### ASA 126th Meeting Denver 1993 October 4-8

## 3aSA13. A regression-based approach for simulating feedforward active
noise control, with regression diagnostics for assessing the impact of
measurement noise.

**C. E. Ruckman
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*Acoust. Technol. Dept., David Taylor Model Basin, Bethesda, MD 20084-5000
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**Chris R. Fuller
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*Virginia Polytech. Inst. and State Univ., Blacksburg, VA 24061
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Current numerical techniques for simulating feedforward active noise
control in the frequency domain are mathematically equivalent to the techniques
required for linear least-squares regression. Measurement error in the control
system error sensors plays a role analogous to that of observation error in a
statistical regression. In the statistics literature, regressions are always
accompanied by regression diagnostics, i.e., computed statistics that help
assess the impact of observation error. However, discussions in the acoustics
literature typically fail to address this issue. The present workmodels
feedforward active control as a regression of complex-valued variables, and
shows how to apply two basic regression diagnostics: the F-test and the t-test.
Also discussed are the physical significant of the ``cost function'' being
minimized by the regression, and the assumptions that must be made regarding
the variance of the measurement error. The techniques are demonstrated by
numerically simulating a simple system in which radiation from an axisymmetric
cylindrical shell is controlled by oscillating forces applied on the shell
surface. [Work supported by David Taylor Model Basin and ONR.]