## 2 Materials and Methods
### Ultrasonic Signal Modelling  
Modelling was performed to study the behaviour of ultrasonic waves propagating through the layers of adhesively bonded aluminum to aluminum with brass inclusion defects located between metal and adhesive, as well as to study their propagation and reflection paths from the sample interfaces to determine time instances of each for determination of gates to be used when selecting the part of the signal of interest for determination of features. According to our previous work [3], it was discovered that the analysis of multiple interface reflections improves the probability of defect detection. Therefore, time instances of ultrasonic impulses that correspond to multiple interface reflections were studied in this part. Figure 4: Schematic of experimental set-up for radiographic inspection. Figure 3: Experimental set-up of ultrasonic pulse-echo immersion. The model that complies with the sample under investigation was modelled in MatLab software. Sample and medium characteristics are presented in Table 1. The distance between the focused transducer and the sample surface was 48 mm. As a result of modelling, pulse responses of each reflection from the structure boundary were obtained. Images with impulse plots characterizing the arrival time of each signal reflected from different sample boundaries with and without defects are presented below in Figure 5. Additionally, in Figure 6 the propagation paths of the ultrasonic wave for each signal impulse reflected from the sample interfaces, as well as their time moments for the non-defective and defective options, are presented. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Material** & **Thickness, mm** & **Density, kg/m3** &
\begin{tabular}{c} **Ultrasound** \\ **Velocity, m/s** \\ \end{tabular} \\ \hline Water & 48.5 & 998 & 1496 \\ Aluminum & 1.6 & 2780 & 6532 \\ Adhesive & 0.16 & 1214 & 2433 \\ Brass inclusion & 0.05 & 8730 & 4430 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the sample materials and medium. Figure 5: Impulses characterizing each signal reflection from the boundaries of the sample: (**a**) without defect; (**b**) with defect. According to obtained plots of impulses, the time moments of multiple reflected signals from the sample interfaces coincided: aluminum-adhesive interface (impulses 2, 5, 7) in the case of the sample without defect and aluminum-brass inclusion (impulses 2, 5, 7) for the sample with defect. In addition, for the sample with defect, there was a change in phase, for multiple interface reflections: aluminum-brass inclusion, which differed from the option of sample without defect. In addition, additional wave reflections from the brass inclusion bottom appear and overlap with other reflections from the boundaries. To obtain time diagrams of the signals propagating in the investigated structure, the convolution of the pulse response and the excitation signal was performed. The excitation signal was a sine burst of 15 MHz frequency 2 periods with a Gaussian envelope. The time diagrams obtained in defect-free and defective objects are presented in Figure 7a,b, respectively. In the case of defect-free objects, individual pulses reflected from different material boundaries were easily distinguished. Pulse no.1 was surface reflection, pulse no.2 was  
Figure 6: Ultrasonic wave propagation paths through the boundaries and time instances for: (**a**) not defected and (**b**) defected options. reflection obtained from aluminum-adhesive boundary, pulses no.3-5 were multiple reflections in adhesive layer, and pulse no.6 was the second reflection from aluminum-adhesive boundary. However, in the case of a defective sample, the analysis of the reflected signals (Figure 7b) was much more complicated: pulse no.1 was surface reflection, while pulse no.2 was the result of interference of pulses reflected from aluminum-brass, brass-adhesive, and adhesive-aluminum boundaries (see Figure 5b pulses 2-7). It can be observed that it was impossible to separate signals reflected from separate boundaries.