ERRORS IN PARAMETER ESTIMATES FROM THE FORCE STATE MAPPING TECHNIQUE FOR FREE RESPONSE DUE TO PHASE DISTORTION
✍ Scribed by C. MESKELL; J.A. FITZPATRICK
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 106 KB
- Volume
- 252
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The force state mapping (FSM) technique, as proposed by Masri et al. [1,2], for a single-degree-of-freedom system uses the response measurements to construct the restoring force surface (which may be non-linear) over the displacement}velocity state plane. A surface which can be described analytically is then "tted to this empirical surface to obtain quanti"ed system parameters. This approach to system identi"cation has been applied to a variety of applications including non-linear and multi-degree-of-freedom systems, undergoing free or forced response [3}7]. The technique requires estimates for the system displacement, velocity and acceleration. In practice, whether these estimates are obtained by three separate instruments [7] or by careful numerical di!erentiation and/or integration of a single measured signal [4], the resulting signals may su!er phase distortion. Furthermore, for forced response, there is a possibility that the force signal may experience phase distortion relative to the response signals. A practical example of how these problems may manifest themselves was given in the experimental study by Worden and Tomlinson [8], in which all the measured signals were phase shifted by a multiplexed analogue}digital converter.
Wright and Al-Hadid [9] have derived expressions for the errors in the parameter estimates obtained by FSM in the presence of phase distortion of the measured signals for a linear system subject only to a sinusoidal excitation force. They have shown that for lightly damped systems, which are often of most interest, the damping parameter is the most susceptible to error particularly with phase distortion in the excitation force. It is possible to use free response data as input to the FSM technique [7] in order to avoid the phase lag between the excitation and the response and so remove the associated error in the parameter estimates. In this case, there will also be a potential for error in the parameter estimates due to relative phase error in the response signals. However, although reach the general conclusion that &&very accurate data appear to be a basic requirement for FSM approach for lightly damped systems'', they also note that di!erent types of excitation are likely to yield di!erent parameter estimates and hence error sensitivity. Thus, it is necessary to evaluate the sensitivity to phase errors of the force state mapping technique using free response data as input.