## 3 Results
### Classification Features Choice  
Detection of defects in dissimilar welded joints by the AE method is reduced to the problem of recognizing time realizations containing a useful AE signal in a noise flow. Since the AE signals corresponding to the propagation of a defect have an impulse waveform and are characterized by a fairly low activity (see Section 3.1), and noise is recorded continuously, it is advisable to divide the data into two classes: \"noise\" and \"signal + noise\". To determine the parameters that allow us to identify the differences between the classes, a wavelet analysis of the noise and AE signals against a noise background was performed. Figure 15 shows the results of wavelet analysis for the case of impulse noise: realization of noise is shown in Figure 15a, and the AE signal against the noise background in Figure 15b. Figure 15c,d show wavelet spectrograms of these signals. The Morlet wavelet was used as a wavelet function; the resolution of the wavelet spectrogram is 10,000 samples along the time axis (10,000 us with a sampling interval of \(\Delta\)T = 1 us) and 150 samples by frequency (300 kHz with a frequency resolution of 2 kHz). The amplitude values were  
Figure 14: Simulated signals at a distance of 0.3 m with azimuthal coordinate 0\({}^{\circ}\) (**a**), with azimuthal coordinate 180\({}^{\circ}\) (**b**) wavelet spectrograms for the simulated signal (**c**), and for the measured signal (**d**). selected so that the signal-to-noise ratio was approximately equal to 3 dB. The noise spectrogram visualizes areas corresponding to the impulse components of noise, localized in time (up to 50-100 \(\upmu\)s) and stretched along the frequency axis. The AE signal against the background of noise (Figure 15d) is characterized by greater energy in the low-frequency region, up to 100 kHz, and a greater duration of the impulse. Figure 16 shows the results of wavelet analysis for the noise of the loading device. As can be seen from the wavelet spectrogram, the noise of this type is continuous and low-frequency, corresponding to the frequency band of 50-100 kHz. The AE signal against the background of noise is revealed on the wavelet spectrogram as a time-localized region of interest corresponding to the low-frequency range. The wavelet transform is a signal decomposition at different scale levels; when choosing a long observation interval (longer than the stationarity interval of stochastic noise), the wavelet decomposition character remains similar for different intervals of long-term noise implementation. Signal detection using the wavelet transform is possible since a short-term impulse signal introduces a change point in the time-frequency decomposition character of the noise signal. Figure 15: Time realization of impulse noise (**a**), time realization of AE signal against the background of impulse noise (**b**), wavelet spectrogram of noise (**c**), and wavelet spectrogram of AE signal against the background of impulse noise (**d**). Therefore, even though in the cases under consideration, the frequency ranges of the noise and useful signals significantly overlapped, and in the case of impulse noise, the signal and noise had close parameters in the time domain, the use of the wavelet transform made it possible to identify the differences between useful AE signals and noise. Various parameters of the time and frequency projections of the wavelet transform coefficients were considered as parameters for detecting the AE signal. The most informative parameter turned out to be the wavelet kurtosis, which represents the kurtosis calculated for wavelet coefficients corresponding to different frequencies (temporal wavelet kurtosis) and different times (frequency wavelet kurtosis) [26, 27]. Figure 17a shows the dependence of time wavelet kurtosis vs. frequency for impulse noise (blue graph) and for the AE signal against the background of impulse noise (red graph).