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This paper presents a simple and effective approach to recognize ultra-high-frequency (UHF) signals of partial discharges (PDs). Six artificial insulation defect models were designed to generate UHF PD signals, which were detected by a Hilbert fractal antenna in a series of experiments. Wavelet packet (WP) decomposition was used to decompose the UHF PD signals into multiple scales. A number of multi-scale fractal dimensions and energy parameters of UHF PD signals were computed and linear discriminant analysis (LDA) was used to reduce the dimensionality of the problem while maximising separation among defected types. The low-dimension data were successfully classified via a simple scheme based on finding the closest class centroid. As a comparison, a back-propagation neural network (BPNN) and a support vector machine (SVM) were also used for recognition of the defects and found to offer no advantage. The recognition experiments were replicated 100 times to establish the robustness of the solutions and the LDA was also found to be superior in this respect. Further results examining the effects of refraction and reflection by transformer components support the conclusion that the proposed approach has potential for the recognition of PDs in practical situations.