Higher-order estimation of active and reactive acoustic intensity

Abstract

The phase and amplitude gradient estimator (PAGE) method can be used to increase the bandwidth of complex acoustic intensity estimates obtained with multi-microphone probes. Despite the increased bandwidth, errors arise when using this method, which is based on linear least-squares gradients, in non-planar fields. Examples of non-planar fields include the acoustic near field of a radiating source or near a null in a standing-wave field. The PAGE method can be improved by increasing the number of microphones and using a Taylor expansion to obtain higher-order estimates of center pressure, pressure amplitude gradient, and phase gradient. For one-dimensional active intensity in a simulated monopole field, a four-microphone probe is shown to converge to less than 0.2 dB error at a closer distance than a two-microphone probe with the same inter-microphone spacing. For reactive intensity in a standing wave field, increasing the number of microphones improves the bandwidth, and applying a higher-order method to traditional reactive intensity estimation outperforms higher-order PAGE.