Predicting leakage in a piston pump using HP filter and ARIMA-GARCH model

Abstract: A piston pump has been widely used in large agricultural equipment, and walking machinery. However, the leakage can often be induced by the performance degradation with the increase of cumulative running time, even threat to the volumetric efficiency and operation safety of the equipment. It is a high demand for the accurate and rapid prediction of the performance degradation state in the piston pump for better working reliability. In this study, the leakage was selected as the characteristic indicator to quantitatively analyze the performance degradation of the piston pump. A Hodrick-Proscott (HP) filtering was first utilized to divide the leakage volume of the piston pump into the long-term trend data and short-term fluctuation data in the modeling. A correlation function graph of long-term trend term data was drawn to observe the effective lag order, and then the Akaike information criterion (AIC) criterion was used to select the optimal order. The autoregressive integrated moving average model (ARIMA(16, 3, 0)) was established to verify the data characteristics of the residual sequence using the statistical analysis. After that, a generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model was established to combine with the data characteristics of nonlinear and heteroscedasticity of long-term trend data. As such, an HP-ARIMA-GARCH model was established for the trend item data to predict the leakage of the piston pump. The residual sequence was approximately normal distribution after testing, fully meeting the requirements of the model. The leakage prediction was performed on the same pump in different time periods and different pumps in the same time period. The accuracy of the proposed model was then determined to compare with the linear ARIMA model and the nonlinear self-excitable threshold autoregression (SETAR) model. The mean absolute error (MAE), mean square error (MSE), and the mean relative error (MRE) of the HP-ARIMA model were significantly reduced in all prediction periods, compared with the traditional ARIMA model, where the maximum average relative error was 2.42%. Therefore, it infers that the HP filtering can be widely expected to effectively extract the long-term trend of leakage data, and then filter out the noise interference for the lower prediction error of the time series model. Furthermore, there was a relatively smaller error in the nonlinear time series model for the higher prediction accuracy, compared with the traditional linear model. Nevertheless, there was a varying prediction of the improved model in the prediction accuracy. The reason was the inconsistent leakage of the piston pumps during the different periods and the rapid fluctuation in the short time during operation. More importantly, the error of unfiltered data was less than that of the filtered, indicating that the nonlinear model performed better than the linear one. The highest prediction accuracy was achieved in the HP-ARIMA-GARCH model, where the average relative error was within 1.5%. Therefore, the improved time series model was more accurate than before, particularly suitable for the leakage prediction of the piston pump. Above all, the finding can provide a theoretical reference to quantitatively predict the performance degradation of piston pump, especially for the decision-making on the equipment reliability and operational safety. The long-term prediction accuracy can be further improved in the time series model in the future. Besides, the fluctuation data by the HP filter can also be expected for the higher prediction accuracy of leakage, considering the valuable information of the time series model, rather than the errors during modeling.