# Health State Prediction Method Based on Multi-Featured Parameter Information Fusion
## 1 Introduction
Currently, the main methods of feature fusion are principal component analysis (PCA) [5], kernel principal component analysis (KPCA) [6], neighborhood component analysis (NCA) [7], linear discriminant analysis (LDA) [8], etc. [PERSON] et al. [9] fused vibration data from sensors by combining the two-phase Bayesian approach with the principal component analysis (PCA) method to diagnose electrical and mechanical faults in rotating equipment. [PERSON] et al. [10] obtained the entropy of a sound signal by variable mode decomposition and then fused the entropy by the kernel principal component analysis (KPCA) method to eliminate the redundancy of high-dimensional feature information, which has high diagnostic accuracy. The above study proves that both methods, PCA and KPCA, can realize data fusion but require dimensionality reduction. The dimension of the data for health state prediction is fixed, and if the dimension is reduced, a lot of useful information is lost. [PERSON] et al. [11] selected the sound signal features by using the Neighborhood Component Analysis (NCA) method and used these selected features as inputs to the model for fault diagnosis. [PERSON] et al. extracted the Fisher features of the vibration signal features by using the Linear Discriminant Analysis (LDA) method, which can reduce the dimensionality of the features and improve the feature accuracy of fault identification [12]. NCA and LDA rely on data labeling for clustering and fusion, although they do not require feature fusion by dimensionality reduction. Cluster analysis is a powerful statistical method for grouping observations in a data set. Among the various clustering methods are K-Means Clustering [13], Hierarchical Clustering [14], and Gaussian Mixture Models (GMM) [15]. All are common choices. Among them, [PERSON] et al. [16] use a K-mean clustering method for sorting automatic diagnosis of rolling bearing defects; this model does not require the use of data measured on a specific machine under bearing failure conditions to train the method. However,K-means has some drawbacks: it is sensitive to the initial center of mass position, and different initial values may lead to different clustering results; it is susceptible to outliers, which will shift the center of mass position and affect the clustering accuracy; and it is only applicable to linearly divisible spherical data and is less effective for non-spherical and unevenly sized data distributions. [PERSON] et al. [17] used an algorithm with improved hierarchical clustering to reduce the computational effort of modeling all motors of a motor system separately. Hierarchical clustering provides a visual tree diagram, which helps to understand the hierarchical structure of the data, but its computational complexity is high and is not suitable for large-scale datasets. [PERSON] et al. [18] analyzed the features extracted from large data during vehicle charging through a Gaussian mixture model to reduce the computational difficulties caused by the complexity of the data. Gaussian mixture models, on the other hand, provide more complex probabilistic models to describe the distribution of data points, with more complex single-parameter estimation and higher computational costs. Currently, health state prediction methods can be broadly categorized into three groups: analytical model-based prediction methods, expert system-based prediction methods, and data-driven prediction methods. Model-based methods represent the actual working process of mechanical equipment components by building mathematical or physical models. However, in practice, it is very difficult to integrate accurate physical models of complex rotating equipment systems, which therefore limits the scope of application of this method.