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Group-sparse mode decomposition (GSMD) is a decomposition method designed based on the group sparse property of signals in frequency domain. It is proved to be highly efficient and robust against noise, showing bright prospects for bearing fault diagnosis. However, the following adverse factors may impede its application for incipient bearing fault feature extraction: Initially, the GSMD method did not consider the impulsiveness and periodicity of the bearing fault feature. As a result, the ideal filter bank generated by GSMD may not accurately cover the fault frequency band because it may produce over-coarse or over-narrow filter bank under the condition of strong interference harmonics, large random shocks and heavy noise. Moreover, the location of informative frequency band was obstructed since the bearing fault signal shows complicated distribution in frequency domain. To overcome the abovementioned limitations, an adaptive group sparse feature decomposition (AGSFD) method is proposed. Firstly, the harmonics, large-amplitude random shocks and periodic transient feature are modeled as limited bandwidth signals in the frequency domain. On this basis, an autocorrection of envelope derivation operator harmonic to noise ratio (AEDOHNR) indicator is proposed to guild the construction and optimization of the filter bank of AGSFD. Also, the regularization parameters of AGSFD are adaptively determined. With the optimized filter bank, the original bearing fault is decomposed into a serial of components with AGSFD method, where the sensitive fault-induced periodic transient component is maintained using the AEDOHNR indicator. Finally, the studies of the simulation and two experimental items are carried out to evaluate the feasibility and the superiority of AGSFD method. The results indicate the AGSFD method can identify the early failure in the presence of heavy noise, strong harmonics or random shocks and has better decomposition efficiency. • An AGSFD method is developed for extracting the weak bearing fault feature. • A new indicator named as AEDOHNR is proposed, which shows better performance for characterizing the periodic impulses feature. • Based on AEDOHNR, the filter bank of the AGSFD is constructed and optimized. • The results demonstrate that the AGSFD method can effectively extract the incipient bearing fault feature. [ABSTRACT FROM AUTHOR]

In this paper, a method for approximating a multi- input multi-output (MIMO) transfer function by a causal finite-im- pulse response (FIR) paraunitary (PU) system in a weighted least- squares sense is presented. Using a complete parameterization of FIR PU systems in terms of Householder-like building blocks, an iterative algorithm is proposed that is greedy in the sense that the observed mean-squared error at each iteration is guaranteed to not increase. For certain design problems in which there is a phase- type ambiguity in the desired response, which is formally defined in the paper, a phase feedback modification is proposed in which the phase of the FIR approximant is fed back to the desired response. With this modification in effect, it is shown that the resulting iterative algorithm not only still remains greedy, but also offers a better magnitude-type fit to the desired response. Simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank (PCFB)-like filter banks and the FIR PU interpolation problem. Concerning the PCFB design problem, it is shown that as the McMillan degree of the FIR PU approximant increases, the resulting filter bank behaves more and more like the infinite-order PCFB, consistent with intuition. In particular, this PCFB-like behavior is shown in terms of filter response shape, multiresolution, coding gain, noise reduction with zeroth-order Wiener filtering in the subbands, and power minimization for discrete multitone (DMT)-type transmul- tiplexers. [ABSTRACT FROM AUTHOR]