Aiming at the nonlinearity, nonstationarity and multi-component coupling characteristics of reciprocating compressor vibration signals, an integrated feature extraction method based on the variational mode decomposition (VMD) and multi-fractal detrended fluctuation analysis (MFDFA) is proposed for a fault diagnosis for a reciprocating compressor valve. Firstly, to eliminate the noise interference, a novel VMD method with superior anti-interference performance was utilized to obtain several components of the quasi-orthogonal band-limited intrinsic mode function (BLIMF) from a strong non-stationarity vibration signal, and a consistent number K of BLIMFs was selected based on a novel criterion for all fault states. Secondly, the MFDFA method, which can describe the multi-fractal structure feature of non-stationary time series, was applied to analyze each BLIMF component, and the parameters of MFDFA were employed as the eigenvectors to reflect the structure characteristics and local scale behavior of the vibration signal. Then, the principal component analysis (PCA) was introduced to refine the eigenvectors for a higher recognition efficiency and accuracy. Finally, the vibration signals of four types of reciprocating compressor valve faults were analyzed by this method, and the faults were identified correctly by pattern classifiers of BTSVM and CNN. Further results comparison with other feature extraction methods verifies the superiority of the proposed method.

Local mean decomposition (LMD) is a new time–frequency analysis method which can decompose a signal adaptively into a set of product function (PF) components, and the construction of local mean function and envelope function plays an important role in the accuracy of its PF components. Aiming at the strong nonstationarity, nonlinearity and multi-component coupling characteristics of reciprocating compressor vibration signals, an improved LMD was proposed by a novel construction method of local mean function and envelope function. By introducing an extreme symmetrical point between two extreme points and using the Monotone Piecewise Cubic Hermite Interpolation (MPCHI) instead of Cubic Spline Interpolation (CSI) to construct the envelopes, a novel construction method of local mean function and envelope function was proposed, and then the improved LMD algorithm was given based on this novel construction method. The improved LMD was applied to decompose the vibration signals of reciprocating compressor fault states, and the comparison of details between different LMD decomposition results verified the superiority of this improved method. The envelope frequency spectrum of PF component gives a more significant peak of fault frequency than that of original signal, which further indicates that this proposed method is competent for the diagnosis of reciprocating compressor oversized bearing clearance fault.

Underdetermined blind source separation (UBSS) has garnered significant attention in recent years due to its ability to separate source signals without prior knowledge, even when sensors are limited. To accurately estimate the mixed matrix, various clustering algorithms are typically employed to enhance the sparsity of the mixed matrix. Traditional clustering methods require prior knowledge of the number of direct signal sources, while modern artificial intelligence optimization algorithms are sensitive to outliers, which can affect accuracy. To address these challenges, we propose a novel approach called the Genetic Simulated Annealing Optimization (GASA) method with Adaptive Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering as initialization, named the CYYM method. This approach incorporates two key components: an Adaptive DBSCAN to discard noise points and identify the number of source signals and GASA optimization for automatic cluster center determination. GASA combines the global spatial search capabilities of a genetic algorithm (GA) with the local search abilities of a simulated annealing algorithm (SA). Signal simulations and experimental analysis of compressor fault signals demonstrate that the CYYM method can accurately calculate the mixing matrix, facilitating successful source signal recovery. Subsequently, we analyze the recovered signals using the Refined Composite Multiscale Fuzzy Entropy (RCMFE), which, in turn, enables effective compressor connecting rod fault diagnosis. This research provides a promising approach for underdetermined source separation and offers practical applications in fault diagnosis and other fields.

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.

Underdetermined blind source separation (UBSS) is a critical technique in the field of intelligent mechanical operation and maintenance, allowing for the disentanglement of source signals from their mixtures without the need for prior knowledge or extensive sensor information. The accuracy of source signal recovery hinges on the estimation of the mixing matrix. To promote sparsity in source signals, we employ methods like sparse representation and sparse component analysis. Traditional approaches, such as Short-Time Fourier Transform (STFT), often suffer from limited time-frequency resolution, motivating the adoption of the Synchronous Extraction Transformation (SET) algorithm, which closely approximates the ideal time-frequency transform. SET significantly enhances the sparsity of the signals, thus facilitating the separation of mixed signals. In the context of sparse component analysis, we introduce an improved Density Peaks Clustering (DPC) method that successfully resolves source number estimation issues and robustly eliminates outliers. This improvement leads to a more accurate mixing matrix estimation. To determine cluster centers, we employ K-means clustering, further refining our source separation process. In summary, our paper presents an innovative approach that combines the Synchronous Extraction Transformation (SET) with ’an improved Density Peaks Clustering (DPC)’ and K-means for mixing matrix estimation. Source signal recovery is achieved through a shortest-path algorithm. Extensive simulations and experiments validate the method’s effectiveness, outperforming traditional techniques. When applied to rolling bearing fault diagnosis, the proposed approach effectively separates complex signals and accurately identifies fault characteristic frequencies.