Error Assessment of Multivariate Random Processes Simulated by a Conditional-Simulation Method

Random processes, such as the wind velocity field and spatially varying ground motions, are usually simulated as N-variate stochastic processes by the conditional-simulation method. However, the temporal power spectral density (PSD) function of a single, simulated sample process may be different from the target PSD. Such differences can usually be assessed by the statistical errors (i.e., the bias and stochastic errors). Therefore, this paper investigates the bias errors and the stochastic errors of the PSD functions produced by the conditional-simulation method. For the bias errors, it was found that the conditional-simulation method might produce the nonzero bias error of the PSD functions in some cases. However, this usually does not occur in the unconditional simulation, and it should be avoided. To avoid the nonzero bias error of the PSD functions, a modified conditional-simulation method was proposed. It was verified using both the theoretical derivation and the numerical example. For the stochastic errors, the closed-form solutions for the PSD functions' stochastic errors produced by a conditional simulation were given by the theoretical derivation and verified by numerical examples. Finally, the PSD functions' stochastic errors produced by a conditional simulation were compared with those produced by an unconditional simulation using the spectral-representation method. (C) 2014 American Society of Civil Engineers.