# Research on Key Technology of Wind Turbine Drive Train Fault Diagnosis System Based on Digital Twin
## 4 Fault Diagnosis Method Based on Digital Twin
### Feature Extraction Based on Improved Variational Modal Decomposition (IVMD)  
Variational mode decomposition (VMD) [18; 19] is an advanced technique for signal processing, particularly suitable for the analysis of nonlinear and non-stationary signals. It decomposes a complex real signal into several Intrinsic Mode Functions (IMFs) with certain central frequencies and finite bandwidths, achieving signal decomposition and reconstruction. These mode functions are independent of each other and have good sparsity, making VMD an effective tool for signal preprocessing and feature extraction. Figure 8: Data transmission method of fault diagnosis system based on digital twin. When using the VMD algorithm to decompose a signal adaptively, the following input parameters are involved: modal decomposition parameter \(K\), modal bandwidth control parameter \(\alpha\), fidelity coefficient \(\tau\), termination condition \(\varepsilon\). Among them, the modal decomposition parameter \(K\) and the modal bandwidth control parameter \(\alpha\) have a great influence on the decomposition effect of the VMD algorithm. The modal decomposition parameter \(K\) determines the number of IMF components after the decomposition of the VMD algorithm; when the \(K\) value is set too large, it produces problems such as modal aliasing and false components, while when the \(K\) value is set too small, it leads to the phenomenon of under-decomposition, and the complex signals are not effectively separated, which causes certain troubles to the subsequent signal processing. The modal bandwidth control parameter \(\alpha\) mainly affects the frequency bandwidth of each IMF component and the convergence speed in the decomposition process. When \(\alpha\) is set too large, the frequency bandwidth of each IMF component becomes narrowed, resulting in signal loss. In addition, a value of \(\alpha\) that is too large also leads to large fluctuations in the center frequency of the IMF components during the decomposition process, long decomposition time, and low signal-to-noise ratio of the decomposed components, which affects the decomposition effect and accuracy of the VMD algorithm. When the value of \(\alpha\) is set too small, although the shock components in the signals can be detected more efficiently, at the same, there are more noise components and modal overlapping problems. Therefore, choosing the appropriate decomposition parameters \(K\) and \(\alpha\) becomes a major problem for the VMD algorithm in signal preprocessing applications. To address this problem, [PERSON] et al. (2020) proposed a method for adaptively selecting the decomposition parameters \((K,\alpha)\) of the VMD algorithm. This method adaptively determines \(K\) and \(\alpha\) by combining the kurtosis index with the energy loss coefficient. The flowchart is shown in Figure 9.  
Figure 9: Improved variational modal decomposition flowchart. The kurtosis index reflects the impulse characteristics of the signal and is sensitive to early weak faults. A series of locally optimal parameter pairs are preliminarily selected based on the maximum kurtosis criterion. The formula for calculating kurtosis is as follows:  
\[e(i)=\frac{1}{N}\underset{i=1}{\overset{N}{\sum}}\left(\frac{u_{i}-\overline{u} }{\sigma}\right)^{4} \tag{22}\]  
Herein, \(u_{i}\) represents the modal component IMFi, \(N\) is the length of the pattern, \(\overline{u}\) represents the average of \(u_{i}\), and \(\sigma\) is the standard deviation of \(u_{i}\). In order to search for the optimal value of the VMD decomposition parameter \(K_{r}\) within the range \([K_{b},K_{e}]\), the step size is set to \(1\), \(\alpha_{s}\in[\alpha_{b},\alpha_{e}]\). The search step size is set to \(\alpha\). Assuming the mode number for decomposition is \(k\), and the bandwidth control parameter is \(\alpha_{s}\), this pair of parameters is used to perform the VMD decomposition.