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Improved GA-PSO algorithm for feature extraction of rolling bearing vibration signal

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Published/Copyright: May 5, 2023
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Paladyn, Journal of Behavioral Robotics
From the journal Paladyn, Journal of Behavioral Robotics Volume 14 Issue 1

Abstract

To better extract the characteristics of rolling bearing vibration signals, the author proposes a method based on improved genetic algorithm-particle swarm optimization (GA-PSO) algorithm. The common time-domain and frequency-domain feature index construction vectors were extracted based on vibration signals, for signal prediction, by establishing an improved particle swarm algorithm, and by optimizing the signal feature model of the support vector machine (SVM), the signal of the rolling bearing was predicted. The experimental results show that: After the author’s improved particle swarm algorithm optimizes SVM, the signal characteristic accuracy of the bearing is significantly higher, the regression fitting curve is smoother, although the fitting trend is basically the same, the error is significantly higher, this shows that it is feasible to optimize SVM’s rolling bearing signal characteristics based on particle swarm optimization, and proved the author’s improvement of the particle swarm algorithm, it is effective in optimizing SVM parameters. It is proved that the improved GA-PSO algorithm can better extract the characteristics of the vibration signal of the rolling bearing.

Keywords: rolling bearing; improved particle swarm algorithm; support vector machine; signal extraction; vibration signal

1 Introduction

With the continuous progress of society and the continuous development of science and technology, great progress has been made in the field of modern industry. In many industrial production fields, the importance of the mechanical equipment system is becoming more and more important. To liberate the labor force, improve industrial production efficiency, and improve the level of modern science and technology, the mechanical equipment system is becoming more integrated, more automated, more complex, and more intelligent [1]. The improvement of machinery and equipment can not only liberate more labor force but production efficiency and product quality have also been qualitatively improved. Although we are enjoying the benefits of modern equipment and mechanical systems, it also caused a series of problems. As the structure of the mechanical equipment system is becoming more complex and integrated, the connection of various components in the mechanical equipment system is also closer than before [2]. This allows the realization of condition-based maintenance of the mechanical equipment system, brings new problems and challenges that have never been seen before. As shown in Figure 1, due to the integration of mechanical equipment systems, the connection between machinery and various components of the equipment has been greatly improved compared to the past. This leads to damage to any part of the mechanical equipment system, may cause the entire mechanical equipment system to malfunction, trigger a series of chain reactions, produce unpredictable safety production accidents, or cause unnecessary economic losses, what’s more, there may be catastrophic accidents such as casualties, which cause extremely bad social adverse effects [3].

Figure 1 Feature extraction of rolling bearing vibration signal.
Figure 1

Feature extraction of rolling bearing vibration signal.

This article contributes in people’s requirements for the safety and reliability of mechanical systems as it is becoming more and more stringent than before. This domain is specifically flourishing especially for the mechanical equipment system and commonly used to accurately predict the remaining useful life of key components (Remaining Useful Life [RUL]) requirements. The work proposed in this article provides improved outcomes and ensures the stable and reliable operation of the mechanical equipment system as far as possible. It has become an important topic in many scientific research fields [4]. Each file contains fan and drive side vibration data, as well as motor speed. In all files, variable names are displayed and interpreted as follows:

DE – drive-end accelerometer data drive-end acceleration data;

FE – fan-end accelerometer data drive fan-end acceleration data;

BA – base accelerometer data drive base acceleration data;

time – time series data time drive series data;

RPM – rpm during testing revolutions per minute, divided by 60 for the rotational frequency.

A total of 4 normal samples, 77 outer ring damage samples, 40 inner ring damage samples, and 40 rolling element damage samples were obtained using the test bench.

The rest of this article is organized as follows: Section 2 represents literature review followed by the mechanism of improved PSO algorithm described in Section 3. Section 4 provides the experimental results and analysis, which is followed by conclusion in Section 5.

2 Literature review

Qu et al. choose empirical mode decomposition to decompose the vibration signal of rolling bearing, extract features, and find the correlation dimension of the vibration signal from the decomposed modal components, and finally, the radial basis function neural network is used to identify the fault of the rolling bearing [5]. Pan et al. proposed an intelligent diagnosis method for rolling bearings. First, they used complementary ensemble empirical mode decomposition, did a modal decomposition of the fault signal of the bearing, and extracted features and constructed feature vectors based on the decomposed modalities. Finally, they used back propagation network to identify the state of the bearing [6]. In the work of Cheng et al., to solve the difficult problem of early fault diagnosis of low-speed rolling bearings, principal component analysis is used to reduce the dimensionality of fault features, diagnose using support vector machine (SVM) and multi-level correlation vector machine respectively, experimental results show, this method still has high classification accuracy after dimensionality reduction [7]. Dumitrescu and Cardos presented a study using morphological wavelet transform to process bearing vibration signals. On this basis, the signal features are extracted and then the least squares SVM classifier is used for fault classification. The result shows that compared with wavelet transform and neural network, the effect of bearing feature extraction is better in this method, and the accuracy of fault classification is higher [8]. Yan et al. studied the fault diagnosis method of rolling bearing based on multiclass SVM, used wavelet transform for pre-signal processing, and then extracted features from the preprocessed signal, and adopted hybrid particle swarm optimization technology to improve the classification accuracy of bearing faults. Experiments have verified that the classification performance of this method is good [9]. Jiang et al. decomposed the vibration signal of the rolling bearing using the empirical mode decomposition method and then calculated the energy characteristics corresponding to each frequency band. Using this as the input of the neural network, the fault diagnosis of the bearing is realized [10].

Soleimani and Kannan proposed the supervised ISOMAP (supervised-isometric feature mapping [S-ISOMAP]); this algorithm adds category information to the ISOMAP algorithm, changes the ISOMAP algorithm from unsupervised to supervised learning, and realizes the visual classification of data [11]. Zhang et al. researched on the laplacian eigenmaps algorithm and found that this algorithm is very effective in eliminating redundant features in data, and that it can improve the recognition accuracy [12]. Shanmukhi et al., aiming at the problem that the locally linear embedding algorithm can only deal with the dimensionality reduction of densely sampled samples, proposed Hessian local linear embedding (HLLE). The result of algorithm verification shows that the HLLE algorithm can maintain the inherent characteristics of the data set corresponding to the manifold; therefore, the dimensionality reduction effect is better [13]. Küükuurlu and Gedikli introduced variational mode decomposition to preprocess bearing signals and then used the manifold learning algorithm for dimensionality reduction; it also shows that the manifold learning itself has poor noise suppression ability [14]. Singh and Chaudhary proposed a dual-tree complex wavelet noise reduction method based on maximum variance unfolding. This method can prevent waveform distortion after noise reduction; at the same time, the effect of removing redundant features is better, and the classification accuracy is higher [15]. Wang et al. proposed a technique for the extraction and classification of image features by employing a Fuzzy SVM. The experimental analysis reveals good performance and a new direction for producing comfortable footwear [16]. Ansari et al. used various mechanical equipment of different sizes for feature extraction from digital images. The extracted features are more informative in their approach when compared with other studies [17]. Nayak et al. proposed an approach for the prediction of stock closing prices by employing neural networks. The performance of the model is evaluated from mean absolute percentage error and average relative error. It is observed from the analysis that their approach is superior in comparison to other existing studies [18]. Talab et al. proposed a statistical feature analysis approach to extract distinctive features from low-resolution images. Their proposed approach has achieved better accuracy by implementing a random forest classifier [19]. Ansari and Ghrera introduced a novel feature extraction method to encode local texture. The experimental analysis presents the effectiveness of intuitionistic fuzzy binary patterns over the extraction approaches of the local binary pattern [20]. Nayak and Ansari presented a framework as an alternative to the solitary algorithm by constructing a cooperative optimization algorithm. The experimental analysis shows the effectiveness of their framework and enhances the prediction accuracy [21]. Ansari and Ghrera proposed an approach for extracting texture features from input images. The proposed technique is an extension of fuzzy local binary pattern approach and the result demonstrates its effectiveness in terms of accuracy [22]. Chen et al. introduced an integrated design to study the noise and frequency generated by mower blades [23]. Internet of things (IoT)-based framework is proposed for monitoring of conditions in power distribution networks [24]. The proposed framework can effectively monitor the healthy operations of the transformer in real time.

Based on this study, a method based on an improved genetic algorithm-particle swarm optimization (GA-PSO) algorithm is proposed. A hybrid model using SVM is implemented as it offers good accuracy and accomplishes quicker prediction. The hybrid SVM outclasses when there are large features and lesser training data. Based on vibration signals, extract time-domain and frequency-domain feature indicators, and then construct feature vectors for signal prediction. By establishing an improved particle swarm optimization algorithm, the feature model of SVM signals is optimized and the signal of rolling bearings is predicted.

3 Improved PSO algorithm

3.1 Basic particle swarm algorithm

The basic principle of particle swarm optimization is to combine the potential solutions of the problem to be optimized as particles in the search space, and then use the function model to be optimized to solve it. In this process, each particle is given a fitness value, and its flight direction and distance are determined by its own speed vector, so that it can fly to the direction of the best particle [25]. The particle update formula is as follows:

(1) v i j ( t + 1 ) = ω v i j ( t ) + c 1 r 1 ( t ) ( p i j ( t ) − x i j ( t ) ) + c 2 r 2 ( t ) ( p g j ( t ) − x i j ( t ) ) ,

(2) v i j ( t + 1 ) = x i j ( t ) + v i j ( t + 1 ) ,

where i = 1,2,…, m; j = 1,2,…, D; m is the population size; D is the particle dimension; t is the current evolutionary algebra; the non-negative numbers c 1 and c 2 are acceleration factors; r 1 and r 2 are random numbers uniformly distributed on [0,1].

Due to the fact that some studies are based on particle swarm optimization, inertia weighting factors ω have been introduced. These algorithms are called elementary particle swarm optimization algorithms, its inertia weight linearly decreasing strategy is,

(3) ω = ω max − ω max − ω min T × t .

The speed update formula is

(4) v i j ( t + 1 ) = ω v i j ( t ) + c 1 r 1 ( t ) ( p i j ( t ) − x i j ( t ) ) + c 2 r 2 ( t ) ( p g j ( t ) − x i j ( t ) ) ,

where ω max and ω min are the maximum and minimum inertia weights, respectively; t is the current evolution algebra; T is the maximum iteration algebra.

3.2 Key parameters of particle swarm algorithm

3.2.1 Inertia weight factor

In the PSO model, the particle flight speed is equivalent to the search step length of the particle in space, which is related to the convergence of the algorithm. The inertia weight factor ω represents the weight of the impact of the current velocity of the particle. To maintain the flight inertia of other areas in the search space, the change in the value of ω affects the ability of the particle’s local search and global search. If the value of ω is large, there is a strong global search ability and can jump out of the local optimum. Conversely, there is a strong local search ability, which can speed up the convergence [26].

3.2.2 Acceleration factor

c 1 and c 2 represent the acceleration factors required for particles to reach the individual and global optimal positions, respectively. The convergence ability of the global search is balanced by adjusting the size relationship between the acceleration factors c 1 and c 2. Among them, c 1 reflects the particle’s own cognitive ability and makes particles have the ability to approach the optimal solution they have experienced; c 2 reflects the population learning ability of particles and makes particles have the ability to approach the overall optimal solution. Six benchmark functions were studied through simulation, and it was pointed out that the optimal range of acceleration factor c 1 is 2.5–0.5, and the optimal range of acceleration factor c 2 is 0.5–2.5. During the early search of the PSO model, a larger value of c 1 and a smaller value of c 2 can make the particles better move in the direction of their own optimal solution, facilitate global search; Late search, a smaller value of c 1 and a larger value of c 2 can make the particles better move toward the global optimal solution of the population, speed up the convergence rate [27].

3.3 Improvement strategy of the particle algorithm

Based on the above analysis, the author proposes an improved particle swarm optimization (IPSO), by judging the inertia weight factor, acceleration factor, and stagnation, and position iteration formulas and other aspects to improve the algorithm.

3.3.1 Inertia weight factor

The inertia weight factor falls within [0.3, 0.7] as the optimal interval; in this interval, the local and global search capabilities of the algorithm can be better balanced [28]. According to the analysis of the inertia weighting factor, the author proposes a non-linear diminishing change strategy, to make ω more in the optimal range in the iterative process, the adjustment formula is as follows:

(5) ω = 3 ω max − ω min 2 − ( ω max − ω min ) × 2 t T + cos π t T 2 ,

where ω max and ω min are the maximum and minimum inertia weights, respectively. Take ω max as 0.9 and ω min as 0.4; t is the current number of iterations; T is the maximum number of iterations.

3.3.2 Acceleration factor

During the iteration process, the acceleration factor c 1 decreases and c 2 increases. It is helpful to improve the performance of the algorithm. A non-linear diminishing change strategy is proposed, in which the acceleration factor c 1 decreases from 2.5 to 0.5, the acceleration factor c 2 increases from 0.5 to 2.5, and the adjustment formula is:

(6) c 1 = 3.5 − 4 t T − sin ( T − 2 t ) π 2 T , c 2 = − 0.5 + 4 t T + sin ( T − 2 t ) π 2 T ,

where t is the current iteration number; T is the maximum iteration number.

3.3.3 Population particle individual optimal solution stagnation perturbation

When the population particles are flying in the search space to find the optimal solution, it is easy to fall into a local optimum. To prevent this situation from causing invalid iterations later, improve algorithm performance. To determine whether individual particles in the population are in a stagnant state, a stagnation processing strategy is proposed [29]. If the individual is in a stagnant state, the particle reaches its local optimal value, and its judgment processing formula is

(7) p i j ′ ( t ) = rand × p i j ( t ) , p i j ( t ) = p i j ( t − 1 ) = p i j ( t − 2 ) ( t > 3 ) p i j ( t ) ( other ) ,

where p ij (t) is the current individual optimal value of the ith particle; p i j ′ ( t ) is the optimal value of the individual after the stagnation determination process; rand is the uniform random number of [0,1]; t is the current iteration number.

3.3.4 Particle velocity and position update formula

In the individual optimal solution processed by Eq. (7), substitute the particle velocity update formula as:

(8) v i j ( t + 1 ) = ω v i j ( t ) + c 1 r 1 ( t ) ( p i j ′ ( t ) − x i j ( t ) ) + c 2 r 2 ( t ) ( p g j ( t ) − x i j ( t ) ) .

Research has shown that introducing a contraction factor into the speed update formula can ensure the convergence of particle swarm optimization and improve the convergence speed. Theoretically, the inertia weight factor and shrinkage factor have equal effects on the performance of the algorithm, therefore, the shrinkage factor in the speed update formula is not discussed here [30]. A new position updating strategy is proposed, in which global optimization is introduced into the position updating formula, which can randomly guide particles to the global optimization and speed up the convergence in the later period. The updated formula for the improved position is as follows:

(9) x i j ( t + 1 ) = λ ⋅ h ⋅ ( x i j ( t ) + v i j ( t + 1 ) ) + ( 1 − λ ) ⋅ h ⋅ p g j ( t ) ,

where λ = 0.6; h = rand, rand is a uniform random number of [0,1]; t is the current iteration number.

4 Experimental results and analysis

Due to the influence of sensor signal acquisition mode and some external factors, the vibration signals obtained during testing often have trend terms and are contaminated by a large amount of noise, resulting in a decrease in signal-to-noise ratio. Therefore, before extracting feature indicators, it is necessary to preprocess the vibration signal data to improve the signal-to-noise ratio. The obtained indicators can more accurately describe the performance decline trend of rolling bearings. The dataset utilized for testing the functionality of the proposed technique is Case Western University vibration dataset, which is a fundamental dataset providing access to the bearing data of normal and faulty bearings [31]. Data preprocessing mainly consists of three parts, one is to remove singular values, the other is to remove trend items, and the third is to process slip average [32].

Figure 2 is the fitness curve diagram of the IPSO optimization SVM; Figure 3 shows the signal characteristics of No. 1 bearing using the method in this article; Figure 4 shows the signal characteristics of the No. 1 bearing by the standard particle swarm optimization SVM model. After using the standard particle swarm optimization algorithm to optimize the SVM signal characteristics of rolling bearings, although the result is roughly the same as the actual degradation trend of bearings, compared with the improved particle swarm optimization model, the error is significantly increased, and the fitting curve is not smooth. This shows that the author’s improvement of the particle swarm algorithm is effective, and that it can make the prediction of the remaining service life of the bearing based on SVM more accurate [33].

Figure 2 Particle swarm optimization SVM fitness curve.
Figure 2

Particle swarm optimization SVM fitness curve.

Figure 3 Signal extraction of no. 1 bearing after SVM optimized by improved particle swarm algorithm.
Figure 3

Signal extraction of no. 1 bearing after SVM optimized by improved particle swarm algorithm.

Figure 4 Signal extraction of no. 1 bearing after SVM optimized by standard particle swarm algorithm.
Figure 4

Signal extraction of no. 1 bearing after SVM optimized by standard particle swarm algorithm.

Bearing No. 2 is used as a test bearing. The final result is shown in Figure 5. Compared with Figure 2, although the error has increased, the predicted trend is basically the same as the actual degradation trend. Compared with Figure 3, its fitting curve is smoother and the error is relatively small. Through the above comparison description, after the improved particle swarm algorithm optimizes SVM, this makes the generalization ability of rolling bearing signal characteristics significantly improved.

Figure 5 Signal extraction of no. 2 bearing after SVM optimized by improved particle swarm algorithm.
Figure 5

Signal extraction of no. 2 bearing after SVM optimized by improved particle swarm algorithm.

Figure 6 shows the signal characteristics of No. 2 bearing after SVM is optimized by the particle swarm optimization algorithm, although the forecast curve also has a downward trend; however, the error is significantly increased compared with Figures 2, 4 and 5. This indicates that the unimproved particle swarm optimization algorithm can perform well in the face of training dataset data, but performs very poorly in the face of test dataset, reflecting the insufficient generalization ability and inaccurate parameter selection of the algorithm [34].

Figure 6 Signal extraction of no. 2 bearing after SVM optimized by standard particle swarm algorithm.
Figure 6

Signal extraction of no. 2 bearing after SVM optimized by standard particle swarm algorithm.

First, perform data preprocessing on the vibration signal of the test bearing, that is, remove singular values, trend items and slip average processing, and the result of data preprocessing. Figure 7 is a rolling bearing signal characteristic model based on the IPSO proposed by the author to optimize SVM and predict the results of the test signal characteristics, Figure 8 is a standard particle swarm algorithm optimization signal feature model and the predicted results of the test bearings [35].

Figure 7 The signal extraction of the test bearing after the improved particle swarm algorithm optimizes the SVM model.
Figure 7

The signal extraction of the test bearing after the improved particle swarm algorithm optimizes the SVM model.

Figure 8 Test bearing signal extraction after standard particle swarm optimization optimizes the SVM model.
Figure 8

Test bearing signal extraction after standard particle swarm optimization optimizes the SVM model.

Comparing the results of Figures 7 and 8, it can be found that using the improved particle swarm optimization algorithm proposed by the author to optimize SVM significantly improves the accuracy of bearing signal features and smoothes the regression fitting curve (Figure 7). Although the fitting trend in Figure 8 is basically the same, the error is significantly higher. This shows that the optimization of SVM rolling bearing signal characteristics based on particle swarm optimization is feasible, and proves that the improvement of particle swarm optimization algorithm by the author is effective in optimizing SVM parameters. The results show that the method can effectively realize the intelligent diagnosis of different fault positions and different damage degrees of rolling bearings, and a method based on the improved GA-PSO algorithm is proposed. First, multifractal detrended fluctuation analysis is performed on the vibration signals of each state, and five multifractal features are extracted. The validity of the method is verified by the test data of the motor bearing. The results show that the proposed method can realize the intelligent diagnosis of the fault location and damage degree of the rolling bearing. The single-feature method and the corresponding single-feature fusion method have higher diagnostic accuracy.

The comparative analysis of proposed SVM-based optimization approach is done using confusion matrix which in turn computes accuracy, sensitivity, and specificity of the model, which is graphically represented in Figure 9.

Figure 9 Comparative analysis of proposed SVM-based optimization approach.
Figure 9

Comparative analysis of proposed SVM-based optimization approach.

The comparative analysis of the proposed vibration analysis approach is done with the other counterpart machine learning methods and also with the state-of-the-art approaches. The comparative results obtained for different approaches proposed in the literature suggest that the proposed SVM-based optimization approach provides the optimal results for all the performance evaluation parameters comparative to the other machine learning methodologies.

5 Conclusion

The author preprocessed the vibration signal using singular value removal, trend term removal, and sliding average processing, and extracted and reduced the features of the preprocessed vibration signal. A total of 23 dimensional time-domain and frequency-domain features were extracted, and the idea of relative feature indicators was introduced to establish an optimized particle swarm algorithm for different indicators. Finally, based on the optimized particle swarm optimization algorithm, a prediction model for the remaining life of rolling bearings was established and experimentally validated. By comparing the unimproved particle swarm algorithm, optimize the remaining life prediction model of SVM, it is proved that the algorithm proposed by the author is effective in improving the particle swarm algorithm, it can predict the remaining life of the bearing more accurately, and the remaining service life of the bearing optimized by the improved particle swarm algorithm, the generalization ability of the predictive model, it has also improved.

Acknowledgement

This work was funded by Science and Technology Project of Hebei Education Department, No. ZC2021219.

  1. Conflict of interest: The author declares that they have no competing interest.

  2. Informed consent: Informed consent was obtained from all individuals included in this study.

  3. Ethical approval: The conducted research is not related to either human or animals use.

  4. Data availability statement: The datasets and stimuli of this study are available upon reasonable request from the corresponding author.

References

[1] F. Moslehi, A. Haeri, and F. Martínez-Álvarez, “A novel hybrid GA–PSO framework for mining quantitative association rules,” Soft Comput. vol. 24, no. 6, pp. 4645–4666, 2020.10.1007/s00500-019-04226-6Search in Google Scholar

[2] Z. Dang, Y. Lv, Y. Li, and G. Wei, “Improved dynamic mode decomposition and its application to fault diagnosis of rolling bearing,” Sensors, vol. 18, no. 6, p. 1972, 2018.10.3390/s18061972Search in Google Scholar PubMed PubMed Central

[3] A. Benvidi, S. Abbasi, S. Gharaghani, M. D. Tezerjani, and S. Masoum, “Spectrophotometric determination of synthetic colorants using PSO–GA-ANN,” Food Chem., vol. 220, pp. 377–384, 2017.10.1016/j.foodchem.2016.10.010Search in Google Scholar PubMed

[4] C. Chen, J. Li, J. Luo, S. Xie, and H. Li, “Seeker optimization algorithm for optimal control of manipulator,” Ind. Robot: An. Int. J., vol. 43, no. 6, pp. 677–686, 2016.10.1108/IR-12-2015-0225Search in Google Scholar

[5] J. L. Qu, L. Yu, T. Yuan, Y. Tian, and F. Gao, “Adaptive fault diagnosis algorithm for rolling bearings based on one-dimensional convolutional neural network,” Chin. J. Sci. Instrum., vol. 39, no. 7, pp. 134–143, 2018.Search in Google Scholar

[6] N. Pan, X. Wu, and Y. Guo, “Bearing compound fault acoustic diagnosis based on improved blind deconvolution algorithm,” Trans. Can. Soc. Mech. Eng., vol. 39, no. 3, pp. 657–667, 2015.10.1139/tcsme-2015-0052Search in Google Scholar

[7] R. Cheng, Y. Bai, Y. Zhao, X. Tan, and T. Xu, “Improved fireworks algorithm with information exchange for function optimization,” Knowl. Syst., vol. 163, pp. 82–90, 2019.10.1016/j.knosys.2018.08.016Search in Google Scholar

[8] H. Dumitrescu and V. Cardos, “Improved formulation for boundary-layer-type flows,” AIAA J. vol. 40, no. 4, pp. 794–796, 2002.10.2514/2.1715Search in Google Scholar

[9] C. H. Yan, T. F. Wang, Y. Y. Li, T. Lv, and S. S. Wu, “An improved arctangent algorithm based on phase-locked loop for heterodyne detection system,” Chin. Phys. B, vol. 28, no. 3, p. 030701, 2019.10.1088/1674-1056/28/3/030701Search in Google Scholar

[10] Y. Jiang, P. Tsai, Z. Hao, and L. Cao, “Automatic multilevel thresholding for image segmentation using stratified sampling and Tabu Search,” Soft Comput., vol. 19, no. 9, pp. 2605–2617, 2015.10.1007/s00500-014-1425-3Search in Google Scholar

[11] H. Soleimani and G. Kannan, “A hybrid particle swarm optimization and genetic algorithm for closed-loop supply chain network design in large-scale networks,” Appl. Math. Model., vol. 39, no. 14, pp. 3990–4012, 2015.10.1016/j.apm.2014.12.016Search in Google Scholar

[12] Q. Zhang, R. M. Ogren, and S. C. Kong, “A comparative study of biodiesel engine performance optimization using enhanced hybrid PSO–GA and basic GA,” Appl. Energy, vol. 165, pp. 676–684, 2016.10.1016/j.apenergy.2015.12.044Search in Google Scholar

[13] K. Shanmukhi, P. R. Vundavilli, and B. Surekha, “Modeling of ECDM micro-drilling process using GA-and PSO-trained radial basis function neural network,” Soft Comput., vol. 19, no. 8, pp. 2193–2202, 2015.10.1007/s00500-014-1400-zSearch in Google Scholar

[14] B. Küçükuğurlu and E. Gedikli, “Symbiotic organisms search algorithm for multilevel thresholding of images,” Expert. Syst. Appl., vol. 147, p. 113210, 2020.10.1016/j.eswa.2020.113210Search in Google Scholar

[15] P. Singh and H. Chaudhary, “Optimal shape synthesis of a metallic flywheel using non-dominated sorting Jaya algorithm,” Soft Comput., vol. 24, no. 9, pp. 6623–6634, 2020.10.1007/s00500-019-04302-xSearch in Google Scholar

[16] C. Wang, Z. Li, N. Dey, Z. Li, A. S. Ashour, S. J. Fong, et al., “Histogram of oriented gradient based plantar pressure image feature extraction and classification employing fuzzy support vector machine,” J. Med. Imaging Health Inform., vol. 8, no. 4, pp. 842–854, 2018.10.1166/jmihi.2018.2310Search in Google Scholar

[17] M. D. Ansari, V. K. Koppula, and S. P. Ghrera, “Fuzzy and entropy based approach for feature extraction from digital image,” Pertanika J. Sci. Technol., vol. 27, no. 2, 2019.Search in Google Scholar

[18] S. C. Nayak, S. Das, and M. D. Ansari, “Tlbo-fln: Teaching-learning based optimization of functional link neural networks for stock closing price prediction,” Int. J. Sens. Wirel. Commun. Control, vol. 10, no. 4, pp. 522–532, 2020.10.2174/2210327909666191202113015Search in Google Scholar

[19] M. A. Talab, S. Awang, and M. D. Ansari, “A novel statistical feature analysis-based global and local method for face recognition,” Int. J. Opt., vol. 2020, pp. 4967034, 2020.10.1155/2020/4967034Search in Google Scholar

[20] M. D. Ansari and S. P. Ghrera, “Intuitionistic fuzzy local binary pattern for features extraction,” Int. J. Inf. Commun. Technol., vol. 13, no. 1, pp. 83–98, 2018.10.1504/IJICT.2018.090435Search in Google Scholar

[21] S. C. Nayak and M. D. Ansari, “Coa-honn: Cooperative optimization algorithm based higher order neural networks for stock forecasting,” Recent. Adv. Comput. Sci. Commun. (Formerly: Recent Pat. Comput. Sci.), vol. 14, no. 7, pp. 2376–2392, 2021.10.2174/2213275912666190902121153Search in Google Scholar

[22] M. D. Ansari and S. P. Ghrera, Feature extraction method for digital images based on intuitionistic fuzzy local binary pattern, 2016 International Conference System Modeling & Advancement in Research Trends (SMART), IEEE, 2016, November, pp. 345–349.10.1109/SYSMART.2016.7894547Search in Google Scholar

[23] Y. Chen, W. Zhang, L. Dong, K. Cengiz, and A. Sharma, “Study on vibration and noise influence for optimization of garden mower,” Nonlinear Eng., vol. 10, no. 1, pp. 428–435, 2021.10.1515/nleng-2021-0034Search in Google Scholar

[24] Z. Wang and A. Sharma, “Research on transformer vibration monitoring and diagnosis based on Internet of things,” J. Intell. Syst., vol. 30, no. 1, pp. 677–688, 2021.10.1515/jisys-2020-0111Search in Google Scholar

[25] A. Rabiei, T. Thiringer, M. Alatalo, and E. A. Grunditz, “Improved maximum-torque-per-ampere algorithm accounting for core saturation, cross-coupling effect, and temperature for a PMSM intended for vehicular applications,” IEEE Trans. Transp. Electrification, vol. 2, no. 2, pp. 150–159, 2016.10.1109/TTE.2016.2528505Search in Google Scholar

[26] T. X. Gu, J. M. Wang, X. Y. Zuo, B. Yang, and X. P. Liu, “RETRACTED ARTICLE: Formal derivation of biconjugate gradient method with its modification for distributed parallel computing,” J. Eng. Math., vol. 91, no. 1, pp. 213–213, 2015.10.1007/s10665-014-9695-4Search in Google Scholar

[27] J. H. Yi, S. Deb, J. Dong, A. H. Alavi, and G. G. Wang, “An improved NSGA-III algorithm with adaptive mutation operator for Big Data optimization problems,” Future Gener. Comput. Syst., vol. 88, pp. 571–585, 2018.10.1016/j.future.2018.06.008Search in Google Scholar

[28] K. Akoussan and M. Hamdaoui, “Improved layer-wise optimization algorithm for the design of viscoelastic composite structures,” Compos. Struct., vol. 176, pp. 342–358, 2017.10.1016/j.compstruct.2017.05.047Search in Google Scholar

[29] G. A. Periçaro, S. R. Santos, A. A. Ribeiro, and L. C. Matioli, “HLRF–BFGS optimization algorithm for structural reliability,” Appl. Math. Model., vol. 39, no. 7, pp. 2025–2035, 2015.10.1016/j.apm.2014.10.024Search in Google Scholar

[30] G. J. Horng, “The adaptive recommendation mechanism for distributed parking service in smart city,” Wirel. Personal. Commun., vol. 80, no. 1, pp. 395–413, 2015.10.1007/s11277-014-2017-3Search in Google Scholar

[31] S. Zhang, S. Zhang, B. Wang, and T. G. Habetler, “Deep learning algorithms for bearing fault diagnostics—A comprehensive review,” IEEE Access, vol. 8, pp. 29857–29881, 2020.10.1109/ACCESS.2020.2972859Search in Google Scholar

[32] R. C. Anderson and J. W. Fitton, “Index theory-based algorithm for the gradiometer inverse problem,” GEM-Int. J. Geomath., vol. 7, no. 1, pp. 147–161, 2016.10.1007/s13137-015-0072-xSearch in Google Scholar

[33] N. He, A. Juditsky, and A. Nemirovski, “Mirror prox algorithm for multi-term composite minimization and semi-separable problems,” Comput. Optim. Appl., vol. 61, no. 2, pp. 275–319, 2015.10.1007/s10589-014-9723-3Search in Google Scholar

[34] D. Li, J. Cheng, and V. C. Leung, “Polarization jones vector distance statistics-based full-duplex primary signal extraction for cognitive radios,” IEEE Trans. Commun., vol. 67, no. 4, pp. 2689–2701, 2018.10.1109/TCOMM.2018.2889950Search in Google Scholar

[35] H. S. Kumar and P. S. Pai, “Classification of rolling element bearing fault using singular value,” J. Qual. Maint. Eng., vol. 26, no. 2, pp. 181–197, 2019.10.1108/JQME-12-2016-0083Search in Google Scholar
Received: 2022-07-05
Revised: 2022-07-30
Accepted: 2022-08-01
Published Online: 2023-05-05

© 2023 Lixia Hao, published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/pjbr-2022-0092
Keywords for this article
rolling bearing; improved particle swarm algorithm; support vector machine; signal extraction; vibration signal
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Article
  2. The role of prior exposure in the likelihood of adopting the Intentional Stance toward a humanoid robot
  3. Review Articles
  4. Robot-assisted therapy for upper limb impairments in cerebral palsy: A scoping review and suggestions for future research
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