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1.
In an earlier paper (1978), Gottfried presented a method for combining distribution data for float-sink coal-cleaning devices into a single generalized distribution curve which, for a given device and feed size, is independent of specific gravity of separation. A non-linear, exponential-type equation was utilized to represent the generalized distribution curve, along with the corresponding generalized probable error. Distribution data for six common coal-cleaning devices have previously been treated by this method.This paper is an extension of two previous studies (Gottfried, 1978, 1980). The method described above is applied to three different float-sink coal-cleaning devices: Baum jig (replacing previously reported results), Batac jig and Dynawhirlpool separator. Results for the Baum jig and Batac jig reflect a two-stage separation process, with a set of generalized distribution curves obtained for each stage and another set for the overall separation. Several different feed size fractions are given for each vessel. 相似文献
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The performance of float-sink coal cleaning devices customarily is characterized by a distribution curve, in which the percent of feed reporting to clean coal is plotted against specific gravity. For a given vessel and a given feed a family of distribution curves can be obtained, each having its own specific gravity of separation.This paper presents a method for combining these distribution curves at different specific gravities of separation, for a given coal cleaning vessel and a given feed, into a single, generalized distribution curve which is independent of the specific gravity of separation. This curve can be expressed in tabular form or it can be represented mathematically by an exponential type equation, known as a Weibull function.A different generalized distribution curve will be obtained for each of several different size fractions. A method is presented for utilizing these curves with feeds which encompass a broad spectrum of sizes.The well-known concepts of error area and probable error are extended to the generalized distribution curve. It is shown that the conventional probable error, and — under certain conditions — the conventional error area, are directly proportional to the specific gravity of separation for a given vessel and a given feed size. 相似文献
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P.C. Kapur 《International Journal of Mineral Processing》1983,10(2):81-88
A method is presented which seeks to overcome a number of disadvantages that are inherent in the conventional practice of plotting the Tromp curve and analysing it for its various measures, e.g., specific gravity of separation, probable error and error area. A sufficient condition is established for extracting the appropriate criteria of the sharpness of classification, which are independent of coal-feed distribution in specific gravity. Partition area, a modified areal measure, similar to the conventional error area, of the equipment's deviation from ideal classification behavior is derived from the theoretical partition function. A purely numerical procedure is developed for locating the specific gravity of separation and the partition area. Unlike the Tromp-curve-based conventional procedure, the proposed histogram-based method is fast, more convenient and objective for analysing the coal-cleaning plant data. 相似文献
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A microcomputer program for simulating coal-cleaning distribution curves has been developed and includes six different models and two different optimization methods. By displaying the simulated distribution curves on a graphic screen, the curves for different models can be compared and the most suitable model selected. The importance of using this graphics criterion as well as the conventional statistical measurements of error is illustrated. This program requires no user knowledge of either computer programming or of the mathematical procedures. 相似文献
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二维声波方程稳健迭代速度反演 总被引：1，自引：0，他引：1
从二维声波方程初、边值问题出发,通过引进一个广义幂指数误差分布函数,以及对波动方程的Ｌｉｐｐｍａｎ－Ｓｃｈｗｉｎｇｅｒ方程的解进行Ｂｏｎ近似,导出一个残差加权迭代最小二乘（稳健迭代）算法,进而实现对地下介质剖面的速度结构以演计算。模拟计算表明,本方法具有较高的精度和较强的抗干扰能力,是求解声波方程反演问题的一种有效方法,同时也为地下介质的速度分布成像提供一种新的技术。 相似文献
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Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation 
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下载免费PDF全文 This paper presents an algorithm and a fully coupled hydromechanical‐fracture formulation for the simulation of three‐dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3‐D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time‐dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3‐D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented. 相似文献
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The solutions of stress and displacement of a circular opening excavated in brittle and strain-softening rock mass incorporating rockbolts effectiveness and seepage force are presented in this study. The evolution equation is reconstructed for the strength parameters that incorporate these factors. Based on the evolution equation, an improved numerical method and stepwise procedure are presented which are compatible with the Mohr–Coulomb (M–C) and the generalized Hoek–Brown (H–B) failure criteria, respectively. Then given three interaction mechanisms between rockbolts and surrounding rock, solutions for stress and displacement are proposed in line with the improved numerical method and numerical stepwise procedure. The proposed approach can be reduced to Fahimifar and Soroush’s (Tunn Undergr Space Technol 20:333–343, 2005) solutions for special cases. The proposed method was validated by field monitoring data and FLAC results of Yanzidong tunnel. Examples under the M–C and generalized H–B failure criteria for rock mass are generated through MATLAB programming. Moreover, parametric studies are conducted to highlight the influence of rockbolts effectiveness in combination with seepage force on the stress and displacement of very good, average, and very poor surrounding rock. Results show that in this case, stress confinement is higher and tunnel convergences are lower than the corresponding stresses and displacements obtained in non-reinforced tunnels. Displacement and plastic radius are also higher than those without considering seepage force. 相似文献
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三维剖面地质界线是构建三维地质结构模型的重要基础数据,其不确定性会影响三维模型的几何形态和属性分布。以单一分布为假设前提的统计学不确定性分析方法掩盖了其他概率分布特征对模型的影响。突破单一误差分布条件的假设前提,本文使用Monte Carlo方法模拟了不同概率分布情况下地质剖面数据中地质界线的抽样采集,以及地质界线空间分布的不确定性;依托地质界线空间位置与地质属性的耦合关系,提出了用地质属性概率分布实现地质界线空间不确定性的定量可视化,并结合实际地质剖面探讨了多种概率分布条件下地质界线的空间不确定性。实例研究表明,基于Monte Carlo模拟的不确定性分析方法可以突破单一误差分布假设条件,结合地质属性概率可充分揭示出建模数据的内在不确定性与模型外在要素形态之间的耦合关系。 相似文献
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ABDON ATANGANA 《Journal of Earth System Science》2014,123(1):101-108
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented. 相似文献
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Generalized Bootstrap Method for Assessment of?Uncertainty in Semivariogram Inference 总被引：1，自引：0，他引：1
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap. 相似文献
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在这篇文章中，分析了一个具有井眼的非均匀介质中似稳电流场的边值问题。采用了三维有限元的直接解法求解三维似稳电流场；给出了微侧向测井仪器的电极表面电流分布、假几何因子以及８英寸井眼的泥饼校正曲线；求出了在具有倾斜地层条件下，微侧向测井仪器对界面的响应。数值结果与发表的文献非常吻合，从而证明了这种方法的正确性。因此，它为新的仪器研制和微侧向测井解释提供了可靠的数据和理论依据。 相似文献
16.
Ajay Jasra David A. Stephens Kerry Gallagher Christopher C. Holmes 《Mathematical Geology》2006,38(3):269-300
In this paper we develop a generalized statistical methodology for characterizing geochronological data, represented by a distribution of single mineral ages. The main characteristics of such data are the heterogeneity and error associated with its collection. The former property means that mixture models are often appropriate for their analysis, in order to identify discrete age components in the overall distribution. We demonstrate that current methods (e.g., Sambridge and Compston, 1994) for analyzing such problems are not always suitable due to the restriction of the class of component densities that may be fitted to the data. This is of importance, when modelling geochronological data, as it is often the case that skewed and heavy tailed distributions will fit the data well. We concentrate on developing (Bayesian) mixture models with flexibility in the class of component densities, using Markov chain Monte Carlo (MCMC) methods to fit the models. Our method allows us to use any component density to fit the data, as well as returning a probability distribution for the number of components. Furthermore, rather than dealing with the observed ages, as in previous approaches, we make the inferences of components from the “true” ages, i.e., the ages had we been able to observe them without measurement error. We demonstrate our approach on two data sets: uranium-lead (U-Pb) zircon ages from the Khorat basin of northern Thailand and the Carrickalinga Head formation of southern Australia. 相似文献
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Laplace方程Cauchy问题的一种数值解法 总被引：2，自引：1，他引：2
研究了Laplace方程Cauchy问题的数值求解，该问题是一个典型的病态问题。利用格林（Green）公式将Laplace方程的Cauchy问题转化为Hausdorff矩问题。本文利用一种新方法，即矩问题的积分方程方法，求解矩问题，设计了二维Laplace方程Cauchy问题稳定的算法，给出了近似解的误差估计，并对二维Cauchy问题进行了数值模拟。 相似文献
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基于台湾66个站点年最大日雨量历史资料、台湾中央气象局2009年8月8~10日莫拉克台风暴雨期间251个台湾雨量站逐时降雨资料和香港地区65个雨量站的历史逐时降雨资料,以及与香港相邻的3个广东省雨量站(西沥站、横岗站和深圳站)资料,利用分时段地形增强因子法(SDOIF),将莫拉克台风暴雨最大24h实测暴雨中的辐合雨分量分割,并将其辐合雨成分移置到香港地区,与香港地区24h平均地形增强因子相结合,估算出香港地区的可能最大降水。结果显示,莫拉克最大24h降雨量中地形的增强幅度约为45%;得出香港地区最大24h平均可能最大降水分布图,其最大中心值1230.2mm(未考虑水汽放大),与香港地区历史暴雨中心一致,均发生在大帽山附近。 相似文献
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A Bayesian linear inversion methodology based on Gaussian mixture models and its application to geophysical inverse problems are presented in this paper. The proposed inverse method is based on a Bayesian approach under the assumptions of a Gaussian mixture random field for the prior model and a Gaussian linear likelihood function. The model for the latent discrete variable is defined to be a stationary first-order Markov chain. In this approach, a recursive exact solution to an approximation of the posterior distribution of the inverse problem is proposed. A Markov chain Monte Carlo algorithm can be used to efficiently simulate realizations from the correct posterior model. Two inversion studies based on real well log data are presented, and the main results are the posterior distributions of the reservoir properties of interest, the corresponding predictions and prediction intervals, and a set of conditional realizations. The first application is a seismic inversion study for the prediction of lithological facies, P- and S-impedance, where an improvement of 30% in the root-mean-square error of the predictions compared to the traditional Gaussian inversion is obtained. The second application is a rock physics inversion study for the prediction of lithological facies, porosity, and clay volume, where predictions slightly improve compared to the Gaussian inversion approach. 相似文献
20.
Li Jiwei Wang Huabin Wei Changfu Lin Fali Liu Zizhen Zhu Zancheng 《Acta Geotechnica》2022,17(5):1803-1814
A generalized analytical solution for one-dimensional nonlinear horizontal infiltration in unsaturated soil is presented. The solution is an improved functional extremum method based on the principle of stationary action. Any prior assumption about the form of moisture diffusion functions is not implemented in the method. By considering a function of time, the water content type governing equation in the horizontal infiltration process is transformed into a function extremum problem. After solving the Euler–Lagrange equation, combined with boundary conditions, a linear relationship between the moisture diffusion function and the ratio of spatial location to the wetting-front distance is proposed. Furthermore, by using the square relationship between the wetting front and time, the spatial and temporal distribution characteristics of the water content profile are finally expressed. In contrast to most other work, the physical meanings of the parameters in this study are clear and can be derived explicitly. By utilizing the simultaneous Brooks–Corey moisture diffusion function, the development and distribution law of the water content profile was explicitly presented. The results of the solution matched well with the existing theoretical results of the four different soil samples. Owing to the high nonlinearity of the van Genuchten moisture diffusion function, the distribution of the water content profile was implicitly found based on the study method. The results obtained using this method were also consistent with the MATLAB routine, pdepe, numerical solutions for different types of soil properties.
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