P-III分布参数的概率权重矩法S函数计算

概率权重矩法是一种估计统计分布参数的方法.本文根据不完全Γ函数在无限区间积分,推导了P-Ⅲ分布参数的S函数的计算公式.通过现有计算公式比较,其计算结果具有较高的计算精度,避免了的大量的数值积分计算.文中公式只要借助于计算编程进行求解,给定超几何函数项一定的截断误差,其运算具有较高的运行速度.文中计算公式是一种P-Ⅲ分布参数S函数的计算途径.     

Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS₁), (ii) calculated using the fourth-order moments with the theoretical sills (GLS₂), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS₃). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS₁ and theoretical GLS₂ are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS₁ can be recommended for future studies using the LMC.     

Frequency analysis of nonstationary annual maximum flood series using the time‐varying two‐component mixture distributions

The most popular practice for analysing nonstationarity of flood series is to use a fixed single‐type probability distribution incorporated with the time‐varying moments. However, the type of probability distribution could be both complex because of distinct flood populations and time‐varying under changing environments. To allow the investigation of this complex nature, the time‐varying two‐component mixture distributions (TTMD) method is proposed in this study by considering the time variations of not only the moments of its component distributions but also the weighting coefficients. Having identified the existence of mixed flood populations based on circular statistics, the proposed TTMD was applied to model the annual maximum flood series of two stations in the Weihe River basin, with the model parameters calibrated by the meta‐heuristic maximum likelihood method. The performance of TTMD was evaluated by different diagnostic plots and indexes and compared with stationary single‐type distributions, stationary mixture distributions and time‐varying single‐type distributions. The results highlighted the advantages of TTMD with physically‐based covariates for both stations. Besides, the optimal TTMD models were considered to be capable of settling the issue of nonstationarity and capturing the mixed flood populations satisfactorily. Copyright © 2016 John Wiley & Sons, Ltd.     

Super-resolution enhancement of UAV images based on fractional calculus and POCS

Abstract

A super-resolution enhancement algorithm was proposed based on the combination of fractional calculus and Projection onto Convex Sets (POCS) for unmanned aerial vehicles (UAVs) images. The representative problems of UAV images including motion blur, fisheye effect distortion, overexposed, and so on can be improved by the proposed algorithm. The fractional calculus operator is used to enhance the high-resolution and low-resolution reference frames for POCS. The affine transformation parameters between low-resolution images and reference frame are calculated by Scale Invariant Feature Transform (SIFT) for matching. The point spread function of POCS is simulated by a fractional integral filter instead of Gaussian filter for more clarity of texture and detail. The objective indices and subjective effect are compared between the proposed and other methods. The experimental results indicate that the proposed method outperforms other algorithms in most cases, especially in the structure and detail clarity of the reconstructed images.     

Appraisal of regional and index flood quantile estimators

Our results illustrate the performance of at-site and regional GEV/PWM flood quantile estimators in regions with different coefficients of variation, degrees of regional heterogeneity, record lengths, and number of sites. Analytic approximations of bias and variance are employed. For realistic GEV distributions and short records, the index-flood quantile estimator performs better than a 2-parameter GEV/PWM quantile estimator with a regional shape parameter, or a 3-parameter at-site GEV/PWM quantile estimator, in both humid and especially in arid regions, as long as the degree of regional heterogeneity is moderate. As regional heterogeneity or record lengths increases, 2-parameter estimators quickly dominate. Flood frequency models that assign probabilities larger than 2% to negative flows are unrealistic; experiments employing such distributions provide questionable results. This appraisal generally demonstrates the value of regionalizing estimators of the shape of a flood distribution, and sometimes the coefficient of variation.     

Approaches for modeling longitudinal dispersion in pore-networks

The purpose of this study is to quantify the dispersivity in the longitudinal direction by upscaling pore scale mixing over a network domain and to verify the dispersivity with that obtained through the more rigorous upscaling technique, the Brownian particle tracking model (BPTM). We model a porous medium with a network of pore-units that are comprised of pore bodies and bonds of finite volume. Such a pore-unit is assumed to be a mixing cell with the steady state flow condition for a single fluid. Dispersivity can be obtained by solving the mixing cell model (MCM) for the concentration in each pore-unit and by averaging the concentrations for a large number of pore units (as a function of time and space). A minimal size of network that ascertains an asymptotic value of dispersivity was determined and verified with large size pore networks. This numerically computed dispersivity is compared with the results from the BPTM for the same porous medium and flow conditions. We show that the dispersivity obtained from the MCM is equally reliable for the heterogeneous pore-networks and can be estimated as a function of pore size heterogeneity. For homogeneous networks with the MCM, the iteration time step plays an important role. On the other hand, for networks with the BPTM, the assumption of intra-bond velocity profile affects the results.     

地形图点状符号自动识别中不变性特征参数的提取

特征参数的抽取,是实现地形图中点状符号自动识别的关键。本文根据点状符号在扫描图中可能出现的旋转、缩放等情况,归纳和总结出了４种易于计算的不变性特征,并给出了这些特征的提取方法和部分实验结果。这４种特征参数是:复杂度——用以描述符号外围的复杂程度;扁率——用以反映符号的扁平程度;比重——符号的黑色部分在其整个覆盖区域中所占的比例;偏心率——用以反映符号重心与符号的几何中心的偏离程度。这４种特征参数具有旋转不变性和大小不变性,且便于提取、容易计算。     

Characterization of Geochemical Distributions Using Multifractal Models

The use of multifractals in the applied sciences has proven useful in the characterization and modeling of complex phenomena. Multifractal theory has also been recently applied to the study and characterization of geochemical distributions, and its relation to spatial statistics clearly stated. The present paper proposes a two-dimensional multifractal model based on a trinomial multiplicative cascade as a proxy to some geochemical distribution. The equations for the generalized dimensions, mass exponent, coarse Lipschitz–Hölder exponent, and multifractal spectrum are derived. This model was tested with an example data set used for geochemical exploration of gold deposits in Northwest Portugal. The element used was arsenic because a large number of sample assays were below detection limit for gold. Arsenic, however, has a positive correlation with gold, and the two generations of arsenopyrite identified in the gold quartz veins are consistent with different mineralizing events, which gave rise to different gold grades. Performing the multifractal analysis has shown problems arising in the subdivision of the area with boxes of constant side length and in the uncertainty the edge effects produce in the experimental estimation of the mass exponent. However, it was possible to closely fit a multifractal spectrum to the data with enrichment factors in the range 2.4–2.6 and constant K₁ = 1.3. Such parameters may give some information on the magnitude of the concentration efficiency and heterogeneity of the distribution of arsenic in the mineralized structures. In a simple test with estimated points using ordinary lognormal kriging, the fitted multifractal model showed the magnitude of smoothing in estimated data. Therefore, it is concluded that multifractal models may be useful in the stochastic simulation of geochemical distributions.     

Flood frequency analysis of Turkey using L‐moments method

The index flood procedure coupled with the L‐moments method is applied to the annual flood peaks data taken at all stream‐gauging stations in Turkey having at least 15‐year‐long records. First, screening of the data is done based on the discordancy measure (D_i) in terms of the L‐moments. Homogeneity of the total geographical area of Turkey is tested using the L‐moments based heterogeneity measure, H, computed on 500 simulations generated using the four parameter Kappa distribution. The L‐moments analysis of the recorded annual flood peaks data at 543 gauged sites indicates that Turkey as a whole is hydrologically heterogeneous, and 45 of 543 gauged sites are discordant which are discarded from further analyses. The catchment areas of these 543 sites vary from 9·9 to 75121 km² and their mean annual peak floods vary from 1·72 to 3739·5 m³ s^?1. The probability distributions used in the analyses, whose parameters are computed by the L‐moments method are the general extreme values (GEV), generalized logistic (GLO), generalized normal (GNO), Pearson type III (PE3), generalized Pareto (GPA), and five‐parameter Wakeby (WAK). Based on the L‐moment ratio diagrams and the |Z_dist|‐statistic criteria, the GEV distribution is identified as the robust distribution for the study area (498 gauged sites). Hence, for estimation of flood magnitudes of various return periods in Turkey, a regional flood frequency relationship is developed using the GEV distribution. Next, the quantiles computed at all of 543 gauged sites by the GEV and the Wakeby distributions are compared with the observed values of the same probability based on two criteria, mean absolute relative error and determination coefficient. Results of these comparisons indicate that both distributions of GEV and Wakeby, whose parameters are computed by the L‐moments method, are adequate in predicting quantile estimates. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.