**Abstract:** Based on analysis of fault mechanism of generator bearings，the EMD － CD method is improved for diagnosis of bearing fault． Firstly，the false basic modal component in conventional empirical mode decomposition is identified and wiped out by calculating the grey correlation degree between IMFs signal and the vibration signal． Secondly，the correlation dimension of real IMF signals is calculated，and the correlation dimension is taken as fault feature component． Finally，the EMD － CD data under normal condition and different false conditions is obtained by using simulation experiment，the state model of bearings is distinguished by using data comparison．

**Key words:** rolling bearing; fault diagnosis; EMD; grey correlation degree; correlation dimension

Bearing damage is one of the common faults in generators, accounting for 30% to 40% of the total faults in the generator. Experiments have shown that the location of bearing faults varies, and the frequency of fault characteristics also varies. It is possible to determine which type of bearing fault occurs based on the presence or absence of fault characteristic frequencies in the vibration signal. At present, the main research methods include Fourier transform and wavelet transform, but both have shortcomings: the diagnostic accuracy of Fourier transform is easily affected by factors such as noise during the diagnostic process; Wavelet transform is essentially a linear transformation and cannot effectively handle nonlinear problems.

When a bearing undergoes a damage fault, corresponding fault characteristic components and higher-order harmonic components will appear in its vibration signal. Due to the structural characteristics of bearings, normal bearings also have quite complex background noise, and the fault characteristic frequency is often a low-frequency component, which is easily submerged by strong background noise. It is very difficult to diagnose faults through simple analysis of bearing vibration signals. Therefore, an attempt was made to combine the improved Empirical Mode Decomposition (EMD) with the Correlation Dimension (CD) to calculate the correlation dimension of the Intrinsic Mode Function (IMF) of the vibration signal under different fault modes of generator bearings, and to diagnose bearing faults through comparison.

**1. Improve EMD algorithm**

1.1 Empirical Mode Decomposition

The empirical mode decomposition algorithm assumes that any signal can be composed of a series of fundamental mode components, each of which characterizes the inherent fluctuation characteristics of the signal. At the same time, it also has localized characteristics of the signal in the time domain, making it suitable for processing vibration signals of bearings. For signal x (t). Due to the nonlinear characteristics of the signal, it is often not possible to fully meet the requirement of zero envelope mean in the EMD process, which will lead to significant end point wing phenomenon at both ends of the signal. If this phenomenon spreads throughout the entire signal range, the signal decomposition will result in false IMF components, thereby causing unnecessary interference to fault diagnosis. Therefore, in order to improve diagnostic accuracy and reliability, it is necessary to identify and eliminate false IMF components.

1.2 Grey correlation degree

General abstract systems such as social and economic systems contain multiple internal factors, and the combined effects of these factors determine the development trend of the system. According to grey theory, each factor plays a different role in determining the development of the system, with some playing a dominant role and others not playing a significant role. The grey correlation degree is an important indicator to describe this relationship, and its basic idea is to determine whether the degree of connection is close based on the similarity of the geometric shapes of curve sequences. The closer the curve is, the greater the correlation between the corresponding sequences, and vice versa.

Based on the above ideas, it is assumed that the vibration signal after a generator bearing failure is the result of system development, and the IMF components obtained after EMD processing of the signal are the various factors that affect system development. Attempt to use the concept of grey correlation degree for identifying false IMF components: calculate the grey correlation degree between each IMF component and the original vibration signal, and compare it with the set threshold to identify and eliminate false IMF components.

Set the system behavior sequence as

For ξ ∈ (0, 1), make

Among them, ξ It is called the resolution coefficient, γ (X0, Xi) is called the grey correlation degree between X0 and Xi, usually denoted as γ 0i.

**2 Correlation dimension**

The concept of fractal opens up a new way to study nonlinear and chaotic systems. The nonlinear characteristics of vibration signals caused by faults in different parts of bearings are also different. Firstly, obtain the real IMF signal of the vibration signal and calculate its correlation dimension, and then characterize the bearing fault based on the distribution of the correlation dimension.

The Phase space with length of Nm and dimension of m can be formed by time delay method for time series with length of N. Let the original signal time series be {x1, x2,..., xN}, and obtain the reconstruction vector sequence {Yi, i=1, 2,..., Nm} through Phase space reconstruction. After constructing the vector, take any reference point Yi, and the distance from the other points to that point is

Then the correlation integral function is

Draw the scale line lnr lnCm (r) according to the formula, and the slope of the line is the correlation function of the corresponding time series.

**3 Simulation verification**

Select 4 sets of 6311-2RS bearings for fault analysis. The parameters of the bearings are: rotational frequency fa=25 Hz, number of steel balls Z=8, steel ball diameter Dw=20.63 mm, ball group pitch diameter Dpw=87.5 mm, contact angle α = 0 °. Cut a wire slot with a depth of 1 mm and a width of 0.15 mm on the inner, outer, and steel balls to simulate different fault forms. According to formula [12], the fault frequency of the outer ring of the bearing fe=73.3 Hz, the characteristic frequency of the inner ring fault fi=118.6 Hz, and the fault frequency of the steel ball fb=96.1 Hz are calculated.

The time-domain and frequency-domain waveforms of vibration signals under different fault states of bearings are shown in Figure 1 and Figure 2. The diagram shows normal status, outer ring fault, inner ring fault, and steel ball fault from top to bottom. From the figure, it can be seen that due to the low frequency of fault features and the strong noise interference in the low-frequency range of vibration signals, the fault feature frequency is easily submerged by strong noise, and the fault features are not obvious in both time and frequency domain signals. It is very difficult to directly use the time-frequency domain signals of vibration signals for fault diagnosis.

Figure 1 Time domain waveform of vibration signal

Figure 2 Vibration Signal Frequency Chart

Taking the fault of the bearing outer ring as an example, EMD processing was performed on the vibration signal, and the results are shown in Figure 3, with IMF1 to IMF8 and trend components from top to bottom.

Figure 3 Empirical Mode Decomposition Process

Assuming the original vibration signal is X0 and the signals of each IMF component are Xi, calculate the grey correlation between Xi and X0. By definition, the resolution coefficient can be determined ξ Different values result in different values of the calculated grey correlation degree. Under the principle of minimum information, the resolution coefficient ξ = 0.5. The results obtained are shown in Table 1.

It can be seen from Table 1 that the grey correlation Degree distribution between IMF components and vibration signals has a wide range, which reflects the different roles of various components on vibration signals. The grey correlation degree between component IMF4 and the original signal is 0.015 8, which is less than 0.1. This indicates that the correlation degree between IMF4 and the original signal is very small, that is, it plays a small role in the original vibration signal. The grey correlation degree between the remaining IMF components and the original signal is above 0.1, based on which it can be determined that IMF4 is a false IMF component.

For the IMF4 component, it is not simply removed, but added to the trend component as the new trend component, and the remaining IMF components are reordered as the true IMF components.

Perform EMD processing on bearing vibration signal data under four different states. Calculate the grey correlation between each IMF component and the vibration signal, remove false IMF components, and obtain a new IMF sequence. Due to the significant differences in signals under different states, the obtained IMF order is also different, which means that the obtained data dimensions are inconsistent. Moreover, the information contained in the signal is mainly concentrated in the first few components. In order to reduce computational complexity and ensure consistent data dimensionality, the first five components are used for calculation and analysis. The distribution of correlation dimensions before and after EMD improvement is shown in Figures 4 and 5.

Figure 4 Dimensional distribution of conventional EMD-CD

Figure 5: Dimension distribution of improved EMD-CD

From Figure 4, it can be seen that although there are generally differences in the distribution of correlation dimensions under different states, there is overlap between the data. This is due to the presence of false IMF, which will reduce diagnostic accuracy.

It can be seen from Figure 5 that the correlation dimension of the first five IMF components obtained from the EMD processing of the bearing vibration signal under normal conditions is the largest. This is because the bearing vibration signal under normal conditions is mainly random noise, the signal is irregular, and the fractal characteristics such as Self-similarity are not obvious. When the bearing has the corresponding surface damage fault, there is a certain harmonic component in the vibration signal, which leads to the enhancement of the local Self-similarity of the signal. The fractal characteristic is more obvious than the normal signal, and its value is smaller than the value of the signal under the normal state. At the same time, the Fractal dimension of bearing vibration signal under different fault forms has different numerical distribution, and the distribution curve has separability, which can distinguish the normal state and different fault modes.

**4 Conclusion**

Based on the analysis of bearing vibration signals, the concepts of empirical mode decomposition and correlation dimension are introduced to improve EMD, which can effectively identify false IMF components in the signal. After eliminating false IMF components, interference can be effectively eliminated and diagnostic reliability can be improved.

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2023-06-09