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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.

详细阐述了随机场的先验信息通过后验信息的插值、外推和更新机制，考虑了均值场和协方差矩阵先验已知的高斯随机场.当样本观测值在有限点处被噪声污染时，基于无偏最小误差协方差方法，在观测点和插值点处分别求出最佳估计量。为了实现样本场的可视化，研究了一种基于观测条件的高斯场模拟方法。考虑了观测值不含噪声的特殊情况，提出了一种有效的模拟方法，即逐步展开法，以避免协方差矩阵的Cholesky分解或模态分解。该方法基于最佳估计量与相应误差之间的正交性，给出了非高斯场的理论公式，用于模拟离散点观测数据条件下的样本场。该方法基于条件概率密度函数，将高斯场作为特殊情况，并将空间点替换为时间点，可应用于非高斯随机过程，数值算例表明了该方法的有效性.