The quantitative calculation of the source contribution is very important and critical for the identification of the main vibration sources and the reduction of vibration and noise in submarine. It is difficult to calculate the source contribution because of the submarine’s complex structure and the large amount of vibration sources. As a typical blind source separation method, independent component analysis (ICA) has recently been proved to be an effective method to solve the source identification problem in which the source signals and mixing models are unknown. However, the outcomes of the ICA algorithm are affected by random sampling and random initialization of variables. In our study, the prior knowledge of the vibration sources can be obtained through the vibration measurement of submarine. Obviously, information in addition to mixed signals from sensors can lead to a more accurate separation. Therefore the contrast function of ICA can be enhanced by the reference signals obtained by the prior knowledge. In this paper, a closeness measurement between the independent components and the reference signals obtained by the prior knowledge is introduced, and the closeness measurement is constructed to have the same optimization direction with the traditional contrast function: negentropy. The closeness measurement is used to enhance the contrast function and then the enhanced contrast function is optimized by means of the Newton iteration and the deflation approach. Thus the simplified independent component analysis with reference (ICA-R) algorithm is obtained. After that a method to quantitatively calculate the source contribution is proposed based on the outcomes of the simplified ICA-R. Finally, the effectiveness of the proposed method is verified by the numerical simulation studies. The performance offered by the proposed method is also investigated by the experiment: it appear as a very appealing tool for the quantitative calculation of the source contribution.
Any statistical manifold has a contrast function---on the $C\sp 3$-functions taking the minimum at the diagonal of the product manifold
