Fault vibration signals of rolling bearings in early stages are affected by complex transmission paths and strong background noise, resulting in weak information about fault characteristics, which is difficult to extract clearly and accurately. To this end, a new diagnosis method for early faults of rolling bearings is proposed. First, the parameter-adaptive multipoint optimal minimum entropy deconvolution adjusted (PA-MOMEDA) algorithm is used to preprocess the fault signals by strengthening their shock components and weakening the influence of noise on their results. Second, the maximum envelope-spectrum characteristic energy ratio is employed as the selection criterion for the optimal truncation order of dynamic mode decomposition (DMD) to decompose and reconstruct the signals. Finally, the processed signals are subjected to the Hilbert envelope spectral transformation to accurately extract early fault characteristic frequencies. An analysis of simulated signals, public database signals, and bearing signals from a wind turbine has shown that the proposed PA-MOMEDA–DMD method can successfully extract the early fault characteristics of rolling bearings. Compared with the traditional pattern decomposition algorithms, the proposed method is much better at extracting fault characteristics and diagnosing early faults of rolling bearings. The facts have proved that the proposed method is promising in engineering applications.

Tool wear condition monitoring during the machining process is one of the most important considerations in precision manufacturing. Cutting force is one of the signals that has been widely used for tool wear condition monitoring, which contains the dynamical information of tool wear conditions. This paper proposes a novel multivariate cutting force-based tool wear monitoring method using one-dimensional convolutional neural network (1D CNN). Firstly, multivariate variational mode decomposition (MVMD) is used to process the multivariate cutting force signals. The multivariate band-limited intrinsic mode functions (BLIMFs) are obtained, which contain a large number of nonlinear and nonstationary tool wear characteristics. Afterwards, the proposed modified multiscale permutation entropy (MMPE) is used to measure the complexity of multivariate BLIMFs. The entropy values on multiple scales are calculated as condition indicators in tool wear condition monitoring. Finally, the one-dimensional feature vectors are constructed and employed as the input of 1D CNN to achieve accurate and stable tool wear condition monitoring. The results of the research in this paper demonstrate that the proposed approach has broad prospects in tool wear condition monitoring.

Multiscale dispersion entropy (MDE) is a common method for measuring the complexity of nonlinear time series. However, the uncertainty results by the MDE tool may be unreliable as the coarse-graining procedure will reduce the number of data points at a large scale. In addition, the essential differences between the matching patterns cannot be extracted by MDE. To effectively alleviate the above limitations of MDE, an improved multiscale weighted-dispersion entropy (IMWDE) method is proposed in this article. Weight coefficients and weight probabilities were assigned to each vector to consider the amplitude information, and an improved coarse grained process is proposed for entropy value refinement. The performance of the IMWDE method is evaluated with synthetic data. Based on a powerful algorithm for key feature extraction, a novel intelligent diagnosis technique is proposed by combining classifiers. Finally, real vibration signals collected from axle-box bearings are used to demonstrate the effectiveness of the diagnosis scheme. Compared with MDE and IMWDE, the results indicate that the proposed method achieves smaller errors, and the highest diagnosis accuracy.

As a powerful tool, dispersion entropy (DE) has good capability to measure the irregularity and complexity of nonlinear systems, so it is extensively utilized in the field of structural health monitoring. However, traditional multiscale dispersion entropy (MDE) will suffer from down-sampling as the scale factor increases, which compresses some intrinsic feature information, so that the representation ability of MDE for nonlinear system is significantly restrained. Aiming at this problem, a new method called cubic spline interpolation-based refined composite multiscale dispersion entropy (CSIRCMDE) is proposed. In this frame, the coarse-graining series are regarded as knots to calculate the interpolative points in different sub-sections. Then, the obtained coarse-graining samples and interpolative samples are used to construct interpolation series to capture the potential vibration characteristics and constrain the down-sampling phenomenon. Finally, the first coarse-graining point is gradually shifted back to make multiple groups of interpolation series, and the entropy values are rectified by calculating mean pattern probabilities at the same scale. Through these steps, CSIRCMDE can grasp sufficient feature information to reduce entropy errors and overcome the dependence on sample size compared with traditional algorithms, which is demonstrated by simulation and noise signals. Furthermore, two types of bearing damage experiments prove that CSIRCMDE has good capability to characterize the bearing states, therefore, based on the proposed algorithm, the classification model that can fully identify different bearing faults is established.