INTEGRATION OF NON-GAUSSIAN FIELDS

The limitations of the validity of the central limit theorem argument as applied to definite integrals of non-Gaussian random fields are emp irically explored by way of examples. The purpose is to investigate in specific cases whether the asymptotic convergence to the Gaussian dis tribution is fast enough to justify that it is sufficiently accurate f or the applications to shortcut the problem and just assume that the d istribution of the relevant stochastic integral is Gaussian. An earlie r published example exhibiting this problem concerns silo pressure fie lds. [Ditlevsen, O., Christensen, C. and Randrup-Thomsen, S. Reliabili ty of silo ring under lognormal stochastic pressure using stochastic i nterpolation. Proc. IUTAM Symp., Probabilistic Structural Mechanics: A dvances in Structural Reliability Methods, San Antonio, TX, USA, June 1993 (eds.: P. D. Spanos & Y.-T. Wu) pp. 134-162. Springer, Berlin, 19 94](1) The numerical technique applied to obtain approximate informati on about the distribution of the integral is based on a recursive appl ication of Winterstein approximations (moment fitted linear combinatio ns of Hermite polynomials of standard Gaussian variables). The method uses the very long exact formulas for the 3rd and 4th moments of any l inear combination of two correlated four-term Winterstein approximatio ns. These formulas are derived by computerized symbol manipulations. S ome of the results are compared with some special exact results for su ms of Winterstein approximations. [Mohr, G. Br Ditlevsen, O. Partial s ummations of stationary sequences of Winterstein approximations, Prob. Engng Mech. 11 (1996) 25-30.](2) For decreasing correlation extension including negative correlation, problems of increasing sensitivity to the recursive approximations show up. For practical use of the method , it may therefore, in special situations with negative correlation, b e necessary to introduce numerical integration checks or simulation ch ecks of the results.