# Improved SE-ResNet Acoustic-Vibration Fusion for Rolling Bearing Composite Fault Diagnosis
## 2 Methods  
### GS-SVR-EEMD with Window Function  
Ensemble empirical modal decomposition aids signal analysis by adding white noise to the EMD approach. Its resistance to miscibility is improved. Support vector machine regression employs an SVM approximation function to establish a nonlinear mapping between the input vectors and the feature space. Subsequently, a linear regression analysis is conducted within the feature space to formulate the decision function. The SVM function expression is as follows:  
\[f(x_{i})=\omega^{T}x_{i}+b, \tag{1}\]  
To address the challenge of SVM regression fitting, [PERSON] and his colleagues introduced an insensitive loss coefficient to the SVM, subsequently evolving it into the SVR method. The insensitivity loss factor \(\varepsilon\) is as follows:  
\[L_{\varepsilon}(f(x_{i})-y_{i})=\left\{\begin{aligned} 0, &\quad\quad\quad\quad\quad\quad\quad\quad\  
In nonlinear regression problems, a kernel function is utilized to transform the nonlinear data into a higher-dimensional feature space, within which linear regression is then performed. The regression function is given as follows:  
\[f(x)=\sum_{i=1}^{N}(\alpha_{i}-\hat{\alpha}_{i})\Phi(x_{i})\Phi(x)+b=\sum_{i=1}^{ N}(\alpha_{i}-\hat{\alpha}_{i})k(x_{i},x)+b, \tag{5}\]  
The kernel function employed is a Gaussian kernel function, expressed as follows:  
\[\mathrm{K}(x_{i},x)=e^{-g|x_{i}-x_{j}|^{2}}, \tag{6}\]  
The GS algorithm is applied to optimize the penalty factor and the parameters of the kernel function in SVR. The details of the GS-SVR process are as follows:  
1. Determine the range of the optimization search for GS.
2. Determine the step size. A grid is constructed based on the varying directions of growth for the parameters. The nodes within this grid represent the corresponding parameter sets.
3. Iterate over each parameter in the range to be searched and take a series of discrete values for each. Train the model by taking all combinations of the values for the parameters to be tested, respectively.
4. The parameters that give the best results in training the model are chosen as the optimal parameter set.
5. The optimal parameters obtained are substituted into the SVR model.  
In the methodology proposed in this paper, the initial signal undergoes endpoint extension. Samples proximal to the endpoints are chosen to constitute the training set. Subsequently, the aforementioned GS-SVR is utilized for data prediction. Predicted values are used as new boundary points for continuous prediction extension to a set value.  
The endpoint extension does not guarantee that the endpoints are extreme. Therefore, a rectangular window and the Hanning window, respectively, are used to window the delayed signal. EEMD decomposition is used after the endpoint extension. Valid IMFs are obtained after removing the delayed part.  
The procedure for noise reduction in the original signal is outlined as follows:  
1. The aforementioned GS-SVR-EEMD method, incorporating a window function, is employed to decompose the original signal, yielding a sequence of IMF components along with residual signals.
2. The correlation coefficient between each IMF component and the original signal is calculated.
3. At the first local maximum in the difference of the correlation coefficients, the preceding IMF component is eliminated.
4. Singular value decomposition noise reduction is conducted for the remaining IMF components.
5. The processed signal data is obtained by accumulating the IMF components after noise reduction.