Feng-yun XIE, Kun LIU, Chun-yun FENG, Yu FU, Shao-shi YAN，Er-hua WANG

(1School of Mechatronics & Vehicle Engineering, East China Jiaotong University, Nanchang 330013, China) (2Mechanical and Electronical School of Engineering,Changzhou College of Information Technology， Changzhou 213164, China)

Abstract: A nonlinear and non-stationary phenomenon is often generated for the loose fault signal of the bolt. In this paper, the bolt loose state recognition method based on the combination of VMD (Variational Mode Decomposition) and LSSVM (Least squares support vector machine) is proposed. The bolt loose test platform is used to collect the vibration signals of the loose state of the bolts under the four working conditions. The vibration signal of each working condition of the bolt loose state is decomposed by using the VMD. The energy entropy of each modal component by the VMD is calculated. The energy entropy of each modal component decomposed by VMD is as a feature structure eigenvector matrix, which is trained and state-recognized by VMD-LSSVM. The experimental results show that the method can effectively identify the loose state of the bolt loosening state, and the VMD-LSSVM has a better performance in states recognition compared with the EMD-LSSVM model.

Key words: Loose bolt, VMD, LSSVM, Energy entropy, State recognition

1 Introduction

The bolt is the most commonly connecting piece in industrial field, and it plays an important role in maintaining the stable operation of mechanical equipment. However, when the bolt is subjected to the cyclic load of external temperature and self-vibration in working, it is easy to cause loose bolt failure which may further cause serious security incident. Therefore, it is important to detect and identify the loose state of the bolt before it fails.

At present, the most widely used method for looseness detection of bolts is to determine whether the bolts are loose or not by the change of the vibration signals of the two connected workpieces in the case of loose bolts. Dong et al. [1-2] studied the connection failure of the missile support base connection bolts respectively. The spectral distance spectrum factor and the wavelet packet combined with the neural network detection method were studied. According to the vibration signal of the support bolts under different preloading forces, the difference of the power spectrum of the signal is analyzed, and the feature extraction method of extracting the spectral distance factor and wavelet packet energy is proposed. The neural network is used to effectively identify the looseness of the connecting bolt of the support. After the bolt is loosened, the structural dynamics will have a nonlinear response. The analysis of the bolt loose response signal from the time-frequency domain can effectively identify the damage. Zhou et al. [3] proposed a bolt based on EMD (Empirical Modal Decomposition). The loose research method is to perform EMD and power spectrum on the high-frequency and random excitation response signals of the frame structure, and extract the high-frequency intrinsic mode function (IMF) number of the EMD to construct the energy damage indicator. However, EMD algorithm’s inefficiency、 mode aliasing and end effect, which often affect the identification of bolt loose state. VMD (Variational Mode Decomposition) is a new non-recursive, adaptive data signal method proposed by K Dragomiretskiy in 2014 [4]. Compared with EMD, the efficiency of the algorithm is high due to its decrease decomposition layers, and can avoid modal aliasing and end effect very well. It is widely used in the field of mechanical equipment fault diagnosis. This paper proposes a bolt loose state recognition method based on VMD and LSSVM (Least squares support vector machine). In the time-frequency domain, the nonlinearity and the smoothness of the signal are well, and the excellent performance of the LSSVM in state recognition is applied to the state recognition of the bolt. Finally, the validity and feasibility of the method are verified by experiments.

2 Variational mode decomposition

VMD uses the loop iteration using the alternating direction multiplier method to find the optimal solution of the constrained variational problem. The center frequency and bandwidth of each component are continuously updated in the frequency domain, and then the components are converted into time by the inverse Fourier transform. The domain signal can thereby adaptively decompose the frequency domain of the original signal into superposition of K narrow-band amplitude modulation-frequency modulation components to achieve effective decomposition of the signal [5].

VMD has been widely used in the field of mechanical equipment fault diagnosis. Zhao et al. [6] proposed a VMD-based fault feature signal extraction method. The permutation entropy is used to determine the noise level of each component after VMD, and the high noise component is eliminated. The low noise component is smoothed to reconstruct the signal, and the VMD is utilized. The decomposition effectively extracts the fault signal characteristics. Ma et al. [10] decomposed the signal into several eigenmode components by using the VMD for the low signal-to-noise ratio (SNR) of the early fault signal of the rolling bearing and the difficulty of extracting the fault features. Then the kurtosis criterion is used to select the maximum component of the kurtosis. The Teager energy operator demodulation is used to obtain the signal Teager energy characteristics, which realizes the accurate diagnosis of the early failure of the rolling bearing. Ren et al [8] improved the VMD method and proposed a method of determining the number of decomposition layers by using energy difference as the evaluation parameter adaptively, determining the optimal decomposition layer number, and then decomposing to k eigenmodes according to the kurtosis criterion. The sensitive components are filtered out for reconstruction, and the fault information of the bearing is accurately extracted. As a new signal decomposition method, VMD overcomes the modal aliasing phenomenon and endpoint effect of the traditional adaptive decomposition method. The anti-noise robustness and high decomposition efficiency are high. Many scholars have applied VMD in the field of fault diagnosis and achieved good results with further improvements, which indicates the superiority of the VMD method compared to the traditional adaptive decomposition method.

3 Case analysis

3.1 Experiment and data collection

In order to obtain the vibration signal generated by the bolted structure in different loose states of the bolt. First, a bolt connection structure model is made, then the bolt test experimental platform was built on the basis of this. Fig.1 shows the bolt connection structure and the bolt test experimental platform.

Fig.1 Bolt test experimental platform

The model material uses two 15mm thick steel plates, and four bolted joints are used to construct the bolt connection structure. Based on this model, an experimental platform for bolting structure looseness detection is built. The experimental platform system scheme is shown in Fig.2.

Fig.2 Experimental platform system plan

The bolt vibration response data was collected in the loose bolt test platform of the built bolt connection structure, and the sampling rate was set to 12 kHz, and the sampling time was 1 second. For the test bolts in Fig.1, the state of the bolts in this experiment is based on the bolt torque. Four working conditions are set to 150 N·m (condition 1, full tight), 100 N·m (condition 2, tight), 50 N·m (Working condition 3, loose), 0N·m (condition 4, full loose). The looseness of the bolt is changed by the torque wrench, and the structural response under each working condition is collected. 30 sets of data were collected under each working condition, and all states were 120 sets. 20 sets of data were randomly selected from each state in the structural response dat used as training samples, and the remaining 40 sets of data were used as test samples for bolt looseness state identification. The data conditions are grouped as shown in Table 1.

Table 1 Bolt status data grouping table

3.2 Experimental results and data analysis

3.2.1 Time domain analysis

The time-domain diagrams under the four working conditions are shown in Fig.3. As can be seen from the figure, the bolts are slightly increased in time domain amplitude during the period of working conditions 1, 2, 3. It is not obvious that the working condition 4 has a significant increase in the time domain amplitude compared to the working conditions 1, 2, and 3 due to the bolt being completely loose. However, in general, the time domain map alone cannot make an accurate judgment on the various working conditions of the bolt loose state.

Fig.3 Time-domain diagram of vibration signal under various working conditions of bolt

3.2.2 VMD decomposition

The collected bolt vibration data is based on the bolt preload force in a total of four states (conditions 1, 2, 3, 4). In each state, each group of 30 groups has 120 sets of data, and each group of data is subjected to VMD. Taking the bolt normal state (condition 1) as an example, theKvalue of the decomposition mode number is first determined according to the principle of close center frequency [9], andK=7 is determined by analysis. The result of VMD decomposition is shown in Fig.4.

Fig.4 VMD decomposition of each modal component map

Fig.5 shows the modal components after decomposing EMD (12 in total), 8 of which contain most feature information. The figure shows that modal aliasing has occurred between the two components of IMF5 and IMF6. And the endpoint effects of the five components from IMF4 to IMF8 are severe. From Fig.5, we can see that there is no modal aliasing between the IMFs decomposed by VMD. At the same time, the end effect is avoided and the number of decomposition layers is less compared with EMD, which is convenient for following data processing. The decomposition results illustrate the advantages of VMD over EMD in avoiding modal aliasing and endpoint effects as well as controlling the number of layers. The 120 sets of sample signals are decomposed by VMD, and 840 sets of eigenmode functions are obtained. The energy entropy of an eigenmode function is obtained according to the energy entropy value definition [8], which is used for subsequent state recognition. The entropy parameter of IMF1～I(xiàn)MF7 is H1～H7.Due to the space reason, the three sets of energy entropy listed in each case are shown in Table 2.

Fig.5 EMD decomposition of each modal component map

Table 2 IMF energy entropy of each layer of VMD decomposition under various working conditions of bolts

4 LSSVM model training and bolt status recognition

According to the experimentally collected bolts, there are 120 groups of data in 4 states and VMD is performed accordingly to obtain the energy entropy of each IMF. The 7-layer IMF energy entropy is composed into the feature vectorH= [H1,H2,H3,H4,H5,H6,H7]. Each group takes 20 sets of data, and 80 sets of data in four states are arranged in order to construct a 80×7 feature vector matrix for the training set for model training. The remaining 40 sets of data use the same method to construct the test set 40×7 feature vector matrix. The 80×1 label set marks the feature data under the four operating conditions (conditions 1, 2, 3, and 4) as 1, 2, 3, and 4, respectively. Then, the constructed training set feature matrix and the training label set test set feature vector matrix are respectively brought into the LSSVM for model training and recognition. In order to verify the recognition effect of the VMD-LSSVM, the EMD-LSSVM is used to process and identify the same data. Finally, the recognition results are compared. The final recognition results are shown in Table 2.

Table 2 Comparison table of recognition rates under two models

From the recognition accuracy analysis of Table 2, the recognition accuracy of the VMD-LSSVM in working conditions 1 and 2 is higher than that of the EMD-LSSVM, and the VMD-LSSVM is the same for the overall recognition accuracy of the four states of the bolt. The performance is even better. This indicates that the VMD-LSSVM is superior in both initial data processing and post-bolt state recognition and can effectively solve the problem of classification and classification under various working conditions of bolt loosening.

5 Conclusion

Aiming to solve the state recognition problem of bolt looseness, this paper proposes a bolt loose state recognition method based on VMD and LSSVM. In order to verify the validity and feasibility of the proposed method, this paper first built a bolt connection structure model, and constructed a bolt loosening test platform with other equipment. According to the bolt preload force, four kinds of working conditions were designed. The vibration response data of the bolt type 4 was decomposed by VMD to establish the LSSVM, and the remaining test data was used to realize the state recognition of the loose bolt. The model was compared with the EMD-LSSVM. The experiment based on the VMD and LSSVM model proves the feasibility and effectiveness of the bolt loose state identification method as well as the superiority of the VMD-LSSVM compared with the EMD-LSSVM. It will be very significant in the bolt loose state detection and equipment safety maintenance.