Stochastic dynamic systems with complex-valued eigensolutions

A dimensional decomposition method is presented for calculating the probabilistic characteristics of complex-valued eigenvalues and eigenvectors of linear, stochastic, dynamic systems. The method involves a function decomposition allowing lower-dimensional approximations of eigensolutions, Lagrange interpolation of lower-dimensional component functions, and Monte Carlo simulation. Compared with the commonly used perturbation method, neither the assumption of small input variability nor the calculation of the derivatives of eigensolutions is required by the method developed. Results of numerical examples from linear stochastic dynamics indicate that the decomposition method provides excellent estimates of the moments and/or probability densities of eigenvalues and eigenvectors for various cases including large statistical variations of input. Copyright q 2007 John Wiley & Sons, Ltd.