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Since the cyclostationarity in vibration signals is the key to judge the rotating machine health state, spectral harmonics-to-interference ratio (SHIR) has been used to construct single node feature learning network (SHIR-based blind deconvolution, BD-SHIR) to realize condition monitoring of machine. However, BD-SHIR still has several obvious limitations, including the need for prior fault information and the tendency to fall into local optimal solutions which will affect its feature learning and state monitoring performance. Therefore, this paper proposes a multi-node feature learning network based on BDSHIR, which does not rely on prior information, multi-node adaptive BDSHIR (MABD-SHIR). It uses each filter in the 1/3 binary tree filter bank to design each initial node (filter) in the learning network correspondingly, and introduces an adaptive fault characteristic frequency (FCF) detection process. Since this initialization can give some filters close to the fault resonant band, iterations starting from these nodes are more likely to detect the precise FCF and converge to the optimal solution. Finally, MABD-SHIR can obtain multiple local optimal solutions, among which the one with the largest SHIR is generally closer to the global optimal solution than the one obtained by BD-SHIR. Simulation and experimental data of defective rotating machinery verify the effectiveness of MABD-SHIR in machinery condition monitoring and fault feature learning. Note to Practitioners—This paper is motivated by the problems that the rotating machine condition monitoring based on BDSHIR is easy to prematurely fall into local optimal solution and requires prior fault information. These problems can be effectively solved by extending BDSHIR from single node structure to multi-node structure and introducing adaptive period detection technique (A-DPT). The core idea is to start iterations from multiple initial filters and to detect the FCF adaptively during each iteration. Multiple features conforming to filtered signals’ SHIR maximization can be finally learned. Therefore, in this paper, MABD-SHIR is proposed, which is equivalent to a multi-node feature learning network. Since the objective function of BD is usually non-convex, MABD-SHIR can obtain multiple local optimal solutions without requiring prior FCFs. This is more likely to achieve a global optimal solution than BDSHIR, which starts iteration from only one initial filter and ends up with one local optimal solution. In addition, the objective function of MABD-SHIR has lower mathematical complexity, which reduces the difficulty of optimization.

Although the frequency band segmentation rules used in fast kurtogram (FK) has made great achievements in locating fault resonance band, it still has the problem of underdecomposition or overdecomposition for resonance band. This will affect the performance of the methods based on this band segmentation rule in fault diagnosis. Aiming at this problem, an adaptive harmonic product spectrum (AHPS) is proposed in this article, which can realize adaptive frequency band segmentation adaptively based on signal power spectral density (PSD) instead of fixed segmentation rules. AHPS can achieve adaptive frequency spectral segmentation by iteratively convolving the PSD with the Gaussian kernel function. The harmonic saliency index (HSI) is used to pave a spectrum plane. The optimal resonance band is determined by maximizing HSI and more accurate fault resonance band location performance is achieved. Both simulation data and measured data are used to verify the performance of the proposed AHPS. The results show that compared with FK and harmonic product spectrum (HPS), AHPS has better robustness and fault diagnosis performance.

Harmonics-to-noise ratio (HNR) is an important health index of rotating machine, which has been applied in blind deconvolution (BD) method to realize periodic impulse detection. However, most fault impulses are not strictly periodic, but pseudo-cyclostationary, which will affect the performance of HNR in fault characterization to some extent. This limits its applications. Therefore, in this paper, a novel BD method, maximum squared envelope spectrum harmonic-to-interference ratio deconvolution (MSESHIRD), is proposed to more effectively achieve fault identification. The proposed method seeks a target filter by maximizing squared envelope spectrum harmonic-to-interference ratio (SESHIR). Since harmonic components corresponding to repetitive fault impulses in SES are less sensitive to random fluctuations, SESHIR can more accurately distinguish repetitive fault impulses from irrelevant interference in vibration signals. Therefore, BD based on SESHIR has better performance than BD based on HNR in measuring fault features in signals. Through simulation and experimental case analysis, the proposed method is compared with several public methods Results show that the proposed method has better performance in fault characteristic extraction. In addition, it is implemented on bearing run-to-failure data for condition monitoring to show that the proposed method has excellent ability of early fault detection. Note to Practitioners—This paper is motivated by the problems of automatic operating condition monitoring and early defect diagnosis of rotating machines. These problems can be effectively solved by designing a BD method based on reliable and efficient health indices. HNR defined on autocorrelation function (AF) is an excellent health index to characterize the signal-to-noise ratio (SNR) of repetitive fault impulse in signals. However, this paper uses mathematical models of HNR to show that it has very strict requirements on the period and SNR of fault impulse signals. A fluctuating fault period or a low SNR might make HNR unable to accurately estimate the energy of fault components in signals, thus weakening its performance in fault characterization. Compared with HNR, SESHIR has better fault characterization ability due to that SES can more accurately obtain the periodicity (frequency) and energy of fault components in signals. Therefore, this paper proposes a novel BD method based on SESHIR maximization for repetitive impulse monitoring. Its effectiveness and robustness are verified by both theoretical justification and experimental results.