NUMERICAL METHODS TO ESTIMATE THE COEFFICIENTS OF THE POLYNOMIAL CHAOS EXPANSION

Abstract eng:
The polynomial chaos expansion, part of the stochastic finite element method, has been studied in recent years as a means of forming finite-dimensional approximations to general random processes. Because the coefficients of this expansion are themselves functions of the process being approximated, their accurate calculation, with minimal computational effort, is of prime importance during implementation. A sampled averages approach has been explored in previous work to estimate these coefficients. This method proves viable, however, only when samples of the process being approximated are computationally inexpensive to attain. In this paper, numerical integration techniques are utilized to estimate the coefficients. In many cases, this method may require significantly fewer function evaluations and, as a result, can be applied to those problems where each function evaluation requires significant computational resources. The method will be demonstrated on a simple example, as well as a complex engineering application.

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