# Research on Prediction Method of Hydraulic Pump Remaining Useful Life Based on KPCA and JITL
## 1 Introduction
[PERSON] et al. [9] defined wavelet packet transform modulus (WPTM) and presented a WPTM-based PQD feature detection method; experiments show that WPTM has advantages in feature detection. [PERSON] et al. [10] proposed an adaptive extraction method based on extreme-point symmetric mode decomposition; it was applied to the trend term of machinery signal analysis, and good results were obtained. [PERSON] et al. [11] applied ensemble empirical mode decomposition to rolling bearing fault feature extraction. At the same time, many signal decomposition methods have been applied to signal denoising. For example, [PERSON] et al. [12] applied local mean decomposition method to hydraulic pump fault signals demodulation. [PERSON] et al. [13] applied weighted singular value decomposition to enhance the detection performance of a vibration sensor. Because of its good time-frequency localization analysis ability, wavelet analysis based on Fourier analysis is commonly used in signal processing and other fields. Based on an improved wavelet packet transform method, [PERSON] et al. [14] proposed the improved denoising method of fractional wavelet packet transformation, which was subsequently used for filtering and reducing noise signals and showed to have good noise reduction effects. [PERSON] [15] combined the denoising method of EMD with the wavelet threshold method, which presents a remarkable signal denoising effect. [PERSON] et al. [16] calculated the maximum singular value modulus of impact signals after wavelet transformation to determine their singular values and subsequently suppressed the maximum singular value to eliminate noise. [PERSON] et al. [17] proposed a novel signal adaptive decomposition algorithm processed in TF domain, which provides adequate information about the time-varying instantaneous frequency. Based on the wavelet theory, [PERSON] et al. [18] proposed the method of multi-wavelet analysis and denoising,which solves the correlation problem of multi-wavelet transform coefficients well and has a good denoising effect. A pressure signal contains a large amount of useful information [19, 20]. Accurate extraction of the key information is not only the basis for hydraulic pump fault diagnosis but also for determining the accuracy of the diagnosis results [21]. The main purpose of feature extraction is to extract and filter out the useful information that can accurately characterize the fault characteristics of a hydraulic pump from pressure signals. At present, the extraction methods of mechanical equipment fault characteristic parameters mainly include time, frequency, and time-frequency domain analysis methods, with the last one combining time and frequency domain features [22]. Because time and frequency domain analyses of gear pumps have the advantages of simple form and convenient calculation, the corresponding characteristic parameters are extensively studied and adopted for identifying the operating state of a gear pump [23, 24]. If the maintenance personnel who repair a mechanical equipment can timely and accurately determine its remaining useful life (RUL), then a scientific and appropriate maintenance plan can be formulated and the property losses and casualties caused by untimely monitoring and maintenance can also be effectively avoided [25, 26]. Therefore, it is essential to predict the RUL of mechanical equipment on time and accurately. In recent years, with the rapid approach of the artificial intelligence and data \"big bang\" era, computer and information technologies have been frequently developed and integrated and artificial intelligence and machine learning methods are being constantly innovated and advanced [27]. In the current research on the analysis and prediction of the RUL of mechanical equipment, artificial intelligence has become a prominent topic [6]. [PERSON] et al. [28] combined collected field data with accelerated life testing data and introduced conversion and environmental difference factors to improve the prediction and evaluation method of RUL. [PERSON] et al.