## 2 Modeling of Initial Health Assessment Based on MSET
### Establish Health Baseline Based on MSET  
MSET is a non-parametric modeling method first proposed by Argonne National Laboratory in the United States and has been successfully applied to nuclear power plant equipment parameter degradation detection, power system state estimation, electronic equipment life prediction and other fields [??????]. MSET is a nonlinear multivariate prediction and diagnosis technology. In essence, MSET is based on the input of the normal operation data of the equipment under historical working conditions, and then the health rule is learned from the normal operation data of the multi-working conditions through the algorithm to establish the health model of the equipment. In this way, when the observation data to be evaluated is input into the model, it calculates and estimates the data during normal operation based on the analysis and comparison of actual monitoring data and the health data during normal operation of the equipment and outputs the health data estimated by the algorithm under the current working condition as the benchmark for the subsequent health assessment of the equipment [??]. The specific application steps of the algorithm are as follows:  
First, select \(n\) feature indicators that characterize the health state of the component, which can be expressed as \(x_{j},j=1,2,\ldots,n\). Then, record the sequence of feature indicators of the component at the moment \(t_{j}\) as the observation vector \(X(t_{j})\). The expression is as follows:  
\[X(t_{j})=\left[x_{1}(t_{j})\quad x_{2}(t_{j})\quad\ldots\quad x_{n}(t_{j})\right] \tag{4}\]  
Then, the observation vectors of the component's historical health status are collected to establish the historical memory matrix \(D\), as is shown in Equation (5). The historical matrix \(D\in R^{n\times m}\), where each column \(X(t_{j})=\left[x_{1}(t_{j})\quad x_{2}(t_{j})\quad\ldots\quad x_{n}(t_{j}) \right]^{T}\) represents the multi-feature observation vector \(t_{j}\) with \(n\) selected indicators, and each row captures the temporal evolution of the \(i\)-th indicator. \[D=\left[X(t_{1})\quad X(t_{2})\quad\ldots\quad X(t_{m})\right]= \begin{bmatrix} x_{1}(t_{1})&x_{1}(t_{2})&\ldots&x_{1}(t_{m})\\ x_{2}(t_{1})&x_{2}(t_{2})&\ldots&x_{2}(t_{m})\\ \vdots&\vdots&&\vdots\\ x_{n}(t_{1})&x_{n}(t_{n})&\ldots&x_{n}(t_{m})\end{bmatrix}  \tag{5}\]The observation vectors of the normal operations under all working conditions are input into the model to construct the memory matrix \(D\). MSET is a data-driven model. The larger the data of the memory matrix and the more working conditions it covers, the more accurate the output estimation vector will be. Constructing the historical memory matrix is a crucial step of MSET, and it is the basis for the subsequent algorithm to learn the normal operation rules of the memory equipment and match the working conditions. Next, the current observation vector of the device to be evaluated \(X_{obs}\) is input into MSET, the working condition is matched with the historical memory matrix \(D\), and the estimated vector \(X_{est}\) is output after calculation. In the process of condition matching, the model will generate a corresponding m-dimension weight vector \(W\) for each observation vector. The expression is as follows:  
\[W=\left[w_{1}\quad w_{2}\quad\ldots\quad w_{m}\right]^{T} \tag{6}\]  
The weight vector \(W\) represents the degree of similarity between the observation vector \(X_{obs}\) and the m-column historical memory matrix \(D\). Therefore, the estimation vector \(X_{est}\) is equal to the historical memory matrix \(D\) multiplied linearly by the weight vector \(W\), calculated as follows:  
\[X_{est}=DW=w_{1}X(t_{1})+w_{2}X(t_{2})+\ldots+w_{m}X(t_{m}) \tag{7}\]  
Given the observation vector \(X_{obs}\) and the estimation vector \(X_{est}\), the residual \(\varepsilon\) can be calculated by subtracting the two.