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

本研究的主要结果可以总结如下：1。阐明了对数正态随机场的几个方面，即：(1)简单Kriging的最优估计等于条件均值；(2)Kriging的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。提出了通用Kriging方法，用于确定未知均值和已知协方差的对数正态随机场的最优估计量。具有已知均值和协方差的简单克里格估计量优于通用克里格估计量。不能对克里格方差进行评价，只能得到方差指标。考虑一个平均场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量、条件方差和误差方差的影响。通过数值算例说明了贝叶斯克里格方法与条件简单克里格方法和/或通用克里格方法的有效性。基于广泛的地震监测和地理信息系统（GIS），开发了大型城市燃气管网地震信息采集和网络预警（SIGNAL）系统。对客户建筑物和管道的损坏情况进行了估计，对震级和震源进行了估计，对响应谱进行了评估，并根据估计结果进行了是否切断或维持供电的决策分析。

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.