Fault diagnosis of gearboxes based on vibration signal processing is challenging, as vibration signals collected by acceleration sensors are typically a nonlinear mixture of unknown signals. Furthermore, the number of source signals is usually larger than that of sensors because of the practical limitation on sensor positions. Hence, the fault characterization is actually a nonlinear underdetermined blind source separation (NUBSS) problem. In this paper, a novel NUBSS algorithm based on kernel independent component analysis (KICA) and antlion optimization (ALO) is proposed to address the technical challenge. The mathematical model demonstrates the nonlinear mixing of source signals in the underdetermined cases. Ensemble empirical mode decomposition is used as a preprocessing tool to decompose the observed signals into a set of intrinsic mode functions that suffers from the problem of redundant components. The correlation coefficient is utilized to eliminate the redundant components. An adaptive threshold singular value decomposition method is proposed to estimate the number of source signals. Then a whitening process is carried out to transform the overdetermined blind source separation (BSS) into determined BSS, which can be solved by the KICA method. However, the reasonable selection of parameters in KICA limits its application to some extent. Therefore, ALO and Fisher’s linear discriminant analysis are adopted to further enhance the accuracy of the KICA method. The separation performance of the proposed method is assessed through simulation. The numerical results show that the proposed method can accurately estimate the number of source signals and attains a higher separation quality in tackling nonlinear mixed signals when compared with the existing methods. Finally, the inner ring fault experiment is conducted to preliminarily validate the practicability of the proposed method in bearing fault diagnosis.
Diesel Engine Bearing Fault Diagnosis Based on Underdetermined Blind Source Separation
