Research on Common Fault Diagnosis of Mud Pump Based on Wavelet Packet Analysis

The utilization of vibration signals to diagnose faults in centrifugal pumps is a crucial research direction in this field. Traditional frequency domain processing methods, such as Fast Fourier Transform (FFT), may not be effective in analyzing complex signals where multiple types of faults occur simultaneously at the same frequency. This paper proposes the use of wavelet packet analysis as an alternative. By analyzing fault conditions caused by blade damage and clearance wear in a mud pump and comparing the results to those obtained through the FFT analysis method, the superior accuracy of wavelet packet analysis is demonstrated.


WAVELET PACKET ANALYSIS THEORY
Vibration signal analysis mainly includes two processes: wavelet packet decomposition and reconstruction [2] .In the wavelet packet decomposition process, the filter bank reduces the number of data points by half each time it is applied.If the original data length is 2 N and it is decomposed L times, the data length of each frequency band becomes N/ 2 L−1 , which is 1/2 L of the original length.Each layer of subbands covers the frequencies occupied by the signal, but the resolution of different layers is different.Therefore, by using wavelet packet decomposition, the corresponding best filter can be selected by choosing the appropriate subbands at each layer.The decomposition structure is shown in Figure 1 below: The acceleration sensor used in this paper for the mud pump has a sampling frequency of 100 Hz and an analysis frequency of 50 Hz.The frequency range represented by each extracted frequency band is shown in Table 1.The frequency range of each band can be extrapolated accordingly for further decomposition.The average energy on the j-th sub-band at the i-th level of the wavelet packet decomposition is given by: where dl (i, j) is the wavelet coefficient.Assuming that a signal is decomposed into M subbands by wavelet packet decomposition, these M subbands are not necessarily at the same decomposition level, and the total energy of the signal is equal to the sum of the energy of each subband, which is E (0, 0).
Normalization of the feature factors in Equation ( 1) can obtain the feature vector extracted by wavelet packet, which is given by: (2)

Rotor imbalance
During high-speed operation of a centrifugal pump, the rotor may vibrate abnormally due to limitations in the material of the centrifugal pump, errors in processing or installation, and rotor wear, resulting in incomplete coincidence between the axis of rotation and the center of mass of the rotor.The imbalance vibration of the rotor refers to forced vibration generated under the influence of periodic centrifugal forces, in which the centrifugal force produces a disturbance at a certain point on the rotor or bearing every revolution, resulting in a corresponding vibration response at that point.The dominant vibration frequency in the frequency domain is the higher frequency vibration, along with smaller second and third harmonic frequencies.

Rotor misalignment
For the centrifugal pump to operate, the rotor needs to be connected by a coupling for rotational motion.Due to installation errors, mismatched impellers, wear during operation, and permanent deformation caused by loads, the rotor is prone to misalignment faults.Rotor misalignment can be divided into bearing misalignment and coupling misalignment, and in practical engineering, the latter is generally referred to as rotor misalignment.Large centrifugal pumps usually use elastic pin coupling, which differs from rigid or gear couplings [3] .Coupling misalignment can be divided into three types: parallel misalignment, angular misalignment, and comprehensive misalignment.Parallel misalignment results in a vibration component dominated by the second harmonic frequency in the radial direction of the shaft; angular misalignment can cause vibration in the axial direction, with the second harmonic frequency component being the largest, along with certain multiples and even harmonics.
Comprehensive misalignment is a combination of parallel misalignment and angular misalignment, and its frequency domain characteristics include both of their performances.The severity of the specific fault can be determined based on the superposition principle [4] .
Other common faults and the frequency domain signal characteristics of rotor imbalance and rotor misalignment are summarized in Table 2  Mainly dominated by power frequency, with complex and intermittent characteristics

EXPERIMENTAL DATA VERIFICATION AND ANALYSIS
This study used a piezoelectric accelerometer installed in a vertical direction on the pump bearing side of the No. 1 hold of a dredger, with a sampling frequency of 100 Hz.The data was classified and labeled into seven types: normal operation, clearance wear, mud pump bearing damage, excessive vacuum suction, shaft seal leakage, impeller blade damage, and impeller cavitation.Due to the large amount of data generated during mud pump operation, this study selected 600 sets of data that were marked as normal operation when faults occurred and 1, 600 sets of data for each blade damage and clearance wear, respectively.The first 1, 200 sets of data, when faults occurred, were used to obtain the feature vectors of the fault signals, and the last 400 sets of data were used to test the accuracy of identifying the fault types through feature vectors.Blade damage corresponds to rotor imbalance faults, while clearance wear may cause both rotor imbalance and rotor misalignment [5] .According to the dredging pump operation record, the actual operating speed was around 306 rpm or 5.1 Hz.When two or more faults occur simultaneously, fault coupling may occur [9] , but its principle is not discussed in this paper.After observing the original signals, it can be seen that there is a considerable amount of noise, which may be caused by irregular impacts of mud blocks in the pump and the friction between the dynamic and static parts of the pump [6] .When a fault occurs, the vibration intensity significantly increases.
By observing the frequency spectra, it can be seen that in the normal state, the vibration of the pump is not significant, mainly concentrated at the power frequency (5.1 Hz) due to the characteristics of the pump during normal operation.However, in the states of blade damage and clearance wear, the vibration mainly concentrates at the power frequency, and there will be smaller secondary (10.2 Hz) and tertiary (15.3 Hz) harmonics, which belong to rotor unbalance fault or rotor misalignment fault.Their frequency domain characteristics are relatively similar, making it difficult to distinguish the specific type through FFT.Without prior labeling in actual production, it is more prone to misjudgment.In addition, the amplitude of the triple harmonic in the frequency spectrum of the fault signal is already very small.Therefore, the focus is on the lower frequency band, and the higher frequency band is no longer studied [10] .
In the wavelet decomposition, after 4 levels of decomposition, based on experience and the reasons mentioned above, the interested frequency bands are selected as shown in the following figure 3. Using the built-in wpdec and wpcoef functions in Matlab, the original data is decomposed and reconstructed by using the db4 wavelet, which has been shown in previous research [7] and [8] to minimize reconstruction error.The energy of each frequency band is calculated according to Equation (1) and then normalized according to Equation ( 2   The feature vector of blade wear is e1=[0.1011,0.5174, 0.1127, 0.1540, 0.0682, 0.0467] T , while the feature vector of clearance wear is e2=[0.0698,0.4863, 0.1580, 0.1579, 0.0828, 0.0453] T .It can be seen that the energy of the fault signals for blade wear and clearance wear is concentrated in the frequency range of 3.125~6.25Hz, which is close to the power frequency, consistent with the results of FFT.Although the distribution of the two faults in the frequency range of 0~12.5 Hz is similar, there are still differences.In each frequency band at low frequencies, the energy distribution of clearance wear is smoother, while the energy distribution of blade wear fault is more concentrated in the power frequency and frequencies lower than the power frequency.
The energy percentage of each frequency band obtained by verifying the remaining 400 data is shown in Table 4 According to the above feature vectors, fault A is a blade wear fault, and fault B is a clearance wear fault, which is consistent with the original data labels.Therefore, the method of using wavelet packet decomposition and fault feature vector identification is effective for cases where FFT is not easy to recognize.

CONCLUSION
The feature extraction method based on the wavelet packet decomposition algorithm is an advanced technique in fault diagnosis of rotating machinery.It not only solves the difficulty of identifying faults with FFT but also overcomes the drawback of wavelet decomposition unable to reconstruct the highfrequency part of the original signal.In this paper, the principle and algorithm of wavelet packet decomposition are briefly described, and experimental data are processed and compared by using both wavelet packet decomposition and FFT.The results show that wavelet packet decomposition can provide rich information, which complements the deficiencies of FFT.By decomposing the two types of fault signals at multiple levels and extracting the feature vectors of the fault signals, the fault types are successfully identified.

Figure 2 .
The original signals and frequency spectrum diagrams of normal operation, blade damage faults, and clearance wear faults are shown in the following figures.Raw time domain signals and spectrograms

Figure 3 .
Figure 3.The wavelet packet decomposition dendrogram used in this article ), or directly calculated by using the wenergy function.The results of the decomposition of the two types of fault signals in Figure 2 are shown in Figure 4.

Figure 4 .
Figure 4. Wavelet packet decomposition of blade wear and clearance wear Table 3 displays the frequency range and energy percentage of the corresponding frequency band obtained by wavelet decomposition for blade wear and clearance wear.

Table
. The range of frequencies represented by each node

Table 2 .
below.Frequency domain characteristics in the event of mud pump failure

Table 3 .
Frequency range and energy distribution of each frequency band after wavelet decomposition of fault signals

Table 4 .
: Frequency range and energy percentage of each frequency band after wavelet decomposition of verification signals