Aimed at nonstationary and nonlinear characteristics of vibration signal of reciprocating compressor, generalized dimensions is a simple, rapid and efficient characteristic parameter extraction method in the multifractal theory. However, the sensitivity of noise for the waved local fractal dimension made the fault state separability is poor. The optimized local mean decomposition (LMD) algorithm was used based on wavelet denoising, in order to highlight the status of the main information by combined with the correlation coefficient to extract the main component of product function (PF). The idea of multiscale integer optimization to generalized dimensions was introduced, based on calculated the maximum of average distance between the states whereby best separability, the feature matrix was constructed. Support vector machine (SVM) and incremental learning K adjacent (IKNNModel) statistical algorithm training and sample recognition were explored. Comparison indicates that the proposed algorithm can improve the fault feature separability and recognition accuracy.