Variational time-domain decomposition of reciprocating machine multi-impact vibration signals

• A variational time-domain decomposition method for multi-impact signals is proposed. • Adaptive adjustment and wide applicability with three designed optimal parameters. • Applications to simulated and measured multi-impact signals achieve good performance. The vibration signal of reciprocating machinery is mainly formed by the superposition of multiple impact time domains related to the crankshaft angle. Impact recognition and decomposition are important for state feature extraction. The existing commonly used methods utilize the characteristics of the impact frequency domain to identify and decompose the impact through frequency-domain decomposition and reconstruction, which has some known limitations when decomposing complex and multi-impact non-stationary signals. In this study, an adaptive variational time-domain decomposition (VTDD) method was proposed for multi-impact vibration signals using the time-domain characteristics of impact waveforms. The method is mainly based on the energy concentration distribution and rapid amplitude change morphological characteristics of the impact signal. A variational model is constructed based on the minimization of high-order amplitude moments, and the alternating direction multiplier method is used to solve it iteratively. Thus, the model can adaptively find the time-domain impact waveform center and borders on both sides. Moreover, in view of the ubiquitous complex multi-impact vibration signals, an automatic solution method for the number of impacts is designed, and the optimized decomposition parameters of each impact can be adjusted adaptively. Simulated and actual mechanical multi-impact signal tests showed that the proposed method could adaptively and accurately identify the number of impacts and the center and boundary of the impact time domain in the multi-impact vibration signal. Finally, the method in this study was applied for engine valve fault vibration signal feature extraction, and the proposed method could effectively identify the additional impact caused by the fault and accurately extract the impact feature, demonstrating promising application prospects in the fault diagnosis of reciprocating machinery.