# Research on Prediction Method of Hydraulic Pump Remaining Useful Life Based on KPCA and JITL
## 1 Introduction
[29] established a set of RUL prediction and evaluation models for gears and bearings. [PERSON] et al. [30] established an RUL prediction and evaluation model for artillery barrels and verified its accuracy with a large amount of actual data. Just in time learning (JITL), a commonly used nonlinear modeling method [31], is also known as lazy learning [32] and locally weighted learning [33]. It uses process data to build local models to achieve high prediction accuracy. Therefore, the JITL modeling method can effectively solve the modeling problems of strongly nonlinear and time-varying industrial processes, and it has been extensively used in the industry [34]. [PERSON] et al. [35] first grouped variables by principal component analysis (PCA), subsequently selected similar sample data for each group of variables using the JITL method, and finally predicted the output by Gaussian process regression. The simulation and experimental results showed that the proposed method has good prediction performance. [PERSON] et al. [36] proposed a JITL method based on second-order similarity, and simulations and experiments verified that it can improve the prediction accuracy of a model. [PERSON] et al. [37] proposed an integrated soft-sensing modeling framework for JITL based on an evolutionary multi-objective optimization method. The experimental results showed the effectiveness and excellence of this method. [PERSON] et al. [38] proposed a JITL framework based on a variational adaptive encoder to solve the problem of non-consideration of the variable uncertainty in industrial processes, and showed the effectiveness of the method based on experiments. Although the JITL method is commonly recognized, its utilization for predicting the RUL of mechanical equipment is rarely reported. Therefore, this study proposes a prediction method based on JITL to predict the RUL of mechanical equipment on time and accurately. The evolution processes of many equipment faults follow a certain change rule. To detect faults on time, appropriate methods can be adopted to monitor the operating state of a mechanical equipment and observe the real-time changes in the equipment state [39]. The performance of a mechanical equipment tends to decline during operation, and the performance degradation process is frequently irreversible. The performance degradation of mechanical equipment makes their continuous operation impossible. Timely early warning of machinery equipment failure can be provided using appropriate monitoring methods to monitor the working state of machinery and equipment in real time. This will not only help equipment users to establish an appropriate maintenance and repair plan to prevent unexpected shutdowns of the mechanical equipment during use but also effectively prolong its normal operation time and avoid the economic losses caused by unexpected equipment failures. The most major feature of data-driven prediction is that it does not require establishing a complex mathematical model for the prediction and evaluation of mechanical equipment. It only needs collection of a large amount of data generated in the industrial field, based on which a model is built. The establishment of a data-driven model can utilize the real-time measurement data sampled by sensors; therefore, the characteristic parameters of the prediction model can be modified on time to accurately reflect the changes in the measured data. Data-driven prediction models mainly include the time-series prediction method [40], artificial neural networks [41], and support vector regression [42]. In this study, the established data-driven prediction model mainly predicts the RUL of a gear pump from two aspects: determining the performance degradation index and constructing an RUL prediction model of a gear pump. The main research steps of this study are shown in Figure 1. First, the gear pump pressure signals at a pressure port were collected by a pressure sensor.