Comparison between KarhunenLove expansion and translation-based simulation of non-Gaussian processes
The KarhunenLove (KL) 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 KL expansion will approach the spectral representation. The non-Gaussian KL 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 KL 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.
karhunenlove expansion spectral representation compatibility translation process non-translation process latin hypercube orthogonalization