## 2 Methodology  
### General Assumptions  
_Research Object_  
In this paper, the authors present the evolution of the previous technique for determining the location of damage in a composite wind turbine blade coating (which was described in [19; 20]) using the statistic approach. The authors have already explained several aspects of the numerical and experimental research methodology. However, these aspects are still included in this section to ensure completeness. From the beginning of the works on the method of assessing the technical condition of composite coatings of wind turbine blades, the authors are guided by the assumption of use classical mechanical quantities, such as modal parameters. In particular, those, which are possible to experimentally obtain without the disassembly of the WT blade. At the same time, by using high-accuracy equipment for non-contact vibration measurements, it is possible to use a computational method that until now has not worked because of its sensitivity to noise. In addition to detecting damage, the method should also indicate the position of its appearance. For this reason, it is necessary to use signals containing information about changes at the local level, at least in one dimension of the spatial domain. Such quantities are undoubtedly mode shapes of natural vibrations of the blade. The general advantage of the damage detection method based on mode shapes analysis is independence from the technique of obtaining modal data. The modern techniques of vibration measurement allow determining the shape of the form with an adequate precision with a measurement time acceptable from the practical point of view. Vibration measurements can be performed using laser vibrometry supplemented by additional devices, such as is a derotator equipped with a special optical system, which synchronizes the laser beam with the rotation of the object under investigation. In recent years, the motion amplification technology, which can also be the basis of the presented method, has been very actively developed. The vibrations modal parameters can also be obtained from an operating wind turbine based on data collected from a system of piezoelectric or fibre optic sensors. Such measurement systems very often are an integral part of the modern blade structure. The basic motions of wind turbine blades can be divided into three types of vibrations depending on their orientations relative to the rotor plane. The following can be distinguished: bending in the plane perpendicular to the rotor plane, bending in the rotor plane and torsion. All three types of movements are schematically shown in Figure 1.  
Due to the blade's profile position relative to the rotor plane, the most significant deformations of the blade exist with vibrations in the direction of the axis of rotation. Therefore, this direction of vibrations was chosen for spatial signal analysis. In the present study, the authors did not include other types of vibrations. As noted, most researchers dealing with similar topics focus on the analysis  
Figure 1: General motion of the wind turbine blade: **a**—bending in the plane perpendicular to the rotor plane, **b**—bending in the rotor plane, **c**—torsion of the blade. of particular forms of vibration. However, the conclusions of previous authors' research, as well as literature sources, suggest there is a significant correlation between the impact of damage on the shape of vibrational forms and the ordering of modes. The best results of the detection process were obtained only when the damage site and local signal extremes overlap. The solution of this problem seems to be analysing the modes with more complex shapes (more local extremes), and in this way increasing the probability that the damage will be at the point of maximum deformation of the blade shape. However, these complex modes forms occur at higher frequencies, which is associated with a decrease in vibration amplitude.