IDENTIFICATION OF CONDITIONAL STOCHASTIC GAUSSIAN FIELD

A general formulation is presented based on the maximum likelihood met hod to identify the best estimator of a stochastic Gaussian field when the observation is made at discrete spatial points. The uncertainty o f;the estimator in terms of the uncertainty of the stochastic field an d in the observation noise are discussed, and the updating of the esti mator's mechanism by observation is clarified. Two methodologies, that is, a simple kriging method and an extended Kalman filtering procedur e are derived as special solutions of the general formulation. The met hod developed here may be applied to updating a general stochastic fin ite-element method (FEM) system by observation, where the system consi sts of a stochastic field of elastic moduli or loading forces or both, and the observation may be for elastic moduli and/or displacements at finite spatial points. A numerical example is carried out with a beam on a continuous elastic foundation, and the efficiency and practical applicability of the method are demonstrated.