## 1 Introduction  
Aircraft engines are essential components of aviation equipment and directly impact flight conditions and the safety performance of aircraft [1]. To ensure an optimal engine performance, prognostics and health management technology is widely used for engine predictive maintenance. This method evaluates the health and remaining useful life (RUL) of the equipment using historical data and provides maintenance predictions to enhance equipment reliability and safety [2]. As one of the cores of the prognostics and health management (PHM) method, aero-engine RUL prediction has been divided into three main approaches by other scholars: physical-model-based methods [3], data-driven methods [4], and hybrid methods [5]. The physical-model-based approach mainly relies on the engine's internal structure to construct a physical model, which has a high uncertainty and increases the prediction difficulty. The data-driven approach uses machine learning tools to mine the implicit relationship between historical monitoring data and RUL to construct a prediction model. The hybrid approach combines both methods, mixing their advantages and disadvantages. Thus, data-driven approaches are currently a hot research topic. While deep learning methods offer some advantages over traditional methods in predicting the RUL of aerospace engines, additional research is needed to explore their potential for fault maintenance and health assessment. [PERSON] et al. [6] estimated the RUL prediction interval of an aeroengine using a multilayer perceptron (MLP) model based on information granularity theory. [PERSON] et al. [7] used the Euclidean distance method to identify the initial lifetime. [PERSON] et al. [8] fused the time-series of different equipment sensors with MLP prediction models. [PERSON] et al. [9] utilized deep learning techniques to extract the sensor time-series signals between hidden dependencies and adapted the DLSTM network structure and parameters with an adaptive moment estimation algorithm, which showed a good performance compared to other neural network models. The historical degradation data of aerospace engines are characterized by a high dimensionality and massive scale. Given the size of the data, the current research focus is on identifying the most valuable information. In terms of feature screening and extraction, [PERSON] et al. [10] utilized a recurrent neural network to convert high-dimensional data monitored by sensors into low-dimensional data, constructing a one-dimensional health index (HI). [PERSON] et al. [11] employed the k-means algorithm to extract degradation features with monotonic trends and employed a deep forest classifier with LSTM to create an RUL degradation trend prediction model. [PERSON] et al. [12] proposed a method for predicting the remaining useful life of engines using a combination of convolutional and recurrent neural networks (CNN-RNN), and the prediction accuracy was further improved by processing and clustering the data. RUL prediction for aero engines using similarity matching methods is a current hot research topic. In their study, [PERSON] et al. [13] evaluated the trajectory similarity prediction (TSBP) method using similarity regression (SLR) based on Pearson correlation coefficients with dynamic time warping (DTW) methods to determine the most similar degradation model to the test data. They used the principle of weighted kernel density estimation to quantify the RUL prediction. [PERSON] et al. [14] used the kernel two-sample test (KTST) similarity matching procedure by fitting a distribution to the RUL prediction results from a historical database of sample data from operating cycles to failure to obtain confidence intervals for RUL predictions. However, most of the similarity matching was performed using a single time scale for the construction of health indicators, resulting in obtaining degradation trajectories with inconsistent lengths. This inconsistency is not conducive to the construction of historical engine degradation trajectories.