# Research on Prediction Method of Hydraulic Pump Remaining Useful Life Based on KPCA and JITL
## 1 Introduction  
With the rapid development of science and technology and the modern manufacturing industry, the structures and functions of mechanical equipment are gradually shifting toward achieving integration, intelligence, refinement, and comprehensiveness. For a mechanical system, a high integration level and high complexity of the structure and function are associated with a high probability of failure. A fault in one of the mechanical components, or even in a tiny part, if not found and repaired in time, may cause the entire system to fail (so that the machine is unable to operate normally) or lead to property damage or even casualties [1]. A gear pump has the advantages of a small volume, lightweight, good technicality, and strong self-suction. It is commonly used in construction engineering, metallurgy, aerospace, automobile manufacturing, shipping, and other fields. As the \"heart\" of a hydraulic transmission system, the stable operation of a gear pump is an important requirement for its normal operation. Therefore, conducting appropriate monitoring and maintenance and providing warnings of early failures of gear pumps are highly significant [2]. At present, the methods of signal analysis, monitoring, and fault diagnosis of mechanical equipment are becoming increasingly mature, practical, and specialized. Themethods of monitoring and fault diagnosis of mechanical equipment that are extensively used worldwide mainly include vibration analysis, sound analysis, oil sample analysis, and temperature monitoring [3]. Among them, fault diagnosis methods based on vibration monitoring and analysis have the following main advantages: (1) Under the condition in which early failure of mechanical equipment is not evident, the collected vibration signals can still be analyzed to determine its position, degree, and cause. For example, [PERSON] et al. accurately identified the fault degree of rolling bearings based on a deep learning method [3]; (2) there are various methods for analyzing vibration signals, and the analysis results are intuitive and reliable. [PERSON] et al. proposed a new method for vibration-based techniques to detect, monitor, and prevent pump cavitations [4]; (3) different characteristic parameters of mechanical equipment vibration signals have different sensitivities to different types of faults, and they have practical physical relevance. [PERSON] et al. proposed a Tennessee Eastman process fault detection and diagnosis method using sparse principal component analysis [5]. Therefore, in the vibration analysis and fault diagnosis of mechanical equipment, fault diagnosis methods based on vibration monitoring and analysis have attracted increasing attention of researchers. [PERSON] et al. pointed out that machinery intelligent fault diagnosis is a promising tool to deal with mechanical big data. [6]. In 2019, [PERSON] et al. first proposed a fault identification method for axial piston pump based on voiceprint characteristics, which solved the problem of inconvenient installation of vibration sensors under special conditions [7]. Because of the uniqueness of a hydraulic system, the installation method and location of a vibration sensor affect the signal acquisition. Moreover, a vibration sensor is frequently installed by pasting or using a magnetic base, which is inconvenient in some cases. Pressure is an important parameter of a hydraulic system, and pressure signals can be conveniently collected. The outlet pressure pulsation of a hydraulic pump is mostly related to its vibration. Therefore, this study considers the outlet pressure signals of a pump as the research object. In the process of collecting the vibration signals of mechanical equipment, there is frequent interference from noise signals. To analyze a vibration signal accurately and yield the correct diagnosis result, it is necessary to alleviate the associated noise and interference. [PERSON] et al. [8] applied the wavelet packets transform method to the fault diagnosis of rolling bearings and achieved good diagnosis results.