The Shannon entropy measure, applied to the time frequency distribution of a signal, is a reliable indicator to quantitatively analyze the health status of a rolling element bearing. Usually, however, conventional time frequency representations rely on the selection of the best scale of a base function in order to deal with the noise components present in a vibration signal. In this context, the time frequency manifold is a relatively new time frequency analysis method, capable of cancelling out or suppressing the majority of noise components by correlating the deterministic information of a faulty signal in its multidimensional phase space representation, rather than depending on the scale selection of a certain base function. With the aim of examining the merits of the time frequency manifold, in this research, the concepts of the time frequency manifold and Shannon entropy are integrated, so as to construct an accurate bearing health monitoring index. The effects of embedding dimension and time delay on the calculation of the proposed health index are studied. Simulated signals are employed in order to study the characteristic properties of the proposed index. Two experimental datasets are used to validate the effectiveness of the proposed method in compare to some conventional and hybrid bearing health monitoring indexes. Our research shows that the proposed index demonstrates a consistently good performance for both inner and outer race failure, in cases of run to failure bearing testing.

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Intelligent fault diagnosis of rotating machinery is a key topic for industrial equipment maintenance and fault prevention. In this study, an intelligent diagnosis approach of rotating machinery via enhanced hierarchical symbolic sample entropy (EHSSE) is proposed. Firstly, a novel indicator termed symbolic sample entropy (SSE) is proposed for complexity measure and representation of fault information. By using symbolic dynamic filtering, the raw continuous time-series will be discretized into symbolic data, and analysis of symbolic data is less sensitive to measurement noise, resulting in superior robustness. Secondly, SSE is combined with enhanced hierarchical analysis to further extract fault characteristics hidden in both low- and high-frequency components. To study the performance of SSE and EHSSE, multiple simulated signals and experimental studies are constructed and three widely used entropy methods are employed to present a comprehensive comparison. The comparison results show that EHSSE performs best in diagnosing various faults of planetary gearbox and rotor system with highest identification accuracy compared with other entropy-based approaches.

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Multisource domain adaptation (MDA) methods have been preliminarily applied in cross-domain fault diagnosis of rotating system due to its correlation ability between different but related fields. However, it still remains challenging to learn domain-invariant representations under multisource scenarios. This article proposes a multi-representation symbolic convolutional neural network (MR-SCNN) for multisource cross-domain fault diagnosis of rotating system. The novelty of our work lies in three aspects. First, the proposed method combines symbolic dynamics with CNN to obtain a coarse-grained description of vibration signals, which could eliminate the negative transfer caused by subtle changes in dynamic characteristics among different source domains. Second, considering that most MDA methods ignore the significant limitations brought by statistical properties of the specific working condition, a multi-representation Softmax (MR-Softmax) is developed to learn domain-invariant discriminative representations by allowing the diversity of the predictions of samples with the same label. In addition, an undifferentiated adversarial training strategies is proposed to narrow the domain discrepancies and reasonably assess the residual negative transfer risk of different source domains. Based on the assessment, confidence coeffients are defined and embedded into MR-Softmax to extract and utilize the useful diagnostic knowledge on each source domain. Compared with several state-of-the-art diagnostic models, the experimental results confirm the validation of the proposed MR-SCNN method.