A method for the efficient construction and sampling of vector-valued translation random fields

作者：Field R V Jr^*; Grigoriu M

来源：Probabilistic Engineering Mechanics, 2012, 29: 79-91.

DOI：10.1016/j.probengmech.2011.09.003

• Monte Carlo simulation
• Optimization
• Random fields
• Stochastic processes
• Translation models

A method is developed for the efficient construction and sampling of vector-valued translation random processes and fields. Given a target marginal CDF and target covariance function, the approach is to approximate the spectral densities of the Gaussian image by a linear sum of shape functions, where each is scaled by a constant. An efficient optimization algorithm is developed to solve for the unknown constants. The objective function to be minimized is equal to the mean-square difference between the target covariance function, and the translated version of the approximate covariance function: a complex set of constraint equations is enforced during the optimization routine to ensure that the resulting covariance function of the Gaussian image is positive definite. It is shown that classical Monte Carlo simulation techniques can be used to generate samples of the Gaussian images of these models and map them into desired non-Gaussian samples. Several examples are considered to illustrate the application of the proposed method and to assess its accuracy.

• 出版日期2012-7