Early identification of weak-signal fault features under very unfavorable environment using adaptive lifting scheme packet

Aim: Early identification of weak-signal fault features is obviously highly desirable but highly difficult. We have worked on this difficult problem for a number of years^{[2, 5, 6]}. We now propose using the adaptive lifting scheme packet and apply it to identifying successfully weak-signal fault features of a certain gearbox. In the full paper, we explain in some detail the lifting scheme packet and its application; in this abstract, we just add some pertinent remarks to listing the four topics of explanation. The first topic is: the principles of the lifting scheme packet. In this topic, we present the three steps of its decomposition process: Splitting, prediction and updating. The second topic is: The construction of the lifting scheme packet. In this topic, we work out the algorithms for decomposing and reconstructing the lifting scheme packet, as given in eqs. (5) through (8) and eqs. (9) through (16) respectively in the full paper. The third topic is: The calculation and adaptive selection of the operators of the lifting scheme packet. In this topic, we adaptively select at each adjacent sample point the operators of the lifting scheme packet that match the weak-signal fault features through using the auto-correlation coefficients of decomposed signals as objective function and determining the values of their auto-correlation coefficients. The fourth topic is: The analysis of vibrational signals. In this topic, we apply the lifting scheme packet to analyzing the vibrational signals of a certain gearbox. We decompose and reconstruct its vibrational signals to identify the fault features of modulation waveform and cyclic impact or impulse signals, as illustrated in Fig. 3 in the full paper. Then we conduct the demodulation analysis, whose results are given in Fig. 5 in the full paper, and reach the conclusion that the rotating frequency of the small gear in the high-speed axle is the faulty source modulation frequency. The application results show preliminarily that the adaptive lifting scheme packet is effective for the early identification of weak-signal fault features.