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.