基于概率模型的随机裂隙优势产状取值

随机裂隙是广泛存在于岩体中的一种规模较小的结构面,由于其发育的随机性,故其产状、规模等结构面性质难于确定。但是,大量研究表明,同一地区相同地质环境下发育的随机裂隙,其结构面性质存在一定的统计规律。利用建立概率模型的方法,对某花岗岩地区水电站左岸坝基随机裂隙组的优势产状取值进行了探讨。通过建立概率模型所绘制出的概率曲线进行研究发现,相对于简单的求样本的算数平均值,取概率曲线峰值点所对应的数值为一组裂隙最佳产状更为合理。     

Proportional Sampling in Life Length Studies

In studying electron tube life, measuring the life of a tube in service in a system whose age is T amounts to lifelength proportional sampling. The problems of estimating mean life from such data are considered for finite T and for “equilibrium” (large T). Several variations on the straight-forward life-biased sampling plan which are avilable to the experimenter are mentioned and conditions are found under which these other sampling schemes would be better than the life-proportional scheme. Particular attention is paid to the gamma and Weibull families of distributions. Other applications of these results are discussed.     

Response Surface Designs for Experiments with Mixtures

In estimating a response surface where the k variables represent proportions in a mixture, the experimenter is often interested in a reasonably well-defined region of interest which may, for example, center about current operating levels. Previously developed designs are difficult to use except in exploring the entire factor space, and even then there are several disadvantages to these designs. A general method of constructing designs from familiar response surface designs in k ? 1 independent variables and the appropriate analysis for a general polynomial is given. Special attention is given to the first and second order polynomials.     

k-Sample tests based on the likelihood ratio

General k-sample tests are developed, including the classical Kolmogorov-Smirnov, Cramér-von Mises and Anderson-Darling k-sample tests, as well as new powerful omnibus tests based on the likelihood ratio. Conventional tests are sensitive to location difference among distributions, but are dull to detect the variation in shape. The new tests are sensitive to both location and shape. In fact, if the distributions of k-sampled populations are different in location only, the new tests are as powerful as the old ones. Otherwise, they are much more powerful.     

A combined nonparametric approach to feature selection and binary decision tree design

An efficient procedure which integrates feature selection and binary decision tree construction is presented. The nonparametric approach is based on the Kolmogorov-Smirnov criterion which yields an optimal classification decision at each node. By combining the feature selection with the design of the classifier, only the most informative features are retained for classification.     

岩石力学参数概率分布的信息熵推断

基于信息论的最大熵原理，直接用牛顿迭代法，由样本矩来推断岩石力学参数的概率密度函数，并且用精度较高的K-S检验法，从理论上证明所求的密度函数的正确性。算例表明，该方法避免了复杂的数值计算，可以满足岩石工程随机可靠性分析的要求。直接根据试验样本信息和统计方法推断，而不是先假定成经典的理论概率分布，具有更充分的数学和物理意义。由于概率分布采用指数形式而不是幂函数系多项式，避免了计算中的震荡等不稳定现象。     

Contributions of empirical and quantile processes to the asymptotic theory of goodness-of-fit tests

This paper analyzes the evolution of the asymptotic theory of goodness-of-fit tests. We emphasize the parallel development of this theory and the theory of empirical and quantile processes. Our study includes the analysis of the main tests of fit based on the empirical distribution function, that is, tests of the Cramér-von Mises or Kolmogorov-Smirnov type. We pay special attention to the problem of testing fit to a location scale family. We provide a new approach, based on the Wasserstein distance, to correlation and regression tests, outlining some of their properties and explaining their limitations. Dedicated to Miguel Martín Díaz whose scientific criticism has greatly inspirated our research by years. Research partially supported by DGICYT, grants PB98-0369-C02-01 and 02. E. del barrio and C. Matrán have also been supproted by PAPIJCL grant VA08/97.     

Assessment of statistical variations in impact resistance of high-strength concrete and high-strength steel fiber-reinforced concrete

The impact resistance variations of high-strength steel fiber-reinforced concrete (HSFRC), versus those of high-strength concrete (HSC), commanded this research. The impact resistance of the high-strength steel fiber-reinforced concrete improved satisfactorily over that of the high-strength concrete; the failure strength improved most, followed by first-crack strength and percentage increase in the number of post-first-crack blows. The two concretes resembled each other on the coefficient of variation values, respectively, on the two strengths, whereas the high-strength concrete was much higher in the value on the percentage increase. The Kolmogorov-Smirnov test indicates that the high-strength concrete was approximately normally distributed in first-crack and failure strengths, high-strength steel fiber-reinforced concrete was poorly normally distributed in the two strengths, and both concretes were hardly normally distributed in the percentage increase. Finally, for both concretes, failure strength regression models were developed, and then, the accompanying 95% prediction intervals for the strength were established.     

基于AR模型的Kolmogorov-Smirnov检验性能退化及预测研究

设备性能退化评估是对现有故障诊断技术的全新拓展,它为更有效地实现智能主动维护提供参考,更有利于实现设备的零停机率。开展对设备的性能退化评估研究,还可以实现对设备的性能预测维护功能,大大提高设备运行的可靠性。提出了基于AR预测白噪化的Kolmogorov-Smirnov检验方法,同时实现了滚动轴承的全寿命实验。通过对轴承全寿命实验数据的分析研究,论证了本方法在设备性能退化评估及预测中的研究价值,相对于有效值等传统方法,它不仅能够显著地表现前期的微弱退化状态,而且还能有条件地更早指示设备的异常状态,对于故障预测的研究具有较大的意义。     

Sample distribution function based goodness-of-fit test for complex surveys

Testing the parametric distribution of a random variable is a fundamental problem in exploratory and inferential statistics. Classical empirical distribution function based goodness-of-fit tests typically require the data to be an independent and identically distributed realization of a certain probability model, and thus would fail when complex sampling designs introduce dependency and selection bias to the realized sample. In this paper, we propose goodness-of-fit procedures for a survey variable. To this end, we introduce several divergence measures between the design weighted estimator of distribution function and the hypothesized distribution, and propose goodness-of-fit tests based on these divergence measures. The test procedures are substantiated by theoretical results on the convergence of the estimated distribution function to the superpopulation distribution function on a metric space. We also provide computational details on how to calculate test p-values, and demonstrate the performance of the proposed test through simulation experiments. Finally, we illustrate the utility of the proposed test through the analysis of US 2004 presidential election data.