15 April 2011 Sensitivity vector fields in embedded coordinates
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Abstract
Identifying variations in system parameters is a crucial task in many diagnostic engineering applications. Although modal methods are typically employed to quantify such parametric variations in dynamical systems, sensitivity vector fields (SVFs) provide an alternative that can be more effective under certain circumstances. Currently, the application of SVFs has been restricted to systems in which it is possible to know the entire state. For physical systems where only a few components of the state can be measured, this represents a significant obstacle to the adoption of SVFs. Fortunately, even with only partial knowledge of the state, time-delay coordinate embedding can be used to reconstruct the attractors of a nonlinear system. This paper presents techniques for computing SVFs in such embedded coordinates, making their application practical in a much wider range of physical systems. Successful construction of embedded SVFs for various simulated time series demonstrate the reliability of the techniques proposed.
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Andrew R. Sloboda, Andrew R. Sloboda, Bogdan I. Epureanu, Bogdan I. Epureanu, } "Sensitivity vector fields in embedded coordinates", Proc. SPIE 7981, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2011, 79813J (15 April 2011); doi: 10.1117/12.880518; https://doi.org/10.1117/12.880518
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