On Stochastic Decomposition and Its Applications in Probabilistic Dynamics

by Yousun Li, Univ of Houston, United States,
Ahsan Kareem, Univ of Houston, United States,

Document Type: Proceeding Paper

Part of: Structural Safety and Reliability


The frequency domain analysis concerning the response of cascade-nested multiple input/output systems requires computation of the cross-spectral density matrix involving the input, intermediate and output vectors. This feature lessens the attractiveness of the frequency domain analysis. In this study, a stochastic decomposition technique has been developed which eliminates the need for estimating the cross-spectral density matrix. Central to this technique is the decomposition of a set of correlated random processes into a number of component random sub-processes. Statistically any two decomposed processes are either fully coherent or noncoherent. A random sub-process is expressed in terms of a decomposed spectrum or bi-spectrum. This paper presents a theoretical basis for this approach by utilizing examples.

Subject Headings: Stochastic processes | Matrix (mathematics) | Dynamic structural analysis | System analysis | Computing in civil engineering | Vector analysis | Statistics | Vibration

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