STOCHASTIC DECOMPOSITION AND APPLICATION TO PROBABILISTIC DYNAMICS

The frequency-domain analysis concerning the response of nested-cascad e multiple input/output systems requires computation of the cross-spec tral density matrices that involve the input, intermediate, and output vectors. Clearly, as the number of nested systems increases, the orde r of the cross-spectral density matrix increases, demanding additional computational effort. This feature lessens the computational attracti veness of the frequency-domain analysis. A stochastic decomposition te chnique is developed that improves the efficiency of conventional freq uency-domain analysis by eliminating the intermediate step of estimati ng cross-spectral density matrices. Central to this technique is the d ecomposition of a set of correlated random processes into a number of component random processes. Statistically, any two processes decompose d in this manner are either fully coherent or noncoherent. A random su bprocess obtained from this decomposition is expressed in terms of a d ecomposed spectrum. A theoretical basis for this approach and computat ional procedures for carrying out such decompositions in probabilistic dynamics are presented.