The health condition monitoring of planetary gearboxes has drawn increasing attention due to the importance for safety operation and failure prevention. A novel diagnosis methodology based on multiscale symbolic diversity entropy (SDivEn) is proposed in this article. Herein, dynamical complexity of measured data is quantified by SDivEn. Compare to other entropy-based descriptors, SDivEn has advantages in its robustness and computation efficiency. To increase the feature representation capability of entropy descriptors, multiscale analysis is performed, where the measurement data in time series is decomposed into multiple scaled series by using the coarse graining process and then processed individually by using SDivEn method. The proposed multiscale SDivEn method is applied for fault recognition of planetary gearboxes. Experimental results indicate that the proposed method obtains the highest accuracy in recognizing seven health conditions of planetary gearboxes in comparison with three other existing entropy-based methods.

Using transfer learning (TL) for fault detection and diagnosis has been a hot topic in prognostic and health management (PHM) field. In this article, a systematic framework is established to solve the cross-domain fault diagnosis for rotary machines of the same type using entropy-based TL. The multiscale symbolic dynamic entropy (MSDE) is first proposed to extract features from vibration signals. Then, TL model is trained to get a mapping matrix, which can preserve the structure properties of prior distribution and minimize the discrepancies between different datasets. The mapped features are called multiscale transfer symbolic dynamic entropy (MTSDE). Finally, the support vector machine (SVM) classifier is utilized to accomplish the cross-domain intelligent fault-type recognition. To demonstrate the superiority of the proposed MTSDE method, the comparative experiments of nine methods are carried out under different datasets including gearboxes and bearings. Experimental results demonstrate that our proposed MTSDE method performs best in recognizing various fault types comparing with other nine methods. To the best knowledge of the authors, this is the first attempt of using entropy-based TL for cross-domain fault diagnosis of rotating machinery.

The entropy-based feature extraction is a promising tool for extracting weak features from rotating machinery. However, the existing research has paid little attention to the state transition process, which brings the problem of accuracy and comprehensiveness in complexity estimation. To address this issue, this paper proposes link dispersion entropy (LDE) based on the theory of the Markov chain for weak feature extraction. By calculating the transition probability of symbol patterns, the LDE can extract the fault information contained in the transition, enabling it to capture the early weak fault. Furthermore, LDE is extended to a multiscale analysis by combining it with the coarse-gaining process for comprehensive feature extraction, termed multiscale LDE (MLDE). Finally, three simulated signals and two different experimental data are utilized to verify the advantage of MLDE in extracting the weak fault features. Results demonstrate that MLDE has the best performance in fault diagnosis of rotating machinery compared with the existing five methods, namely sample entropy, fuzzy entropy, permutation entropy, dispersion entropy and symbolic dynamic entropy.

As a nonlinear measure, Lempel–Ziv complexity (LZC) can be considered as a suitable parameter for characterizing bearing health status by measuring the complexity of vibration signals. However, in continuous monitoring scenario under noisy condition, all components of a multicomponent bearing signal are not equally sensitive toward a change of LZC value. As a result, a direct application of LZC for bearing health monitoring not only suffers from its inefficient early fault warning but also fails to infer the fault progression. In this article, instead of direct utilization of a whole vibration signal, its fundamental component (FC) sensitive to LZC calculation is separated with the help of continuously adjustable parameterized tunable $Q$ factor wavelet transform (TQWT). In this context, a study based on sparsity indices has been done for $Q$ factor selection of TQWT. Since TQWT uses an oscillation-based bearing FC separation scheme for LZC calculation, the proposed measure is termed as oscillatory Lempel–Ziv complexity (OLZC). Two experimental cases are used for validation. Performance of OLZC is compared with original LZC, representative sparsity indices and recently proposed multiscale symbolic Lempel–Ziv complexity. Results demonstrate that the proposed OLZC can not only overcome the limitations of the original LZC but also performs better than other indices in comparison to continuous monitoring of bearing health.