## 4 Results and Discussion
A similar cluster analysis was performed and is presented in Figure 16 for symptoms \(s_{7}\), \(s_{11}\), \(s_{12}\), and \(s_{16}\). In Figure 16a, four clusters are formed, of which well-recognizable objects are marked as (C\({}_{2}\), C\({}_{3}\), C\({}_{6}\)). The combination of the representation from the symptoms \(s_{7}\) and \(s_{11}\) does not allow the creation of separate clusters for the other aggregates, so they were labeled as C\({}_{y}\) because they contain other objects than C\({}_{x}\). In the next combination of symptoms, \(s_{7}\) and \(s_{12}\), the clusters from the previous partial results were confirmed (see Figure 16b). The best results were obtained with the \(s_{11}\) and \(s_{12}\). It was possible to recognize seven clusters of objects in Figure 16c based on the symptoms. The unrecognizable object is just the motor and the pump working together. This combination of symptoms and determination of clusters of objects represents a significant achievement in identifying and classifying the drill stand and its aggregates. The opposite case is shown in Figure 16d with symptoms \(s_{12}\) and \(s_{16}\). It can be seen that only four clusters could be formed. The significance is that these were clusters (i.e., C\({}_{2}\), C\({}_{3}\), and C\({}_{6}\)) for aggregates considered as objects (i.e., \(\mathbf{O}\equiv\mathbf{C}\)) that are weakly or hardly recognizable in other symptoms. All other objects form another cluster (C\({}_{2}\)). It is also important that the results of displaying the clusters in the plane represent a variant in which the symptoms are from different areas of signal processing. While the symptom \(s_{12}\) norm of autocorrelation of the signal is calculated in the time domain, the symptom \(s_{16}\) is in the frequency domain. The fact that the autocorrelation function of the signal and its power spectrum are equivalent and mutually transformable characteristics of the process also plays a role here. However, their numerical form in the structure of the symptom vector from which they are calculated is different. Figure 5:0 Cluster graphs of all objects in two-dimensional symptom space with symptoms \(s_{1}\), \(s_{2}\), \(s_{4}\), \(s_{5}\): (**a**) graph of symptoms \(s_{1}\) and \(s_{2}\) in the plane; (**b**) graph of symptoms symptoms \(s_{1}\) and \(s_{4}\) in the plane; (**c**) graph of symptoms \(s_{1}\) and \(s_{5}\) in the plane; (**d**) graph of symptoms \(s_{2}\) and \(s_{4}\) in the plane. The selected and displayed symptoms of objects and the created clusters in a two-dimensional plane are significant partial results from the presented research. They provide valuable information about suitable symptoms for forming clusters and classifying the drill stand's objects. In the following section of the paper, Figure 17 shows the clusters of symptom vectors of the drill stand aggregates in the three-dimensional symptom space. For such a display, three symptoms were used, making it possible to assume the differentiability of the aggregates. From the many research results, only the representative ones were selected. This three-dimensional representation comprised the following symptoms, i.e., \(s_{1}\)--mean values; \(s_{2}\)--dispersion values; \(s_{9}\)--energy values (see Figure 17a). There was sufficient diversity of the uniform clusters of aggregates created (i.e., C\({}_{1}\), C\({}_{2}\), C\({}_{5}\), C\({}_{6}\), C\({}_{7}\), and C\({}_{8}\)). A cluster could not be created for the hydrogenerator, motor, and pump objects. This makes their classification more difficult. For Figure 17b, where the symptoms (i.e., \(s_{9}\)--energy values; \(s_{11}\)--entropy values; and \(s_{12}\)-norm autocorrelation values) were displayed, it was possible to, at least partially, display the cluster (i.e., C\({}_{4}\)--for the motor and pump together) despite being located between the two defined C\({}_{5}\) and C\({}_{8}\). Similar results are provided in Figure 17c,d. Partial results are also presented in Figure 18a-d.