An inverse acoustic method is presented in this work, which allows to determine the spatial and temporal distribution of unsteady rotating forces from microphone array measurements. The method is based on the usage of a space–time regularization with a mixed norm. The proposed method can take advantage of a prior knowledge of the space–time characteristics of the unsteady rotating forces to ensure an accurate force reconstruction in real-time, using a smaller number of input signals compared to more conventional inverse methods. Different properties of the proposed method are initially investigated by using synthetic acoustic signals radiated from rotating point sources and computed via an acoustic analogy formulation. Finally, the method is validated by using experimental acoustic signals radiated from the rotor of an unmanned aerial vehicle.

In the original publication of the article, the first affiliation “School of Public Administration, Hunan University, Changsha, China” was incorrectly repeated as fourth affiliation. The fourth affiliation should be “Building and Real Estate Dept. Hong Kong Polytechnic University, Hong Kong SAR”. The original article has been corrected.