An optimal control approach to extreme local maxima for stochastic duffing-type oscillators

Dunne, Julian F (1996) An optimal control approach to extreme local maxima for stochastic duffing-type oscillators. Journal of Sound and Vibration, 193 (3). pp. 597-629. ISSN 0022-460X

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A new way is presented to calculate extreme exceedance probabilities associated with the height of local maxima on stationary sample paths of a non-linear oscillator driven by narrow-band Gaussian excitation. Deterministic “least effort” optimal control functions are used to construct a linear filter which is applied to the excitation process. By defining suitable form of conditioning on the filter output local maxima, the most difficult problem can be switched around, so that use can be made of the conventional theory for a normal process. With subsequent simplifications, the required probabilities can be expressed just in terms of an unknown conditional mean and variance. An efficient numerical scheme is developed to estimate these two moments via non-linear regression using a small set of simulated oscillator sample paths. In testing the method on a Duffing-type oscillator with strongly non-linear stiffness and damping, comparison with conventional Monte Carlo simulation is concentrated in a probability range 10(−2)−10(−5) but using only about 1% of the local maxima normally required. The method offers a practical tool for use in the analysis of extreme non-linear random vibration.

Item Type: Article
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Subjects: T Technology > TJ Mechanical engineering and machinery > TJ0170 Mechanics applied to machinery. Dynamics
Depositing User: Julian Dunne
Date Deposited: 24 Apr 2012 11:50
Last Modified: 10 Jul 2012 12:15
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