# Fault Diagnosis Approach of Main Drive Chain in Wind Turbine Based on Data Fusion
## 2 Fault Features Extraction of Wind Turbine Main Drive Chain Based on Data Fusion
### Fault Features Extraction of Wind Turbine Main Drive Chain Based on Data Fusion
Dimensionality reduction of fault features  
For each type of typical fault, enough fault features should be extracted to determine the type of fault accurately. However, too many redundant fault features will not help increase the accuracy of fault determination, and contradictory samples inside will reduce  
Figure 4: Process of fault feature extraction based on fusion of two types of data. the accuracy of fault diagnosis. Therefore, it is necessary to reduce the dimensionality of fault features. In order to judge each type of typical fault, we require not only low-frequency fault and high-frequency fault features data, but also the combination of how the main shaft and generator rotational speed of the wind turbine are segmented according to the sizes and how the operation control mode of the wind turbine is classified according to the power-up and power-down operations. Therefore, it is necessary to take the rotational speed of the main shaft and generators and the operation control mode of the wind turbine as fault features when reducing the dimensionality of fault features. In this paper, the dimensionality reduction algorithm using Principal Component Analysis (PCA) is used to reduce the dimensionality of the fused eigenvectors. Based on the original n-dimensional features, the k-dimensional orthometric eigenvector is extracted as the principal component through centralized processing and calculation of covariance. It uses orthogonal transformation as the mapping matrix, calculates the covariance matrix of data matrix, obtains an eigenvalue and eigenvectors of the covariance matrix, and then selects the eigenvectors corresponding to the k characteristics with the largest eigenvalue (that is, the largest variance) from the matrix. In this way, the data matrix can be transformed into a new space, and dimensionality reduction of data characteristics can be realized. The main processing steps for a high-dimensional space data sample \(x\in\mathbb{R}^{d}\) are: use the orthogonal matrix \(A\in R(k\times d)\) to map the sample to a low-dimensional space \(Ax\in\mathbb{R}^{k}\), where \(k\ll d\) states that the purpose of dimensionality reduction is to alleviate the curse of dimensionality and classify data better. The specific algorithm is as follows:  
Input: n-dimensional sample set \(D=\left(x^{(1)},x^{(2)},\ldots,x^{(m)}\right)\), the dimension to be reduced to is k.  
Output: the sample set \(D^{\prime}\) after dimensionality reduction. 1. Centralize all samples:  
\[x^{(i)}=x^{(i)}-\frac{1}{m}\sum_{j=1}^{m}x_{j}^{(i)} \tag{2}\]  
where m is data volume of sample \(x^{(i)}\),
2. Calculate the covariance matrix \(XX^{T}\) of the sample,
3. Perform singular value decomposition on the matrix \(XX^{T}\),
4. Take out the eigenvectors \(w_{1},w_{2},\cdots,w_{k}\) corresponding to the largest k singular values, and normalize all the eigenvectors to form an eigenvector matrix \(W\),
5. For each sample \(x^{(i)}\) in the sample set, transform it into a new sample:  
\[z^{(i)}=W^{T}x^{(i)} \tag{3}\]
6. Obtain the output sample set:  
\[D^{\prime}=z^{(1)},z^{(2)},\cdots,z^{(k)} \tag{4}\]  
Through the dimensionality reduction processing using the PCA algorithm, the dimension of the fault characteristic vector can be reduced from hundreds to dozens, which can markedly reduce the complexity of the following step of data processing.