Diagnosis model of noise-type defects for dry-type transformer based on time–frequency-space tensors and improved prototypical network under small sample conditions

•TFS tensor represents transformer states, facilitating input to deep models and capturing multi-dimensional data efficiently.•TFS method enhances diversity; model generalizes better with samples increased 8 times.•HyperPCA-based method reduces TFS tensor channels from 64 to 11, cutting training time by 45% and improving accuracy by 15%.•A custom residual network boosts prototype network efficiency, increasing speed by 15% and accuracy by 10%.•Experiments show the prototype network’s stability with an average precision of 96.0% ± 2.1% for 15 samples per defect type.