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Author Farrell, Brian F. ♦ Ioannou, Petros J.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Uncertain System ♦ Perturbation Growth ♦ Uncertain Flow ♦ Pure Structure ♦ Optimal Excitation Analysis ♦ Fluid Flow ♦ Time Mean Quantity ♦ Physical Connection ♦ Central Role ♦ Certain System ♦ Ergodic Assumption ♦ Operator Fluctuation ♦ Simple Solution ♦ Ensemble Perturbation Growth ♦ Stability Boundary ♦ Optimal Excitation Problem ♦ Generalized Stability Theory ♦ Bounded Second-moment Statistic ♦ Fundamental Limitation ♦ Excited System ♦ Ensemble Mean Covariance ♦ Optimal Initial Excitation ♦ Initial Condition ♦ Second-moment Dynamic ♦ Ensemble Statistic ♦ Mixed State ♦ Stochastic Excitation ♦ Forced Stable Uncertain System ♦ Optimal Stochastic Excitation ♦ Inverting Covariance ♦ Eof Structure ♦ Covariance Evolution Equation ♦ Steady State ♦ Stochastic System ♦ Primary Physical Realization ♦ Illustrative Physical Example
Abstract Perturbation growth in uncertain systems associated with fluid flow is examined concentrating on deriving, solving, and interpreting equations governing the ensemble mean covariance. Covariance evolution equations are obtained for fluctuating operators and illustrative physical examples are solved. Stability boundaries are obtained constructively in terms of the amplitude and structure of operator fluctuation required for existence of bounded second-moment statistics in an uncertain system. The forced stable uncertain system is identified as a primary physical realization of second-moment dynamics by using an ergodic assumption to make the physical connection between ensemble statistics of stable stochastically excited systems and observations of time mean quantities. Optimal excitation analysis plays a central role in generalized stability theory and concepts of optimal deterministic and stochastic excitation of certain systems are extended in this work to uncertain systems. Remarkably, the optimal excitation problem has a simple solution in uncertain systems: there is a pure structure producing the greatest expected ensemble perturbation growth when this structure is used as an initial condition, and a pure structure that is most effective in exciting variance when this structure is used to stochastically force the system distributed in time. Optimal excitation analysis leads to an interpretation of the EOF structure of the covariance both for the case of optimal initial excitation and for the optimal stochastic excitation distributed in time that maintains the statistically steady state. Concepts of pure and mixed states are introduced for interpreting covariances and these ideas are used to illustrate fundamental limitations on inverting covariances for structure in stochastic systems in the event that only the covariance is known. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Publisher Date 2002-01-01