Causally constrained active sound power control in an enclosed space

Abstract

In this paper the causality problem is considered of an active sound power control system that attempts to reduce total acoustic potential energy in an enclosed space by total source power minimization. To find the causally constrained optima under the white random sound field, time domain analysis based on the classical Wiener filtering technique for the active sound power control system in the enclosed sound field is accomplished. For simplicity, a two-monopole source system surrounded by an arbitrary acoustic impedance condition at the enclosure boundary is considered, which turns out to be a multiple-error Wiener filtering problem that has six errors. Theoretical causal and non-causal optimal filters for the white random noise are derived, and their frequency characteristics are also analyzed by the spectral factorization theorem. Simple numerical simulation for a one-dimensional sound field considering plane waves is performed to compare the control performance of non-causal filtering with that of causal filtering. The simulation result shows an important characteristic of the causally constrained optimal filtering; the basic acoustic controllability determined by the wavelength and location of control source is still maintained, even if the control performances in the overall frequency range are degraded due to the lack of predictability of the primary random excitation signal. The simulation result also reveals that large portions of the control source power show negative power, which means that the control source behaves as an active sound power absorber. This result is different from the well-known property of an optimal control source to minimize the total source power output in the deterministic sound field where the primary excitation is harmonic; i.e., the control source neither radiates nor absorbs any net acoustic power under optimal conditions to minimize the total sound power of the sources. (C) 1997 Academic Press Limited.