# Impact Features Extracting Method for a Reciprocating Compressor Based on the ABC-SGMD Model
## 1 Introduction  
Piston air compressors are widely used as the typical volumetric compressors in industrial processes. Due to the complex motion mechanisms and differentiated fault mechanisms, various forms of failure during service are exhibited. with over 60% of failures occurring in the gas valves. However, the state characteristics of reciprocating air compressors are often obscured by the impact characteristics of vibration signals. Given the nonlinear, non-stationary, and multi-component coupling characteristics of its vibration signals, traditional analysis methods bring with them many limitations, making effective fault diagnosis difficult [1; 2]. Currently, the mainstream methods for processing and modeling vibration signals still rely on time-frequency domain analysis. However, classical time-frequency domain methods, such as those referenced in Table 1[3; 4; 5; 6; 7], do not perform satisfactorily when dealing with complex nonlinear systems. The widely used method of Empirical Mode Decomposition (EMD) [8] suffers from endpoint effects, mode mixing, over/under-sifting, and lacking robustness against noise. In contrast, nonlinear relationships between data are efficiently captured, dimensionality is reduced, and features are extracted by the Symplectic Geometric Modal Decomposition (SGMD) [9] method, based on symplectic geometry spectral analysis [10]. This innovative signal processing technique preserves the integrity of the original time series while exhibiting good decomposition and adaptability. SGMD has also been proposed and applied in bearing fault studies [11], which primarily demonstrates its feasibility. However, limited by the high computational complexity of differential geometry and the lack of adaptive dimensionality selection, the performance of the SGMD method is less reliable when facing non-stationary signals. After decomposing the original sequence, introducing entropy algorithms to assess the complexity of each decomposition component and reorganizing them based on entropy similarity can reduce the modeling complexity [12]. Researchers often employ single-scale entropy algorithms such as sample entropy [13], permutation entropy [14], and fuzzy entropy [15]. Among these, the refined composite multiscale dispersion entropy (RCMDE) offers unique advantages. It effectively analyzes nonlinear and non-stationary signals under different scales and time transformations, providing richer information [16]. Compared to other algorithms, RCMDE demonstrates better robustness and is applicable to various signal types. Therefore, selecting multiscale dispersion entropy for signal analysis yields more accurate and comprehensive feature extraction and analysis results. However, a single refined composite multiscale dispersion entropy cannot guarantee complete recognition rates. Thus, this paper utilizes the amplitude variation index and peak-to-peak values, which best reflect reciprocating compressor fault characteristics, to assist in fault identification [17]. In this study, the algorithm of the SaDE-ELM method for pattern recognition is proposed. Compared to methods such as Support Vector Machine (SVM) [18], Artificial Neural Networks (ANNs) [19], and Decision Trees, SaDE-ELM not only demonstrates a faster training speed and better generalization ability but also allows for the simplification of the model structure, reducing the complexity of hyperparameter tuning. Especially for small- to medium-scale pattern recognition problems, SaDE-ELM may be considered as an efficient choice [20]. However, the selection of the appropriate pattern recognition method needs to be based on specific circumstances for large-scale complex datasets and deep learning tasks. Passively, the challenges encountered by traditional methods in extracting faults from reciprocating air compressors are investigated in this study.