Carassale, L. & Solari, G., (2002). Probabilistic Engineering Mechanics, 17, 157-166.

Abstract
Load on structural systems is often represented by a multi-dimensional and/or multi-variate random process. The cross-correlation often existing between loading components acting in different points of the structure introduces conceptual and computational difficulties in many practical problems. It is the case, for example, of the projection of the external load on the vibration modes in the modal analysis of linear systems or of the simulation of multi-correlated time series for a Monte Carlo-based analysis of nonlinear structures. The use of the Proper Orthogonal Decomposition (POD) introduces some formal simplifications in the solution of the aforementioned problems, but requires the evaluation of the eigenquantities of some statistical representations of the loading process. The knowledge of such quantities in analytic form yields computational advantages and enables important physical interpretations. In the present paper, an analytic expression of POD is developed for a class of processes, which includes models usually adopted to represent the atmospheric turbulence. Examples of linear analysis of a wind-excited slender structure and of simulation of turbulence fields are presented.

http://www.sciencedirect.com/science/article/pii/S0266892001000364