# CEEMDAN-IHO-SVM: A Machine Learning Research Model for Valve Leak Diagnosis
## 3 Results
### Valve Leakage Diagnostic Experiments  
We collected acoustic emission signals from internal valve leakage under varying pressure intensities and valve opening degrees for subsequent classification experiments. The data acquisition platform comprises two components. First, we used the internal valve leakage experimental platform, which integrates adjustable valves and pressure gauges to ensure stable and accurate simulation of various leakage scenarios. The valves used are manual gate valves with diameters of 200 mm, 300 mm, and 500 mm. The second component is the acoustic emission acquisition system, which includes an acoustic emission sensor, a preamplifier, a high-speed data acquisition card, and acoustic emission signal acquisition software, thereby enabling real-time signal collection. The acoustic emission sensor utilized in this study is the GI40, manufactured by Qingcheng Company, which operates within a frequency range of 15 kHz to 80 kHz. The data acquisition card employed is the USB-3200 from Altai Company, which is capable of achieving a maximum sampling frequency of 500 kHz. The valve used in the experiments is a ball valve with a diameter of 15 mm. Figure 5 shows the components of the experimental platform. Figure 4: Convergence curves of the four algorithms. After the system was set up, debugging began. The valve to be tested was closed, the pressure-reducing valve was opened, and the pressure was adjusted at the valve inlet. Once the pressure gauge stabilized at 0.2 MPa, the experiment commenced. First, the signal was recorded when the valve was in the closed position; then, the valve was gradually opened, adjusting the opening incrementally. The data on the valve scale were documented and the acoustic emission signals of valve leakage at openings of 5%, 10%, 15%, 20%, and 25% were collected. After completing this set of experiments, the pressure at the valve inlet was increased to 0.4 MPa, 0.6 MPa, and 0.8 MPa, and the experiment was repeated. After finishing the experiment, valves with different diameters were selected and subjected to the aforementioned method to continue the experiments until all valve leakage detection tests were completed. The overall frame diagram is shown in Figure 6.  
Figure 5: Experimental platform device. Figure 6: Overall frame diagram. According to the literature, the acoustic emission signals from internal valve leaks ranged from 10 kHz to 50 kHz. Therefore, the sampling frequency of the signal processing terminal should be set to 500 kHz, in accordance with the Nyquist sampling theorem, to effectively reconstruct the signal. Additionally, the recording duration was set to 2 s to ensure that 1,000,000 data points were collected each time. Taking the data under the diameter of 200 mm and the pressure of 0.2 MPa as an example, the fault classification and labels are shown in Table 4.  
The CEEMDAN algorithm was employed to decompose the original signals, thereby yielding the IMFs corresponding to each state. Given that the number of IMFs generated through decomposition varies across different states, the Pearson correlation coefficients between the original signal and the resulting IMFs were computed. The top five IMFs, based on the correlation coefficients, were selected for further analysis. The calculation of the Pearson correlation coefficient is defined as follows: \(\sigma\) is the standard deviation, \(\mathbf{E}\) is the mean value, and \(\mathbf{cov}\) is the covariance. \[\rho_{X,Y}=\frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}}=\frac{E(XY)-E(X)E(Y)}{\sigma_ {X}\sigma_{Y}} \tag{33}\]  
The fuzzy entropy values of the IMFs corresponding to each fault type form a \(100\times 5\) fault feature matrix. In this study, 80% of the samples for each fault type were designated as training samples while the remaining 20% were utilized as test samples.