Development of Conditional Simulation Techniques and Its Engineering

条件模拟技术及其工程的发展

基本信息

批准号：
05555131
负责人：
HOSHIYA Masaru
金额：
$ 9.15万
依托单位：
Musashi Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Developmental Scientific Research (B)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1995
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-05555131/
关键词：
Conditional Simulation Linear Interepolation Kriging Conditional FEM Random Field Earthquake Wave Propagation Soil Profile Maximum Likelihood Estimation Conditional Simulation Conditional F・E・M Random Field Earthquake wave Propagatio

项目摘要

The interpolation, extrapalation, and updating mechanism of a-priori information, by a-posteriori information, for a stochastic random field are clarified in detall.A Gaussian random field is considered, whose mean field and covariance matrix are known a priori. When a sample observation contaminated with noise at some finite points is obtained, the best estimators are evaluated at observation points as well as at interpolation points, based on an unbiased least error covariance procedure. To visualize a sample field, a method to simulate the Gaussian field conditional on observation, is investigated. A special case is considered, in which the observation is free of noises and an effective method of simulation is proposed, which is a step by step expansion procedure to avoid the Cholesky or modal decomposition of the covariance matrix. This method is based on the orthogonality property between the best estimator and the corresponding error.A theoretical formulation of non-Gaussian field is presented to simulate sample fields conditioned by observed data at discrete points. The formulation is based on a conditional probability density function, which includes Gaussian field as special case and the formulation can be also applied to non-Gaussian random process when spatial points are replaced by temporal points.Numerical examples are demonstrated to show the potential usefulness of simulation methods.

通过a-posteriori信息，对于随机随机场的插值，外推和更新机制在detall中阐明。当获得在某些有限点处被噪声污染的样品观测值时，基于公正的最小误差协方差程序，在观测点和插值点上评估了最佳估计器。为了可视化样品场，研究了一种模拟高斯野外观测条件的方法。考虑了一种特殊情况，其中观察没有噪音，并提出了一种有效的仿真方法，这是避免协方差矩阵的choleskyky或模态分解的逐步扩展程序。该方法基于最佳估计器和相应误差之间的正交性。提出了非高斯字段的理论公式，以模拟在离散点上观察到的数据调节的样本字段。该公式基于条件概率密度函数，其中包括高斯字段作为特殊情况，当空间点被时间点取代时，该公式也可以应用于非高斯随机过程。