Blind signal separation (BSS) is an interesting project in the field of signal processing. The technique of BSS can be applied in rotating machine vibration signal processing, speech signal processing, image processing, communication processing, water voice signal processing, biomedical signal processing, data mining and many others. Because of wide usage of BSS, many researchers have devoted to the research of BSS, and the technique of BBS has been greatly improved. Research on BSS has been going on for about twenty years. However, the problem of BSS has not been totally solved. All above stimulate us to be engaged in researches on BSS algorithm and application.The main parts of thesis are research on BSS theory and modification to BSS algorithm in difference practical field based on linear and nonlinear mix model. The main work and innovation are abstracted as follows.1) The basic knowledge of BSS has been first introduced, including the statistics theory and information theory that are necessary to understanding and mastering BSS technique. Then the basic principle of BSS has been introduced and primary theory and research trends of blind source separation algorithm are analyzed.2) Aim at the problem that the choice of time invariant function and step influence convergent rate and stability of most of BSS algorithms. Proposed an algorithm of blind source separation based on maximum signal to noise ratio. The merit of this new algorithm is very low computational complexity and without any iterative.3) This paper research on post-nonlinear BSS, Post-nonlinear is a weak nonlinearity. Nonlinear BSS have more good robust and separation performance through research the RBF algorithm.4) A new process monitoring method is presented based upon wavelet transform and blind source separation. At first, wavelet transform is employed to de-noise measured signals to remove the process noise. Then blind source separation based on second order statistics(SOS) is used to extract blind source signals of the process. The simulation and experiment testing results show the proposed method that compare with other method based on blind source analysis directly with process information can effectively extract the quantitativefeature extraction.BSS theory is a developing theory, future research should focus on better usage in fault diagnosis.