# Research on Key Technology of Wind Turbine Drive Train Fault Diagnosis System Based on Digital Twin
## Case Study
### Experimental Verification of Fault Diagnosis Model
To validate the feasibility and superiority of the proposed IVMD algorithm, this section decomposes the experimental data using both the conventional VMD algorithm and the IVMD algorithm and compares the decomposition results. Taking the outer ring fault vibration signal in Figure 15 as an example, based on a previous experience [25], the mode decomposition parameter K in VMD is set to 4, and the mode bandwidth control parameter \(\alpha\) is set to 2000. The decomposition results are shown in Figure 16a. It can be seen that the original signal is decomposed into four IMF components, each with an independent characteristic frequency, and the frequency bands between the components are distinctly separated. This indicates that each component obtained through the VMD algorithm can effectively retain the frequency characteristics of the original signal and effectively eliminate invalid components. However, there is evident over-decomposition in IMF2 and IMF3, and the central frequencies of IMF3 and IMF4 are too large, indicating possible under-decomposition. Next, we use IVMD to decompose this set of signals. The search range and step size of \(K\) and \(\alpha\) are preliminarily set as \(K\in[2,7]\) and \(\alpha\in[1000,10,000]\), respectively, and the search step size \(\Delta\alpha=500\). Select the best VMD parameters according to the above IVMD algorithm flow. By calculating the minimum ELC value, the optimal decomposition parameters for IVMD (5, 2000) were determined. Using (5, 2000) as the IVMD decomposition parameters, the signal is decomposed, and the results are shown in Figure 16b. It can be seen that the components obtained through the IVMD algorithm do not exhibit cross-phenomena, demonstrating that the IVMD algorithm can effectively mitigate the mode mixing problem. The central frequencies of the IMF components are closely spaced without under-decomposition, proving that the modal components obtained through IVMD decomposition can comprehensively reflect the frequency characteristics of the original signal and effectively eliminate false components and noise. To further validate the effectiveness of the IVMD algorithm, we selected the IMF3 component from VMD and the IMF4 component from IVMD based on the minimum envelope entropy criterion for envelope analysis. The results are shown in Figure 17. From Figure 17a, it can be seen that the envelope spectrum of the signal decomposed by IVMD clearly shows the fault characteristic frequency and harmonics. In contrast, Figure 17b shows that the fault characteristic frequency in the signal decomposed by VMD contains  
Figure 15: Time domain waveform of vibration signals in different states of rolling bearing. many interferences, hindering the extraction of fault characteristics. In summary, the proposed IVMD algorithm can effectively decompose signals. The optimal IMF component of the rolling bearing under each working condition is obtained from the above section, and then the NCMDE algorithm is used to extract the feature of each IMF component to construct the feature vector set for the following fault mode recognition. Figure 16: Decomposition of the result and the resulting frequency domain graph: (**a**) VMD decomposition result; (**b**) IVMD decomposition result. In order to test the performance of the classification model, we use four different fault diagnosis models to conduct the fault classification experiment, namely, IVMD-LSSVM, VMD-PSO-LSSVM, IVMD-PSO-SVM, and IVMD-PSO-LSSVM. According to the previous experience [20], in each state, 29 sets of data are extracted at a ratio of 1:1 as the training set for the subsequent fault recognition model and 29 sets of data as the test set for the model, so there are 116 training sets and 116 test sets in the experimental rolling bearing vibration dataset. We input the mentioned data into these models for training and testing.