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

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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.