Predictive Maintenance of Power Transformers: A Thermodynamic Fuzzy Logic Approach for Severely Imbalanced DGA Data

The ageing power transformer is one of the most important components of an electrical transmission grid, and it is important that diagnostic tools can be developed that can be applied in the field for reliable identification of faults when there is a significant data imbalance. In this paper, a new predictive maintenance model is introduced that combines Reliability, Availability, Maintainability and Safety (RAMS) engineering with Weibull parametric distributions to model combustible gas evolution within the normative limits of the IEEE C57.104-2019 standard. A forced-zero-probability matrix is introduced into the data generation pipeline so that all concentration ratios generated are within the thermodynamic plausibility range, which helps to overcome the thermodynamic implausibility that arises when using conventional oversampling algorithms like SMOTE. A Mamdani Fuzzy Inference System (FIS) was applied to evaluate all 2,000 synthetic DGA profiles, including 60 ground-truth critical fault cases (3.00%) deterministically injected to stress-test diagnostic boundary conditions. The framework achieved a 100% high-priority capture rate: all 60 ground-truth critical cases were classified into intervention-required states (39 as 'Critical' and 21 as 'Poor'), and no false 'Critical' alarm was recorded among the 1,940 non-injected records. Control-surface analysis verified Ethylene (C2H4) and Acetylene (C2H2) as the main reasons for Health Index appraisal, and directly indicated known high-energy degradation mechanisms. By maintaining complete end-to-end mathematical traceability, this architecture provides grid operators with an interpretable, standard-compliant predictive tool that resolves the operational opacity of black-box models.