ESTIMATION OF ACOUSTIC SOURCE STRENGTH BY INVERSE METHODS: PART I, CONDITIONING OF THE INVERSE PROBLEM

This paper deals with the discrete inverse problem in acoustics. It is assumed that a number of acoustic sources are located at known spatial positions and that the acoustic pressure is measured at a number of spatial positions in the radiated field. The transfer functions relating the strengths of the acoustic sources to the radiated pressures are also assumed known. In principle, the strengths of the acoustic sources can be deduced from the measured acoustic pressures by inversion of this matrix of transfer functions. The accuracy of source strength reconstruction (in the presence of noise which contaminates the measured pressures) is crucially dependent on the conditioning of the matrix to be inverted. This paper examines the conditioning of this inverse problem, particularly with regard to the geometry and number of sources and measurement positions and the non-dimensional frequency. A preliminary investigation is also presented of methods such as Tikhonov regularization and singular value discarding which can improve the accuracy of source strength reconstruction in poorly conditioned cases. Results are also presented which enable the solution of the inverse problem when the time histories of the acoustic sources are time-stationary random processes and the spectra and cross-spectra are measured at a number of positions in the radiated field. The paper illustrates the possibilities and limitations of the use of inverse methods in the deduction of acoustic source strength from radiated field measurements.