# A Hybrid Degradation Modeling and Prognostic Method for the Multi-Modal System
## 1 Introduction  
Prognostic health management is a critical piece of technology for providing early warnings of system failure [1], aiming to minimize economic loss and potentially catastrophic accidents. As a vital issue of prognostic health management, the remaining useful life (RUL), which is defined as the duration from the current time to the failure time, should be predicted accurately. Therefore, remaining useful life prediction has drawn much attention from both industry and academia. An engineering system can work under a single operating condition or multiple operating conditions depending the application scenario. The sensor data often have stationary aging trends or features when the system works under a simple condition. Most researchers concentrate on the prognostic health management of system with the single operation condition [2; 3; 4; 5; 6; 7; 8; 9; 10]. However, in practice, the engineering system often works under multiple operating conditions [11] and switches operation modes according to the changes in the operating environment and its states. For example,the battery charger typically works either on the constant-current (CC) mode or constant-voltage (CV) mode, depending on the battery voltage [12]. When the system works under multiple operating conditions, the stationary feature is difficult to select and cannot be utilized merely to master the underlying physical processes [13]. Therefore, it is necessary to extract and utilize the features of the collected information to the maximum extent. In conclusion, there are two problems for the prognostic analysis of multi-modal systems. On the one hand, the different number and order of mode switching makes the aging trend of systems more complicated. The aging data of the single-mode system is often used to predict remaining useful life directly. But for multi-modal systems, inter-frame dynamic information hides in aging data [14]. Thus, there is an urgent requirement to study the physical description of mode switching in the life and the cumulative effect of mode switching on the aging degree of the system. Ref. [15] used sensor sequence information to reveal the hidden characteristics of the data with multiple operating conditions to some extent. However, the work ignores the time interval between signals in the same operating mode to make the degradation characteristics of signals under varying operating modes. Health indicator (HI) has shown superiority in the problem of systematic health management [16]. The suitable health indicator could simplify prognostic modeling and calculate accurate prediction results [17]. Some work has constructed physics health indicators related to the physics of degradation from sensor signals based on statistical methods or signal processing methods, such as root mean square [18] and kurtosis [19]. Each physical feature can be considered as a physical health indicator [20] which contains partial information about the aging process. For multi-modal systems, many physical indicators will be proposed based on the mode switching rule. Remaining useful life prediction with only one physical feature is one-sided [21], but information overlaps between a large number of physical features. Besides, the collected sensor data usually includes noise signals, which may lead to mutual exclusion or invalid information between features. Using all physical health indicators of sensors to predict consumes a lot of computing resources, especially for large-scale datasets. Therefore, the physics health indicators are fused to construct the virtual health indicator. Virtual health indicators usually present the degradation trends without physics meanings; see [22; 23]. Therefore, the establishment of an explanatory health indicator applicable to the complex working state of multi-modal systems is a challenge for the accurate prediction of remaining useful life. The system aging is a long-term cumulative process.