The dissertation considers methods of representation and synthesis of random fields and examines variance reduction techniques in conjunction with reliability analysis of engineering systems. The dissertation presents new approaches to the scale type method, the ARMA method, and the covariance method for random field simulation. The scale type method is formulated by using the wavelet representation of random fields. In this regard it is shown that a large class of random fields is amenable to a simplified representation. Also this dissertation presents a new efficient two-stage procedure for ARMA approximation of target stochastic processes. It is shown that this method yields quite low order ARMA models and reduces the requisite numerical computations for synthesizing samples of stochastic processes. Criteria are established for efficient representation of random fields by a small number of random variables in conjunction with the covariance method of random field simulation. A variance reduction method is developed by extending the Galerkin projection to stochastic mechanics problems. This method improves the Monte Carlo based reliability analysis of engineering systems with random properties. The methods developed in this dissertation aim to expedite the application of stochastic mechanics concepts to design applications
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