# A Novel Feature Selection Based on VMD and Information Gain for Pipe Blockages
## 4 Experimental Results and Analyses
### Sensitive IMF Selection  
VMD is applied to the acoustic signals for buried pipe conditions. The center frequency values of the components of the inherent mode function obtained by VMD decomposition are distributed from low to high, and the number of IMF components K is evaluated from 1. If the center frequency of the last IMF reaches its maximum value for the first time, it means  
Figure 4: Time-frequency map: (**a**) clean; (**b**) lateral connection; (**c**) 55 mm blockage; (**d**) 55 mm + 40 mm blockage. that no insufficient decomposition occurs, and the value of K increases gradually until the maximum center frequency remains relatively stable. The parameter of decomposing mode number K was decided in advance, where it was determined according to a previous study [38]. Therefore, the K value in the paper was set as 12. As played in Figure 5, a set of acoustic signals with the coexistence of 40 mm, 55 mm blockages, and lateral connections in the pipe were selected for VMD processing, the K value of 9 pipe operating conditions was finalized at 12 after the pre-setting process and the analysis of maximum center frequency for various components. Thereby deriving a total of 12 IMF components. The 12 IMF components after VMD decomposition represent the signal characteristics at different frequency scales, but the effective components were different for different operational conditions in the pipeline. The goals of component filtering were to simplify the feature space, eliminate complexity, and enhance the system performance. A component is considered more important if it can bring richer information to the classification model. Its presence or absence in the classification model leads to a larger change in the amount of information, and the difference in information amount before and after its addition is precisely the information gain it brings to the model. Utilizing the information gain, M effective components were selected from the 12 original components, which were used for the identification of different pipe conditions. The major steps for information gain based filtration of effective components are as follows:  
Step 1: Computation of the given sample set D. Nine types of pipe conditions are selected, each of which has 300 samples, totaling 2700 samples. For each sample, 12 components form a dataset D.  
Step 2: Computation of information gain. The information gains of the 2700 samples are calculated according to formula (3), as well as the corresponding partition points. Step 3: Selection of root node. As shown in Figure 6, the information gain value of \"IMF1\" is the largest among the 12 components, which is thus selected as the root node of the decision tree. The data set D is split into two parts based on the calculated partition points. Figure 5: VMD component decomposition diagram. Step 4: Selection of subnodes. For the remaining 11 components, the information gains are calculated as per Step 2, and the component with the largest information gain is selected as the leaf node of the decision tree. As shown in Figure 6, \"IMF3\" is the largest component making the dataset D less than or equal to the information gain in IMF1, which is thus selected as the subnode of the left subtree at the second layer. Meanwhile, \"IMF11\" is the maximum value making the dataset D greater than the information gain in IMF1, which is selected as the subnode of the right subtree at the second layer. After passing through the second layer, the data are divided into four parts. Step 5: For the remaining nine discrete wavelet packet components, their information gains are calculated as per Step 2, where the given threshold for information gain is 0.5.