## 3 Simulation Analysis
### Transfer-Entropy Simulation  
In order to apply the transfer-entropy algorithm to the analysis of the vibration-transmission path of the hydropower house, it is necessary to determine the efficiency of the transfer-entropy algorithm in the identification on the direction of information transmission. Construct two correlated simulation signals \(A\) and \(B\):  
\[A=\cos(2\pi x_{1}t)+0.2\sin(2\pi x_{2}t) \tag{21}\]  
\[B=\mu A+0.1\cos(2\pi x_{1}t)\cos(2\pi x_{2}t)-\cos(2\pi x_{2}t) \tag{22}\]  
where \(x_{1}=40\); \(x_{2}=4\); \(\mu\) is the correlation coefficient. As shown in Equations (21) and (22), it can be seen that the signal \(B\) consists of the signal \(A\) with correlation coefficient \(\mu\) and part of the interference signal. From the perspective of the signal composition, as the correlation coefficient \(\mu\) increases, the proportion of signal \(A\) in signal \(B\) increases and the proportion of interference signal decreases. The signal \(A\) should be more easily considered as the source of the \(B\) signal. On the basis of this, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Denoising Methods** & \(SNR\) & \(RMSE\) \\ \hline SVD & \(-2.04\) & 2.38 \\ EEMD & 1.85 & 1.49 \\ CEEMDAN & 3.66 & 1.19 \\ CEEMDAN-SVD & 4.35 & 1.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of \(SNR\) and \(RMSE\) results of four denoising methods. this section identifies the applicability of transfer entropy in the direction identification and quantitative analysis of transfer effects between signals by varying the correlation coefficient \(\mu\) in the signal \(B\) and analyzing the changes in \(T_{A\to B}\) and \(T_{B\to A}\) with different correlation coefficients \(\mu\). The correlation coefficients \(\mu\) of signals \(A\) and \(B\) are set to 0.2, 0.4, 0.6 and 0.8, respectively, and the transfer entropy \(T_{A\to B}\) and \(T_{B\to A}\) between the simulated signals \(A\) and \(B\) is calculated. The curves of the transfer-entropy values with the change in time are shown in Figure 5 and the information-transmission rate with different correlation coefficients are shown in Table 2.  
From Figure 5 and Table 2, the following conclusions can be drawn:  
(1) When the correlation coefficient \(\mu\) is 0.2, 0.4, 0.6, 0.8, \(T_{A\to B}\) are all greater than \(T_{B\to A}\), indicating that a large amount of information is transmitted from \(A\) to \(B\), and the pure signal \(A\) is the source of information transmission. This is consistent with the actual simulation signal-information-flow direction; the \(B\) signal is constructed according to signal \(A\) and the signal \(A\) has no interference signals and has the main characteristics of the \(B\) signal. From the perspective of calculating transfer entropy, the amount of information flowing from \(A\) to \(B\) is much larger than that in the opposite direction, and more significant transfer effect can be obtained. (2) When the correlation coefficient \(\mu\) is 0.2, the values of \(T_{A\to B}\) and \(T_{B\to A}\) are close to each other, which is not conducive to the identification of the transmission direction between two signals, and \(ITR_{A\to B}\) is 12.30%. As the correlation coefficient becomes larger, the difference between \(T_{A\to B}\) and \(T_{B\to A}\) becomes larger, and the transmission effect becomes more and more obvious. When the correlation coefficient \(\mu\) is 0.8, \(ITR_{A\to B}\) is 93.57%. This result indicates that the transfer entropy is highly sensitized to the transmission direction of the information flows between two signals, and the transfer-entropy curve can accurately reflect the direction of information transmission between two signals. (3) In this section, simulation signals \(A\) and \(B\) are constructed, and the reasonableness of the transfer entropy for judging the direction of information transmission between two signals is verified by changing the magnitude of the correlation coefficient \(\mu\). \(ITR_{A\to B}\)