3 Result analysis and discussion

3.1 Analysis of optimal VMD component envelope spectrum

The biting and throwing stage signals of the four kinds of signals were removed, and 6,000 sample points were intercepted to make time domain diagrams of vertical, axial and horizontal vibration signals, as shown in Figure 5.

After PSO VMD decomposition, the decomposition parameters of signals in each direction of the four kinds of bearings are shown in Table 1. In order to speed up the computing speed of PSO, the optimization range of K for PSO is set as [4~10], the optimization range of α is set as [2 000~3 000], and the search step size of α is set as 50. Among them, 6 IMF components are obtained from the vertical vibration signals of spalling bearing of rolling body. The correlation coefficient, kurtosis and variance contribution rate of each IMF component of the spalling fault signals of rolling body of experimental rolling mill and the original signals are calculated, as shown in Table 2. Based on the correlation coefficient, kurtosis and variance contribution rate indexes of each component, it is concluded that the IMF2 component contains more fault characteristic information and is the optimal component.

The IMF2 envelope spectrum of bearings with rolling faults is shown in Figure 6. The frequency corresponding to the first dominant peak is 0.091Hz, which is about the bearing rotation frequency; 0.351Hz is the rolling failure frequency; 0.732 4 and 1.068Hz are the double and triple frequency of the rolling failure frequency. Due to the limited length of the rolled sheet, the limited normal data is less in practice when the biting and throwing stages are removed, resulting in sparse envelope spectrum images and low frequency resolution.

As shown in Figure 5, after signal processing by VMD decomposition, the optimal component is selected and envelope analysis is carried out, and the characteristic frequency of rolling body fault can be found from the spectrum diagram. However, due to the small amount of data, the effect is not perfect, and the small amount of data makes the rolling body wear and cage breakage relatively weak, so it is difficult to identify the fault frequency in the fault envelope spectrum. Therefore, feature extraction is still needed to further improve the accuracy of diagnosis. 3.2 Analysis of VMD decomposition and MMPE algorithm results The VMD calculation method was used to decompose all directional vibration signals to obtain K fractions. The first four optimal components were selected to calculate the three-dimensional MMPE values of the components of vibration signals in the order of IMF1~IMF4. And according to the number of components to arrange, and peak-peak value to form a 5-dimensional feature vector for PSO SVM recognition and classification; The first 4 optimal IMF components processed by EEMD and LMD algorithm were selected to calculate MMPE value, and then grouped into feature vectors for PSO SVM model recognition and classification.

Similarly, the MPE algorithm is used to extract and compare the features of the signals. Because the embedding dimension m is too large, the algorithm is affected, resulting in too many sequences and combinations of signals. Existing studies show that good results can be achieved when m is set to 3~7. Therefore, the embedded dimension m of the algorithm is set to 3, and only 6 permutation and combination modes will appear for each group of signals, which greatly saves the computing time. The optimal scale factor is found in the scale space of 1~20, and the diagnostic accuracy rates of VMD‑MMPE and VMD‑MMPE of model input vibration signals under different scale factors are calculated, and the variation curve of accuracy is drawn, as shown in Figure 7. Finally, the scale factors of MMPE and MPE were selected as 14 and 13.

The four components processed by the three algorithms, EEMD, LMD and VMD, are segmented according to 6 000 samples, and 10 time-domain features are extracted. The signals are input into the PSO SVM model as input vectors, and identification, classification and comparison are carried out. Various fault labels of experimental rolling mill are shown in Table 3. In all kinds of fault labels of the experimental rolling mill, 30 feature vectors were randomly calculated as the test set, and the time-domain index of the optimal VMD component signal was used as the input. The prediction and classification results were shown in Figure 8. Among them, no fault 2 points were misclassified, rolling body spalling 2 points were misclassified, rolling body wear 18 points were misclassified, the classification accuracy was 81.67%. Because the roller wear degree is low, the signal is similar to normal bearing, and the fault free and rolling wear are seriously misclassified.

The EEMD component MPE value feature vector of the experimental rolling mill was used as input prediction classification results, as shown in Figure 9. Among them, 2 fault free points were misclassified, 4 cage fault points were misclassified, and 5 rolling wear points were misclassified. The classification accuracy of the model was 90.83%. The error score was improved after MPE calculation.

The feature vector of MPE value of VMD component was used as the input to predict the classification results, as shown in Figure 10. Among them, 3 points of no fault were misclassified, 2 points of cage damage were misclassified, and 4 points of rolling body wear were misclassified. The accuracy of mold classification was 92.50%. When MPE feature vector is used as input, the error classification of similar faults is obviously improved compared with that of classification signal directly. Compared with EEMD algorithm, the diagnostic accuracy is improved.

The feature vector of MMPE value of VMD component of the experimental mill was used as input to predict the classification results, as shown in Figure 11. Among them, three points without fault were misclassified, one point was misclassified when the rolling body was peeled off, two points were misclassified when the cage was damaged, and one point was misclassified when the rolling body was worn. The correct classification rate of the model was 94.17%. Compared with time domain index input and MPE feature input, the accuracy is further improved.

PSO SVM and SVM algorithm diagnostic accuracy rate and program running time are shown in Table 4 and Table 5. In the rolling mill operation process, there are axial channeling, metal deformation flow, friction between rolls and roll system deformation, which will lead to the generation of axial force, so the rolling mill multi-row roller bearing in the rolling process of axial force, need to compare the axial vibration signal input. The statistical calculation time is the time required by the entire fault diagnosis flow path.

It can be seen from Figure 8-11 and Table 4,5 that the VMD algorithm has a high classification accuracy in the three input cases, and the VMD‑MMPE combined feature vector as input to process the two types of data has the highest accuracy of 94.17%. MPE algorithm was used to extract feature vectors, and after optimizing input, SVM diagnosis accuracy and diagnosis speed were significantly improved. The combination of MMPE feature vector as input improves the classification effect of fault degree of the same fault and different parts of the model. MMPE optimizes the input of PSO SVM, and verifies that VMD‑MMPE value has good effect as the characteristic characterization of shaft bearing fault.

To further verify the effectiveness of the VMD‑MMPE feature extraction method in this study, it was combined with multiscale entropy, multiscale fuzzy entropy (MFE) and weighted permutation entropy. Simply called WPE) in line comparison. MSE parameters are set to: m=3, r=0.15σ, τ=1, s= 15. MFE parameters are set to: m=3, τ=1, s=15. WPE parameters are set to: m=3, τ=1. As shown in Table 6, it can be seen that VMD‑MSE, VMD‑MFE and VMD‑WPE are not as effective as VMD‑MMPE in this study.

4 Conclusion

1) Experimental rolling mill data analysis results show that VMD combined with row entropy processing is better than EEMD and LMD algorithm, MMPE can well extract bearing fault characteristics, can effectively realize bearing fault diagnosis.

2) Component time domain feature input, MPE combination feature vector input and MMPE combination characteristic vector input result ratio is shown, MMPE value can greatly optimize the input of PSO SVM, reduce the input dimension, realize the characterization of all kinds of bearing faults, shorten the diagnostic calculation time, Improve the diagnostic accuracy.

3) The MMPE algorithm is better than the existing MSE, MFE, MPE and WPE algorithms in signal feature extraction.

4) The established fault diagnosis model can realize the fault diagnosis of rolling block and cage, and can effectively realize the diagnosis and classification of early rolling block scratch fault.

Source: China National Knowledge Network

Author: Ji Jiang, Zhao Chen, and Wang Yongqin

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