Studies on observation, identification and renewal theory for conditional stochastic field

1.阐明了对数正态随机场的几个方面：(1)简单Kriging最优估计等于条件均值；(2)Kriging无偏最小误差方差不同于条件方差；(3)估计误差方差不依赖于观测数据，而条件方差依赖于观测数据；(4)条件模拟与估计误差方差无关。提出了一种识别具有未知均值和已知协方差的对数正态随机场的最优估计的通用克立格方法。已知均值和协方差的简单Kriging估计优于普适Kriging估计。不能计算克立格方差，只能得到方差指标。考虑了均值和协方差矩阵参数不确定的高斯离散场。讨论了观测数据对最优估计、条件方差和误差方差的影响。给出了数值算例，说明了贝叶斯克立格法与条件简单克立格法和/或泛克里格法的有效性。基于广泛的地震监测和地理信息系统(GIS)技术，开发了大型城市燃气管网地震信息采集与网络预警(信号)系统。进行了对客户建筑物和管道的破坏估计，震级和震源估计，反应谱评估，以及根据估计结果进行切断或维持供应的决策分析。

The main results of this study may be summarized as follows :1. Several aspects of a logmormal stochastic field were clarified, namely : (1) the optimal estimation by the simple Kriging is equal to conditional mean value, (2) unbiased least error variance by the Kriging differs from conditional variance, (3) estimated error variance does not depend upon observation data while conditional variance does, and (4) conditional simulation is not related to estimated error variance.2. The universal Kriging was proposed as a method for identifying the optimal estimator of a lognormal stochastic field with unknown mean and known covariance. The simple Kriging estimator with known mean and covariance is superior to the universal Kriging estimator. The Kriging variance is not able to be evaluated, and only the variance indicator can be obtained.3. A Gaussian discrete field was considered whose parameters of mean field and covariance matrix are uncertain. Discussions were made on the effect of observation data on the optimum estimator, conditional variance and error variance. Numerical examples were given to illustrate the effectiveness of the Baysian Kriging compared with the conditional simple and/or universal Kriging approaches.4. A seismic information gathering and network alert (SIGNAL) system for a large-scale city gas network was developed based on extensive earthquake monitoring and geographic information system (GIS). The damage estimation to customers' buildings and pipelines, estimation of the magnitude and hypocenter, evaluation of the response spectrum, and decision analysis whether to shut-off or maintain the supply based on the estimated results were conducted.