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1.
一种求带约束的离散Minimax问题的区间算法 总被引：2，自引：0，他引：2
进一步讨论了目标函数和约束函数都是Lipsehitz连续的带约束的离散minimax问题，给出了罚函数的区间扩张，提出了解该约束离散minimax问题的区间算法。算法给出了问题的minimax值所在范围以及minimax点所在位置。定理和数值算倒说明该算法是可靠的。 相似文献
2.
Slope reliability analysis using a support vector machine 总被引：6，自引：0，他引：6
The first-order second-moment method (FOSM) reliability analysis is commonly used for slope stability analysis. It requires the values and partial derivatives of the performance function with respect to the random variables for the design. Such calculations can be cumbersome when the performance functions are implicit. Implicit performance functions are normally encountered when the slope is geologically complicated and the limit equilibrium method (LEM) is used for the stability analysis.
To address this issue, this paper presents a support vector machine (SVM)-based reliability analysis method which combines the SVM with the FOSM. This method employs the SVM method to approximate the implicit performance functions, thus arriving at SVM-based explicit performance functions. The SVM method uses a small set of the actual values of the performance functions obtained via the LEM for complicated slope engineering. Using the SVM model, a large number of values and partial derivatives of the performance functions can be obtained for conventional reliability analysis using the FOSM. Examples are given to illustrate the proposed SVM-based slope reliability analysis. The results show that the proposed approach is applicable to slope reliability analysis which involves implicit performance functions. 相似文献
3.
The luminosity and mass functions of a group of Galactic open clusters are constructed by applying a statistical method to photometric data from the USNO-A1 catalog. Despite some limitations, this catalog can be used for statistical analyses in Galactic astronomy. Pairwise comparisons of the derived cluster luminosity functions are performed for five age intervals. The differences between the luminosity functions of the open clusters are not statistically significant in most cases. It is concluded that the luminosity functions are approximately universal throughout a large volume in the solar neighborhood. Combined luminosity and mass functions are constructed for six age intervals. The slope of the mass spectrum may vary somewhat from cluster to cluster, and the mean slope may be somewhat higher than the Salpetervalue. 相似文献
4.
Calibrating functions play a substantial role in the determination of earthquake magnitudes. Their shape and character is closely connected with the internal structure of the Earth, the distribution of velocities and attenuation of seismic waves in the Earth's body. These facts have been considered during the establishment of the Eurasian Homogeneous Magnitude System (EuHMS). The paper summarizes the procedures used for constructing the new complete set of calibrating functions for body and surface waves (vertical and horizontal components of P, S and L waves from medium period instruments, and vertical component of P waves from short period instruments).The calibrating functions were derived in the distance range between 20° and 100°, being based on several thousands of homogeneous observations for each wave type. The application of a HMS gives a possibility to derive the magnitude calibrating functions with a considerable degree of reliability due to the method of simultaneous optimization of the calibrating functions and the systems of station corrections. The magnitude calibrating functions for EuHMS represent the first complete set of calibrating functions, which are derived by the same standard method and initial observational material. A comparison with the existing calibrating functions shows that the application of σ and Q functions, presently used in the seismological practice for magnitude determinations, may lead to errors exceeding
of magnitude unit at certain epicentral distances, specific for each wave type. It appears that the internationally recommended Q functions are not admissible for magnitude determinations from short-period P waves. 相似文献
5.
The effectiveness and accuracy of the superposition method in assessing the dynamic stiffness and damping coefficients (impedance functions) of embedded footings supported by vertical piles in homogeneous viscoelastic soil is addressed. To this end, the impedances of piled embedded footings are compared to those obtained by superposing the impedance functions of the corresponding pile groups and embedded footings treated separately, with the magnitude of the relative average differences being around 10–30%. The results are presented in a set of dimensionless graphs and simple expressions that can be used to estimate the dynamic stiffness and damping of piled embedded footings, provided that the impedance functions of the two individual components are known. This is precisely the reason why the superposition approach studied here is appealing, because such impedance functions for both embedded footings and pile groups are available for a wide range of cases. How to estimate the kinematic response functions of the system when those of the individual components are known is also discussed. To address the problem, parametric analyses performed using a 3D frequency‐domain elastodynamic BEM‐FEM formulation are presented for different pile–soil stiffness contrasts, embedment depths, pile‐to‐pile separations and excitation frequencies. Vertical, horizontal, rocking, and cross‐coupled horizontal‐rocking impedance functions, together with translational and rotational kinematic response functions, are discussed. The results suggest that the superposition concept, in conjunction with a correction strategy as that presented herein, can be employed in geotechnical design. For kinematic effects, the response functions of the embedded footing are found to provide reasonable estimates of the system's behaviour. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
6.
Moisture Movement Through Cracked Clay Soil Profiles 总被引：1，自引：0，他引：1
Delwyn G. Fredlund Sandra L. Houston Quan Nguyen Murray D. Fredlund 《Geotechnical and Geological Engineering》2010,28(6):865-888
A continuum mechanics approach is used for the formulation of unsaturated hydraulic conductivity functions and the water storage
functions for fractured or cracked clay soils in this parametric study. Suggested procedures are based on available research
literature related to the behavior of cracked unsaturated porous media. The soil–water characteristic curve, hydraulic conductivity
and water storage functions take on the character of bi-modal unsaturated soil property functions. The bimodal character arises
out of the independent behavior of the cracks and the intact clay soil. Matric suction changes beneath a slab-on-grade foundation
placed on a cracked clay soil profile are modeled for varied surface flux conditions using the proposed unsaturated hydraulic
conductivity and water storage functions. The impact of various levels of surface cracking on soil suction distributions is
discussed. Suction distribution patterns are dependent on the initial soil surface suction. In particular, the results are
dependent upon whether the initial matric suction is less than or greater than the air entry of the cracked clay. There is
an extremely wide range of possible conditions that could be modeled but the parametric study results presented in this paper
are limited to a series of selected crack widths and densities for an exfiltration case and an infiltration case. 相似文献
7.
《Ore Geology Reviews》2003,22(1-2):117-132
A data-driven application of the theory of evidential belief to map mineral potential is demonstrated with a redefinition of procedures to estimate evidential belief functions. The redefined estimates of evidential belief functions take into account not only the spatial relationship of an evidence with the target mineral deposit but also consider the relationships among the subsets of spatial evidences within a set of evidential data layer. Proximity of geological features to mineral deposits is translated into spatial evidence and evidential belief functions are estimated for the proposition that mineral deposits exist in a test area. The integrated maps of degrees of belief for the proposition that mineral deposits exist in a test area is classified into a binary mineral potential map. For the Baguio district (Philippines), the binary gold potential map delineates (a) about 74% of the training data (i.e., locations of large-scale gold deposits) and (b) about 64% of the validation data (i.e., locations of small-scale gold deposits). The results demonstrate the usefulness of a geologically constrained mineral potential mapping using data-driven evidential belief functions to guide further surficial exploration work in the search for yet undiscovered gold deposits in the Baguio district. The results also indicate the usefulness of evidential belief functions for mapping uncertainties in the geologically constrained integrated predictive model of gold potential. 相似文献
8.
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast. 相似文献
9.
Statistical assignment of upscaled flow functions for an ensemble of geological models 总被引：1，自引：0，他引：1
Upscaled flow functions are often needed to account for the effects of fine-scale permeability heterogeneity in coarse-scale
simulation models. We present procedures in which the required coarse-scale flow functions are statistically assigned to an
ensemble of upscaled geological models. This can be viewed as an extension and further development of a recently developed
ensemble level upscaling (EnLU) approach. The method aims to efficiently generate coarse-scale flow models capable of reproducing
the ensemble statistics (e.g., cumulative distribution function) of fine-scale flow predictions for multiple reservoir models.
The most expensive part of standard coarsening procedures is typically the generation of upscaled two-phase flow functions
(e.g., relative permeabilities). EnLU provides a means for efficiently generating these upscaled functions using stochastic
simulation. This involves the use of coarse-block attributes that are both fast to compute and correlate closely with the
upscaled two-phase functions. In this paper, improved attributes for use in EnLU, namely the coefficient of variation of the
fine-scale single-phase velocity field (computed during computation of upscaled absolute permeability) and the integral range
of the fine-scale permeability variogram, are identified. Geostatistical simulation methods, which account for spatial correlations
of the statistically generated upscaled functions, are also applied. The overall methodology thus enables the efficient generation
of coarse-scale flow models. The procedure is tested on 3D well-driven flow problems with different permeability distributions
and variable fluid mobility ratios. EnLU is shown to capture the ensemble statistics of fine-scale flow results (water and
oil flow rates as a function of time) with similar accuracy to full flow-based upscaling methods but with computational speedups
of more than an order of magnitude. 相似文献
10.
Spherical harmonics in texture analysis 总被引：1，自引：0，他引：1
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3
3 or hypersphere Ω4
4, respectively, they belong at least to the space of measurable and integrable functions
1(Ωd), d=3, 4, respectively.
Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of 1(Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements. 相似文献
11.
湿地是流域水循环和水量平衡的重要调节器,在维护流域水量平衡、减轻洪旱灾害和应对气候变化等方面发挥极其重要的作用。流域湿地水文调蓄功能是湿地生态水文学研究的重要内容,科学认识和理解流域湿地水文调蓄功能对流域湿地恢复保护、水资源综合管控与应对气候变化具有极其重要的意义。本文阐述了流域湿地水文调蓄功能的概念与内涵,剖析了流域湿地水文调蓄功能时空变异性、阈值性和多维性三大特征及其影响因素（包括湿地土壤特性、植被特征和初始水文条件等内在因素和流域特征、降雨特征、气候变化和人类活动等外在因素）,探讨了流域湿地不变情景下和变化情景下水文调蓄功能评估方法,并介绍了流域湿地水文调蓄功能定量评估模型与应用情况。最后,从学科发展和实践需求的视角提出了流域湿地水文调蓄功能未来亟需加强研究的重点方向。 相似文献
12.
The variogram matrix function is an important measure for the dependence of a vector random field with second-order increments, and is a useful tool for linear predication or cokriging. This paper proposes an efficient approach to construct variogram matrix functions, based on three ingredients: a univariate variogram, a conditionally negative definite matrix, and a Bernstein function, and derives three classes of variogram matrix functions for vector elliptically contoured random fields. Moreover, various dependence structures among components can be derived through appropriate mixture procedures demonstrated in this paper. We also obtain covariance matrix functions for second-order vector random fields through the Schoenberg–Lévy kernels. 相似文献
13.
Peter K. Kitanidis 《Mathematical Geology》1985,17(2):195-208
The parameters of covariance functions (or variograms) of regionalized variables must be determined before linear unbiased estimation can be applied. This work examines the problem of minimum-variance unbiased quadratic estimation of the parameters of ordinary or generalized covariance functions of regionalized variables. Attention is limited to covariance functions that are linear in the parameters and the normality assumption is invoked when fourth moments of the data need to be calculated. The main contributions of this work are (1) it shows when and in what sense minimum-variance unbiased quadratic estimation can be achieved, and (2) it yields a well-founded, practicable, and easy-to-automate methodology for the estimation of parameters of covariance functions. Results of simulation studies are very encouraging. 相似文献
14.
Multivariate Intrinsic Random Functions for Cokriging 总被引：2，自引：0，他引：2
In multivariate geostatistics, suppose that we relax the usual second-order-stationarity assumptions and assume that the component
processes are intrinsic random functions of general orders. In this article, we introduce a generalized cross-covariance function
to describe the spatial cross-dependencies in multivariate intrinsic random functions. A nonparametric method is then proposed
for its estimation. Based on this class of generalized cross-covariance functions, we give cokriging equations for multivariate
intrinsic random functions in the presence of measurement error. A simulation is presented that demonstrates the accuracy
of the proposed nonparametric estimation method. Finally, an application is given to a dataset of plutonium and americium
concentrations collected from a region of the Nevada Test Site used for atomic-bomb testing. 相似文献
15.
Sonia Pérez-Plaza Fernando Fernández-Palacín Manuel Berrocoso Raúl Páez Belén Rosado 《Mathematical Geosciences》2018,50(6):659-677
This paper demonstrates the usefulness of approaching the dynamic study of the precise positioning of a network of permanent global positioning system (GPS) stations through functional data analysis. The displacement data for each GPS station, obtained from observations of the global navigation satellite system, are a discrete sample of the positioning curve. The aim of this paper is to reconstruct the original functions in order to use them as functional data. In the method presented in this paper, the geodetic series are obtained first by processing the GPS data with respect to a reference station. Second, for each station, a cleaning process is applied to eliminate the values considered as outliers, and the missing values are imputed by using a Kalman filter. Finally, the original functions are reconstructed by using smoothing techniques and by evaluating several bases of functions. Moreover, these functions are treated with statistical techniques for functional data. This procedure is applied to the permanent stations of the south of the Iberian peninsula and the north of Africa (SPINA) network. The topocentric series: east, north and up are analysed. In the analysis of the positioning curves, there is observed a synchronized behaviour of the functions in those periods of time with important seismic activity. This behaviour also appears in the analysis of the second principal component of the East and up dimensions. Furthermore, the first two principal components of the East coordinate enable us to make a classification of the stations in the SPINA network. The classification made is consistent with the previous knowledge of the tectonic plates in the studied area. 相似文献
16.
Guocheng Pan 《Mathematical Geology》1993,25(5):603-631
This paper presents a regionalized method for the estimation of a favorability function through generalization of all relevant variables (explanatory and target) into random functions. The new method allows the use of cross-covariance functions in addition to ordinary covariances for extracting spatial joint information, which is virtually overlooked in the conventional analyses. The optimal weights for a favorability equation are derived from solving a generalized eigen-system established by the maximization of covariances between a favorability function and the principal components of a set of pre-selected target variables. Various correlation coefficients may be computed to assist in interpretation of the favorability estimates. Both favorability functions and correlation coefficients may be estimated for a point or a block. The regionalized favorability theory can be compared to cokriging in that both use the sample-sample covariances to account for the sample-sample relations and the point-sample covariances to account for the point-sample configurations. The new technique is demonstrated on a test case study, which involves the integration of geochemical, airborne-geophysical, and structural data sets for the target selection of hydrothermal gold-silver deposits. 相似文献
17.
DPFT is a lumped approach for operational flash flood forecasting, based on the unit hydrograph. Using a multi-event alternating iterative algorithm, it identifies a robust and stable average transfer function and a consistent set of effective rainfall series associated with each event at the same time. This key ingredient allows an objective calibration of different loss functions, relating gauged precipitation and effective rainfall. A case study based on an operational French basin (545 km2) is presented. Three lumped production functions have been calibrated and compared. The results show that more elaborate models of loss functions must be proposed, and some possible directions for this are pointed out. 相似文献
18.
Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
19.
Least squares collocation is a very comprehensive method for gravity field modelling, since it may use known noise characteristics of the data. In many earlier applications the errors affecting the data were considered uncorrelated, mainly due to the difficulty in estimating the systematic character of such kind of errors. In this study, error covariance functions of airborne gravity gradiometer data are estimated by comparing model covariance functions with empirical covariance functions of the gravity gradiometer data. The model covariance functions were estimated from accurate surface gravity data and continuated upward to the height of the airborne measurements using the covariance propagation law. The estimated error covariance functions were modeled as finite ones and used as an additional information for the prediction of gravity anomalies from gravity gradiometer data. The assessment of the prediction results was made by comparing the gravity values predicted from the airborne gradient data and showed up to 25% improvement compared to not using correlated errors. 相似文献
20.
S. M. J. R. Goel S. K. Malasi P. S. Moharir H. R. Wason K. N. Khattri V. K. Gaur 《Journal of Earth System Science》1983,92(3):223-237
Whether the earthquake occurrences follow a Poisson process model is a widely debated issue. The Poisson process model has
great conceptual appeal and those who rejected it under pressure of empirical evidence have tried to restore it by trying
to identify main events and suppressing foreshocks and aftershocks. The approach here is to estimate the density functions
for the waiting times of the future earthquakes. For this purpose, the notion of Gram-Charlier series which is a standard
method for the estimation of density functions has been extended based on the orthogonality properties of certain polynomials
such as Laguerre and Legendre. It is argued that it is best to estimate density functions in the context of a particular null
hypothesis. Using the results of estimation a simple test has been designed to establish that earthquakes do not occur as
independent events, thus violating one of the postulates of a Poisson process model. Both methodological and utilitarian aspects
are dealt with. 相似文献