## 1 Introduction  
The major factor that contributes to the deterioration of the insulation characteristics of dielectrics is partial discharges (PD), which occur under the influence of high-intensity electric fields. Partialdischarges occur on the surface of or inside dielectrics, causing deterioration of their electrical insulating characteristics. PD in solid dielectrics often entails electrical treeing, which involves the formation of conductive or semi-conductive channels in the shape of trees inside the dielectric. Discharges in the channels result in further development of trees and finally lead to the low-resistance short-circuit of electrodes. That is why the forecasts for insulation in which treeing occurs are disastrous. Therefore, the information on whether treeing has been initiated in the insulation becomes of supreme importance for the purposes of high voltage (HV) insulation condition diagnostics. Early studies on partial discharges (PD) occurring in dielectrics were carried out at the beginning of the Twentieth Century by [PERSON], who investigated the impact of partial discharges on breakdown [1]. The development of the studies was stimulated by the development of power engineering and the high unreliability of paper and oil insulation used in HV cables, transformers, and generators. The studies were continued in the 1930s by [PERSON] [2] and [PERSON] [3], who demonstrated that partial discharges in paper and oil insulation caused electrical treeing, which involves the formation of channels in the shape of trees or shrubs, or a sight in a dielectric, and are the main cause for the low durability of high-voltage cables with this type of insulation. The main direction of studies in the second half of the Twentieth Century included the following: electrical treeing initiation [4], studies on the relationship between tree length, voltage impact time, and time to breakthrough [5; 6], studies on the properties of cables with solid polyethylene insulation [7], and insulation breakthrough tests [8]. There have also been studies on partial discharge detection and measurement methods. Initially, mainly oscilloscopic methods were proposed by [PERSON] [9]. Some studies on the development of insulation ageing models were also carried out [10]. In addition to detailed papers, several publications summarized and systematized the current knowledge status [11; 12]. The turn of the Twenty-first Century saw studies related to forecasting treeing in dielectrics. Engineering progress contributed to the use of modern and sophisticated methods of partial discharge testing. [PERSON] [13; 14] pointed out the possibility of examining treeing incubation by means of electroluminescence. Papers by [PERSON] [15] and [PERSON] [16] discussed the ways to predict treeing propagation using the theory of fractals and deterministic chaos. Since trees have a fractal-like nature, the authors used fractal size to identify the shape of the tree being formed. The theory of deterministic chaos was, in turn, used to identify the probable directions of tree development. One can observe a tendency for the development of non-invasive partial discharge methods, and the acoustic emission method in particular [17; 18; 19; 20; 21; 22]. Advanced signal analysis methods, such as wavelet transformation or artificial neural networks, used for analysis parameters of solid insulation systems and identification of the discharge source and type have been employed [23; 24; 25; 26; 27; 28; 29]. Among the methods used for the detection of partial discharges (e.g., in the transformer tank), the acoustic emission method is common, focusing on the recording and analysis of an acoustic wave propagating in the material as a result of external impact exerted on it. The sources of the impact may include mechanical pressure (testing the stress inside the material) [30; 31; 32; 33; 34], electric field (partial discharge testing), or magnetic fields (used for Barkhausen noise analysis).