A new intelligent diagnosis method based on a hybrid algorithm of multi-scale permutation entropy and multi-core limit learning machine was proposed to address the complex internal structure of reciprocating compressors, difficulties in extracting bearing clearance fault features, and low recognition accuracy. Firstly, a generalized multi-scale permutation entropy (GMPE) algorithm was proposed to solve the problem that the mean coarse-grained method of multi-scale permutation entropy in the multi-scale process "neutralized" the dynamic mutation behavior of the original signal to a certain extent and reduced the accuracy of entropy analysis. Then, in order to solve the limitations of kernel extreme learning machine in dealing with complex data sample classification, Gaussian kernel function, polynomial kernel function and perceptron kernel function were linearly superimposed to construct a hybrid kernel function, and a multiple kernel extreme learning machine (MKELM) model was proposed. The simulation results show that the fault diagnosis accuracy of the proposed method is as high as 98%, and the intelligent diagnosis of different types of bearing faults is realized efficiently.