Sound Field Reconstruction In An Enclosed Space With Reverberation Using Equivalent Source Method

Technological advancements have resulted in the development of sophisticated vehicles and aircrafts for human use,and this has equally led to higher demand for comfort in these cabins.Noise control engineers need to eliminate or reduce every form of noise emanating from these vehicles and aircraft cabins to the least minimum.To reduce or eliminate noise,the first priority is to identify the noise sources in the cabin.Once the noise source is identified,it is much easier for the engineers to reduce,remove or modify the overall sound pressure level of the aircraft cabin.Noise source can be identified by the reconstruction of the sound field on the cabin boundary using any of the modern sound field reconstruction methods.One problem faced for noise source reconstruction in a large cabin,is the presence of reverberation,which tends to distort the reconstructed image,making it difficult to locate the noise source.In this situation,the direct source component needs to be separated from the reverberant source component before the reconstruction process.This thesis proposed a method for sound field separation of the direct source component away from the reverberant source component,and then reconstruct the sound field on the cabin boundary for noise source identification.The sound field separation is done in frequency – time domain.Short-time Fourier transform is used to transform the measured sound pressure from time-domain to frequency – time domain,exposing the different components of the sound field.A search algorithm is implemented to sort and identify the direct source component.Because reverberation decays with time,the search algorithm tends to identify the direct source components by its pressure magnitude.A test was conducted to validate the accuracy of the proposed sound field separation method,comparing speech obtained in a highly reverberant chamber with a speech made by same person in an anechoic chamber.The obtained result was almost same as the speech made in an anechoic chamber.To reconstruct the sound field in an enclosure,an inverse model is needed.The equivalent source method is developed in this thesis for the reconstruction.It is chosen because of the many advantages it has over the boundary element method,some of which include its simplicity,reduced computational cost,and avoidance of the singularity and non-uniqueness problems which are associated with the boundary element method.The Tikhonov regularization technique is employed to solve the underdetermined system of equation,and the L-curve method is used to select the regularization parameter.Numerical simulation was conducted to validate the accuracy and robustness of the developed method,using spherical enclosure,rectangular enclosure and a 2D source plane.The microphone field measurement was calculated using analytical models.The reconstructed result obtained in all matched well with the true pressure on the boundaries,validating the effectiveness of the developed method.Another approach also considered here is the use of sound field decomposition method to estimate the sound field around the microphone array,using different frequency bin and time frame output by the field separation,and then provide output to the equivalent source method for reconstruction on the whole cabin.This is to improve the robustness of the reconstructed image.Numerical simulation was also done to validate the method,and it was able to locate the sound source.To validate the effectiveness of the proposed sound field separation and the developed equivalent source method combined for practical application,an experiment was conducted using an improvised reverberation chamber.The reconstructed image was able to identify the location of the source in the room.This validates that the proposed sound field separation technique,in combination with the developed equivalent source method can accurately reconstruct the sound field in an enclosed cabin with reverberation.In conclusion,a new method is proposed that can separate out the direct sound from the reverberant sound in a cabin,for when the source is located outside,and then reconstruct effectively the sound field on the cabin boundary for noise source identification.The direct sound component is separated using Short time Fourier transform technique and a search algorithm.The boundary pressure field is reconstructed using an equivalent source method and a sound field decomposition method...