## 2 Materials and Methods
### Information and Kinetic Approach  
A distinctive feature of this approach is that, rather than record the acoustic emission signal first, the physical processes are first modeled to assess the current state of the test object by means of concentration and kinetic indicators of the AE process and universal physical constants found by processing the results of AE tests and using reference s-n curves. The method uses a multilevel model [16] based on fracture micromechanics, the kinetic concept of strength, and the statistical regularities of elastic wave radiation. The strength and AE parameters of structural materials are the result of superposition and depend on the results of fracturing and plastic deformation processes simultaneously occurring in the material. The diagram of the multilevel model is created with its mathematical description being expressed by Equation (1) [16]. The multilevel model of acoustic pulse flow parameters combines statistical and physical approaches to testing. It allows for obtaining information that reduces the uncertainty of strength properties at the macro-, micro-, and nano-levels of strength tests to make a reasonable choice of AE indicators. The approach is described in more detail in [16; 17], but it is the first time it has been applied to quality control in the area of strengthening technologies. \[\xi(t)=k_{AE}C(t)=V\int\int\int_{\Delta t,f,u}\Phi(\Delta t,f,u)dudfd\Delta tC( t), \tag{1}\]  
where \(\xi\) is the primary informative AE parameter (number of pulses, relative amplitude, energy, etc. ); \(k_{AE}\) is the acoustic emission coefficient; \(C(t)\) is the concentration of fractured structural elements; \(V\) is the volume of the material being tested; \(\Phi\left(\Delta t,f,u\right)\) is the probability density of the distribution of AE signals by intervals \(\Delta t\) between them, frequency \(f\), and amplitude \(u\). Given the stochastic nature of elastic wave radiation, the triple integral included in the expression has the meaning of detection probability, that is, the probability that the parameters of elastic waves coming from the AE source fall into the range of frequencies, AE signal amplitudes, and time intervals recorded by the measuring device. The approach is based on the idea that the test object is a combination of structural elements whose individual states determine the state of the object as a whole. The strength indicator is the time until the structural elements become fractured, which is described by the Zhurkov formula [18; 19; 20], and the key factor determining the moment of fracturing is the rate of damage accumulation until reaching a critical value. As the strength parameters of the material are not homogeneous, the equation for describing the growth in the concentration of fractured elements has the following form:  
\[C(t)=C_{0}\int_{\omega_{0}}^{\omega_{0}+\Delta\omega}\Psi(\omega)\bigg{\{}1- exp\bigg{[}-\int_{0}^{t}\frac{dt^{\prime}}{\theta_{avg}}(U_{0},\omega(t)) \bigg{]}\bigg{\}}d\omega, \tag{2}\]  
where \(C_{0}\) is the initial concentration of structural elements in the material before failure; \(\omega_{0}\) is the lower limit of the range of \(\omega\); \(\Delta\omega\) is a representative dispersion range of \(\omega\) values by structural elements; \(\Psi(\omega)\) is the distribution density function of the values of \(\omega\) by structural elements; \(\theta_{avg}\) is the average time before one structural element fails, which is found by the Zhurkov formula; \(U_{0}\) is the energy that activates the process of fracturing; \(\omega=\gamma\sigma/KT\) is the strength parameter of the structural element, where: \(\gamma\) is the activation volume [21; 22] (nanostructure parameter); \(\sigma\) is tensile stresses in the structural element; \(K\) is the Boltzmann constant; and \(T\) is the absolute temperature. The ratio between the parameters of the function \(\Psi(\omega)\) reflects how heterogeneous the strength parameters of the material are.