Since it is difficult for the traditional fault diagnosis method based on dissolved gas analysis (DGA) to meet today’s engineering needs in terms of diagnostic accuracy and stability, this paper proposes an artificial intelligence fault diagnosis method based on a probabilistic neural network (PNN) and bio-inspired optimizer. The PNN is used as the basic classifier of the fault diagnosis model, and the bio-inspired optimizer, improved salp swarm algorithm (ISSA), is used to optimize the hidden layer smoothing factor of PNN, which stably improves the classification performance of PNN. Compared with the traditional SSA, the sine cosine algorithm (SCA) and disruption operator are introduced in ISSA, which effectively improves the exploration capability and convergence speed. To verify the engineering applicability of the proposed method, the ISSA-PNN model was developed and tested using sensor data provided by Jiangxi Province Power Supply Company. In addition, the method is compared with machine learning methods such as support vector machine (SVM), back propagation neural network (BPNN), multi-layer perceptron (MLP), and traditional fault diagnosis methods such as the international electrotechnical commission (IEC) ratio method. The results show that the proposed method has a strong learning ability for complex fault data and has advantages in accuracy and robustness compared to other methods.