**1. Introduction**

Diaphragm pump is a kind of transmission power equipment in the metallurgical industry, which provides power for slurry pipeline transmission. The safe operation of the diaphragm pump ensures the supply of mineral raw materials, and improves the production efficiency and the quality of steel products. The poor operating environment, stress, and load will cause damage to the diaphragm pump, which cause significant economic losses [1]. Therefore, the maintenance of the diaphragm pump is important. Bearing and check valve are the most frequently damaged parts in diaphragm pump, and the price of check valve is high. The maintenance personnel often detect the faults of bearing and check valve through abnormal sounds of diaphragm chamber and bearing seat, slurry leakage trace, pressure, and flow. These methods rely on subjective experience seriously. The excessive maintenance will cause the risk of shutdown, and the frequent replacement will cause the waste of spare parts, which will cause serious economic losses. Insufficient maintenance will lead to mechanical failure. Besides, a too late replacement of parts will lead to secondary failure of other parts, which will bring immeasurable losses and safety accidents. Therefore, it is urgen<sup>t</sup> to propose a reliable fault detection method to guide the formulation of maintenance and replacement strategy.

Tracking the fault state of parts and determining the early fault point have important guiding significance for the design, assembly, and maintenance of the diaphragm pump.

**Citation:** Zhou, C.; Jia, Y.; Bai, H.; Xing, L.; Yang, Y. Sliding Dispersion Entropy-Based Fault State Detection for Diaphragm Pump Parts. *Coatings* **2021**, *11*, 1536. https://doi.org/ 10.3390/coatings11121536

Academic Editors: Ke Feng, Jinde Zheng and Qing Ni

Received: 1 November 2021 Accepted: 11 December 2021 Published: 14 December 2021

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The time domain, frequency domain, and time-frequency domain features of the vibration signal excited by faults will change in real time with the state degradation. However, it is difficult to track and detect the fault states of the diaphragm pump because the vibration signal is interfered by the pulsation of the slurry and the vibration of parts. In addition, the signal has nonlinear and non-stationary characteristics due to the influence of transmission path and hydraulic, mechanical, and electrical factors, which brings grea<sup>t</sup> challenges to the fault state tracking and detection.

There are few researches on fault detection of diaphragm pumps at home and abroad, but the researches on bearing fault detection still have good reference significance. Mixed domain features are the most commonly used methods in fault detection, including time domain, frequency domain, and time-frequency domain features. Li extracted 24 timefrequency features and selected sensitive feature through monotonicity and correlation coefficient, finally tracked the bearing degradation state through gate recurrent unit and 3σ criteria [2]. Gao extracted the degradation features from the mixed domain features of the bearing through isometric mapping, then established a reliability model by logistic regression [3]. Hua extracted the mixed domain features of the bearing and constructed a fault warning line based on the 3σ principle, and finally predicted the degradation state through the support vector machine [4]. Li selected the effective features from the mixed domain features of bearing and obtained a degradation curve by self-organizing feature mapping [5]. Bilendo extracted the mixed domain features and selected effective degradation features through local linear embedding (LLE) [6]. However, the single features, mixed domain features, and its fusion features have not achieved satisfactory results in the fault detection of the bearing and check valve. The reasons for this are that single features are only sensitive to the specific fault in a specific stage, the fusion features are redundant and depend on dimensionality reduction methods. Besides, the construction and dimensionality reduction of mixed domain features depend on the experience of technicians. The deep learning method can solve the above problems [7]. Ding proposed a domain adaptive long short-term memory (LSTM) to predict the bearing degradation state [8]. Hu extracted modes by convolutional neural network and evaluated the bearing degradation process by fuzzy C mean clustering [9].

Although the above-mentioned deep learning-based methods can avoid the subjective experience problems in mixed domains, the time cost of deep learning is higher and neural network structure seriously affects the feature extraction performance. Entropy can measure the complexity and uncertainty of signal [10] and has the advantages of simple calculation and high calculation efficiency [11]. Kumar extracted the Shannon entropy, permutation entropy (PE) and approximate entropy (AE) degradation features of the bearing and then constructed a bearing degradation trend model by gaussian process regression [12]. Noman first separated the oscillating eigenvalues from the vibration signal, then took the PE of the oscillation signal as the bearing degradation feature [13]. Minhas obtained several modes by empirical mode decomposition, then extracted the weighted multi-scale entropy degradation features of sensitive modes by Hurst index [14]. Li proposed a degradation feature combining composite spectrum and relative entropy, which can characterize the degradation trend of hydraulic pump effectively [15]. Mostafa tracked the fault evolution process of gear and bearing through sample entropy (SE), PE, and dispersion entropy (DE) [16]. Experiments show that the DE [17] is not sensitive to noise, but sensitive to instantaneous frequency, amplitude, and sequence bandwidth, which is in line with the feature extraction requirement of vibration signal.

However, the entropy methods also have their own defects, SE is sensitive to signal length, PE ignores the amplitude information, and they both have poor anti-noise performance. Although the performance of DE is slightly better than that of single features, mixed domain features and traditional entropy features in the fault detection of diaphragm pump, DE has not achieved satisfactory results in the fault detection. The problems can be summarized as follows. Firstly, the vibration signal segmen<sup>t</sup> used to extract the DE feature is discontinuous and irrelevant, which greatly reduces the tendency of the degradation

feature. Secondly, the results obtained by the normal cumulative distribution function (NCDF) used in the DE deviate from the actual distribution of vibration signals, which makes the traditional DE feature unable to well characterize the true characteristics of vibration signals. Thirdly, the anti-noise performance of DE degradation feature still does not meet the fault detection requirements of mechanical equipment in the actual industrial environment. In addition, there is still a lack of an effective fault point detection and early warning method, which can track the degradation state of parts in real time and warn the key fault points.

The sliding dispersion entropy (SDE) and its state warning line are proposed and used for fault state detection and degradation state tracking in this paper. In order to enhance the tendency of DE degradation feature, a sliding window is added to the signal segmen<sup>t</sup> and the root mean square of the signal in the window is used to replace the signal segmen<sup>t</sup> to achieve down-sampling. In order to improve the characterization performance of DE feature, the down-sampling sequences are mapped to different categories by introducing hyperbolic tangent sigmoid function (TANSIG) mapping. Because the TANSIG mapping is closer to the actual empirical distribution of vibration signal, the proposed SDE enhances the monotonicity of the degradation feature. To enhance the anti-noise performance, locally weighted scatterplot smoothing (LOWESS) is introduced to remove the small fluctuations and burrs of the SDE feature curve. At the same time, an adaptive early warning line based on 2σ criteria is proposed, which can determine the fault warning point effectively. In summary, the proposed method solves the above problems well. The method can track the fault state of the parts and determine the fault warning point and provide technical guidance for the maintenance and replacement of the parts.

The remainder of this paper is organized as follows: in Section 2, the theory of the proposed sliding dispersion entropy (SDE) and its fault state warning line are introduced. Then, a state detection method based on SDE is proposed, and the specific steps are described in detail. In Section 3, the effectiveness of the SDE and its state warning line is proved by analyzing the bearing data in the laboratory environment, then the proposed SDE is applied to the fault detection of check valve in the actual industrial environment, and the proposed SDE was compared with many existing methods. Finally, some conclusions are presented in Section 4.
