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- Hongde Dai
^{1}, Juan Li^{2}, Yu Kuang^{3}, Jian Liao^{4}, Qieshi Zhang^{5,*}, and Yuhang Kang^{5}

Human-centric Computing and Information Sciences volume **11**, Article number: 25 (2021)

Cite this article **3 Accesses**

https://doi.org/10.22967/HCIS.2021.11.025

Abstract

The fault diagnoses of the airborne fuel pumps are important to the safety and performance of flight tasks. Therefore, fault information extraction and the methods of fault diagnoses for airborne fuel pumps have become critical areas of study. In this paper, a fault state extraction method for airborne fuel pump is proposed by combining multiscale fuzzy entropy (FE) and particle swarm optimization support vector machine (PSO-SVM). The vibration signals of airborne fuel pumps are non-linear and non-stationary, which makes it difficult to extract fault features. Firstly, a coarse-graining process is applied to address vibration signals of an airborne fuel pump, and several coarse-grained sequences are obtained under different scales. Secondly, the FE is used to calculate the fault features, which contains the main fault information in the first few scales. Then, the feature vectors of fault are divided into training data and test data which used for the fault diagnoses model. The training data is used to train the PSO-SVM model, and the testing data is used to verify the effectiveness of the proposed method. Finally, the vibration signal of the airborne fuel pump on our designed experimental platform is collected, and the dataset is used to test the proposed method. Also, the experimental results show that the proposed method can successfully diagnose faults in airborne fuel pumps.

Keywords

Airborne Fuel Pump, Multiscale Fuzzy Entropy, Entropy, Fault Diagnoses, Support Vector Machine

Introduction

The function of airborne fuel pumps affects the flight stabilization, which plays an essential role in the fuel system [1]. If an airborne fuel pump fails in flight, it can lead to uncontrollable economic losses and affect the safety of pilots [2]. Therefore, fault diagnoses for airborne fuel pump have attracted significant attention of engineers andresearchers [3–5].

In the process of airborne fuel pump fault diagnoses, the research process can be divided into three steps: fault sample collection, fault features extraction, and different fault pattern classifications [6]. The vibration signal and pressure signal can be used as fault samples for conditionmonitoring and fault diagnoses, so fault features extraction isan essential step in airborne fuel pump diagnoses. In the process of fault features extraction, the pressure signal contains less fault information, which is not enough to summarize the fault features of airborne fuel pumps. Therefore, vibration signals are mainly used for fault feature extractions, such as the rolling bearing vibration signal data set of Case Western Reserve University, which provides a wealth of research on mechanical system fault diagnoses [7]. Muralidharan and Sugumaran[8] extracted fault features with the discrete wavelet transform (DWT) from the vibration signals of centrifugal pumps, and then the features are used to be classified intofive states, including normal, cavitation, bearing fault, impeller fault, and impeller. For these fault samples, the fault features was extracted with a wavelet transform (WT) and classified with a support vector machine (SVM) [9], which proves the rationality of applying vibration signals to summarize the fault information of centrifugal pumps [10].

Time domain statistical information such as the peak index, kurtosis index, impulsion index, tolerance index and root mean square are used as fault features to summarize the fault information of vibration signals [11]. When an airborne fuel pump works with high intensity, its operational state often appears uncertainty, and the vibration signals also present non-linear and non-stationary state. Therefore, it is necessary to extract the fault state featuresof vibration signals accurately [12]. In the analysis of non-linear vibration signals, the traditional time domain and frequency domain statistical information can not accurately and completely summarize the fault features. With the development of non-linear analysis theory, many classical non-linear algorithms have been used for fault feature extraction.For the fault diagnoses of bearings, correlation dimension and naïve Bayes are combined by Zhang et al.[13]; Kappaganthu and Nataraj[14] focused on developing a non-linear model for the rotor-bearing system on roller bearings with Lyapunov. However, in the calculation process of the correlation dimension, the requirement of the vibration signal is much stricter; Lyapunov estimation rarely relies on noise in the data, and the result of Lyapunov is usually unstable.

Entropy is a measurement of the disorder or randomness of system energy, which can be used for information extraction of vibration signals. In 1991, the approximate entropy (ApE) was proposed by Pincus[15] to measure the percentage of new patterns in time series, butthe effectiveness of ApE depends on the series length largely. In 2000, Richman and Moorman[16]defined the theory and characteristics of sample entropy (SE) to enhance the performance of ApE. Nevertheless, a definite time series model is required to calculate the SE. Fuzzy entropy (FE) is used to measure the probability of a new model when the dimension of the time series is modified and to reflect the complexity and irregularity of the time series, which can be used in the research of electromyography signal analysis [17,18], autism spectrum disorder signal analysis [19], and rolling bearing vibration signal analysis [20]. However, due to the sophistication and integrity of airborne fuel pumps, the non-linear fault feature of the vibration signals shows different characteristics in different scales, which makes it difficult and fragmentary to extract the characteristics of vibration signal by FE.Therefore, it is essential to extract fault feature of vibration signals with FE at different scales.

After the extraction of fault features from vibration signals, fault pattern classification is accomplished. For fault state recognition problems, many classification algorithms can be adopted, such as SVMs and artificial neural networks (ANNs) [21]. An airborne fuel pump is a complex electromechanical system, and its mathematical or physical model is difficult to establish accurately; hence, there are few fault samples from airborne fuel pumps. SVM is based on the minimization of statistical and structural risks and itcan be successfully applied with a few fault samples. Particle swarm optimization (PSO) is applied to adaptively pick out the optimum penalty parameter and kernel function parameters of the SVM model, which can enhance the accuracy of SVM [22].

Aiming at the fault diagnoses problems of airborne fuel pumps acquired from different sensors and motivated by the works above, a multiscale FE-based fault diagnoses method is proposed. The vibration signal of airborne fuel pumps is processed by coarse graining, and several coarse-grained series under different scale factors are obtained. Then, the FE of the first few scale factors is calculated as the fault features, and the fault diagnoses model is obtained by a PSO-SVM. Finally, the fault diagnoses of airborne fuel pumps are accomplished successfully.

The rest parts are structured as follows: in Section 2, we describe the experimental platform for airborne fuel pumps, and the fault information extraction algorithm based on multiscale FE is introduced in Section 3. Then the fault samples and experimental results are discussed in Section 4. Lastly, the conclusion can be found in Section 5.

Verification Platform for Airborne Fuel Pump

To study and monitor the working characteristics and fault state of an airborne fuel pump system, an experimental verification platform is designed. The platform is mainly composed of centrifugal airborne fuel pump, a secondary fuel tank, a main fuel tank, a valve, a real fuel pump and an experimental device. The structure of the fuel pump calibration system is shown in Fig. 1 which includes three vibration sensors and one pressure sensor, data acquisition equipment, a mainframe, a monitor, etc., which are used to collect the vibration and pressure signals of the normal state and different fault states during the operation of the fuel pump.

To collect the fault samples on the experimental platform, several vibration sensors are mounted on the shell of the fuel pump through the magnetic base. Here we use three vibration sensors to capture the single as Fig. 2 shown. The pressure sensors are located 60cm and 80cm away from the pump outlet port.

The functions of the four sensors are as follows: vibration sensor 1 is used to measure the axial vibration acceleration of the fuel pump, vibration sensors 2 and 3 measure the radial vibration acceleration of the fuel pump, and pressure sensor 4 measures the outlet pressure, and then convert the measured vibration signal and pressure signal into an electrical signal. The sampling frequency is 6,000Hz. Signals from the four sensors are transmitted to the data acquisition equipment in a parallel way. The data acquisition equipment filters the electrical signal transmitted by the sensor, and then converts the analog signal into digital signal through an A/D converter. Then the data acquisition equipment will input the processed vibration signal and pressure signal into the computer, and the computer will save these experimental data in text format.

All the time-domain airborne fuel pump signals of the three vibration sensors and one pressure sensor are shown in Fig. 3, which are the acceleration of three vibration sensors and pressure from the pressure sensor. From Fig. 3, the signals are non-linear and non-stationary.

At present, there are few studies on the failure modes of airborne fuel pumps, and there is a lack of failure samples in the process of fault diagnoses. In this paper, first, a verification platform for an airborne fuel transmission system is designed to simulate the working process of a fuel pump in a fuel tank. Second, for the classic failure mode of an airborne fuel pump, fault experiments are carried out through the design, production, and collection for faulty parts, and data collection is carried out.

Fault Information Extraction Method Based on Multiscale Fuzzy Entropy

Fuzzy Entropy

A new measure of time series regularity was proposed by Chen et al.[17]in 2007, which can be used for the characterization of surface electromyography signals. Compared to SE, FE is a negative natural logarithm of the conditional probability that two vectors similar to m points remain similar for the next m+1 points [23]. The FE procedures are detailed as follows.1) A normalized time series {$x(i),1≤ i ≤ N$} with length N is defined, and a vector set series $X_i^m$ is designed in the following form:

*(1)*

*(2)*

*(3)*

3) The similarity value $D_{ij}^m$ between $X_i^m$ and $X_j^m$ can be defined as:

*(4)*

4) Function $ϕ^m (n,r)$ is defined as:

*(5)*

*(6)*

*(7)*

*(8)*

Multiscale Fuzzy Entropy

Based on coarse-grained theory [24], multiscale FE (MFE) is defined in the following steps.
1) Define a N length normalized time series {$x(i),1≤i ≤ N$}, and a coarse-graining series {$y_j^{(τ)}$}:
*(9)*

2) The FE value of each coarse-graining time series is collected and described as a function of the scales. The FE value at different scales is called the MFE value [25].

To calculate the MFE, four parameters will be set: the embedding dimension m, the boundary width r, the boundary gradient n, and the scale factor τ. The embedding dimension delay m has a large effect on the calculation of FE. Classically, m is selected as 2. The boundary width r and boundary gradient n determine the characteristics of FE. If the value is too small, it will be sensitive to noise, while a large value will result in the loss of information. Generally, r is selected to be 0.1–0.25, and n is selected to be 2. The scale factor τ has an indirect effect on the calculation of MFE. Classically, τ is selected to be 5–10.

Entropy is the measurement parameter of the disorder or randomness of energy in a time series and it can be used to reflect the feature of signals. In [17], the authors developed FE as the feature information on electromyography time series, which indicated that FE has a much stronger relation than SE. In [21], FE was used to represent the characteristic feature of a bearing vibration signal. The FE value of the fixed length vibration signal sequence is calculated as the characteristic value of the vibration signal to realize the feature representation of the vibration signal with different fault types.

Fault Classification Algorithm Based on PSO-SVM

After fault feature of vibration signals is extracted, fault pattern described using fault features need to be classified. In the process of mechanical system fault diagnoses and analysis, fault state recognition can be defined as a tool based on data processing and fault feature extraction. Therefore, the method for fault state identification should be concise and adaptive. On this basis, the classical SVM algorithm can be used as a tool for fault state recognition, which is fast and simple. It can also be used to prove the effectiveness of fault feature extraction method. Furthermore, applying PSO as an adaptive optimization algorithm can improve the adaptability of SVM. To realize the classification of fault features, a fault diagnoses algorithm based on MFE and SVM is proposed. SVM is an intelligent algorithm which has been extensively used in machine learning fields [26].

The SVM is used to enhance the original feature vector to a high-dimensional feature space with non-linear mapping [27]. The SVM model is defined as follows:

(1) The given samples are defined as ($x_i,y_i$),$i=1,2,…,l,$ where $x_i$ is the input value and $y_i ϵR$ is the output value.

(2) Kernel function selection. In the SVM model, the kernel function K(∙,∙) is important. There are four functions: the linear function, polynomial function, radial basis function,and sigmoid kernel function. In this paper, the radial basis function is selected as the kernel function,

*(10)*

(3) According to the maximal-margin rule, the target function and the constraint condition can be defined,

*(11)*

(4) According to the Karush-Kuhn-Tucker (KKT) conditions, the SVM model is converted to:

*(12)*

In PSO, each particle in the problem space maintains its position and velocity, and the initial position and velocity are randomly generated [28]. In the n-dimensional space the position and velocity of the i-th particle can be defined as:

*(13)*

The updated positions and velocities of the particles are calculated by

*(14)*

When the airborne fuel pump fails, both the vibration signal and the pressure signal contain abundant fault information. Domestic and foreign scholars have widely implemented the intelligent fault diagnoses of fuel pumps by extracting the fault characteristics of vibration signals and pressure signals. However, fault diagnoses can be obtained by comparing vibration signal with pressure signal. In the fault diagnoses of mechanical system, the vibration signal is easier to obtain and more stable. The fault diagnoses algorithm of airborne fuel pump proposed in this paper is as follows.

Fault sample collection. The vibration signals of the (x, y,z) axis and the pressure signals are collected. It was found in our previous study [30] that the output signal of the second vibration sensor (y-axis) contained more obvious fault information, so the vibration signal of they-axis was selected for fault feature extraction. In step (1), the combination of the vibration signals and pressure signals is usually used in traditional airborne fuel pump fault diagnoses. Applying MFE as the feature information can achieve data feature extraction with fewer signals, reducing the sensors needed in the condition monitoring systems of airborne fuel pumps, which is of great important significance in engineering practice.

Feature extraction. The y-axis vibration signal is used to calculate the MFE values of each fault sample from the airborne fuel pump while establishing parameters. The scale factor τ=10, thus 10 features are collected to express the fault information.

According to the analysis in [31], the complexity change usually emerges into a higher frequency, and airborne fuel pumps' fundamental fault information tends to concentrate on higher frequency components. Therefore, the first 5 MFE values that fundamentally express the complexity of fault samples at a higher frequency are collected to build the feature vectors for diagnoses. The analysis shows that the variation of complexity often presents a higher frequency, and the basic fault information of the onboard fuel pump is usually concentrated on the higher frequency components.

Inputs of classifier setting. The extracted feature vectors are set as the inputs of the PSO-SVM classifier.

The results of the testing samples are output to automatically fulfill fault diagnoses. The proposed algorithm for MFE-PSO-SVM-based airborne fuel pump fault diagnoses algorithm is described briefly in Fig. 6.

Experiment Results

To evaluate the capability of the fault diagnoses algorithm, experimental analysis on airborne fuel pump faults is conducted. The length of the airborne fuel pump vibration signal sequences is 2048. There are seven types of faults and each type has 30 vibration signals, and 210 samples are randomly selected from all fault samples. In these 30 samples, the training data and test data are half of the random samples.

In the experiment, the feature vectors based on MFE are set as the input of classifier, and the output is the diagnostic type label corresponding to each fault state, label-1 is normal, label-2 is diffusion tube damage, label-3 is diffusion tube damage with impeller rub, label-4 is leakage, label-5 is blade damage, label-6 is the back of the impeller with diffusion tube rub, and label-7 is the pump port with impeller rub. In our previous study we found that the vibration signals of the y-axis are contained enough information to diagnoses the fuel pump [1, 25], so only the vibration sensor of the y-axis was used for the fault diagnoses. All the time-domain airborne fuel pump vibration signals with the seven states on the y-axis are shown in Fig. 7, and it is difficult to completely distinguish the states of airborne fuel pump vibration signals from the time-domain signals.

Results

(a) SVM diagnoses and (b) PSO-SVM diagnoses.

The accuracy of the SVM classifier for 105 test sets composed of FE feature vectors is 67.619% (71/105), and the accuracy of the PSO-SVM classifier is 76.191% (80/105). As shown in Fig. 8, many samples in the fault diagnoses results have been misclassified based on FE. In other words, FE cannot ideally summarize the vibration signals’ fault information. The outputs and classification results of SVM and PSO-SVM for all test data are as Fig. 8(a) and 8(b) shown, from which it can be found that the amount of misclassified data by PSO-SVM is less than that by SVM; therefore, the comparison results show that the PSO-SVM can obtain a better result than others.

The classification results as Fig. 10(a) shown, which include the desired and trained SVM outputs, and the results of PSO-SVM are shown in Fig. 10(b).

(a) SVM diagnoses results and (b) PSO-SVM diagnoses results.

1) Multiscale signals are obtained by EMD, which decomposes an original vibration signal of an airborne fuel pump into the IMF.

2) The cross-correlation criterion is used to select IMF as the study of[32] described.

3) The feature vector is computed and obtained by FE of each IMF with fault information.

4) The SVM classifier is used to classify the feature vectors for fault diagnoses.

The classify result of SVM is 91.429% (91/105) which uses 105 testing sets with the feature vectors consisted of EMD-FE, and the accuracy of the PSO-SVM classifier is 95.238% (96/105). As shown in Fig. 11, PSO-SVM misclassified fewer samples than FE in the fault diagnoses results, which shows that the multiscale time series contains more fault information than the original time series. Compared with the results in Fig. 10, the feature vectors based on MFE contain more fault information than those in EMD-FE.

The classification results of different algorithms are shown in Table 1. Values such as “2” and “6” in the table represent correct results, which are classified by different classification algorithms for different samples of the 15 test sets in each state.

Overall, the experimental shows that:

1) The experimental platform represents the different working status of airborne fuel pumps, and can provide fault samples for fault diagnoses.

2) The vibration signal contains abundant fault information, and the fault diagnoses can be completed only by the vibration signal acquired from the y-axis. Compared with the combination of the vibration signal and pressure signal, MFE can express fault features with less sensor data.

3) MFE is used to analyze the fault samples at multiple scales due to the non-linear and non-stationary vibration signals, and the results show that MFE has the advantages in accuracy and has good application prospects in analyzing non-linear feature information correctly.

4) PSO algorithm is applied to the adaptive selection of kernel function parameters and optimal penalty parameters, which improves the classification performance of SVM algorithm.

5) As shown in the experiment, each class has 15 samples for training and 15 samples for testing. Therefore, 105 and 105 samples were used for training and testing, respectively. Due to the limited number of fault samples, the next step of research can consider the ability to extract fault information in large samples.

(a) SVM diagnoses results and (b) PSO-SVM diagnoses results.

Fault diagnosis method | Fault type label | Accuracy (%) | ||||||
---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | ||

FE-SVM | 2 | 15 | 15 | 1 | 14 | 12 | 12 | 67.619 |

FE-PSOSVM | 6 | 8 | 15 | 14 | 14 | 8 | 15 | 76.1905 |

EMD-FE-SVM | 15 | 13 | 15 | 15 | 7 | 11 | 15 | 86.6667 |

EMD FE-PSOSVM | 15 | 13 | 15 | 14 | 13 | 12 | 14 | 91.4286 |

MFE-SVM | 10 | 15 | 15 | 15 | 15 | 15 | 15 | 95.2381 |

MFE-PSOSVM | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 100 |

Conclusion

In this paper, a method based on multiscale FE and PSO-SVM is proposed for fault state diagnoses to ensure airborne fuel pumps safe. We applied the coarse-graining process to process the vibration signals of the airborne fuel pump, and obtain several coarse-grained sequence under different scale factors. Then, the FE is used to calculate the fault characteristics.The collected dataset is decomposed into training set and test set to train and test our proposed method to perform the fault diagnoses. Finally, a PSO-SVM based fault diagnoses method of airborne fuel pumps is achieved.In order to verify the reliability and validity of the proposed method, extensive experiments are carried out. The results show that our proposed method achieves the best performance.

Acknowledgements

Not applicable.

Author’s Contributions

Conceptualization, HD, JuL, YK, JiL.Investigation and methodology, HD, JuL, YK, QZ. Writing of the original draft, HD, JuL.Writing of the review and editing, HD, YK, JiL, QZ, YHK. Validation, HD, JuL, YK, YHK. Visualization, HD, JuL, YK. Supervision, JiL, QZ, YHK.

Funding

This work was supported by the Shandong Natural Science Foundation of China (No. ZR2017MF036), Defense Science and Technology Project Foundation of China (No. F062102009), The Young innovation team of colleges and universities in Shandong province (No. 2020KJN003), Science & Technology Project of Jiangxi Educational Committee (No. GJJ201410), and National Natural Science Foundation of China (No. U1913202 and U1813205).

Competing Interests

The authors declare that they have no competing interests.

Author Biography

**Name : Hongde Dai**

**Affiliation :** School of Basic Sciences for Aviation, Naval Aviation University

**Biography :** He received the Ph.D degree in Northwestern Polytechincal University China. Now he is an Associate Professor with School of Basic Sciences for Aviation, Naval Aviation University. His main research interests include inertial technology and integrated navigation,filtering and estimation theory, and reliability theory. E-mail：dihod@126.com

**Name : Juan Li**

**Affiliation :** College of Mathematics and Information, Lu Dong University

**Biography :** She received the Ph.D degree in Air Force Engineering University, China. Her main research interests include Prognostic and health management, Statistic analysis and reliability theory. E-mail：daidaiquanquan123@126.com

**Name : Yu Kuang**

**Affiliation :** Sun Yat-sen University, China.

**Biography :** Yu Kuang obtained the B.S. degree in software engineering from East China Jiaotong University in 2011 and the M.S. degree in computer science and technology from JiangxiAgricultural University in 2014. Since 2020, he has been working at Sun Yat-sen University, China. His research interests include flight simulation, intelligent algorithm and computer vision.

**Name : Jian Liao**

**Affiliation :** Gannan Normal University, China

**Biography :** Jian Liao received the B.S. degree in measurement and control engineering, the M.S. degree in control science and engineering and Ph.D. degree in control science and engineering from Naval Aeronautical and Astronautical University, China, in 2007, 2009 and 2014, respectively. Since 2020, he has been working at Gannan Normal University, China. His research interests include fault diagnosis, artificial intelligence and machine learning.

**Name : QieshiZhang**

**Affiliation :** Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences

**Biography :** Qieshi Zhang received the Ph.D.degrees from Waseda University, Japan. From 2010 to 2012, he was a Research Fellow with the Japan Society for the Promotion of Science (JSPS), Japan. From 2012 to2019, he was Research Assistant, ResearchAssociate, and Adjunct Researcher with the Information, Production andSystems Research Center (IPSRC), WasedaUniversity, Japan. He is currently an Associate Professor with the Shenzhen Institutesof Advanced Technology, Chinese Academy of Sciences, China. He hasauthored or co-authored over 70 scientific articles in international journalsand conferences. His current research interests are artificial intelligence,unmanned drive, robot etc.

**Name : YuhangKang**

**Affiliation :** Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences

**Biography :** Yuhang Kang received the B.S. degree in measurementand control engineering, the M.S. degreein control science and engineering and Ph.D. degreein control science and engineering from NavalAeronautical and Astronautical University, China, in2011, 2013 and 2017, respectively. Since 2018, hehas been with the Shenzhen Institutes of AdvancedTechnology, Chinese Academy of Sciences, wherehe is currently an Assistant researcher with theHuman Machine Control Laboratory. His researchinterests include cooperative control of multi-agentsystem and consensus problem.

References

[1] J. Li, B. Jing, H. Dai, X. Jiao, and X. Liu, “Remaining useful life prediction based on variation coefficient consistency test of a Wiener process,” Chinese Journal of Aeronautics, vol. 31, no. 1, pp. 107-116, 2018.

[2] J. Li, B. Jing, Z. Sheng, F. Lu, X. Jiao, and H. Dai, “GARCH based degradation modeling of solder joint under vibration loading,” in Proceedings of 2017 Prognostics and System Health Management Conference (PHM-Harbin), Harbin, China, 2017, pp. 1-5.

[3] Y. Zhang, L. You, and C. Jia, “Fault detection and diagnosis using Bayesian-network inference,” in Proceedings of the43rd Annual Conference of the IEEE Industrial Electronics Society (IECON), Beijing, China, 2017, pp. 5049-5053.

[4] S. Chakraborty, E. Keller, and A. Ray, “Data driven anomaly detection via symbolic identification of complex dynamical systems,” in Proceedings of 2009 IEEE International Conference on Systems, Man and Cybernetics, San Antonio, TX, 2009, pp. 3745-3750.

[5] B. Cai, H. Liu, and M. Xie, “A real-time fault diagnosis methodology of complex systems using object-oriented Bayesian networks,” Mechanical Systems and Signal Processing, vol. 80, pp. 31-44, 2016.

[6] L. M. Wang and Y. M. Shao, “Crack fault classification for planetary gearbox based on feature selection technique and k-means clustering method,” Chinese Journal of Mechanical Engineering, vol. 31, article no. 4, 2018. https://doi.org/10.1186/s10033-018-0202-0

[7] W. A. Smith and R. B. Randall, “Rolling element bearing diagnostics using the Case Western Reserve University data: a benchmark study,” Mechanical Systems and Signal Processing, vol. 64, pp. 100-131, 2015.

[8] V. Muralidharan and V. Sugumaran, “Rough set based rule learning and fuzzy classification of wavelet features for fault diagnosis of monoblock centrifugal pump,” Measurement, vol. 46, no. 9, pp. 3057-3063, 2013.

[9] M. J. J. Ghrabat, G. Ma, I. Y. Maolood, S. S. Alresheedi, and Z. A. Abduljabbar, “An effective image retrieval based on optimized genetic algorithm utilized a novel SVM-based convolutional neural network classifier,” Human-centric Computing and Information Sciences, vol. 9, article no. 31, 2019. https://doi.org/10.1186/s13673-019-0191-8

[10] V. Muralidharan, V. Sugumaran, and V. Indira, “Fault diagnosis of monoblock centrifugal pump using SVM,” Engineering Science and Technology, an International Journal, vol. 17, no. 3, pp. 152-157, 2014.

[11] N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung,and H.H. Liu, “The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings Mathematical Physical & Engineering Sciences, vol. 454, no. 1971, pp. 903-995, 1008. https://doi.org/10.1098/rspa.1998.0193

[12] X. Jiao, B. Jing, Y. Huang, J. Li, and G. Xu, “Research on fault diagnosis of airborne fuel pump based on EMD and probabilistic neural networks,” Microelectronics Reliability, vol. 75, pp. 296-308, 2017.

[13] N. Zhang, L. Wu, J. Yang, and Y. Guan, “Naive Bayes bearing fault diagnosis based on enhanced independence of data,” Sensors, vol. 18, no. 2, article no. 463, 2018. https://doi.org/10.3390/s18020463

[14] K. Kappaganthu and C. Nataraj, “Nonlinear modeling and analysis of a rolling element bearing with a clearance,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 4134-4145, 2011.

[15] S. Pincus, “Approximate entropy (ApEn) as a complexity measure,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 5, no. 1, pp. 110-117, 1995.

[16] J.S. Richman and J.R. Moorman, “Physiological time-series analysis using approximate entropy and sample entropy,” American Journal of Physiology Heart & Circulatory Physiology, vol. 278, no. 6, pp. 2039-2049, 2000.

[17] W. Chen, Z. Wang, H. Xie, and W. Yu, “Characterization of surface EMG signal based on fuzzy entropy,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 15, no. 2, pp. 266-272, 2007.

[18] F. Hao, G. Min, M. Lin, C. Luo, and L. T. Yang, “MobiFuzzyTrust: an efficient fuzzy trust inference mechanism in mobile social networks,” IEEE Transactions on Parallel and Distributed Systems, vol. 25, no. 11, pp. 2944-2955, 2014.

[19] Z. Cao and C. T. Lin, “Inherent fuzzy entropy for the improvement of EEG complexity evaluation,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 1032-1035, 2017.

[20] J. Zheng, Z. Jiang, and H. Pan, “Sigmoid-based refined composite multiscale fuzzy entropy and t-SNE based fault diagnosis approach for rolling bearing,” Measurement, vol. 129, pp. 332-342, 2018.

[21] J. Zheng, H. Pan, and J. Cheng, “Rolling bearing fault detection and diagnosis based on composite multiscale fuzzy entropy and ensemble support vector machines,” Mechanical Systems and Signal Processing, vol. 85, pp. 746-759, 2017.

[22] E. Garcia-Gonzalo and J. L. Fernandez-Martinez, “A brief historical review of particle swarm optimization (PSO),” Journal of Bioinformatics and Intelligent Control, vol. 1, no. 1, pp. 3-16, 2012.

[23] Y. Li, B. Miao, W. Zhang, P. Chen, J. Liu, and X. Jiang, “Refined composite multiscale fuzzy entropy: localized defect detection of rolling element bearing,” Journal of Mechanical Science and Technology, vol. 33, no. 1, pp. 109-120, 2019.

[24] J. Zheng, D. Tu, H. Pan, X. Hu, T. Liu, and Q. Liu, “A refined composite multivariate multiscale fuzzy entropy and Laplacian score-based fault diagnosis method for rolling bearings,” Entropy, vol. 19, no. 11, article no. 585, 2017. https://doi.org/10.3390/e19110585

[25] J. Zheng, J. Cheng, Y. Yang, and S. Luo, “A rolling bearing fault diagnosis method based on multi-scale fuzzy entropy and variable predictive model-based class discrimination,” Mechanism and Machine Theory, vol. 78, pp. 187-200, 2014.

[26] X. Zhang, Y. Liang, and J. Zhou, “A novel bearing fault diagnosis model integrated permutation entropy, ensemble empirical mode decomposition and optimized SVM,” Measurement, vol. 69, pp. 164-179, 2015.

[27] J. Zhu, P. Sun, Y. Gao, and P. Zheng, “Clock differences prediction algorithm based on EMD-SVM,” Chinese Journal of Electronics, vol. 27, no. 1, pp. 128-132, 2018.

[28] C. M. Lee and C. N. Ko, “Time series prediction using RBF neural networks with a nonlinear time-varying evolution PSO algorithm,” Neurocomputing, vol. 73, no. 1-3, pp. 449-460, 2009.

[29] J. Ma, J. D. Wu, Y. G. Fan, X. D. Wang, and Z. K. Shao, “Fault diagnosis of rolling bearing based on the PSO-SVM of the mixed-feature,” Applied Mechanics and Materials, vol. 380, pp. 895-901, 2013.

[30] J. Li, B. Jing, X. Qiang, and X. Liu, “Fault states feature extraction and experimental study for airborne fuel pumps based on sample quantile,” ActaAeronautica et AstronauticaSinica, vol. 37, no. 9, pp. 2851-2863, 2016.

[31] Y. Li, M. Xu, R. Wang, and W. Huang, “A fault diagnosis scheme for rolling bearing based on local mean decomposition and improved multiscale fuzzy entropy,” Journal of Sound and Vibration, vol. 360, pp. 277-299, 2016.

[32] H. Wang, R. Li, G. Tang, H. Yuan, Q. Zhao, and X. Cao, “A compound fault diagnosis for rolling bearings method based on blind source separation and ensemble empirical mode decomposition,” PLoS One, vol. 9, no. 10, article no. e109166, 2014. https://doi.org/10.1371/journal.pone.0109166

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Hongde Dai^{1}, Juan Li^{2}, Yu Kuang^{3}, Jian Liao^{4}, Qieshi Zhang^{5,*}, and Yuhang Kang^{5}, Multiscale Fuzzy Entropy and PSO-SVM Based Fault Diagnoses for Airborne Fuel Pumps, Article number: 11:25 (2021) Cite this article 3 Accesses

**Recived**31 March 2021**Accepted**29 May 2021**Published**15 June 2021

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