Traditional signal-decomposition methods require manual setting of the basis function, which cause uncertainty and other problems. Accordingly, a self-driven Fourier decomposition method (FDM) can be used for signal processing and a feature extraction and recognition method based on FDM energy entropy is proposed in this paper. First, FDM decomposition is performed on the vibration signal to obtain several Fourier intrinsic band functions. The signal is then reconstructed based on the autocorrelation principle, and the signal FDM energy entropy feature is extracted. Finally, the fused feature vectors are sent to a support vector machine for training, and damaging vibrations are identified. Experimental results show that the proposed method can correctly identify different types of vibration signals with high accuracy. This method will enable improved recognition of damaging vibrations in optical fiber prewarning systems, thus aiding the development of pipeline protection technology.