## 3 Results
### Neural Network Classifier  
The data sample for training the neural network was generated according to the approach presented in Section 2.1. The data set for the \"noise\" class was generated based on long-term noise realizations (Figures 6b and 7b) by reducing them to a certain peak level (from 40 to 60 dB). The data sample for the \"signal + noise\" class is generated in a more complex way. In the first stage, the acoustic signals obtained using FEM are converted from displacement units to voltage units using convolution with the impulse response of the AE sensor. Then, using weighting coefficients, the signal amplitudes are brought into conformity with the power-law distribution typical of welded joints with diffusion interlayers (Figure 10c--blue-point graph), and at the final stage, noise is added to the signals. The flow chart of the data retrieval algorithm is shown in Figure 19. On the basis of this algorithm, a training sample was formed, consisting of 1000 data sets--50 realizations of noise and 500 realizations of \"signal + noise\". A neural network of radial basis functions (RBF) and a multilayer perceptron (MLP) with different activation functions were considered as a neural network for constructing the classifier. The best classification result was achieved using an MLP with a sigmoid activation function of a neuron. The architecture of the neural network, the number of hidden layers and the number of neurons in each layer were determined by selection to minimize classification errors. The best result with classification error was achieved for a neural network with one hidden layer of 32 neurons (MLP 446-32-2); however, when \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Parameter** & **Parameter’s Equation** & **Initial Dimension** & **Pre-Processing Method** & **Final Dimension** \\ \hline \multirow{3}{*}{1} & Wavelet & \multirow{3}{*}{\(S_{f}(f)=\frac{1}{N}\sum\limits_{t=0}^{I_{max}}W(t,f)\)} & \multirow{3}{*}{250 \(\times\) 1} & Compresses 26 times with & \multirow{3}{*}{62 \(\times\) 1} \\  & coefficients & & & the help of DWT & \\  & averaged in time & \(N\)—number of samples & & approximation order 6 & \\ \hline \multirow{3}{*}{2} & Frequency wavelet & \multirow{3}{*}{\(E_{f}(f)=E(W(t,f))\)} & \multirow{3}{*}{250 \(\times\) 1} & Compresses 26 with the & \multirow{3}{*}{62 \(\times\) 1} \\  & kurtosis & & & & \\ \hline \multirow{3}{*}{3} & Wavelet & \multirow{3}{*}{\(S_{t}(t)=\frac{1}{N_{f}}\sum\limits_{t=0}^{I_{max}}W(t,f)\)} & \multirow{3}{*}{10,000 \(\times\) 1} & Compresses 26 times with & \multirow{3}{*}{161 \(\times\) 1} \\  & coefficients & & & the help of DWT & \\ \cline{1-1}  & averaged in frequency & \multirow{3}{*}{\(N_{f}\)—number of frequency coefficients} & \multirow{3}{*}{10,000 \(\times\) 1} & Compresses 26 times with & \multirow{3}{*}{161 \(\times\) 1} \\  & & & & the help of DWT & \\ \cline{1-1}  & time wavelet & \multirow{3}{*}{\(E_{t}(t)=E(W(t,f))\)} & \multirow{3}{*}{10,000 \(\times\) 1} & Compresses 26 times with & \multirow{3}{*}{161 \(\times\) 1} \\  & kurtosis & & & the help of DWT & \\ \cline{1-1}  & & & approximation order 6 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Classification features. Figure 19: Flowchart of the data sampling algorithm. varying the number of neurons in the hidden layer from 19 to 41, the classification error changed by no more than 2%. Figure 20 reveals the best training results for neural networks for the case of impulse noise (Figure 20a) and for the case of stationary noise (Figure 20b) for the different noise levels. At a noise level of no more than 50 dB, the classification accuracy was at least 90%; at a noise level of up to 55 dB, the classification accuracy decreased to 80%.