## 4 Health Prognostics
### Empirical Degradation Model
#### 4.3.2 Machine Learning Method  
Due to the complexity of MSAE and the diversity of equipment, there are great differences between different ships. MSAE is usually composed of multiple components with multiple failure modes. It is almost impossible to understand all potential failure physics and their interactions of complex systems [153]. Consequently, the model-based method has some limitations in this field. With the development of modern sensor systems and data storage and processing technology, the RUL prediction method based on machine learning has been widely used and popularized. The following is a review of common machine learning methods. ANN  
A variety of neural network models have been applied to RUL prediction [220]. [PERSON] et al. constructed an ANN model with historical age and multi-state monitoring measurements as inputs and life percentage as output for more accurate RUL prediction of pumps [263]. [PERSON] et al. established an ANN model and applied the degradation signal database to realize the RUL prediction at any time during the service life of the bearing [264]. [PERSON] et al. used the feed-forward neural network (FFNN) model based on Levenberg Marquardt's (LM) training algorithm to predict the RUL [265] [PERSON] et al. developed a dynamic wavelet neural network prediction model [266]. In addition to typical neural network models, many deep learning models have been developed for RUL prediction. [PERSON] et al. used the dual CNN model to intelligently predict RUL only using the original signal [205]. [PERSON] et al. proposed an adaptive performance degradation assessment method of marine turbochargers based on component generalized feature mapping [267]. [PERSON] et al. used long short-term memory (LSTM) recurrent neural networks (RNN) to predict RUL independently of offline training data and can predict RUL earlier than traditional methods when offline data are available [268]. [PERSON] et al. used the deep TL network based on SAE to transfer the SAE trained by historical fault data to a new object, and RUL predicted the new target without supervision information [269]. The ANN method can achieve good results in tendency, monotonicity, and scale similarity. It often uses a signal processing method to extract equipment degradation features, and then uses the deep learning method to learn the mapping relationship between health indicators and degradation key features, to realize equipment RUL prediction. However, the neural network method is a typical \"black box\" model, which has low transparency and needs a large number of high-quality training data. The nodes and weights also need to be preset manually or optimized by using the optimization algorithm, which reduces their generalization ability in different situations. SVM/RVM  
The least-squares SVM (LS-SVM), OC-SVM, and multi-class SVM have been successfully used in RUL prediction. [PERSON] et al. proposed a bearing degradation prediction method based on PCA and optimized LS-SVM [270]. [PERSON] et al. realized RUL prediction of equipment through OC-SVM [271]. [PERSON] et al. modified LSSVM into OC-LS-SVM based on Bayesian inference-aided for accurate TTS point detection and applied recurrent least-square support vector regression (RLS-SVR) model for robust RUL estimation by predicting the future degree-of-defectiveness HI (DDHI) value [272]. [PERSON] et al. presented isometric feature mapping to construct the HI and forecasted it using an SVR method to estimate the bearing RUL [273]. However, it is difficult to determine the penalty coefficient of SVM, and the kernel function must satisfy the Mercer theorem. To overcome the shortcomings of SVM, a supervised learning RVM is developed as its alternative method. In addition to the unrestricted use of any kernel function, its advantages also include the automatic estimation of complex parameters without cross-validation, the generation of a probability output, and the use of Bayesian approximation to solve the uncertainty of prediction in SVM.