## 1 Introduction  
Damage can be defined as a change in the state of a material that disrupts the functioning of the structural element currently or may cause it in the future and which can lead to the destruction of this element or, in the worst-case scenario, the entire structure. Defects usually have the form of delamination, cracks or local destruction of the material due to corrosion or fatigue. They may also be in the form of voids or undesirable inclusions. Their cause may be external factors, such as exceeding the structure working time and various types of errors: service, maintenance, renovation, assembly and technological. The issue of early detection, location and estimation of the structural damage is one of the most important engineering problems because it is closely related to the safety and durability of the facility. Non-destructive defect identification methods are a relatively young, continually developing field, e.g., a contactless method implementing the thermovision camera [1]. New directions of research are indicated, different approaches are used, and many advanced methods are developed. Many of these are based on the analysis of structural response signals. A very promising tool for signal analysis, based on mathematical theory, is a wavelet transform (WT), which allows non-stationary signals to be effectively analyzed. Due to the possibility of multiresolution decomposition/analysis (MRA), it manages to extract even small, local signal disturbances from the global structural response, which often requires taking into account a considerable number of data. Moreover, if the wavelet analysis is used to identify the defect, it is enough to process the data obtained from the damaged structure without the need to compare it with the signal of the undamaged system. This is the main advantage of the method because in real experiments, the undamaged structure response signal is usually unavailable, and the numerical model may not be a precise representation of reality. Wavelet transform was first used to detect defects in the mid-1990s, in which [2] the vibration signal obtained in a computer-simulated experiment for a beam with a crack was analyzed. Numerically simulated experiments were also presented in [3; 4; 5], in which the effectiveness of the WT in detectingdamages in plates, beams and trusses, based on the analysis of static or dynamic structural response signals, was demonstrated. Experimental verification, conducted with the use of a laser scanning vibrometer, of numerical tests for eight vibration modes of the cantilever beam with cuts of 5, 10 and 20% of the beam height is presented in [6]. The effectiveness of the discrete wavelet transform (DWT) for detecting damage and the influence of the wavelet order on the reliability of the obtained results was tested in real dynamic tests of concrete slabs in [7]. Another non-destructive diagnostic method is the acoustic emission method (AE). In this method, elastic waves generated during physical, chemical or biological processes are analyzed. The analysis of the parameters of the recorded signals allows locating the emission source, which may be, for example, partial discharges occurring in the insulation of electrical power devices [8; 9]. Online acoustic emission monitoring in order to observe damage progression in the filler-loaded glass/epoxy samples and characterize different fracture mechanisms associated with loading was presented in [10]. The literature provides information on the use of wavelet analysis of acoustic signals concerning, for example, the identification of micro damages in composite materials [11], analysis of changes in the structure of glass fiber under load [12] and the location of AE sources based on the amplitudes of wavelet transform [13].