A novel approach is suggested for improving the accuracy of fault detection in distribution networks. This technique combines adaptive probability learning and waveform decomposition to optimize the similarity of features. Its objective is to discover the most appropriate linear mapping between simulated and real data to minimize distribution differences. By aligning the data in the same feature space, the proposed method effectively overcomes the challenge posed by limited sample size when identifying faults and classifying real data in distribution networks. Experimental results utilizing simulated system data and real field data demonstrate that this approach outperforms commonly used classification models such as convolutional neural networks, support vector machines, and k-nearest neighbors, especially under adaptive learning conditions. Consequently, this research provides a fresh perspective on fault detection in distribution networks, particularly when adaptive learning conditions are employed.