To reasonably process the complex signals and improve the diagnosis accuracy of inter-shaft bearing incipient faults, this paper develops wavelet energy spectrum exergy (WESE) and random forest (RF) (short for WESE-RF) method with respect to acoustic emission (AE) signals. Inter-shaft bearing faults, which contain inner race fault, outer race fault, rolling element faults and normal status under different measuring points and different rotational speeds, are simulated based on the test rig of inter-shaft bearings, to collect the AE signals of these faults. Regarding the AE signals of inter-shaft bearing faults, the WESE values, one signal feature, are extracted from an information exergy perspective, and are applied to structure feature vectors. The WESE values of these AE signals are regarded as the sample set which include the training samples subset used to establish the WESE-RF model of fault diagnosis and the test samples subset applied to test the effectiveness of the developed WESE-RF model. The investigation on the fault diagnosis of inter-shaft bearing demonstrates the fault diagnosis method with the WESE-RF has good generalization ability and high diagnostic accuracy of over 0.9 for inter-shaft bearing fault. The efforts of this paper provide a useful approach-based information exergy and wavelet energy spectrum for inter-shaft bearing fault diagnosis.

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