Considering that the inadequacy of the inferior performance of the symmetric difference analytic energy operator (SD-AEO) technique in the presence of vibration interferences with higher amplitudes

an improved analytic energy operator (AEO) based on SD-AEO is proposed in this work. This proposed energy measure takes advantage of the higher-order symmetric difference to substitute the symmetric difference for the sake of boosting the signal-to-interference ratio (SIR)

which can enhance the ability to detect the weak fault signal in the presence of vibration interferences with larger magnitude. Furthermore

the energy transformation of this proposed energy operator is weighted by absolute value to prevent the negative values in the transformed signal. Under the simulated tests

the superiority of the immunity to intensive noise and interferences as well as the non-negative property is demonstrated. Finally

the proposed energy detector is applied to the real-world data measured from the defective bearings

and it is found that this proposed fault detection tool can successfully identify the weak fault signatures under a severe working condition.