# A Hybrid Degradation Modeling and Prognostic Method for the Multi-Modal System
## 1 Introduction
[24] selected a recurrent neural network for remaining useful life prediction from the perspective of long-term prediction performance and obtained an excellent prediction effect. To get better results for long sequences, the long short-term memory neural network was used to estimate remaining useful life in [25]. Less computation was required in [26] based on the gated recurrent unit. However, these works did not consider the impact of the switching of the working state on the machine. The prediction model should be established more suitably for cumulative aging characteristics of a multi-modal system. On the other hand, the system's ability to withstand the damage is different for the system in different aging states. The ability decreases gradually with the increase of action times. The same shock will cause more severe damage to the system in a relatively late aging stage than in an earlier aging stage. Thus, it is significant to study the latest physical degradation description of mode switching in the life and the effect of mode switching on the aging degree of the system. The authors in [27] used the time window to extract the data features in segments, but did not consider the change of the system's ability to withstand damage. The statistical features of short sequence sensor data were extracted in [28], but the frequency-domain features of wave data remained unexplored. It is necessary to study a comprehensive local feature extraction method to analyze the latest-stage aging predictions specifically. The multi-dimensional local features lead to a large amount of computation for the prediction model. Thus, the algorithm with less computational overhead is selected as the prediction model that could improve the prediction speed. The decision tree ensemble methods are popular in solving practical prediction problem based on the interpretability and effectiveness, such as gradient boosting decision tree [29] and extreme gradient boosting [30]. However, these methods calculate the information gain and find the optimal partition point by scanning all samples. Efficiency and scalability are difficult to satisfy when calculating large amounts of data. The light gradient boosting machine (LightGBM) has proven to have a faster and more accurate performance in [31]. In addition, the light gradient boosting machine has great potential in remaining useful life estimation when the sensor data contains a lot of noise, which is very common in industrial applications. After solving the above problems, a decision-level fusion model is needed to get the final aging prediction result. Most previous researchers intended to remedy the lack of performance of one of the algorithms, such as convergence and computational complexity [32; 33], rather than focusing on the physical characteristics of the system, which are important for remaining useful life prognostic and are analyzed in this paper. The averaging method has the advantages of low computational complexity and the ability to adjust parameters online. In [34], the strategy, which uses different methods to construct the degradation models and combines them for remaining useful life prediction, is defined as the hybrid prognostics approach. In this paper, a hybrid degradation modeling and prognostic method for multi-modal systems is proposed to address shortcomings mentioned above. First, a cumulative dynamic differential health indicator (CDD-HI) is proposed based on the physical characteristics with the existence of mode switching. The proposed health indicator is used to predict long-term cumulative degradation by the gated recurrent unit network. Then, local features are constructed to predict latest-stage degradation by light gradient boosting machine. Finally, based on averaging method, the results of the gated recurrent unit and light gradient boosting machine are integrated to obtain remaining useful life.