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

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

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

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

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

6. WAVELET SCHEME f8 f9
f10

7. 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

8. 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