Multiple-Factor Effective Independence Method for the Optimal Mode Decomposition Array

Mode decomposition provides the foundational characteristics of sound fields in flow ducts. However, when numerous modes propagate and multiple working conditions are considered, this problem often becomes ill-posed due to the singularity of modal matrices caused by inadequate spatial independence among measuring points. To this end, the multiple-factor effective independence (MFEI) method is developed for mode decomposition array design, simultaneously satisfying multiple Mach number and frequency combinations. This method quantifies each measuring point’s contribution to the linear independence of the modal matrix and sequentially eliminates the least contributive point from an initial candidate set to yield the optimal array. Additionally, an efficient array coordinate transformation scheme is introduced to transform the MFEI-designed array from one rectangular duct to another without repeating the design process. Furthermore, validations of an MFEI-designed array are conducted: 1) an uncertainty analysis of the mode decomposition of analytical sound fields based on Monte Carlo simulation confirms the robustness, 2) an experiment in which microphones are incrementally added to the array exhibits convergent decomposition results, and 3) the transmission loss of a liner derived from the experimental decomposition agrees satisfactorily with finite element simulations. These results demonstrate the effectiveness of the design methodology and the decomposition accuracy of the array.