一种新的估计非高斯分布含水层渗透系数场的方法

集合卡尔曼滤波(ensemble Kalman filter,EnKF)是最流行的数据同化方法之一。然而,在处理非高斯问题时,EnKF存在局限性。为了解决非高斯问题并准确描述含水介质连通性,将正态分数变换(normal-score transformation,NST)与多重数据同化集合平滑器(ensemble smoother with multiple data assimilation,ES-MDA)相结合,提出NS-ES-MDA方法。通过对比实验,验证了NS-ES-MDA方法估计非高斯分布含水层渗透系数场的有效性。相较于重启正态分数集合卡尔曼滤波器(restart normal-score ensemble Kalman filter,rNS-EnKF)方法,NS-ES-MDA在吸收相同数据后,参数估计精度提升约34%,计算效率提升约35%。此外,NS-ES-MDA方法受“异参同效”现象的影响较小,具有较强的更新能力,能够保障得到较准确的参数估计值。研究可为非高斯分布含水层参数估计提供一种有效的求解方法。

一种简单、可靠的分数正态化及标准化换算方法

考试是教育行为中检验学生对某门学科知识掌握程度的重要手段,如何科学地处理考生成绩,使其成为分布合理、具有可比性的分数,是教育测量学中的一个重要方面.本文提出一种利用映射原理,对考生卷面分进行正态化及等值处理的简便换算方法.

使用“地区常模表”对不同的测验分数进行比较

通过测验所直接得到的分数，叫原始分：由于各个测验的难度不同，各原始分的价值也不相同。为了使不同的测验分数可以进行比较，必须把原始分数转换成导出分数，如百分等级分或标准分：百分等级分可以十分直观、准确地表示某原始分所在的百分位置，但由于它是一个循序量数，不能进行数学运算，给进一步的分析带来了困难。通常采用标准分Z(或T)对不同的测验分数进行比较和进一步的分析：

高校学生评估教师课堂教学质量分析

目的:探讨学生评估教师课堂教学质量的效果。方法:选取某校学生为研究对象,随机抽取57名授课教师的由245名学生评估的教师课堂教学质量分数,采用单水平和多水平模型进行统计分析。收集57名授课教师的教龄资料,分析教龄对教师课堂教学质量的影响。结果:对不同授课教师课堂教学质量做单水平模型分析,差别有统计学意义(P<0.001),对不同授课教师课堂教学质量做多水平模型分析,差别有统计学意义(P<0.001),教龄对教师课堂教学质量有影响(P<0.001)。结论:由学生评估的教师课堂教学质量具有良好的效能和信度。

Method for calculating the capacity of bus bay

The bus operating characteristics are analyzed at the bus bay using the trajectories depending on the current status of buses. On this basis, a method for calculating the capacity of the bus bay is developed, which considers the queue probability, the dwell time distribution and the waiting time for a gap in the traffic stream at the curb lane. Then, the distribution model of the dwell time is developed using the survey data of Hangzhou city. And the log-normal distribution shows the best fitting performance. The capacities of the bus bay are computed with the Matlab program under different distribution parameters of the dwell time and different traffic volumes at the curb lane. The results show a large range of traffic capacity as the distribution parameters and traffic volumes change. Finally, the proposed model is validated by measurement and simulation, and the average relative errors between the calculated values and the measured and simulated values are 8.78% and 5.28%, respectively.

An Introduction to the Theory of C~*-modules

This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.

Experimental Study on the Initial Position Distribution of Taylor Bubbles in Cryogenic Upward Inclined Tubes

An experimental study was carried out to understand the phenomena of the boiling flow of liquid nitrogen in inclined tubes with closed bottom by using the high speed digital camera.The tubes in the experiment are 0.018 m and 0.014 m in inner diameter and 1.0 m in length.The range of the inclination angles is 0-45° from the vertical.The statistical method is employed to analyze the experimental data.The experiment was focused on the effect of the inclination angle on the initial position distribution of Taylor bubbles.The formation criterion of Taylor bubbles was confirmed by analyzing the images of Taylor bubbles.The experimental results show that the initial position of Taylor bubble increased first,and then decreased with the increasing inclination angle,with the maximum at 30°.The standard deviation of the initial position of Taylor bubble in tubes was different with different inner diameters.The lognormal shape was fitted to the measured the initial position distributions of Taylor bubbles in the cryogenic tubes.

Classification of tight sandstone reservoirs based on NMR logging

The traditional reservoir classification methods based on conventional well logging are inefficient for determining the properties,such as the porosity,shale volume,J function,and flow zone index,of the tight sandstone reservoirs because of their complex pore structure and large heterogeneity.Specifically,the method that is commonly used to characterize the reservoir pore structure is dependent on the nuclear magnetic resonance(NMR)transverse relaxation time(T2)distribution,which is closely related to the pore size distribution.Further,the pore structure parameters(displacement pressure,maximum pore-throat radius,and median pore-throat radius)can be determined and applied to reservoir classification based on the empirical linear or power function obtained from the NMR T2 distributions and the mercury intrusion capillary pressure ourves.However,the effective generalization of these empirical functions is difficult because they differ according to the region and are limited by the representative samples of different regions.A lognormal distribution is commonly used to describe the pore size and particle size distributions of the rock and quantitatively characterize the reservoir pore structure based on the volume,mean radius,and standard deviation of the small and large pores.In this study,we obtain six parameters(the volume,mean radius,and standard deviation of the small and large pores)that represent the characteristics of pore distribution and rock heterogeneity,calculate the total porosity via NMR logging,and classify the reservoirs via cluster analysis by adopting a bimodal lognormal distribution to fit the NMR T2 spectrum.Finally,based on the data obtained from the core tests and the NMR logs,the proposed method,which is readily applicable,can effectively classify the tight sandstone reservoirs.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Spatial Variability of Soil Organic Carbon in a Watershed on the Loess Plateau

Soil organic carbon (SOC) has great impacts on global warming, land degradation and food security. Classic statistical and geostatistical methods were used to characterize and compare the spatial heterogeneity of SOC and related factors, such as topography, soil type and land use, in the Liudaogou watershed on the Loess Plateau of North China. SOC concentrations followed a log-normal distribution with an arithmetic and geometric means of 23.4 and 21.3 g kg-1, respectively, were moderately variable (CV = 75.9%), and demonstrated a moderate spatial dependence according to the nugget ratio (34.7%). The experimental variogram of SOC was best-fitted by a spherical model, after the spatial outliers had been detected and subsequently eliminated. Lower SOC concentrations were associated with higher elevations. Warp soils and farmland had the highest SOC concentrations, while aeolian sand soil and shrublands had the lowest SOC values. The geostatistical characteristics of SOC for the different soil and land use types were different. These patterns were closely related to the spatial structure of topography, and soil and land use types.

A Storm Surge Intensity Classification Based on Extreme Water Level and Concomitant Wave Height

Storm surge is one of the predominant natural threats to coastal communities. Qingdao is located on the southern coast of the Shandong Peninsula in China. The storm surge disaster in Qingdao depends on various influencing factors such as the intensity, duration, and route of the passing typhoon, and thus a comprehensive understanding of natural coastal hazards is essential. In order to make up the defects of merely using the warning water level, this paper presents two statistical distribution models(Poisson Bi- variable Gumbel Logistic Distribution and Poisson Bi-variable Log-normal Distribution) to classify the intensity of storm surge. We emphasize the joint return period of typhoon-induced water levels and wave heights measured in the coastal area of Qingdao since 1949. The present study establishes a new criterion to classify the intensity grade of catastrophic storms using the typhoon surge estimated by the two models. A case study demonstrates that the new criterion is well defined in terms of probability concept, is easy to implement, and fits well the calculation of storm surge intensity. The procedures with the proposed statistical models would be useful for the disaster mitigation in other coastal areas influenced by typhoons.

A Statistical Analysis of the Modulus of Elasticity and Compressive Strength of Concrete C45/55 for Pre-stressed Precast Beams

Random behavior of concrete C45/55 XF2 used for prefabricated pre-stressed bridge beams is described on the basis of evaluating a vast set of measurements. A detailed statistical analysis is carried out on 133 test results of cylinders 150 ~ 300 mm in size. The tests have been running in laboratories of the Klokner Institute. A single worker took all specimens throughout the period, and the subsequent measurements of the static modulus of elasticity and the compressive strength of the concrete were performed. The measurements were made at the age of 28 days after specimens casting, and only one testing machine with the same capping method was used. Suitable theoretical models of division are determined on the basis of tests in good congruence, with the use of Z2 and the Bernstein criterion. A set of concrete compressive strength （carried out on 133 test results of cylinders 150 ~ 300 mm after test of static modulus of elasticity） shows relatively high skewness in this specific case. This cause that limited beta distribution is better than generally recommended theoretical distribution for strength the normal or lognormal. The modulus of elasticity is not significantly affected due to skewness because the design value is based on mean value.

Quadratic Radical Function Better Than Fisher z Transformation

A new explicit quadratic radical function is found by numerical experiments,which is simpler and has only 70.778%of the maximal distance error compared with the Fisher z transformation.Furthermore,a piecewise function is constructed for the standard normal distribution:if the independent variable falls in the interval(-1.519,1.519),the proposed function is employed;otherwise,the Fisher z transformation is used.Compared with the Fisher z transformation,this piecewise function has only 38.206%of the total error.The new function is more exact to estimate the confidence intervals of Pearson product moment correlation coefficient and Dickinson best weights for the linear combination of forecasts.

Reliability-based service life prediction of existing concrete structures under marine environment

Chloride-induced corrosion of the reinforcement is considered as one of the major mechanisms resulting in the reduction of structural resistance of reinforced concrete structural elements located in marine and other aggressive environments. A study of reinforced concrete structures located at the Fangcheng dock in the Beibu Gulf port, China, was present. The result from field survey indicates that the concrete cover depth and chloride diffusion coefficient fit best normal distribution and lognormal distribution, respectively. The service life of structure is about 55 a, while initiation time is 45 a. Sensitivity analysis indicates that the most influential factor of the structure service life prediction is concrete cover, followed by diffusion coefficient, diffusion decay index, critical chloride concentration, surface chloride concentration, current density and localized pitting corrosion. Finally, the effects of diffusion decay index and critical chloride concentration on structure service life prediction are discussed.

Reliability and maintainability analysis of electrical system of drum shearers

The reliability and maintainability of electrical system of drum shearer at Parvade. 1 Coal Mine in central Iran was analyzed. The maintenance and failure data were collected during 19 months of shearer operation. According to trend and serial correlation tests, the data were independent and identically distributed （iid） and therefore the statistical techniques were used for modeling. The data analysis show that the time between failures （TBF） and time to repair （TTR） data obey the lognormal and Weibull 3 parameters distribution respectively. Reliability-based preventive maintenance time intervals for electrical system of the drum shearer were calculated with regard to reliability plot. The reliability-based maintenance intervals for 90%, 80%, 70% and 50% reliability level are respectively 9.91, 17.96, 27.56 and 56.1 h. Also the calculations show that time to repair （TTR） of this system varies in range 0.17-4 h with 1.002 h as mean time to repair （MTTR）. There is a 80% chance that the electrical system of shearer of Parvade. 1 mine repair will be accomplished within 1.45 h.

Size Distributions and Source Function of Sea Spray Aerosol over the South China Sea

The number concentrations in the radius range of 0.06 – 5 μm of aerosol particles and meteorological parameters were measured on board during a cruise in the South China Sea from August 25 to October 12, 2012. Effective fluxes in the reference height of 10 m were estimated by steady state dry deposition method based on the observed data, and the influences of different air masses on flux were discussed in this paper. The number size distribution was characterized by a bimodal mode, with the average total number concentration of（1.50 ± 0.76）×10~3 cm^（-3）. The two mode radii were 0.099 μm and 0.886 μm, both of which were within the scope of accumulation mode. A typical daily average size distribution was compared with that measured in the Bay of Bengal. In the whole radius range, the number concentrations were in agreement with each other; the modes were more distinct in this study than that abtained in the Bay of Bengal. The size distribution of the fluxes was fitted with the sum of log-normal and power-law distribution. The impact of different air masses was mainly on flux magnitude, rather than the shape of spectral distribution. A semiempirical source function that is applicable in the radius range of 0.06 μm

A New Proposal to Adjust a Straight Line to a Normal Q-Q Plot

In this paper a new proposal of a straight line, the ＂modified Tukey＇s line＂, for fitting to a normal quantile-quantile Plot, or normal Q-Q plot, is presented. This probability plot allows us to determine whether a set of sample observations is distributed according to a normal distribution. For this, the sample quantiles are represented against the quantiles of a theoretical probability model, which in this case is the normal distribution. If the data set follows the above mentioned distribution, the plotted points will have a rectilinear configuration. To verify this, there are different alternatives for fitting a straight line to the plotted points. Among the straight lines which can be fitted to a Q-Q plot, in this paper, besides the proposed straight line, the following straight lines are considered： straight line that passes through the first and third quartiles, straight line that passes through the 10th and 90th percentiles, straight line fitted by the method of least squares, straight line with slope s and constant the average of the data set, Theil＇s line and Tukey＇s line. In addition, an example, in which there are represented the different straight lines considered and the proposed straight line on a normal Q-Q plot obtained for the same set of observations, is developed. In this example the existing differences among the straight lines are observed.

Study of Vertical Breakwater Reliability Based on Copulas

The reliability of a vertical breakwater is calculated using direct integration methods based on joint density functions.The horizontal and uplifting wave forces on the vertical breakwater can be well fitted by the lognormal and the Gumbel distributions,respectively.The joint distribution of the horizontal and uplifting wave forces is analyzed using different probabilistic distributions,including the bivariate logistic Gumbel distribution,the bivariate lognormal distribution,and three bivariate Archimedean copulas functions constructed with different marginal distributions simultaneously.We use the fully nested copulas to construct multivariate distributions taking into account related variables.Different goodness fitting tests are carried out to determine the best bivariate copula model for wave forces on a vertical breakwater.We show that a bivariate model constructed by Frank copula gives the best reliability analysis,using marginal distributions of Gumbel and lognormal to account for uplifting pressure and horizontal wave force on a vertical breakwater,respectively.The results show that failure probability of the vertical breakwater calculated by multivariate density function is comparable to those by the Joint Committee on Structural Safety methods.As copulas are suitable for constructing a bivariate or multivariate joint distribution,they have great potential in reliability analysis for other coastal structures.

Improving S/N ratio for pre-stack seismic data from western China

The seismic data from western China is very noisy. Two main reasons are static corrections and low S/N ratio problems. By seismic data processing and study these problems have been effectively solved by iterating the static corrections and improving the S/N ratio for pre-stack seismic data. Suppression and elimination of various other distortions has been implemented as well. Due to the fact that the S/N ratio is improved, the resolution of the seismic data is also improved.

Large Deviations for Sums of Heavy-tailed Random Variables

This paper is a further investigation of large deviations for sums of random variables Sn=i=1∑n Xi and S（t）=i=1∑N（t）Xi,（t≥0）, where {X_n,n≥1） are independent identically distribution and non-negative random variables, and {N（t）,t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.