Considering the advantages of contactless fault diagnosis, a novel sound based fault diagnosis method for railway point machines (RPMs) is proposed. Firstly, a denoising method based on empirical mode decomposition (EMD) is proposed. The useful intrinsic mode functions (IMFs) are selected using kurtosis and energy criteria to reconstruct the denoised signal. Then, multi-scale fractional permutation entropy (MFPE) is proposed inspired by fractional calculus, which is more powerful than the classical multi-scale permutation entropy (MPE). And a two-scale algorithm is developed to avoid neglecting the information contained at the end of the signals in the coarse-graining process. Finally, the feasibility and superiority of the proposed method (D-FMPE-T) based on denoising method and two-scale algorithm are verified using support vector machine optimized by particle swarm optimization (PSO-SVM) through comparing with some commonly used feature extraction and classification methods. Besides, CWRU is also utilized for verification of the superiority of the proposed method. Experiment results show that the proposed method performs best. The identification accuracies on normal-reverse and reverse-normal switching processes, and CWRU data sets reach 99.3%, 99%, and 99.17% respectively, demonstrating the feasibility and effectiveness of the proposed method.