A fuzzy clustering method for periodic data, applied for processing turbomachinery beamforming maps

In the present paper, the fuzzy c-means method is extended, and an algorithm is proposed for fuzzy clustering of data lying in a feature space of arbitrary dimensions, with one of them being periodic. To aid in determining the optimal number of clusters, the Xie-Beni validity index is extended, to account for the periodicity. Furthermore, the relative weights of the dimensions in the calculation of distances are investigated. The method is incorporated into a procedure for processing turbomachinery beamforming maps. Thus, an objective, robust way of identifying the sound sources being present in such machines is obtained. These properties are ensured by selecting the required parameters through parameter studies. Presented through a case study, the method is used to determine the most significant sound source mechanisms in an axial fan.