## 3 Program Design
### Verification of Validity Based on Seasonal Decomposition  
For long-term data on the stable operation of components, the use of empirical modal decomposition (EMD), while capable of extracting accurate trends, suffers from two shortcomings. Firstly, the influence of unknown factors, such as the orbital environment, can lead to data embodying health that is not ideally monotonically decreasing. When performing nonmonotonic trend extraction, a suitable modal function (e.g., IMF) needs to be selected for decomposition based on experience or expert knowledge. This involves subjective judgement and parameter selection, which can lead to subjective bias in the results for complex variation data. Secondly, EMD is highly sensitive to data specificity. When anomalies with nonsmooth, nonlinear, or noisy data are encountered, EMD may produce inaccurate or unstable results [45; 46].  
In contrast, the seasonal decomposition (SD) algorithm is widely used in time series analysis and offers distinct advantages. It decomposes time series data into three components: seasonal, trend, and stochastic. Compared with EMD, SD has the advantages of deterministic decomposition, targeting periodic data, providing trend analysis, and handling periodic noise [47; 48]. At the same time, SD does not require human selection of modal functions or adjustment of parameters. Subjectivity and human intervention are avoided, providing more consistent and repeatable results. This makes it very suitable when dealing with data with fixed periodic variations, such as satellite component data. It is based on the principle of analyzing periodic and trend changes in time series and decomposing the data into components of different frequencies [49].  
SD can be expressed in Equation (9):  
\[\mathrm{Y(t)}=\mathrm{T(t)}+\mathrm{S(t)}+\mathrm{R(t)} \tag{9}\]  
where Y(t) represents the time series data, T(t) represents the trend component, S(t) represents the seasonal component, and R(t) represents the stochastic component.  
The main steps of the algorithm are as follows:  
1. First, the trend component is estimated using smoothing techniques (e.g., moving averages):  
\[\mathrm{T(t)}=\mathrm{f(T(t))} \tag{10}\]
2. Next, the trend component is subtracted from the raw data to obtain the detrended data:  
\[\mathrm{Y^{\prime}(t)}=\mathrm{Y(t)}\ -\ \mathrm{T(t)} \tag{11}\]
3. The data are then detrended by calculating the cyclical variation at each point in time. The seasonal component is estimated:  
\[\mathrm{S(t)}=\mathrm{g(Y^{\prime}(t))} \tag{12}\]4 Finally, the seasonal component is subtracted from the detrended data to obtain the remaining stochastic component:  
\[\text{R(t)}=\text{Y}^{\prime}(\text{t})\ -\ \text{S(t)} \tag{13}\]  
Through such a decomposition process, the time series data can be split into three components: trend, seasonality, and stochastic. Analysis of the data and trend extraction are achieved.  
The advantages of this method are illustrated in particular in reaction flywheel case temperature data that appear to be anomalous. As can be seen in Figure 7, the shell temperature data for this component are complex and, at the same time, anomalous at around day 1200. EMD for such data can only extract the trend of late rising changes through global description. This is not fully consistent with the real data trend; however, the characteristics of SD make it possible to extract an accurate trend of change for these data. The fact that accurate descriptions can also be generated in detail illustrates the strength of this method.