# Health State Prediction Method Based on Multi-Featured Parameter Information Fusion
## 2 Methods
### Som  
SOM is an unsupervised competitive learning algorithm that does not require pre-labeled data and learns the intrinsic connections of data through a self-organizing process. Its structure is shown in Figure 4, which mainly consists of an input layer and a map layer. The topology of the input data is preserved in the low-dimensional output layer by self-organizing the weights of the adjusting neurons [25]. Thus, it can discretize the input of any dimension into a 1D or 2D-dimensional discrete space. The specific steps for the implementation of this algorithm are as follows:  
1. Stochastically initialize the network weight.
2. The input vibration signal feature vector is \(X=\big{[}x_{1},x_{2},\cdots x_{n}\big{]}^{T}\). Calculate the Euclidean distance between the neurons in the topology layer and \(X\). The formula is as follows: \[d_{j}=\parallel X-w_{j}\parallel=\sqrt{\sum_{i=1}^{m}(x_{i}(t)-w_{ij}(t))^{2}}\] (7) where \(w_{ij}\) is the weight vector between neurons in the topology layer.
3. The neuron with the smallest distance is selected as the winning neuron C and the set of its neighborhood neurons is given.
4. Weight learning to correct the weights of the output neuron C and its neighborhood neurons. \[\Delta w_{ij}=w_{ij}(t+1)-w_{ij}(t)=\eta(t)\big{(}x_{i}(t)-w_{ij}(t)\big{)}\] (8) where \(\eta(t)\) is the gain function.
5. Train steps 2-5, until the maximum number of training sessions is reached.  
Figure 4: Structure of the SOM network.  
Figure 3: Structure of the BiLSTM network.  
Calculate the distance between the input feature vector and the winning unit C at each time point, Minimum Quantization Error (\(MQE\)). \[MQE=\parallel X-w_{c}\parallel\] (9) where \(w_{c}\) is the weight vector of the winning unit. Since there are many burrs and perturbations in the calculated \(MQE\), the accuracy of the prediction will be affected if it is directly used as HI; therefore, this paper decomposes the \(MQE\) into db5 wavelet packets and uses the low-dimensional trend term as the HI curve.  
The wavelet packet transform (WPT) is an analytical method that decomposes a signal into different frequencies and scales, providing a more detailed frequency resolution than traditional wavelet computing. The db5 wavelet is the fifth wavelet basis of the Daubechies wavelet family. It is performed as follows:  
1. Obtain the filter coefficients for the db5 wavelet: Let the original signal be \(x[n]\). The low-pass filter coefficients of the db5 wavelet are \(h[k]\). The high-pass filter coefficients are \(g[k]\) Low-frequency component: \[A[n]=\sum_{k}x[2n-k]h[k]\] (10) High-frequency component: \[D[n]=\sum_{k}x[2n-k]g[k]\] (11)
2. Recursive decomposition: Apply the low-pass and high-pass filters again to each new component A and D and continue the decomposition to obtain more detailed frequency components. Repeat the steps until a predetermined level of decomposition is reached.
3. Reconstructing the signal: wavelet packet reconstruction is the inverse of the decomposition process, where the signal is reduced by reconstructing filters for the low- and high-frequency components. Low-frequency reconstruction: \[x[n]=\sum_{k}A[\frac{n-k}{2}]h[k]\] (12) High-frequency reconstruction: \[x[n]=\sum_{k}D[\frac{n-k}{2}]g[k]\] (13)