Abstract: The issue of multi-source mixing in the vibration signals of the booster cylinder of hydraulic-driven reciprocating hydrogen compressors is addressed. A novel adaptive decomposition method, called variational cyclic impact mode decomposition (VCIMD), is proposed. This method combines the characteristics of variational models and cyclic impact modes, and through an optimized iterative process, it effectively decomposes multi-source mixed vibration signals, extracting relevant fault-related information. VCIMD assumes that the energy of cyclic impact modes and interference components in the signal is concentrated within a limited bandwidth and exhibits peak values that repeat at fixed periods. By minimizing the sum of the L2 norms of frequency and time center shifts for each mode, and constraining the error between the sum of cyclic impact modes and the original signal, the decomposition of the mixed signals is achieved. Compared to traditional methods, VCIMD can effectively handle multi-source mixed signals and decompose the impact signals from the single-cylinder piston. To address the lack of fault mechanism indicators in the diagnostic process for the booster cylinder of hydraulic-driven reciprocating hydrogen compressors, a Piston Vibration Harmonic Amplitude Accumulation Index (PVHAAI) is proposed. By extracting the amplitude of the piston’s reciprocating frequency and its harmonics, this index enables the detection of piston faults. Finally, the experimental results from a real hydraulic-driven reciprocating hydrogen compressor test platform demonstrate that the VCIMD method, combined with the PVHAAI, is highly feasible. It outperforms existing methods in terms of accuracy and precision, validating its effectiveness and advancement.

Key words: homogeneous multi-source mixing, variational cyclical impulse mode decomposition, vibration analysis, booster cylinder fault diagnosis, hydrogen compressor