Estimation of acoustic source strength within a cylindrical duct by inverse methods

One method for deducing the strength of an acoustic source distribution from measurements of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution. This method uses the singular value decomposition (SVD) as the primary analysis tool and has shown some promise. In the transformation process associated with the SVD, the strength of the discretized point source can be simply represented by the pressure field and the inversion of corresponding matrix of the frequency response function and the transformed pressures and source distribution are related by single real numbers only (i.e., the singular values). Therefore, the resolution and the accuracy of the reconstruction produced by such inversion methods will be highly dependent on how these small singular values are treated during the inversion process. In the present work, the emphasis is placed on the description of the inverse method for the investigation of the characteristics of acoustic sources within a circular duct. Firstly, an analytical model is developed of the internal field from a finite duct with open ends. An examination is presented of the capability of the inverse method in dealing with in-duct sound source problems. These guide the design of an optimal sensor array which can make the condition number as small as possible for the assumed source distribution. Also, a series of experimental demonstrations are given of the proposed in-duct sensor array for producing high-resolution information regarding in-duct sources.