Degradation Feature Extraction of Quay Crane Gearbox Based on Static Divided Symbol Sequence Entropy

doi:10.21203/rs.3.rs-1630377/v1

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Degradation Feature Extraction of Quay Crane Gearbox Based on Static Divided Symbol Sequence Entropy

https://doi.org/10.21203/rs.3.rs-1630377/v1

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Gearbox is an important transmission equipment of quay crane hoisting mechanism. In order to accurately extract the degradation features from the vibration monitoring signal, a degradation feature extraction technique based on the static divided symbol sequence entropy is proposed. Considering the uniformity of the symbolization standard, the technique takes the root mean square of the signal in health condition as the basis, and combines the scale coefficient to establish a uniform basic scale. At the same time, the symbol set is expanded to enhance the information content and the ability of characterizing complexity of signal in large-value region. The Logistic chaotic sequence and the lifetime signal of hoisting mechanism gearbox are used for analysis respectively. The results show that the proposed technique is able to characterize the complexity of the nonlinear time series, and sensitively describe the performance degradation of the hoisting mechanism gearbox. The calculation speed is fast, which will lay a method foundation for further evaluating the health condition of large-scale quay crane in the port.

Quay crane

Degradation feature extraction

Entropy

Symbol sequence entropy

Gearbox

The quay crane is a widely used large-scale port hoisting machinery, which mainly completes loading and unloading functions for port containers. Hoisting reduction box is a key transmission component of the hoisting mechanism and its running condition will directly affects the safety and reliability performance. The quay crane usually works in harsh natural environment and special working condition, therefore, the vibration monitoring signal of hoisting reduction box presents nonlinear, non-stationary and non-periodic characteristic. At the same time, the vibration signal is also mixed with large number of noise and shock components under working conditions, which increases the difficulty of vibration signal analysis[1]. In addition, the quay crane has a long liftime and harsh working environment, so it is difficult to monitor online and verify the technique’s effectiveness. Therefore, how to extract the degradation features that characterize the operating condition from the complex and special monitoring signals is of great research significance for accurately assessing the health condition of quay crane and implementing Condition-Based Maintenance (CBM) [2].

As the basis of health condition evaluation, the purpose of degradation feature extraction is to mine performance degradation principle contained in the signal quantitatively, In view of the nonlinear, non-stationary and non-periodic characteristics of vibration monitoring signals, in recent years, signal analysis methods based on complexity theories including information entropy, fractal dimensions and chaos had been widely used in degradation features extraction for rotating machinery such as rolling bearings and gears. Some techniques had been proposed such as fuzzy entropy [3], permutation entropy [4], dispersion entropy [5], amplitude spectrum entropy [6–7], fractal dimension [8–9] and so on. On account of the difficulty of collecting lifetime vibration monitoring signals, accelerated test data from IMS [10] and IEEE PHM 2012 [11] are usually introduced for verification. Compared with the accelerated lifetime signals above, vibration signals of the quay crane is more complex, and some effective methods verified in accelerated test data are proved out of work when processing the vibration signals from the quay crane.

Symbol dynamics is a signal symbolization theoretical method which has been successfully applied in fields of network security [12], biomedicine [13], and mechanical engineering [14]. This method is used by means of digitizing the original time series and extracting the main trend. At the same time, the noise components can be reduced and thereby greatly improving the effect and calculation efficiency. The combination of symbol dynamics and complexity theory is able to effectively extract the complexity quantitatively and characterize complex nonlinear systems.

Based on the above analysis, in order to effectively extract the degradation features of the quay crane hoisting gearbox, combining the symbol dynamics theory and information entropy, on the basis of the existing Basic Scale Entropy, a degradation feature extraction based on static divided symbol sequence entropy is proposed. The analysis and verification are carried out with the Logistic sequence and the lifetime dataset from the gearbox respectively. The paper is organized as follows: Section 2 briefly introduces Basic Scale Entropy and Section 3 proposed the new technique named static divided symbol sequence entropy. The simulated analysis of Logistic sequence is proposed in Section 4. In Section 5, the proposed method is verified and the results are discussed. Finally, the conclusion of this paper is given in Section 6.

Basic Scale Entropy (BSE) is a typical feature analysis method based on static symbol division. It is mainly used in ECG signal processing in medical field [15]. In recent years, it has also some preliminary applications in field of mechanical equipment fault diagnosis [16]. The principle of the basic scale entropy method is as follows:

Supposing u is a one-dimensional time series with length N. Transforming the sequence in phase space:

X(i)=[u(i),u(i + L),…,u(i+(m-1)L)] (1)

Among them, m is the transformation dimension, L is the delay factor which demands i+(m-1)L ≤ N. Generally, L = 1, and the structure of matrix X is: (N-m + 1)×m. Later, symbolizing each m-dimensional vector and converting it to a sequence S with m-dimensional vector symbols.

S_i(X_i)={s(i),s(i + L),…,s(i+(m-1)L)} (2)

In the formula above, s∈A:A={0,1,2,3}, and the principle of symbol symbolization are as follows.

$${S_i}({X_i})=\left\{ \begin{gathered} 0:\overline {u} <{u_{i+k}} \leqslant \overline {u} +a \times BS \hfill \\ 1:{u_{i+k}}>\overline {u} +a \times BS \hfill \\ 2:\overline {u} - a \times BS<{u_{i+k}} \leqslant \overline {u} \hfill \\ 3:{u_{i+k}} \leqslant \overline {u} - a \times BS \hfill \\ \end{gathered} \right.$$

Among them, ū and BS represent the mean and basic scale of the i^th m-dimensional vector, respectively, and BS is defined as follows:

$$BS(i)=\sqrt {\frac{{\sum\limits_{{j=1}}^{{m - 1}} {[u(i+j) - u(i+j - 1)]{}^{2}} }}{{m - 1}}}$$

In the formula above, the arguments a is used as basic scale parameter, which needs to be properly selected in practical applications. This method uses a⋅BS as the symbolization standard.

Counting and calculating the symbol pattern distribution probability P in sequence S. The total pattern of the four symbols is π = 4^m, and the probability of the symbol pattern in S is calculated as follows:

$$p(\pi )=\frac{{Num\{ t|({u_t},{u_{t+}}_{1},...,{u_{t+m - 1}})~~hastype~~\pi \} }}{{N - m+1}}$$

Among them, 1 ≤ t ≤ N-m-1, and Num represents the number.

Finally, the basic scale entropy BSE is calculated as follows:

$$H(m)=\frac{{ - \sum {p(\pi ){{\log }_2}p(\pi )} }}{{{{\log }_2}({4^m})}}$$

According to the principle of basic scale entropy, this method is able to describe the fluctuation pattern of the sequence. The larger the value, the more complex the fluctuation pattern, and vice versa.

The basic scale entropy method takes a⋅BS as the symbolization standard to quantitatively measure the fluctuation pattern, and each series needs to calculate the basic scale BS according to formula (4). This will bring about two shortcomings, firstly, the inconsistency of the basic scale means the difference of the symbolization standard, and it is difficult to uniformly measure the changing of sequence complexity. Secondly, the length of time sequence will affect calculation speed, and the value of the parameter a will affect the symbolization standard.

Based on the above considerations, a feature extraction method of Static Divided Symbol Sequence Entropy (DSSE) is proposed. The principle is as follows:

Step1: Assuming that u is a one-dimensional time series with length N, converting u into an m-dimensional vector X.

X(i)=[u(i),u(i + L),…,u(i+(m-1)L)] (7)

Step2: Symbolizing each m-dimensional vector in turn and converting it into an m-dimensional vector symbol sequence S.

S_i(X_i)={s(i),s(i + L),…,s(i+(m-1)L)} (8)

where s∈A:A={0,1,…,K}, the conversion principle is as follows:

$${S_i}({X_i})=\left\{ \begin{gathered} 1,\left| {u(i)} \right| \leqslant B{S_0} \hfill \\ 2,B{S_0}<\left| {u(i)} \right| \leqslant 2 \times B{S_0} \hfill \\ \cdots \hfill \\ j,(j - 1) \times B{S_0}<\left| {u(i)} \right| \leqslant j \times B{S_0} \hfill \\ \cdots \hfill \\ K,\left| {u(i)} \right|>K \times B{S_0} \hfill \\ \end{gathered} \right.$$

Among them, K means the number of symbols, the symbols set is A={1,2,3,4,5} when K = 5. BS₀ is the basic scale of symbolization, and this parameter adopts a fixed value. In this paper, this parameter is set as the product of the root mean square value of the first group of health condition signal and the coefficient a as follows.

BS ₀ = a*rms(u₁), 0 < a < 2 (10)

In this method, K represents the size of the symbols set that is the number of symbolized regions. The base scale representation represents the size of the symbolized area.

Step3: Counting the symbol pattern distribution probability P in S. The arrangement pattern of K symbols is π = K^m, and the calculation method is the same as formula (5).

Step4: Calculating the entropy DSSE of the static divided symbol sequence entropy as follows:

$${H_0}(m)= - \sum {p(\pi ){{\log }_2}p(\pi )}$$

In order to compare and analyze the influence of parameters selection on the results, the calculation of sequence entropy is not normalized in this paper.

Logistic model, also known as ‘Pest model’ [17], is a typical second-order recursive polynomial, x_t+1 = λ.x_t(1-x_t), which is mainly used in nonlinear dynamics and chaos analysis. The bifurcation diagram of the Logistic model (the initial value is 0.4, the sequence length is 2000) is shown in Fig. 1. When λ is greater than 3.446, the Logistic model begins to oscillate, and when λ is approximately equal to 3.567, it begins to enter a chaotic state. As λ increases, the complexity of the sequence also increases but it also includes non-chaotic sequences, such as the islands of stability phase between λ = 3.829 and 3.86 when the sequence returns from the chaotic state to the initial oscillating state.

The Logistic model is processed by the proposed static divided symbol sequence entropy, where a = 0.2, the effective value of the first group of sequences is 0.666, so the basic scale BS₀ = a*0.666. The number of symbols is set as K = 6, and the DSSE degradation feature curve is shown in Fig. 2. It is obvious that the DSSE curve effectively characterize the process of model complexity from low to high, and at the same time, it is also sensitive to the initial oscillation at λ = 3.446 and the islands of stability phase, indicating that this method is able to effectively characterize the complexity of the nonlinear time series.

A horizontal comparison is made using typical complexity calculation methods, including Basic Scale Entropy [16], Fuzzy Entropy [18], Sample Entropy [19], and C0 complexity [20], the degradation curves of the four methods are shown in Fig. 3. As to the four methods, the overall upward trend is well reflected during the evolution process, but the Basic Scale Entropy and Sample Entropy curves fail to reflect the initial oscillation of the curve, and the complexity of Fuzzy Entropy in the initial oscillation process appears ‘distorted’.

The parameters and computational performance of the above methods are shown in Table 1. The operating environment is Intel Xeon® CPU E5-2450L, Memory 16.0GB, Matlab 2014a. In terms of operation time, C0 complexity is the fastest, while both Fuzzy Entropy and Sample Entropy are slower. The main reason lies that the C0 complexity is a typical structural complexity and only involves Fourier transform and statistical analysis, so it is the fastest in calculation. Fuzzy Entropy and Approximate Entropy are two typical behavioral complexities, due to the phase space transformation involved in the calculation, the calculation amount is large and the calculation time is long. The phase space transformation is also included in calculation proess of DSSE technique, the amount of calculation is greatly reduced however due to the symbolization process. Therefore, the operation speed and structural complexity are almost the same order of magnitude. Therefore, the proposed static divided symbol sequence entropy is able to reflect the changing trend of signal complexity, and the operation is accurate and the speed and time are fast. It is suitable for degeneration feature extraction of mechanical equipment.

Table 1

Typical complexity degradation features setting and calculation time
Methods	Parameters setting	Time(second)
Basic Scale Entropy	m = 4,a = 0.5	0.8931
Static Divided Symbol Sequence Entropy	BS₀ = 0.2*rms(u₁), u₁ is the first group signal	0.8433
Fuzzy Entropy	m = 4, r = 0.2*std(s), n = 10	32.5798
Sample Entropy	m = 4, r = 0.2*std(s)	10.9290
C0 Complexity	a = 0.8	0.3937

5.1 Quay Crane gearbox lifetime vibration loading spectrum

The study object is a gearbox of quay crane hoisting mechanism of a container terminal in Shanghai port, and the signal monitoring platform is the network crane condition monitoring and assessment system (Net-CMAS) and this system monitored vibration, temperature and stress signals online. The full lifetime data is derived from the vertical vibration sensor of the high-speed input shaft of the hoisting gearbox shown in Fig. 4. The signal sampling frequency is 24 kHz and sampling time is 1s, the sampling interval is set as 10s. Every time the data is collected, the system automatically calculates the effective value and stores it as a sample point of vibration loading spectrum sequence. After nearly 7 years and 8 months of on-line monitoring of the crane, some faults occurred at the hoisting gearbox. After shutting down for maintenance, it was found that the faults location was the high-speed input shaft roller bearing of the gearbox, and the failure mode was roller wear as shown in Fig. 5.

During the monitoring period, the Net-CMAS system collected the whole lifetime vibration loading spectrum of the hoisting gearbox from health to failure (the effective value sequence of each sampled signal). In order to facilitate the analysis, the massive loading spectrum is stored in the form of matrix with the 4608*2048 structure, and each row represents the loading spectrum sequence of approximately one day, including a total of 4608 rows of data.

5.2 Loading spectrum static symbolization

Firstly, the process of static symbolization of loading spectrum is introduced. The effective value of the first group of vibration loading spectrum is 1.8784, the parameters are set as a = 0.6, K = 8, so the basic scale of divided symbol BS₀ = a*0.666 = 1.1270. Taking a section of loading spectrum in Fig. 6(a) as an example, the amplitude is symbolized according to the basic scale standard, and the symbolization sequence is shown in Fig. 6(b). Through the static symbolization of the amplitude, the amplitude of the continuous vibration loading spectrum is symbolized as a ‘digitized’ symbol sequence {1,2,3,4}, and the symbol sequence retains the amplitude distribution and variation of the original signal.

5.3 Analysis on effectiveness

Feature extraction is performed on each group of vibration loading spectrum in turn according to the above parameter settings, the entropy sequence dsse_i(i = 1,…,4608)is calculated as shown in Fig. 7. For comparison, the Basic Scale Entropy parameters are set as a = 0.6 and m = 4, and the BSE degradation curve of the lifetime loading spectrum is also obtained and shown in Fig. 8.

It is obvious from the comparison that through the improvement in static symbolization, the DSSE curve shows a relatively regular changing trend. With the deepening of the performance degradation degree, the value gradually increases, and the degradation phase is more obvious. The main reason is that unified basic scale BS0 is used in static symbolization. The deeper the degradation degree, the more large-scale shocks, and the more even in distribution of symbolized sequence pattern. Therefore, the value of the information entropy will increase. At the same time, while maintaining the overall increasing trend, the curve is mixed with a certain volatility, which is determined by large noise and many shocks in vibration signal. In contrast, the basic scale entropy curve is less regular and more volatile, making it difficult to accurately evaluate the degradation condition.

Therefore, the proposed static divided symbol sequence entropy is able to reflect the complexity evolution principle contained in signal amplitude during the performance degradation process. The deeper the performance degradation degree, the larger the value of degradation feature, and compared with the basic scale entropy method, the fluctuation of the curve is greatly reduced, and the overall trend is more obvious, which is more conducive to accurately tracking the performance degradation condition.

5.4 Influence analysis of the parameters

Three groups of vibration loading spectrum are taken as examples to analyze the influence of parameters. The samples include the 1st, 2000th, and 4200th groups and named as G₁, G₂₀₀₀, and G₄₂₀₀ respectively. The loading spectrum time series is shown in Figure.9, the larger the loading spectrum group, the larger the proportion of the large amplitude component. At the same time, since the loading spectrum stores the root mean square value of each group signals, they are all positive values.

The number of symbols K determines the size of symbols set. Setting the parameters as m = 4, a = 0.6, the basic scale of divided symbolization is set as BS₀ = a*0.666 = 1.1270. The number of symbols is set from 3 to 18. Under the condition of each symbol number, calculating three groups of the DSSE value changing curves, the result is shown in Fig. 10. It can be seen that as the number of symbols increases, the DSSE value gradually increases, but remains stable after a certain number of symbols. The main reason is that the number of symbols directly determines the number of symbol sequence patterns (K^m). The initial number of symbols is small, and the pattern distribution of the symbol sequence is uneven. As the number of symbols increases, the pattern of the symbol sequence tends to more uniform, therefore, the value gradually increases. As the value of K increases, when the newly added symbol standard is too high to symbolize the amplitude of this sequence, the DSSE value will not increase any more. At the same time, it can be seen that the lower the group, the smaller the number of symbols when DSSE value is stable, which is consistent with the above analysis, that is, the number of symbols is able to gradually increase the information expression ability of the symbol sequence for high-amplitude signals and improve the complexity resolution of high-amplitude signal regions. Considering that the three sets of curves are stable when K > 7, when using the DSSE technique, K is set as 8 in this paper.

DSSE degradation character curves when symbols number is set as 4, 5, 6, and 7 are shown in Fig. 11 respectively. It is cleared from the comparison that the more the number of symbols, the larger the overall value, and with the increase of the symbols numbers, the DSSE value in the low-amplitude area is gradually stable, and the value of high-amplitude area gradually increases, improving the ability in distinguishing. This is consistent with the analysis conclusion of the above figure.

The value of the basic scale coefficient a will determine the size of the symbol area. Setting the parameters m = 4, K = 8, the basic scale of divided symbolization is set as BS₀ = a*0.666 and the value of a is set from 0.1 to 2. The DSSE curves of three groups under different scale coefficient are shown in Fig. 12. It is clear that with the increase of the scale coefficient, the symbolized area also increases, and the DSSE value gradually increases, but the value gradually decreases after a certain level. The main reason lies that the larger the scale factor, the wider the symbolized area. As to the same group, when the number of symbols is unchanged, with the increase of the coefficient, the symbol sequence pattern can be made more uneven, and the coverage of symbol sequence will increase, so the entropy value of the sequence will increase. After reaching the maximum value, the symbolized area will continue increasing. At this time, the coverage pattern will tend to be uneven, and the high-amplitude symbol sequence pattern will increase, thereby reducing the DSSE value.

At the same time, the lower the group, the value will be smaller when reaching the DSSE maximum. Therefore, the basic scale factor is able to control the accuracy of the symbol sequence's ability to express signal information. When the value is greater than 0.8, the DSSE curves of the three groups are basically stable. Therefore, this parameter is suitable to be set to a > 0.8.

The comparison of DSSE degradation character curves when the basic scale coefficients are set as 0.1, 0.4, 0.8, and 1.2 respectively in Fig. 13. It is clear from the comparison that when the coefficient is small, the overall degradation curve is distorted, which indicates that the parameter selection is unreasonable. As the value increases, the overall resolution gradually increases and becomes stable, which is consistent with the analysis conclusion in the above figure.

In order to extract the degradation feature of quay crane hoisting gearbox, a degradation feature extraction method based on static divided symbol sequence entropy is proposed and the technique is validated with simulation and lifetime vibration signals. The following conclusions are obtained.

(1) The proposed static divided symbol sequence entropy technique improves the basic scale entropy method, the basic scale of symbolization is unified, the symbols number variable and basic scale coefficient are added meanwhile to control the symbolic regions more flexibly. The verification of Logistic model and lifetime loading spectrum shows that this technique is able to sensitively describe the complexity of nonlinear time series. The higher the complexity, the larger the value, thus it is convenient to track the progress of equipment performance degradation.

(2) The symbols number variable and basic scale coefficient are added in this technique, the two parameters are able to change symbol pattern of the symbol sequence, thus affecting the value of DSSE. Among them, the increase of symbols number will gradually increase the information expression ability in high-amplitude region, improving the complexity resolution of the high-amplitude signal region. In addition, the basic scale coefficient is proposed to control the accuracy of symbol sequence's ability in signal information expressing.

(3) Compared with the four common complexity algorithms, namely fuzzy entropy, sample entropy, and C0 complexity, the proposed technique has high computational efficiency and strong anti-noise ability while ensuring the effect of degradation feature extraction. It is suitable to be applied to the degradation feature extraction for mechanical equipments.

FUNDING

This research received specific grant from National High Technology Research Development Plan(2013AA041106), National Natural Science Foundation(62073213), China Postdoctoral Science Foundation(2014M561458).

ACKNOWLEDGMENT

The authors declare no conflict of interest in preparing this article

Data Availability Statements

The data that support the findings of this study are available on request from the corresponding author Bing Wang. The data are not publicly available because they contain information that could compromise research participant privacy.

Hou Meihui, Hu Xiong, Wang Bing,etc. Degradation feature extraction for the ship-to-shore crane turning point based on Weibull distribution, JOURNAL OF VIBRATION AND SHOCK,2019,38(22):198-203+243.
Jagtap H P , Bewoor A K , Kumar R . Failure analysis of induced draft fan used in a thermal power plant using coordinated condition monitoring approach: A case study, Engineering Failure Analysis, 2020, 111:104442.
Tang Zhanjun, Sun Runfa. Fan Bearing Fault Diagnosis Based on Multi-scale Fuzzy Entropy and STOA-SVM,Motor and Control Application,2021,48(12):66-70.
Wang Gongxian, Zhang Miao, Hu Zhihui, etc.Bearing fault diagnosis based on multi-scale mean permutation entropy and parametric optimization SVM, JOUＲNAL OF VIBＲATION AND SHOCK, 2022,41(01):221-228.
Wang Mian, Liu Yong. Fault Diagnosis Method of Rolling Bearing Based on Time-shifted Multi-scale Dispersion Entropy and SVM, Machine Design and Research,2021,37(05):83-87.
Peng Ruitao, Luo Xiuqiang, Luo Yue, etc.Rolling Bearing Fault Diagnosis Based on Information Entropy and Alpha Stable Distribution, Machine Design and Ｒesearch,2021,37(04):92-98.
Chen Mang, Yu Dejie, Gao Yiyuan. Fault diagnosis of rolling bearings based on graph spectrum amplitude entropy of visibility graph, JOUＲNAL OF VIBＲATION AND SHOCK, 2021,40(04):23-29.
Du Xiaolei, Chen Zhigang, Wang Yanxue, etc.Application of morphological empirical wavelet transform and IFractalNet in bearing fault identification. Journal of Vibration Engineering,2021,34(03):654-662.
Xi Maosong, Xu Xin, Pan Hongxia. Early Fault Diagnosis of Supply and Delivery System based on k Value Optimization for VMD and Matrix Fractal, Machine Design and Research,2020,36(02):208-211+215.
Lee Jay, Qiu Hai, Yu Gang,et al. Bearing dataset from IMS of university of Cincinnati and NASA ames prognostics data repository,http://ti.arc.nasa.gov/tech/dashpcoe/prognostic-data-repository.
NECTOUX P,GOURIVEAUR,MEDJAHER K, et al. PRONOSTIA: an experimental platform for bearings accelerated degradation tests, IEEE International Conference on Prognostics and Health Management. Denver,CO,2012.
Yang Baowang. Low-rate-denial-of-service attack detection by symbolic dynamics method,Jounal of XIDIAN University,2018,45(01):140-144.
Xin Yi, Zhao Yizhang, Mu Yuanhui. ECG Feature Analysis Based on Poincare Plot and Symbolic Dynamic, Transactions of Beijing Institute of Technology, 2017,37(10):1084-1089.
Ding Chuang, Feng Fuzhou, Zhang Bingzhi, etc. MMSDE and its application in feature extraction of a planetary gearbox, JOUＲNAL OF VIBRATION AND SHOCK,2020,39(13):97-102+147.
Zhao Tingting, Duan Xiaoli, Yan Bige. Multiscale base-scale entropy analysis of heart rate variability signals in the young and the elderly,Chinese Journal of Medical Physics,2019,36(01):88-91.
Wang Bing, Hu Xiong, Li Hongru, etc. Rolling bearing performance degradation state recognition based on basic scale entropy and GG fuzzy clustering, JOUＲNAL OF VIBＲATION AND SHOCK, 2019,38(05):190-197+221.
Bryson B, Kunze H , Torre D L , et al. A Generalized Multiple Criteria Data-Fitting Model With Sparsity and Entropy With Application to Growth Forecasting. IEEE Transactions on Engineering Management, 2021, (99):1-12.
Li Y , Wang S , Yang Y , et al. Multiscale symbolic fuzzy entropy: An entropy denoising method for weak feature extraction of rotating machinery. Mechanical Systems and Signal Processing, 2022, 162(7):108052.
Sidorenko A V, Saladukha M A. Evaluation of operator's state under the influence of electromagnetic noise generator. System analysis and applied information science, 2021(4):45-53.
Wang Wei, Hu Xiong,Wang Bing,etc.Identification of Degradation State for Bearing Performances Based on C0 Complexity and GG Fuzzy Clustering, Bearing, 2019(12):51-57.

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Degradation Feature Extraction of Quay Crane Gearbox Based on Static Divided Symbol Sequence Entropy

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Abstract

Figures

1 Introduction

2 Theory Of Basic Scale Entropy

3 Proposed Of Static Divided Symbol Sequence Entropy

4 Simulated Analysis Of Logistic Sequence

5 Instance Data Analysis

5.1 Quay Crane gearbox lifetime vibration loading spectrum

5.2 Loading spectrum static symbolization

5.3 Analysis on effectiveness

5.4 Influence analysis of the parameters

6 Conclusion

Declarations

References

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