Journal of Engineering Mechanics · 2002 · 200 citations · 5 references
ComputingComputational EngineeringPhysicsFinite Element MethodsStochastic ModelingStochastic ProcessesChaos TheoryGaussian Process ModelingGaussian ProcessesPolynomial Chaos ExpansionsSimulation MethodsStochastic Systems ModelingKarhunen-loève ExpansionPolynomial DecompositionProbability Density FunctionsStochastic Process AnalysisStochastic Process SimulationTransformations
The authors develop a method to represent and synthesize random processes defined by their two‑point correlation functions and nonstationary marginal probability density functions. They model the target process as a polynomial transformation of a Gaussian process, decompose its correlation structure using a Karhunen–Loève expansion, and apply successive polynomial transformations to match the one‑point marginal distributions. The resulting representation is well suited for implementation with the spectral stochastic finite element method and for general simulation of realizations of such processes.
A method is developed for representing and synthesizing random processes that have been specified by their two-point correlation function and their nonstationary marginal probability density functions. The target process is represented as a polynomial transformation of an appropriate Gaussian process. The target correlation structure is decomposed according to the Karhunen–Loève expansion of the underlying Gaussian process. A sequence of polynomial transformations in this process is then used to match the one-point marginal probability density functions. The method results in a representation of a stochastic process that is particularly well suited for implementation with the spectral stochastic finite element method as well as for general purpose simulation of realizations of these processes.
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