## 2 Methodology
### Signal Preprocess and Determination of State Boundaries  
#### 2.3.1 EEMD Denoise Algorithm for System Signal  
Due to the complex and dynamic operating environment of ship lubrication systems, hardware information sensors are prone to various external disturbances, such as mechanical vibrations, temperature fluctuations, and electromagnetic interference. These disturbances result in significant noise in the signals collected by the sensors, thereby affecting the accurate assessment of the lubrication system's status. Therefore, before data analysis, it is essential to perform denoising on the sensor fluctuation signals to extract more accurate operational state information. Ensemble Empirical Mode Decomposition (EEMD) has demonstrated good performance in denoising nonlinear, non-stationary signals [29]. Consequently, this paper uses the EEMD method to preprocess the fluctuation signals collected by the lubrication system sensors. The EEMD method decomposes the raw fluctuation signals into a series of Intrinsic Mode Function (IMF) components and a residual term. The correlation coefficient between each IMF component, residual term, and the original signal is then calculated to assess their contribution to the original signal. IMF components and the residual term with higher correlation coefficients are selected to reconstruct the signal, completing the denoising process. To verify the denoising effect of the EEMD method, a known signal X is first generated, and noise is added to form a noisy signal Y. The noisy signal Y is then decomposed using EEMD, resulting in five IMF components and a residual term (denoted as the sixth IMF component). The correlation coefficients of each IMF component are then calculated. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Output Parameter** & **AMESim Result** & **Simulink Result** & **Relative Error** \\ \hline Total Lubricating Oil Supply/(L/min) & 48.52 & 48.49 & 0.062\% \\ Main Oil Line Temperature/(\({}^{\circ}\)C) & 56.09 & 57.69 & 2.77\% \\ Gearbox Oil Supply/(L/min) & 25.42 & 24.59 & 3.27\% \\ Oil Pump Pressure/(MPa) & 0.54 & 0.55 & 1.85\% \\ Cooling Water Outlet Temperature/(\({}^{\circ}\)C) & 69.59 & 70.05 & 0.657\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of AMESim and Simulink simulation results. In order to determine the effect of the experimental signal, we simulated and designed a signal with an interval of \((-1,1)\), and tested the effect by adding noise and denoising. Figure 3(top) shows an idealized, noise-free original signal. The signal consists of the superposition of two sine waves with frequencies of 10 Hz and 30 Hz. Its waveform shows obvious periodicity and smoothness, which is representative of the \"clean signal\" in signal processing. The horizontal axis represents time (in seconds) and the vertical axis represents the amplitude of the signal. This plot is the reference point for all subsequent signal processing and reflects the real characteristics and frequency structure of the signal. In practical applications, bioelectrical signals and mechanical vibration signals often have similar characteristics but are often contaminated by the interference of the external environment or measurement errors. Figure 3(middle) illustrates the noisy signal obtained after adding white Gaussian noise to the original signal. This kind of noise widely exists in the natural environment and measurement system. It is characterized by strong randomness and a wide spectrum coverage, and easily masks the structural information of the original signal. It can be observed that the signal fluctuates violently, locally presents a random jitter phenomenon, and the periodicity and structure become difficult to identify. The traditional filter has difficulty completely removing this kind of noise without loss of signal characteristics. Figure 3(bottom) shows the signal results after noise reduction by the EEMD method.