Aiming at the problem that the traditional multifractal detrended fluctuation analysis (MFDFA) using the least squares method to fit the trend term is prone to overfitting and takes a long time, this paper proposes a new non-stationary signal analysis method-smoothed prior analysis multifractal (SPA-MF).Firstly, the time sequence data is adaptively decomposed by smooth prior analysis (SPA) to eliminate the local trends of sequence data at different scales, and then the multifractal analysis is performed on the detrended data obtained by the decomposition. At the same time, the sparrow search algorithm (SSA) is used to optimize the parameter of the SPA, so as to eliminate the trend item data more accurately. Through the simulation signal which composed of the BMS signal and noise signal, the feasibility of SPA-MF for feature extraction is proved. Finally, SPA-MF is applied to extract the features of the reciprocating compressor valve vibration signal, and the extracted reciprocating compressor valve features are input into support vector machine (SVM) for classification and recognition. Through the analysis of the experimental results, it can be seen that the recognition rate of the valve features obtained by the traditional MFDFA method is only 87.5%, and the recognition rate of the SPA-MF method proposed in this paper reaches 96.87%, and the time spent on feature extraction using SPA-MF is only about 36% of that of MFDFA method, which proves the SPA-MF method is a feature extraction method with high accuracy and effectiveness.INDEX TERMS reciprocating compressor valve, smooth prior analysis, MFDFA, SPA-MF.

Aiming at the long-term unpredictability of the reciprocating compressor vibration signal, a non-parametric prediction method of reciprocating compressor time series based on the prediction credibility scale is proposed in this paper. The method is to take the multifractal singular spectrum as the prediction parameter and use the Smoothness Priors Approach (SPA) method to obtain the singular spectrum parameters of different components, and construct the phase space reconstruction dynamic modeling domains. It enables the prediction model to reflect the real-time characteristics of the dynamics evolution of complex systems and highlights the independent influence of each component on the prediction. Meanwhile, the information entropy saturation principle is introduced into the K-Nearest Neighbor (KNN) model to establish the improved K neighborhood dynamic non-parametric prediction model based on the maximum prediction credibility scale, which improves the credibility of the prediction results. Finally, a complete SPA&PSR_KNN prediction algorithm is proposed. Through example validation and error analysis, compared with KNN, BP, and SVM, it can be seen that the prediction results of spectral characteristic parameters obtained by this algorithm have smaller error and higher reliability, and faster operation speed. Thus, the prediction of vibration signal time series of reciprocating compressor is realized.