Reconstruction of aeroacoustic source strength distributions by inverse techniques

An investigation is presented of the reconstruction of aeroacoustic source strength distributions by inverse techniques based on the least squares method. The essence of the discrete inverse problem enabling the source strength reconstruction is the conditioning of the matrix to be inverted. A study is made of the behaviour of the condition number associated with the matrix of radiation transfer functions of each of three elemental acoustic source types. In order to enhance the accuracy of reconstruction, methods such as Tikhonov regularisation and singular value discarding are applied. A description is also given of methods for choosing the regularisation parameter and the singular values to be discarded by using the generalised cross-validation technique. It is concluded that aeroacoustic source strength distributions can be reconstructed with reasonably acceptable accuracy if we choose a good geometrical arrangement of microphone array together with an appropriate choice of the regularisation parameter and the singular values to be discarded.