Studies on real-time estimation method of earthquake ground motions under imperfect information

这项研究提出了一种在一些离散点的观测数据可用时有效地估计地震动指数空间分布的理论方法。提出了已知位置和几何形状的块体上过程平均值的空间估计方法。给出了在离散点观测时条件对数正态随机场估计的理论公式。然后，当估计已知位置的未知值时，将块平均值的最优估计器和最小均方估计误差与通过点克里格法获得的结果进行比较。数值算例分析了块大小对最优估计器和估计误差方差的影响。结果表明，除了非常小的块大小外，块克立格法是一种重要的方法。条件非高斯场…随机内插外推的近似算法更多的LDS产生具有特征最小误差方差的非线性无偏估计。然后利用扩展卡尔曼滤波方法将条件估计问题转化为高斯随机场进行求解。以对数正态随机场为例。并与简单克立格法的理论解进行了比较，讨论了该方法的精度和效率。结果表明，该方法不存在计算最优估计器和估计误差方差的困难。给出了条件非高斯平移随机场在离散点观测时最大熵估计及其相关熵指数的计算理论。通过六种分布随机场的分析发展和数值算例，比较了克立格法和最大熵法在空间估计中的应用。研究发现：1)最大熵估计和条件熵依赖于观测数据的值；2)平均条件熵与观测值无关，不大于平均无条件熵。较少

This study presents a theoretical procedure for efficiently estimating the spatial distribution of earthquake ground motion indices when observed data at some discrete points are available.1. The spatial estimation method of the average of the process over a block whose location and geometry are known was proposed. A theoretical formulation is presented to estimate conditional lognormal stochastic field when observation is made at some discrete points. The optimum estimator and minimized mean-squared estimation error of a block average value are then compared with the results obtained by point kriging when an unknown value at a known location is estimated. Numerical examples were carried out to examine the influence of block size on the optimum estimator and estimated error variance. Except for very small block sizes, the results indicate that the block kriging is critical method.2. The approximate algorithm for stochastic interpolation and extrapolation of conditional non-Gaussian fie … More lds produces a nonlinear unbiased estimator with the characteristic minimum variance of errors. The extended Kalman filtering procedure is then used for solving the conditional estimation problem transformed into the Gaussian stochastic field. A lognormal stochastic field is taken up as an example. The accuracy and efficiency of the proposed method is discussed compared with the theoretical solutions of simple kriging. It is found that the proposed method does not suffer from the difficulties associated with computing the optimum estimator and estimated error variance.3. A theory for evaluating the maximum entropy estimators and their associated entropy indices for conditional non-Gaussian translation stochastic fields was proposed when observation is made at some discrete points. Through analytical development and numerical examples of stochastic fields with the six types of distribution, kriging and maximum entropy techniques for spatial estimation are also compared. It was found that : 1) the maximum entropy estimate and conditional entropy are dependent on the values of observed data ; and 2) the average conditional entropy has an independence on the observations, and is not larger than the average unconditional entropy. Less