG算法中,低收敛指标使得计算精度有所提高,但稳定性却明显降低;计算精度对PCG算法中的阻尼因子的敏感性比对SIP算法中的加速因子敏感性低,二者的减小均导致计算精度降低;SIP算法中,计算过程中的迭代次数、运行时间与水头变化的收敛指标值呈明显的反比关系。当收敛指标设定小于一定值时,迭代次数和收敛指标的对数值呈现明显的线性关系。     

井眼轨道的软着陆设计模型的改进解法

井眼轨道的软着陆设计模型的求解可以归结为一个七元非线性方程组的求解问题。前人给出了数值迭代求解算法,然而并没有证明该迭代算法的收敛性,并且该算法是否收敛严重依赖于用户给出的迭代初始值。通过一系列的消元、化简的数学技巧,将七元非线性方程组化简为一元多项式方程,并在此基础上给出了软着陆设计模型的一个新算法。理论分析和实际算例表明,新算法的主要计算工作量是求多项式方程的非负实数根,其他未知数与实数根是简单的函数关系,计算量很小。新算法克服了迭代算法的初值依赖性以及迭代过程可能发散等缺陷,并且在设计模型有多个解的情况下,可以同时求出这些解。     

基于遗传算法的煤层注水渗透特征参数反演

煤层注水是防治矿井冲击地压灾害发生的最有效的方法。确定煤层渗透特征参数，是合理确定注水工艺参数、有效控制防灾效果的关键，有很强的现实意义。遗传算法是全局收敛的方法，用该算法对煤体导水、贮水等渗透特征参数反演，方法稳定可靠。以观测水分增值与计算结果的相对偏差作为最优搜索目标函数，建立GA反演适应度函数及迭代收敛准则；GA操作采用无条件保护最优个体、种群个体无死亡及每个体只有1次参与交换机会等规则。提出通过对已知参数正向问题结果(水分增值)的反演计算，验证遗传算法精度。算例结果表明，繁衍迭代至第41代时，反演参数结果与理论参数几乎完全拟合。达到最优解，精度符合工程要求。     

光滑粒子流体动力学二阶算法精度研究

光滑粒子流体动力学(SPH)由于无需网格生成和拉格朗日特性,对求解带有自由表面和大变形的力学问题有优势。但是该方法存在计算精度不高,计算效率较低等缺点。为此重点对SPH方法的精度提高进行研究。介绍了传统算法的基本公式,根据误差分析指出该算法精度不高的原因,提出了SPH二阶精度算法。通过精度验证分析,证明了该方法的精度的确能够达到二阶。通过二维计算实例,给出传统方法和二阶方法在粒子均匀分布和非均匀分布时函数值以及函数的一、二阶导数的误差分布,证明二阶算法能够克服传统算法的一些缺点,且计算精度有较大提高。     

非饱和渗流问题的自适应欠松弛变量变换方法

在使用有限元方法求解非饱和土渗流问题时,土-水特征曲线和渗透率函数的强烈非线性经常会造成计算中出现迭代不收敛、计算误差大等问题。基于变量变换的思想,结合时间步长自适应技术提出了一种求解非饱和渗流问题的新方法--欠松弛RFT变换方法（ATUR1）。ATUR1方法通过变量变换,大大降低了Richards方程中未知数在空间和时间上的非线性程度,从而改善这种非线性所带来的计算收敛困难和精度差等问题。欠松弛技术的引入减少了迭代过程中的振荡现象,进一步提高了非线性迭代计算的效率。时间步长自适应技术则有效地控制整个计算过程的误差。数值算例结果说明,ATUR1可以有效地提高计算效率和精度,是一种准确有效的计算方法。     

基于线性互补的非连续变形分析

非连续变形分析(DDA)方法是一种新的用来分析块体系统运动和变形的非连续介质数值计算方法。研究的核心工作是致力于对现有DDA接触问题处理方法的改进。DDA主要采用罚函数法和Lagrange乘子法处理接触问题,合理设定罚参数很困难,此外,因开闭迭代而引起的刚度矩阵的不连续变化也会导致收敛方面的困难。为避免引入罚参数及传统意义上的开闭迭代,用混合线性互补模型(LCDDA)对DDA方法进行了重新描述。在此基础上,综合基于非光滑分析的Newton法的局部平方收敛和最速下降法的全局线性收敛的优势,提出求解LCDDA模型的有效算法。根据上述思想及理论研究成果编制了完整的计算程序,算例计算结果证明了方法的精度及可行性。     

水平层状各向异性地层多分量感应测井数据的快速参数化反演算法

利用传输线理论、Sommerfeld积分快速计算以及最小平方拟合技术研究建立多分量感应测井数据的一种新的快速参数化迭代反演算法,同时重构水平层状横向同性地层的纵、横向电阻率以及水平层界面深度。首先,通过Fourier变换与传输线理论给出频率波数域中电磁场并矢Green函数在各个地层中的解析解,并利用三次样条插值和贝塞尔函数递推公式建立Sommerfeld积分的半解析算法,快速计算多分量感应的测井响应。然后在此基础上,利用摄动理论建立磁场并矢Green函数与模型向量间变化关系的摄动方程,并将摄动方程中各个积分转化为Sommerfeld积分,实现正演模拟的同时用半解析算法快速确定多分量感应测井响应的Fréchet导数。最后,利用归一化处理和奇异值分解技术,同时反演所有地层的纵、横向电阻率和层界面深度,实现输入数据和反演模型的模拟数据优化拟合。理论模型的数值结果验证了该反演算法的有效性及抗噪性。     

P—Ⅲ型分布Φ值数值计算方法比较

皮尔逊Ⅲ型频率曲线的数值计算方法是水文频率计算中的难点之一。本文对近年来提出的几种数值计算方法进行了分析比较，并推导出了各数值计算方法试算离均系数Φ值的迭代公式。最后推荐计算精度高、运算速度快、收敛范围广的级数展开法迭代公式。     

宾汉钻井液圆管轴向层流压降的数值计算

在计算宾汉钻井液在钻具中的层流压降时,需要求解一个非线性方程,以往通常使用近似公式进行计算。对于求解这个非线性方程,提出了一个数值迭代算法,并对该算法的收敛性进行了证明,给出了最大迭代步数的上限值。理论分析和大量实际算例表明：本文算法具有非常稳定的收敛性和非常快的收敛速度,并且能够给出压降的精确计算值。     

混沌控制反演系统构造及算法逻辑设计

给出了适用于非线性反演的混沌控制反演系统构造方法及求解控制矩阵的算法逻辑设计。该方法在迭代反演控制参数和迭代反演输出结果之间建立耦合关系，通过时时修改控制参数保证迭代稳定收敛到预期的解空间。在求解过程中，应用数据结构方法分析了混沌控制理论中计算控制矩阵的数据结构，采用树形结构表述出控制矩阵计算过程中下标的取值逻辑，利用可以复读栈中元素的中序遍历来遍历每一棵树，寻找各元素的组合序列，给出的数值算例说明了混沌控制反演方法及其算法的有效性。     

变参数DCD算法在岩土工程位移反分析中的应用

常规DCD(dynamic canonical descent)算法具有全局优化能力且无需考虑目标函数的可微性,只要预先定义优化空间即可,但是该算法的收敛速度有限,为此提出了变参数DCD算法,并建立了其相应的算法迭代格式。在数值试验和工程应用中将该变参数DCD算法与常规的DCD算法进行比较,其结果均表明：变参数DCD算法在全局优化能力和收敛速度上找到了一个均衡点,该算法不仅具有DCD算法的全局优化能力,而且收敛时所需的目标函数评估次数少,在优化过程中该算法展示出了稳定性强且优化结果可靠度高的一面。     

Determining elastic constants of transversely isotropic rocks using Brazilian test and iterative procedure

The elastic constants of rocks are the basic parameters for rock mechanics, and play a very important role in engineering design. There are many laboratory methods to determine the elastic constants of transversely isotropic rocks, and the Brazilian test is a popular method. This paper presented a method combination of the Brazilian test, back calculation, and iterative procedure to evaluate the five independent elastic constants of transversely isotropic rocks in laboratory. The strain data at the centre of discs were obtained using Brazilian test. The stresses at the centre of discs were computed using numerical programs. By using back calculation, the temporary elastic constants were computed after the stresses and stains were substituted into elastic mechanics equations. After iterative procedure, the convergent values of the elastic constants can be obtained. One numerical example and three experimental cases were proposed to show the applicability of this method. The convergent values of the five independent elastic constants can be obtained in no more than 10 iterative cycles. The results coming from numerical analysis method exhibited satisfactory outcome in accordance with those of generalized reduced gradient method. The merits of this method include convenient specimen preparation of the Brazilian test, simple iterative procedure, and readily available commercially numerical programs, so that this method can be easily popularized in research and engineering analysis. Copyright © 2007 John Wiley & Sons, Ltd.     

Damped least-squares inversion of confined aquifer pumping data based on singular value decomposition

An iterative method for calculating the transmissivity and storage coefficient from pumping test data for a confined aquifer is presented. The method optimizes the fit between the measured and the theoretical data (computed using the Theis equation) in the leastsquare sense. Unlike the existing schemes, this method employs the Levenberg-Marquardt method and the singular value decomposition technique resulting in a stable and rapidly convergent data inversion algorithm. The inverse procedure is initialized by an automatically created starting model derived using a novel technique that operates on the timederivative of the drawdown curve. An important feature of the algorithm is that all the computations are done in logarithmic space which effectively linearizes the pmblem. The proposed method has several advantages over the conventional iterative inversion algorithms because of the linearizing parameterizations at both the forward and inverse stages of the problem. Detailed derivations of the basic equations are provided to guide the potential users as well as applications to field data to demonstrate the usefulness of the proposed algorithm.     

基于PSONN的大坝监控实时预报模型

将粒子群算法（PSO）引入大坝监测领域,提出一种基于粒子群神经网络（PSONN）的大坝监控预报模型。该模型充分发挥PSO的全局寻优能力和BP神经网络局部细致搜索优势,给BP神经网络提供了良好的初始权值。对逐一粒子群（SPSONN）、整体粒子群（WPSONN）、逐一BP（SBPNN）及整体BP（WBPNN）4种预报模型的对比分析表明：逐一预报模型（SPSONN和SBPNN）的预报精度明显高于对应的整体预报模型（WPSONN和WBPNN）的预报精度;与BP神经网络模型相比,PSONN模型不仅收敛速度明显加快,而且预报精度也有较大提高,尤其是SPSONN模型,其高精度和短历时性完全满足实时预报的需要,可以准确、有效地应用于大坝监测量的实时预报。     

Geophysical constraints on geodynamic processes at convergent margins: A global perspective

Convergent margins, being the boundaries between colliding lithospheric plates, form the most disastrous areas in the world due to intensive, strong seismicity and volcanism. We review global geophysical data in order to illustrate the effects of the plate tectonic processes at convergent margins on the crustal and upper mantle structure, seismicity, and geometry of subducting slab. We present global maps of free-air and Bouguer gravity anomalies, heat flow, seismicity, seismic Vs anomalies in the upper mantle, and plate convergence rate, as well as 20 profiles across different convergent margins. A global analysis of these data for three types of convergent margins, formed by ocean–ocean, ocean–continent, and continent–continent collisions, allows us to recognize the following patterns. (1) Plate convergence rate depends on the type of convergent margins and it is significantly larger when, at least, one of the plates is oceanic. However, the oldest oceanic plate in the Pacific ocean has the smallest convergence rate. (2) The presence of an oceanic plate is, in general, required for generation of high-magnitude (M > 8.0) earthquakes and for generating intermediate and deep seismicity along the convergent margins. When oceanic slabs subduct beneath a continent, a gap in the seismogenic zone exists at depths between ca. 250 km and 500 km. Given that the seismogenic zone terminates at ca. 200 km depth in case of continent–continent collision, we propose oceanic origin of subducting slabs beneath the Zagros, the Pamir, and the Vrancea zone. (3) Dip angle of the subducting slab in continent–ocean collision does not correlate neither with the age of subducting oceanic slab, nor with the convergence rate. For ocean–ocean subduction, clear trends are recognized: steeply dipping slabs are characteristic of young subducting plates and of oceanic plates with high convergence rate, with slab rotation towards a near-vertical dip angle at depths below ca. 500 km at very high convergence rate. (4) Local isostasy is not satisfied at the convergent margins as evidenced by strong free air gravity anomalies of positive and negative signs. However, near-isostatic equilibrium may exist in broad zones of distributed deformation such as Tibet. (5) No systematic patterns are recognized in heat flow data due to strong heterogeneity of measured values which are strongly affected by hydrothermal circulation, magmatic activity, crustal faulting, horizontal heat transfer, and also due to low number of heat flow measurements across many margins. (6) Low upper mantle Vs seismic velocities beneath the convergent margins are restricted to the upper 150 km and may be related to mantle wedge melting which is confined to shallow mantle levels.     

Generalized trapezoidal numerical integration of an advanced soil model

This paper investigates the numerical performance of the generalized trapezoidal integration rule by using an advanced soil model. The generalized trapezoidal integration rule can include many other integration algorithms by adjusting a single parameter α ranging from 1 to 0. The soil model used is the recently developed middle surface concept (MSC) sand model which simulates different soil response characteristics by using different pseudo‐yield functions. The generalized trapezoidal rule and MSC sand model are used to simulate the responses of sand samples with different relative densities under various initial and loading conditions. Instead of a single step, multiple loading steps bring the sample to the vicinity of failure. These comprehensive investigations examine and compare the influences of various values of α on the numerical solution of integrated constitutive equations, the convergence of Newton's iterative scheme, and the integration accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

基于?－SVR和GA的初始地应力场位移反分析方法研究

基于一种改进的支持向量机（?－SVR）和改进的遗传算法（GA）,提出一种初始地应力场位移反分析方法。该方法通过正交设计方法安排较少次数的正分析方案,用?－SVR对正分析中测点位移值与参数构成的样本集进行学习,建立参数取值与观测点测值的非线性隐式方程;采用确定性或随机反分析的思路确定反分析的优化目标函数,并利用GA搜索最优参数取值。采用?－SVR方法建立的参数取值与位移量测点测值的非线性隐式方程,能够以很高的精度拟合和预测不同参数取值时的观测点测值,因此,可以用该隐式方程代替正分析,减少计算量;采用改进的GA方法能够准确搜索到最优参数;搜索到的最优参数值与理论值相当吻合。算例表明,基于?－SVR和GA的初始地应力场位移反分析方法是一种行之有效的初始地应力场位移反分析方法,可以广泛用于初始地应力场确定性反分析和随机反分析。     

Combination of Dependent Realizations Within the Gradual Deformation Method

Gradual deformation is a parameterization method that reduces considerably the unknown parameter space of stochastic models. This method can be used in an iterative optimization procedure for constraining stochastic simulations to data that are complex, nonanalytical functions of the simulated variables. This method is based on the fact that linear combinations of multi-Gaussian random functions remain multi-Gaussian random functions. During the past few years, we developed the gradual deformation method by combining independent realizations. This paper investigates another alternative: the combination of dependent realizations. One of our motivations for combining dependent realizations was to improve the numerical stability of the gradual deformation method. Because of limitations both in the size of simulation grids and in the precision of simulation algorithms, numerical realizations of a stochastic model are never perfectly independent. It was shown that the accumulation of very small dependence between realizations might result in significant structural drift from the initial stochastic model. From the combination of random functions whose covariance and cross-covariance are proportional to each other, we derived a new formulation of the gradual deformation method that can explicitly take into account the numerical dependence between realizations. This new formulation allows us to reduce the structural deterioration during the iterative optimization. The problem of combining dependent realizations also arises when deforming conditional realizations of a stochastic model. As opposed to the combination of independent realizations, combining conditional realizations avoids the additional conditioning step during the optimization process. However, this procedure is limited to global deformations with fixed structural parameters.     

Comparative Evaluation of Neural Network Learning Algorithms for Ore Grade Estimation

In this paper, comparative evaluation of various local and global learning algorithms in neural network modeling was performed for ore grade estimation in three deposits: gold, bauxite, and iron ore. Four local learning algorithms, standard back-propagation, back-propagation with momentum, quickprop back-propagation, and Levenberg–Marquardt back-propagation, along with two global learning algorithms, NOVEL and simulated annealing, were investigated for this purpose. The study results revealed that no benefit was achieved using global learning algorithms over local learning algorithms. The reasons for showing equivalent performance of global and local learning algorithms was the smooth error surface of neural network training for these specific case studies. However, a separate exercise involving local and global learning algorithms on a nonlinear multimodal optimization of a Rastrigin function, containing many local minima, clearly demonstrated the superior performance of global learning algorithms over local learning algorithms. Although no benefit was found by using global learning algorithms of neural network training for these specific case studies, as a safeguard against getting trapped in local minima, it is better to apply global learning algorithms in neural network training since many real-life applications of neural network modeling show local minima problems in error surface.     

Integration of local–global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations

We propose a methodology, called multilevel local–global (MLLG) upscaling, for generating accurate upscaled models of permeabilities or transmissibilities for flow simulation on adapted grids in heterogeneous subsurface formations. The method generates an initial adapted grid based on the given fine-scale reservoir heterogeneity and potential flow paths. It then applies local–global (LG) upscaling for permeability or transmissibility [7], along with adaptivity, in an iterative manner. In each iteration of MLLG, the grid can be adapted where needed to reduce flow solver and upscaling errors. The adaptivity is controlled with a flow-based indicator. The iterative process is continued until consistency between the global solve on the adapted grid and the local solves is obtained. While each application of LG upscaling is also an iterative process, this inner iteration generally takes only one or two iterations to converge. Furthermore, the number of outer iterations is bounded above, and hence, the computational costs of this approach are low. We design a new flow-based weighting of transmissibility values in LG upscaling that significantly improves the accuracy of LG and MLLG over traditional local transmissibility calculations. For highly heterogeneous (e.g., channelized) systems, the integration of grid adaptivity and LG upscaling is shown to consistently provide more accurate coarse-scale models for global flow, relative to reference fine-scale results, than do existing upscaling techniques applied to uniform grids of similar densities. Another attractive property of the integration of upscaling and adaptivity is that process dependency is strongly reduced, that is, the approach computes accurate global flow results also for flows driven by boundary conditions different from the generic boundary conditions used to compute the upscaled parameters. The method is demonstrated on Cartesian cell-based anisotropic refinement (CCAR) grids, but it can be applied to other adaptation strategies for structured grids and extended to unstructured grids.