Quantitative identification of independent and dependent sources based on bounded component analysis

The quantitative identification of vibration sources can provide the basis and guidance for the vibration and noise reduction of mechanical systems. Since the vibration sources in a mechanical system are not necessarily mutually independent, this paper proposes a quantitative identification method suitable for both independent and dependent sources based on bounded component analysis (BCA). Firstly, the new BCA algorithm is adopted to separate source signals and normalized boundary minimization is used as the objective function, which is optimized by a modified subgradient method with the introduction of the probability mass function and an adaptive step size, and thus the noise resistance and convergence performance are enhanced. Secondly, the source contribution is extracted by taking the separated signal as the input and boundary minimization of the residual signal as the criterion. Thirdly, the projection of the source contribution in the mixed signal is calculated by the inner product and the proportion of the calculated projection on the mixed signal is taken as the contribution index to evaluate the influence of the vibration source on the vibration of the observation point of the system. Finally, the effectiveness and superiority of the proposed method are tested by simulation analysis and experimental verification. The results show that the proposed method has high accuracy in the quantitative identification of both independent and dependent sources.