The accuracy and stability of the envelope estimation function are enduring issues throughout the research process of LMD. This paper presents double interpolation and mutation interval reconstruction local mean decomposition (DIMIRLMD) to improve the stability of the demodulation process and the accuracy of PF components. DIMIRLMD first proposes a mutation interval reconstruction envelope algorithm using extreme symmetry points to suppress the demodulation mutation phenomenon, which disturbs the stability of the demodulation process, and then selects the optimal PF component from a double interpolation PF component library based on the index of orthogonality (IO) for a better hierarchical property. DIMIRLMD was employed to analyze the simulation signal and vibration signal of a reciprocating compressor in an oversized bearing clearance state, and the results illustrate its performances are more excellent than those of three other LMD methods. Furthermore, the envelope frequency spectrum obtained from the proposed LMD presents a clear double rotation fault frequency and lower noise disturbance.

The effectiveness of feature extraction is a critical aspect of fault diagnosis for petrochemical machinery and equipment. Traditional entropy analysis methods are prone to disruption by noise, parameter sensitivity, and sudden entropy variations. This study establishes a high-dimensional mapping entropy (HDME) method characterized by robust noise resistance, addressing the issues of parameter sensitivity and inadequate noise suppression inherent in traditional feature extraction methodologies. A mapping theory of high-dimensional space based on kernel function pattern recognition is proposed, which reassembles the sample vector after phase space reconstruction of time series. The multi-scale high-dimensional mapping entropy (MHDME) and refined composite multi-scale high-dimensional mapping entropy (RCMHDME) algorithms are further studied based on the idea of refined composite multi-scale. Application to simulated signals shows that the suggested methods reduce parameter sensitivity and enhance entropy smoothness. The development of a methodology to identify faults through MHDME is proposed. This approach integrates signal preprocessing and intelligent preference techniques to achieve pattern recognition of reciprocating compressor bearings in various wear conditions. Moreover, the identification findings demonstrate that the suggested approach can effectively extract the characteristics of the signal and accurately distinguish the effects caused by different faults.