Comparison between Karhunen-Loeve expansion and translation-based simulation of non-Gaussian processes

摘要

The Karhunen-Loeve (K-L) expansion has been successfully applied to the simulation of highly skewed non-Gaussian processes based on the prescribed covariance and marginal distribution functions. When the stationary random process is indexed over a domain that is much larger than the correlation distance, the K-L expansion will approach the spectral representation. The non-Gaussian K-L technique is applied in the popular spectral representation as a special case to facilitate comparison with translation-based spectral representation. Processes with both incompatible and compatible spectral density and marginal distribution functions are simulated numerically. It is demonstrated that K-L expansion can be used to address the situation with incompatible target functions where the commonly used translation approach may not be applicable. It is therefore a more robust method for simulation of non-Gaussian processes because it can generate different processes satisfying the same target spectral density function and the same target marginal distribution function regardless of their compatibility.