# Damage Detection in Wind Turbine Blades Based on an Improved Broad Learning System Model
## 3 Damage Detection in Wind Turbine Blades Based on the CBNLM-BLS
### Construction of the CBNLM-BLS  
The CBNLM-BLS performs feature extraction on input data X. The input data are mapped into multiple feature nodes, which are classified as mapped features \(Z_{1},\ldots,Z_{n}\) in that part of the data. \(Z_{1},\ldots,Z_{n}\) are first multiplied by a set of random weights, \(W\), and then biased. The activation function is processed as the output of the enhancement node layer, noted as \(H_{1},\ldots,H_{m}\). Finally, \(Z_{1},\ldots,Z_{n}\) mixed with \(H_{1},\ldots,H_{m}\) is noted as \(A=[Z\mid H]\). The output is noted as \(Y=AW_{m}\). The core of the CBNLM-BLS is to find the pseudo-inverse of the feature nodes and enhancement nodes to the target value. The CBNLM-BLS is constructed in three steps as follows: generation of feature nodes, generation of enhancement nodes and finding the pseudo-inverse. The input layer data set is noted as \((s\times f)\times H_{1}\), where \(s\) denotes the number of samples and \(f\) denotes the number of features. For two-dimensional images, the code pulls it into a one-dimensional vector; the feature node layer contains \(N_{1}\) feature node windows, each containing \(N_{2}\) feature nodes and the enhancement layer contains \(N_{3}\) enhancement nodes. The construction of the CBNLM-BLS consists of the following steps. 1. The generation of feature nodes. A mapping of input data to feature nodes is created. The Z-score normalization is carried out for \(H_{1}\) to ensure that the input data have been normalized to between 0-1 of its expansion, making it \(H_{1[s\times(f+1)]}\). In order to generate feature nodes, bias terms can be added directly by matrix operations. Feature nodes are generated for each window. An \((f+1)\times N_{2}\)-dimensional random weight matrix, \(W_{e}\), is generated. The features of each sample are convolved and biased once with random weights to obtain the new features, \(A_{1}=H_{1}\times W_{e}\). The new features are sparsely represented and normalized, resulting in a window of feature nodes \(T_{1}\). \(N_{2}\) feature nodes are generated for each of the \(N_{1}\) feature windows. Each feature node is an \(s\)-dimensional feature vector. For the whole network, the feature node matrix \(y\) is a matrix of dimension \(s\times(N_{1}\times N_{2})\). 2. Enhancement nodes are generated. The CBNLM-BLS can make use of enhancement nodes to complement the random feature nodes, which are linear. The enhancement nodes are introduced with the aim of enhancing the non-linear elements in the network. A mapping of feature nodes to enhancement nodes is created. As with the feature nodes, the feature node matrix \(y\) is first normalized and expanded to obtain \(H_{2}\). Unlike the feature node, the coefficient matrix of the enhancement node is not a random matrix, but is a random matrix normalized orthogonally. The coefficient matrix of the enhancement nodes, \(W_{h}\), can be \(N_{1}\times N_{2}>N_{3}\) expressed as an \(N_{1}\times N_{2}\times N_{3}\) dimensional orthogonal normalized random matrix, which allows the feature nodes to be mapped to a higher dimensional subspace through non-linearity, making the network more expressive and provides an 'augmentation' effect. Afterwards, activation operations are performed on the augmented nodes to maximize the activation of the features expressed by the augmented nodes to generate \(T_{2}\). \(T_{3}\) is the final input of the generated network. Compared with the feature nodes, the enhancement nodes did not require a sparse representation or window iterations. Although the iterations of orthogonalization consumed some computational time, the time to add augmented nodes was often less than adding feature nodes, and the final input \(T_{3}\) of the network can be expressed as \([y,T_{2}]^{T}\), where each sample feature dimension is \(N_{1}\times N_{2}+N_{3}\). 3. Pseudo-inversion is sought. Let \(yy\) be the output value of the network, i.e., \(yy=T_{3}\times W\).