## 4 Health Prognostics
### HI Construction
#### 4.1.2 Synthesize HI  
Many MSAE are systems composed of multiple components, and the complexity improvement leads to the lack of dominant failure features. Therefore, it will be challenging to describe the changes in system functions with a single HI. Although multiple single HIs could be used for separate analysis, it usually leads to a large deviation from RUL prediction. Consequently, it is an effective method to reasonably fuse all sensor signals related to degradation into one dimension to construct the synthesized HI [173]. Synthesize HI construction can be divided according to whether the method is optimized or not. [PERSON] et al. used EMD and auto associated kernel regression model to combine different features to reflect the weighted sum of HS, which is a non-optimization-based method [174]. [PERSON] et al. applied the PCA method to build synthesize HI for compressor valve failure, hoping to reduce information loss [175]. [PERSON] et al. used reduced kernel recursive least squares simplified kernel recursive least squares algorithm to build synthesized HI [176]. To overcome the problem that the trend of some HI is not obvious in the whole life cycle and could not be used to predict RUL, [PERSON] et al. proposed genetic programming method to automatically find the high-level features in degraded signals and improve the monotonicity of HI [177]. Compared with non-optimization methods, the optimization-based methods focus on the construction of HI according to the needs of their respective models, to purposefully improve its service performance and make it a more efficient HI construction method. Different fusion methods of synthesizing HI are divided into two categories: data-level fusion and feature-level fusion. Data-level fusion directly fuses the measured multi-sensor information into 1D, which can more accurately describe the health condition of the system than a single sensor signal. [PERSON] et al. developed a data level fusion method to fuse multiple sensor data under multiple operating conditions into one synthesized HI to describe degradation [178]. Feature level fusion integrates the feature information generated by independent analysis methods. A priori knowledge about degradation mechanisms and physical laws is usually employed to create the required features. [PERSON] et al. applied the feature level fusion method cascade correlation neural network to multi-sensor data fusion [179]. In contrast, the synthesized HI constructed based on data level fusion is more conducive to health condition visualization and more suitable for degradation model and RUL prediction [158]. Most fusion methods constructed synthesize HI by the linear combination of original sensor signals [180; 181; 182; 178], but for more and more complex systems, multi-sensor signals usually have multiple sources and are affected by various degradation factors. Therefore, nonlinear fusion models have attracted more and more attention. [PERSON] et al. proposed an HI construction method based on a profound multilayer perceptron revolution neural network, which considered outlier regions simultaneously [183]. [PERSON] et al. used wavelet packet-empirical mode decomposition combined with self-organization mapping neural network to construct confidence value as HI to realize performance degradation evaluation and RUL estimation [184]. [PERSON] et al. utilized the Gaussian mixture model and Jensen-Renyi divergence to construct the HI to ensure monotonicity when bearing conditions deteriorate [185]. [PERSON] et al. used the automatic encoder based on a bidirectional recurrent neural network to convert the run-to-failure data of multiple units of the same system collected by multiple sensors to construct one-dimensional HI to reflect the health degradation mode [186]. The traditional data fusion method requires the researchers to determine the relevant characteristics in advance. [PERSON] et al. developed the method of HI automatic construction based on genetic programming, which reduced the user's preliminary work [187].