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 Lognormal Beta
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