###### Abstract  
During the service life of brake systems, performance degradation of the components is inevitable. In order to grasp the health status of components of brake systems, and aiming at the problem that the performance degradation trend of the components of the brake system is not completely clear due to signal coupling between components, the influence of variable working conditions, and the long performance degradation cycle, a performance degradation prognosis method of the components of the brake system based on relative characteristic (RC) and the long short-term memory (LSTM) network was proposed. The input and output signals of the components were isolated and fused, the working condition-independent RC was extracted to construct the health indicator (HI), and the validity of the HI was tested by using the monotonicity, correlation, and robustness metrics. Moreover, considering the time memory characteristics, the trend prediction of the HI curve of the components of the brake system was carried out based on the LSTM network. Furthermore, data augmentation for the training and testing sets was performed. Taking the typical component of brake systems as an example, a performance degradation test was carried out. The analysis results of the test data show that the accuracy of the performance degradation prognosis of the intake filter was over 99%, which validates the effectiveness and accuracy of the proposed method. The research results could provide a reference for health management and to improve the active safety protection capability of brake systems of in-service trains. in-service trains; components of brake system; performance degradation prognosis; relative characteristic; long short-term memory +
Footnote †: journal: Applied  
conducted fault diagnosis for the solenoid valve of brake systems with embedded sensor signals and physical interpretation. However, few reports on performance degradation prognosis for components of brake systems of in-service trains have been reported. Generally, prognosis methods are mainly divided into two categories: model-based prognosis methods, and data-driven prognosis methods [10; 11; 12]. As a brake system is typically a mechanic-electric-pneumatic-coupled and time-varying nonlinear system with a complex structure and multiple operating modes [13], it is not easy to establish an accurate degradation mathematical model, while data-driven prognosis methods focus on data characteristics [14; 15], and a large amount of operational data is generated during the service period of components of brake system. Therefore, data-driven methods are more suitable for performance degradation prognosis for components of brake systems, and there are two main steps to achieve this process: constructing a health indicator and selecting a suitable prognosis algorithm. To address the problem of health indicator construction, [PERSON] [16] extracted time-domain characteristic parameters of vibration signals as health indicators for bearing performance degradation prediction. [PERSON] [17] extracted the recursive graph entropy characteristics of vibration signals to predict the performance degradation process of bearings. In addition to the direct extraction of feature parameters as health indicators, some scholars have also used indirectly obtained health indicators for degradation prediction by fusing multiple source feature parameters. [PERSON] [18] fused time domain feature parameters by using a self-organizing mapping method and treated the minimum quantization error obtained as the health indicator of rolling bearings. [PERSON] [19] used the minimum quantization error as a health indicator and proposed a residual life prediction method for ball bearings. [PERSON] [20] used a dynamic PCA method to obtain the principal elements and calculate the equine distance to construct a health indicator.