Development of Conditional Simulation Techniques and Its Engineering

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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.