DISCUSSION ON “ISSUES IN SIMULATION BASED RELIABILITY ASSESSMENT” by GEORGE R. FEGAN PHOON KK, QUEK ST & HUANG SP

KARHUNEN-LOEVE EXPANSION Potentially useful to simulate a wide range of second-order processes QUESTION: Can we do this cheaply on a PC?

LENGTH OF PROCESS Eigensolutions are functions of length of process Need more K-L terms for long process a/b = 5 a/b = 10

COVARIANCE MODEL Eigenvalues decrease faster for “smooth” covariance model Need more K-L terms otherwise

PRACTICAL PROBLEM are solutions of the homogenous Fredholm integral equation of the second kind Difficult to solve ACCURATELY & CHEAPLY Need LOTS OF THEM

WAVELET SCHEME f8 f9 f10

NON-GAUSSIAN PROCESS Can modify K-L expansion to get non-Gaussian distribution Tail does not match well in some cases Brown-bridge Beta Lognormal

CONCLUSIONS K-L has practical potential for simulation Can address wide range of second-order processes But may need lots of eigensolutions to be accurate Non-Gaussian processes possible but not perfect