Variance decomposition of nonlinear systems

The motivation for assessing closed-loop performance was to evaluate the effect of the controller on the output variation of linear systems. Far less has been written on assessing the multivariate noise case for nonlinear dynamic systems. In this paper, we develop a strategy to quantify the effects of different types of noise on nonlinear dynamic systems using an ANOVA-like decomposition method. We test the proposed strategy using nonlinear autoregressive moving average models which represent an important class of nonlinear systems. To reduce the computational burden, we use the Fourier amplitude sensitivity test (FAST) method to estimate the partial variances which we can compare with the less efficient Monte-Carlo strategy. The results of this paper can be used in investment problems, biomathematics and control theory where multivariate disturbances are frequently encountered.