## 3 Evidential Reasoning Algorithm
### Decomposition Model and Transformer Condition Assessment  
In order to assess the condition of a complex technical system, such as a power transformer, it is necessary to collect, process and interpret a large amount of qualitative and quantitative information [2; 7; 15; 23; 25; 35; 40]. The required information is obtained by measuring and evaluating the observed object itself or by using remote monitoring and continuous information gathering. Regardless of the way the information is collected, it is necessary to transfer it to the qualitative domain using the appropriate semantic apparatus and the methods described in the previous chapter. Let us assume that the information has been successfully collected and transferred to the appropriate qualitative domain, that the attributes from Equation(3) have been successfully evaluated with the set of ratings defined by Equation (4) and that the attribute ratings have been given according to Equation (5). Considering all of the above, a general attribute or property based on the attributes directly or via lower-order attributes can be estimated depending on the used decomposition model. For instance, the condition of liquid or solid insulation of a power transformer can be determined by a chromatographic analysis and by measuring physical and electrical parameters. Chromatographic analysis determines the percentage of characteristic gases dissolved in oil (hydrogen, methane, acetylene, ethylene, etc. ), the measurement of physical parameters determines the oil moisture, paper insulation, borderline surface tension, oil temperature, etc., while the measurement of electrical parameters determines insulation resistance, dielectric loss factor, oil dielectric strength and other quantities, as shown in Figures 4-6, with Figure 5 showing a multi-stage decomposition model for a power transformer. Figure 6 shows the decomposition of a second-level attribute, i.e., it shows the decomposition of liquid rigid insulation. In the decomposition from general to baseline attributes, several levels of attributes can be seen. Each attribute \(e_{i}\) from a set of baseline attributes \(E\) should have a defined weight \(\omega_{i}\) and a confidence rating \(\beta i\) regarding the grade \(H_{n}\). For the purpose of this paper, a power transform [18; 41; 42; 43; 44] has been chosen as a proof of concept (PoC) example for a technical system and a decomposition model has been created for the same, with the corresponding general and baseline attributes. All attributes \(e_{i}\) of the given model have been assigned their appropriate weights \(\omega_{i}\). For the baseline attributes, values for which appropriate measurements can be carried out or be estimated for which confidence rating \(\beta i\) can be determined to its respectable grade \(H_{n}\). Since this is an extremely complex technical system consisting of several subsystems, determining the decomposition model is not a simple task. By creating a decomposition model, an attempt was made to decompose the power transformer into as many independent baseline elements of the system as possible, the condition of which can be determined by measurement or evaluation. The system elements in the decomposition model are called system attributes (3), and in the following text, the term system attribute will refer to the element of the decomposed system. Figure 5 shows the proposed power transformer decomposition model. There is a clear split into seven general attributes, which represent certain parts of the observed technical system and give an insight into the generally derived attributes, winding condition, liquid or solid insulation condition, boiler condition, conductor condition, control cover condition and cooling system condition. Each of the listed seven general attributes is divided into lower-order attributes down to the baseline attributes.