Development of Conditional Simulation Techniques and Its Engineering

详细阐述了随机随机场先验信息通过后验信息的插值、外推和更新机制。考虑一个高斯随机场，其平均场和协方差矩阵是已知的。当得到在有限点上被噪声污染的样本观测值时，基于无偏最小误差协方差过程，在观测点和插值点上求出最佳估计量。为了使样本场可视化，研究了一种以观测为条件的高斯场模拟方法。考虑了观测值无噪声的特殊情况，提出了一种有效的模拟方法，即采用逐级展开法避免协方差矩阵的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。提出了一种非高斯场的理论公式来模拟以离散点观测数据为条件的样本场。该公式基于一个条件概率密度函数，其中包括高斯场作为特例，该公式也适用于将空间点替换为时间点的非高斯随机过程。数值算例表明了仿真方法的潜在有效性。

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.