## 3 Evidential Reasoning Algorithm
### Decomposition Model and Transformer Condition Assessment
#### 3.5.2 Condition Assessment
For the condition comparison of two or more points in time, the terms from (26-28) can be used. All computations required to perform the aggregation procedure were performed numerically using the condition assessment application developed by the authors. To describe the computation procedure, the computation of the condition of the power transformer for the latest point in time is presented in abbreviated steps. The chosen example is interesting due to the largest amount of available data. In order to successfully commence the calculation procedure, it is assumed that all available quantitative data for the basic attributes have been collected and weights have been set for all attributes, both general and baseline. According to the qualitative data presented in Table 2, the aggregation procedure starts with the baseline attributes and general attributes. Complex mathematical steps in performing the aggregation procedure are omitted here, and the procedure is presented in detail in [3; 37], so only the final values of the general attribute ratings are shown. Taking into account the confidence ratings \(\beta i\) in grade \(H_{n}\) for baseline attributes \(e_{i}\) and their assigned weights \(\omega_{i}\), and after carrying out the aggregation procedure for the second level general attributes, the following distributions are obtained: \begin{tabular}{l} S (Load) = ([excellent, 1)] \\ S (Remaining life cycle) = ([excellent, 1)] \\ S (Aging momentum) = ([excellent, 1)] \\ S (General derived attributes) = ([excellent, 1)] \\ S (Winding capacity) = ([excellent, 1)] \\ S (Magnetizing current) = ([excellent, 1)] \\ S (Winding active resistance) = \{([excellent, 1)] \\ S (Winding shift control) = ([excellent, 1)] \\ S (Windings) = ([excellent, 1)] \\ S (Chromography) = \{(unsatisfactory, 0.0295), (very good, 0.2489), (excellent, 0.7216)] \\ S (Physical values) = (very good, 0.0454), (excellent, 0.08275), (H, 0.1271)] \\ S (Electric values) = \{(excellent, 0.7895), (H, 0.2105)] \\ S (Liquid/solid isolation) = \{(unsatisfactory, 0.0084), (very good, 0.0823), (excellent, 0.8306), (H, 0.0787)] \\ S (Boiler air dry) = ([excellent, 1)] \\ S (Boiler oil level) = ([excellent, 1)] \\ S (Seal loosening) = \{(excellent, 1)] \\ S (Boiler) = ([excellent, 1)] \\ S (Conductor insulation dielectric loss factor) = \{(good, 0.0563), (very good, 0.2550), (excellent, 0.6886)] \\ S (Conductor insulation capacity) = \{(excellent, 1)] \\ S (Conductor thermal imaging) = \{(H, 1)] \\ S (Primary side capacity shift index) = \{very good, 0.2951), (excellent, 0.7409)] \\ S (Secondary side capacity shift index) = \{very good, 0.1212), (excellent, 0.8788)] \\ S (Contductors) = \{(good, 0.0035), (very good, 0.1492), (excellent, 0.7920), (H, 0.0554)] \\ S (Number of operations) = \{(excellent, 1)] \\ S (Total switched current) = \{(excellent, 1)] \\ S (Top changer motor power) = \{(excellent, 1)] \\ S (Top changer) = \{(excellent, 1)] \\ S (Pump condition) = \{(excellent, 1)] \\ S (Ventilator condition) = \{(excellent, 1)] \\ S (Cooler efficiency) = \{(excellent, 0.5355), (H, 0.4645)] \\ S (Cooking system) = \{(excellent, 0.9934), (H, 0.0606)] \\ which results with the following distribution: \\ S (ET)\({}_{\text{event/M}_{\text{M}_{\text{M}_{\text{M}_{\text{M}_{\text{M}_{\text{M}_{\text{M}_{\text{M}_{\text{M}}}}}}}}}} =\{(unsatisfactory, 0.019), (good, 0.0005), (very good, 0.0385), (excellent, 0.9331), (H, 0.0261)] \\ which represents the overall condition assessment of the power transformer for the chosen point in time. \\ \end{tabular}   
From the above, it can be seen that the overall condition of the power transformer is rated as unsatisfactory with a confidence rating of 0.019, good with a rating of 0.0005, very good with a rating of 0.0385 and excellent with a rating of 0.9331. The uncertainty of the assessment is 0.0261 and results from the absence and/or unfamiliarity of all defined input data. To obtain a more comparable grade, it is possible to calculate the final assessment.