Trackside acoustic signals are useful for non-contact measurements as well as early warnings in the diagnosis of train wheelset bearing faults. However, there are two important problems when using roadside acoustic signals to diagnose wheel-to-wheel bearing faults; one is the presence of strong interference from strong noise and high harmonics in the signal, and the other is the low efficiency of bearing fault identification caused by it. Therefore, from the viewpoint of solving the two problems, a sparse operation method is proposed for denoising and detuning the modulation of the roadside acoustic signal, and a machine learning classifier with a Genetic Algorithm (GA)-optimized Radial Basis Neural Network (RBFNN) is proposed to improve the rate at which the features of roadside acoustic signal faults are recognized. Firstly, the background noise is filtered out from the Doppler-corrected acoustic signal using the Sparse Representation method, and the inverse wavelet transform is reconstructed into a noiseless signal. Secondly, the interference high-harmonic signal in the signal is filtered out using the Resonant Sparse Signal Decomposition (RSSD) method. Then, the GA is selected to optimize the parameters of the RBF neural network and build a fault diagnosis model. Finally, the extracted acoustic signal feature set is trained on the network model, and the trained model is used for testing. In summary, the sparse operation on the roadside acoustic signal processing and the GA-RBFNN diagnosis model were verified as being very effective in the diagnosis of roadside acoustic train wheel pair faults through the simulation experiment.