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Exploring Issues in Simulation-Based Reliability Assessment Using K-L Expansion

This discussion delves into the challenges and potentials of simulation-based reliability assessments, particularly using the Karhunen-Loève (K-L) expansion method. The focus is on simulating second-order processes efficiently on standard PC systems. Key considerations include the impact of process length on eigenvalues, the requirements for numerous K-L terms for accurate representations in long processes, and the necessity of effective covariance models. The dialogue also addresses non-Gaussian processes and the viability of adapting K-L expansions to achieve accurate simulations, despite limitations in matching distributions.

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Exploring Issues in Simulation-Based Reliability Assessment Using K-L Expansion

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  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 Lognormal Beta

  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

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