Convergence study of the truncated Karhunen-Loeve expansion for simulation of stochastic processes

A random process can be represented as a series expansion involving a complete set of deterministic functions with corresponding random coevecommon covariancemode ls. Theconve rgenceand accuracy of theK–L expansion are investigated by comparing the second-order statistics of the simulated random process with that of the target process. It is shown that the factors a?ecting convergence are: (a) ratio of the length of the process over correlation parameter, (b) form of the covariance function, and (c) method of solving for the eigen-solutions of the covariance function (namely, analytical or numerical). Comparison with the established and commonly used spectral representation method is made. K–L expansion has an edge over the spectral method for highly correlated processes. For long stationary processes, the spectral method is generally more e