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

Abstract

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.

Convolutive blind source separation in the frequency domain of mechanical noise for gas turbines based on bounded component analysis

“…BSS based on BCA can not only separate independent sources but also separate dependent sources. Gong et al [19] proposed a normalized boundary objective function for instantaneous mixing case, whose expression is:…”

“…Consider the energy minimization of subtracted mixed signals as a criterion. Let h ij represents the contribution coefficient of the ith source signal in the jth mixed signal, and then the coefficient h ij can be solved by equation (19):…”

“…In this section, simulation experiments are performed to validate the effectiveness of CBSS_FDBCA and its superiority compared to other methods. CBSS_FDBCA is aimed at the separation of dependent source signals, but it also has good separation ability for independent signals, which has been studied by many researchers [18,19,21]. This section only considers the separation ability of independent and dependent sources in the case of convolutive mixing, and no longer studies the case where the source signals are only independent signals.…”

“…All these BCA methods are computationally cumbersome in terms of objective functions. To solve this problem, Gong et al [19] proposed a normalized boundary objective function, which simplified the objective function of BCA, and validated the effectiveness of the method through simulation and experiments. The above-mentioned BSS methods based on BCA are all based on the instantaneous mixing of source signals.…”

A Blind Source Separation Method Based on Bounded Component Analysis Optimized by the Improved Beetle Antennae Search

“…The computational complexity of all these BCA approaches is high in terms of the objective function. To solve this problem, Gong et al [6] proposed a normalized boundary objective function that simplified the objective function of BCA and verified the effectiveness of this method via simulation and experiment. Babatas et al [7] proposed that the PCA algorithms can be applied to temporal or spatially dependent sources, as well as independent sources.…”