Accounting for Estimation Optimality Criteria in Simulated Annealing

This paper presents both estimation and simulation as optimization problems that differ in the optimization criteria, minimization of a local expected loss for estimation and reproduction of global statistics (semivariogram, histogram) for simulation. An intermediate approach is proposed whereby an initial random image is gradually modified using simulated annealing so as to better match both local and global constraints. The relative weights of the different constraints in the objective function allow the user to strike a balance between smoothness of the estimated map and reproduction of spatial variability by simulated maps. The procedure is illustrated using a synthetic dataset. The proposed approach is shown to enhance the influence of observations on neighboring simulated values, hence the final realizations appear to be better conditioned to the sample information. It also produces maps that are more accurate (smaller prediction error) than stochastic simulation ignoring local constraints, but not as accurate as E-type estimation. Flow simulation results show that accounting for local constraints yields, on average, smaller errors in production forecast than a smooth estimated map or a simulated map that reproduces only the histogram and semivariogram. The approach thus reduces the risk associated with the use of a single realization for forecasting and planning.     

改进的模拟退火-变尺度优化方法在测井解释中的应用

实际中的测井参数反演是一个多参数、非线性优化问题,所采用的目标函数,即度量由参数化的理论模型得出的预测值与观测值的吻合程度,往往存在多解的现象。针对这种状况我们提出了模拟退火与变尺度综合反演方法用于参数计算,经过实际试算证明该方法效果很好。     

Slope stability analyzing using recent swarm intelligence techniques

Slope stability analysis of soil with a weak layer sandwiched between two strong layers is considered as a complex geotechnical problem. In this problem, the objective function is non‐convex and discontinuous with the presence of multiple strong local minima. Classical optimization techniques fail to converge to a valid solution unless a proper initial trial is adopted. Even though many new optimization algorithms have emerged, they have not been applied to geotechnical problems yet. In the present study, some recent swarm intelligence algorithms are adopted for some complicated example of slope stability problems and benchmarked with the traditional particle swarm optimization algorithm. From the results, it seems the levy flight krill herd algorithm is the most efficient method over proposed algorithms for this kind of problem. Copyright © 2014 John Wiley & Sons, Ltd.     

An adaptive grid technique for minimizing heterogeneity of cells or elements

Geostatistical techniques allow simulation of properties such as porosity or conductivity on a fine scale. Typically, porous media flow modeling is performed at a coarser scale. Upscaling properties from the fine scale to the coarser scale introduces potential errors which are constrained by the degree of homogeneity of the cell or element. Adaptive grid techniques can be used to minimize the heterogeneity in the individual cells or elements, thus minimizing potential upscaling errors. A geostatistical adaptive grid (GAG) algorithm based on local minimization of heterogeneity is introduced. Local minimization allows greater control over the type of distortion permitted. Comparisons are made with a general elastic grid adjustment (GEGA) algorithm based on global minimization of heterogeneity. Several sample problems are used to test and demonstrate the two approaches.     

双重变异遗传算法及其在临界滑动面搜索中的应用

针对传统的优化算法难以在具有变量多、约束条件复杂、局部极值点多的边坡临界滑动面搜索中取得较好效果的问题,提出双重变异遗传算法（DMGA）。一方面,该算法通过探测变异操作提升算法的局部寻优能力,通过直接变异操作提升算法的全局寻优能力,两者的结合使算法能够在搜索的广度与深度上达到较好的平衡;另一方面,算法采用考虑个体适应度值与进化代数的自适应交叉概率及自适应变异概率,使算法在进化的早期能够增加种群的多样性,在进化的后期能够保护较优的个体不受破坏。将该算法与简化Bishop法相结合,对澳大利亚计算机应用协会（ACADS）提供的考核题及一个海堤边坡工程实例进行分析,计算结果表明:（1）对于均质边坡和非均质边坡,该方法均能准确搜索到边坡的临界滑动面及相应的安全系数;（2）与仅进行直接变异或探测变异的遗传算法相比,双重变异遗传算法具有更强的全局搜索能力及更好的鲁棒性,具有广阔的应用前景。     

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。     

Popperian geophysics and tunnelling algorithm

Parasnis has observed in a presidential address that geophysics is not a Popperian science in a major way. That is, hypotheses are not consciously put forth in a falsifiable format and much of the effort goes in seeking supporting evidence for favoured hypotheses. Parker evolved a parameter extremization strategy, initially to tackle the problem of non-uniqueness in geophysical inference. Later he based a hypothesis testing proposal on it, which is refreshingly Popperian. It has not been adopted widely, partly because it requires global extrema, and not local and this has been regarded as a problem with no solution. Attention is drawn towards tunnelling algorithm, which solves the problem of global optimization successfully, makes Parker’s Popperian proposal practical and extends the range of Popperian geophysics.     

利用温度全局优化法探测堤坝多重集中渗漏

利用地温探测堤坝工程中的多重集中渗漏通道位置是一种反问题,为取得全局最优解及突破现有方法的局限性,采用不同优化算法相互配合的温度全局最优化方法,以达到有效准确探测显著集中渗漏通道的位置。结合各算法优势及目标函数不连续性等特点,选用全局搜索(GS)、多初始点(MS)及遗传算法(GA)3种方法联合补充优化。首先利用GS搜索局部最优点; 然后结合目标函数不连续点及上述局部最优点,人工增加MS优化起始点进行多初始点优化; 最后依据上述局部解,利用GA混合算法优化,从而有效提高全局最优化的概率。根据堤坝工程集中渗漏通道低温补给的特点,对优化目标函数进行了具有特定物理意义的修正; 为减少每次迭代的优化参数,基于温度测试精度提出分步优化方法,根据温度或修正目标函数残差吸引盆特征确定某步优化的集中渗漏数量; 由修正残差与温度测量精度相对大小确定优化是否终止,对应修正残差最小的优化结果为集中渗漏通道位置的真实解。结合工程实例,计算了某水库左坝肩的多重集中渗漏通道位置,分步优化了两个主要的集中渗漏位置,直接法优化3个集中渗漏位置。文献及工程实践证明了该法的正确性及有效性,为了堤坝等水利工程岩土体的集中渗漏整治提供了科学依据。     

Practical considerations in the application of simulated annealing to stochastic simulation

Realizations generated by conditional simulation techniques must honor as much data as possible to be reliable numerical models of the attribute under study. The application of optimization methods such as simulated annealing to stochastic simulation has the potential to honor more data than conventional geostatistical simulation techniques. The essential feature of this approach is the formulation of stochastic imaging as an optimization problem with some specified objective function. The data to be honored by the stochastic images are coded as components in a global objective function. This paper describes the basic algorithm and then addresses a number of practical questions: (1) what are the criteria for adding a component to the global objective function? (2) what perturbation mechanism should be employed in the annealing simulation? (3) when should the temperature be lowered in the annealing procedure? (4) how are edge/border nodes handled? (5) how are local conditioning data handled? and (6) how are multiple components weighted in the global objective function?     

基于RAGA的供水库群水资源配置模型研究

针对动态规划在供水库群优化调度中存在"维数灾",且难以获得真正最优解这一缺点,将改进的加速遗传算法应用到供水库群的水资源优化配置之中。在加速遗传算法中,嵌入局部搜索,以加强算法的全局寻优能力。以库群间的水利联系为线索,设计了相应的算法框架,并提出了供水策略区间的概念。为了体现该算法的优越性,以二个串联供水水库的水资源优化配置为例,选用该方法与基于动态规划的轮库迭代法进行比较研究。结果表明该方法合理可行、收敛速度快,有一定的实用性。     

基于MPSO的RBF耦合算法的桩基动测参数辨识

变异粒子群优化算法（MPSO）是一种基于群体智能的改进全局优化技术,其优势在于减小陷入局部极值的机率,增加全局搜索能力。将变异粒子群算法与径向基函数（RBF）神经网络结构进行结合,建立了变异粒子群神经网络（MPSO-RBF）耦合算法,充分发挥了MPSO算法的全局寻优能力和RBF算法的局部搜索优势。数值计算结果表明,所建立的方法能够对桩基动测进行多参数的识别和非线性优化问题的求解,具有良好全局收敛能力,是一种行之有效的智能算法。     

A derivative-free methodology with local and global search for the constrained joint optimization of well locations and controls

In oil field development, the optimal location for a new well depends on how it is to be operated. Thus, it is generally suboptimal to treat the well location and well control optimization problems separately. Rather, they should be considered simultaneously as a joint problem. In this work, we present noninvasive, derivative-free, easily parallelizable procedures to solve this joint optimization problem. Specifically, we consider Particle Swarm Optimization (PSO), a global stochastic search algorithm; Mesh Adaptive Direct Search (MADS), a local search procedure; and a hybrid PSO–MADS technique that combines the advantages of both methods. Nonlinear constraints are handled through use of filter-based treatments that seek to minimize both the objective function and constraint violation. We also introduce a formulation to determine the optimal number of wells, in addition to their locations and controls, by associating a binary variable (drill/do not drill) with each well. Example cases of varying complexity, which include bound constraints, nonlinear constraints, and the determination of the number of wells, are presented. The PSO–MADS hybrid procedure is shown to consistently outperform both stand-alone PSO and MADS when solving the joint problem. The joint approach is also observed to provide superior performance relative to a sequential procedure.     

一个新的全局优化算法在岩土工程反分析中的应用

DCD(dynamic canonical descent)算法是一个新的全局优化算法,运用该法进行优化时,无需考虑目标函数的可微性,只要正确给定优化变量的优化区间,且该区间具有凸性,那么此算法就能很好地收敛于该区间的全局极小点.针对该算法,建立了相应的算法迭代格式.对数值试验和在岩土工程位移反分析的应用中引入该算法的迭代格式进行全局优化反演,其结果表明:该算法稳定性强,优化结果的可靠度高,收敛速度较快.     

基于三次插值的大地电磁自适应有限元二维正演模拟

大地电磁(MT)数值模拟中通常使用有限单元法,通过伽辽金(Galerkin)法将微分方程转化为与其等价的泛函形式,对泛函求取极值并在单元上定义插值基函数,得到节点上电磁场值的线性方程组,最终形成大型复对称稀疏矩阵。要达到较高的有限元计算精度,一般采用密集的网格或高次插值的方法,这样做大大的减慢了正演的速度。结合两者的优点利用三次插值和h-型自适应相结合的有限元法来实现MT的正演算法。首先从一个粗网格出发并利用三次插值,通过后验误差估计方法局部加密网格,在计算量较小的情况获得较高的计算精度。这种方法可以针对目标区域和介质分界面发生突变处进行网格加密,不需要全局加密网格。最后通过对国际标准模型COMMEMI-2D1的模拟,分别比较二次插值与三次插值的自适应网格数量和数值模拟结果,证明了三次插值自适应有限元算法的可行性。     

An Initial Guess for the Levenberg–Marquardt Algorithm for Conditioning a Stochastic Channel to Pressure Data

A standard procedure for conditioning a stochastic channel to well-test pressure data requires the minimization of an objective function. The Levenberg–Marquardt algorithm is a natural choice for minimization, but may suffer from slow convergence or converge to a local minimum which gives an unacceptable match of observed pressure data if a poor initial guess is used. In this work, we present a procedure to generate a good initial guess when the Levenberg–Marquardt algorithm is used to condition a stochastic channel to pressure data and well observations of channel facies, channel thickness, and channel top depth. This technique yields improved computational efficiency when the Levenberg–Marquardt method is used as the optimization procedure for generating realizations of the model by the randomized maximum likelihood method.     

Point-block covariance: A general solution for the two-dimensional stationary random functions

The application of the theory of random functions to problems of ore evaluation may involve computations of the covariance between the mean value of a given block and the functional value at a given point. However, an analytical solution for such a covariance does not exist for nonspherical blocks and for commonly applied models of covariance functions. Further, because this covariance is a function of the spatial arrangements of the block and the point, it has to be evaluated numerically each time for given point—block arrangements. This paper presents a readily available general solution to this problem in the form of a series of graduated curves which, together with some geometric manipulations, may be used to compute the covariance between a pointand a two-dimensional block for all possible point—block arrangements. The availability of the graph thus eliminates the necessity of using the time-absorbing programs on computers for such computations. Finally, many of the approximations that are made in order to avoid cumbersome covariance evaluations are no longer necessary due to the ease of such computations with the help of the graph provided.     

改进麻雀搜索算法的自然电位数据反演

自然电位法是一种成本低廉,野外观测操作简便的天然源地球物理勘探方法。自然电位数据反演具有病态和非线性的特征。常规反演算法分为局部优化类和全局搜索类,但基于梯度运算的局部优化算法难以求得全局最优解且反演效果依赖于初始模型的构建,而传统全局搜索算法又存在收敛速度慢,易陷入局部极值和不稳定的缺点。基于此,对一种新的全局优化策略(麻雀搜索算法)进行改进,通过混沌映射叠加反向学习策略初始化麻雀种群,再依随机概率使用Levy飞行策略更新麻雀个体位置来进一步提升算法对于解空间的探索能力和增强算法跳出局部极值的可能性。将改进前后的麻雀搜索算法分别应用于合成自然电位数据(不含与含10%、30%的随机噪声)与来自印度和法国的实测数据的反演解释中以对比检验改进算法的反演效果。理论测试结果表明：麻雀搜索算法(SSA)在无噪声干扰下的垂直圆柱和倾斜板模型数据反演误差为0.42%和0.25%,相同情况下改进麻雀搜索算法(ISSA)的反演误差为0.06%和0.07%,改进后算法拟合精度提高到3～7倍,对比目标函数收敛曲线图中ISSA的收敛速度与收敛精度都要明显优于SSA;SSA反演参数的稳定性、精度和异常响应曲线拟...     

A mathematical model for orientation data from macroscopic cylindrical folds

An asymptotic form of Bingham's distribution on the sphere is applied to orientation data from cylindrical folds. Data from cylindrical folds typically form two clusters, one cluster for each fold limb. A bimodal distribution is obtained by fitting a unimodal distribution to each cluster. One parameter of the distribution gives the fold axis, another parameter is directly related to the curvature of the fold limb. Certain tests of hypotheses based on this distribution are the same as tests based on the Dimroth—Watson (symmetric girdle)distribution. One such is the test of whether two folds have the same fold axis.     

Human sociogeophysics — Phase II (continued): Criticality in the diffusion of ethnicity produces civil society

After a Phase I expansion at a constant population density, the earth's surface —the habitable niche of man — becomes filled. The subsequent global Malthusian constant (birth rate minus death rate) however remains unchanged. A criticality in density is thereupon reached, and a phase transition ensues. The most marked feature of Phase II is an onset of condensations, of settlements in place. The kinematics of Phase II involved (a) continued low growth rate of total population; (b) the continued diffusion of ethnicity with remixing; (c) fluctuating condensations involving local urban densifications; (d) local convective process fluxes (flows) carried on via trade and war rather than simple diffusive flow processes carried on via extensive local migrations; and (e) civilizational flow processes of convection governed by man-made rules for the diffusive transports of matter, energy, action and population.The diffusion of ethnicity continues at an expanded space-time scale. The spatial scale is enlarged to the order of 300 km, with a corollary time scale of 1/2 to 1 millennium. This estimate is based on two physical notions: (a) a stability criterion for the transition, which provides an estimate for the number (density) of neighboring condensed population centers that need be involved in the trade-war convections (on the order of 16) and the range domain for these centers (on the order of 200–300 km); and (b) continuance of the diffusion of ethnicity as marked by a diffusivity relation (d₁ ²/t₁ = d₂ ²/t₂) where d₁ = 50–80 km (prior hunter-gatherer spatial scale), t₁ = 30 years (prior hunter-gatherer time scale), d₂ = 300 km (subsequent settlement spatial scale), so that t₂ (subsequent settlement temporal scale) approximates 500 to 1000 years.While the total human ensemble represents a unitary human culture (in Braudel's term, a world-economy), it also contains a plurality of cultures in the anthropologist's sense, which now continuously diffuse and rediffuse, mix and remix. This continuing diffusion of ethnicity at the longer and larger scales produces longer and larger-scale fluctuations — fluid-like, transitory, large moving — which begin to constitute the politics and economics of civilizations. Trade and war become civilization's macroscopic flows, surplus production and states and empires its macroscopic patterns and forms.