## 5 Conclusions  
This paper explores a vibration-transmission-path identification method based on CEEMDAN-SVD-TE, verifies the effectiveness of the algorithm through simulation signal analysis, analyzes the vibration-transmission path caused by tailwater fluctuation of the Quxue hydropower house, and obtains the following conclusions:  
1. The transfer-entropy (TE) algorithm, as a method for judging the information-transmission effect between signals, can effectively identify the source of information transmission, but the results of this algorithm are easily affected by noise; CEEMDAN-SVD, as a secondary filtering signal-processing approach, can retain the useful information in the signal and filter out the noise effectively. The innovative combination of CEEMDAN-SVD and TE method can give full use to the advantages of each method and obtain accurate and true information-transmission paths. 2. The transmission path identification method of CEEMDAN-SVD-TE provides a new method and innovative perspective for the analysis of vibration response and vibration mechanism in hydraulic structures. Based on CEEMDAN-SVD-TE, the vibration response due to tailwater fluctuation was analyzed, and it was found that the vibration-transmission path of the hydropower house under different working conditions is tailwater pipe (top cover measurement point)\(\rightarrow\)turbine pier (stator foundation measurement point, lower frame foundation measurement point)\(\rightarrow\)generator floor (generator floor measurement point). 3. Combining all the identified transmission paths under the three operating conditions, it can be found that the lower frame foundation is transmitted the largest amount of information, while the least amount of vibration information is transferred through the lower frame foundation. This indicates that the lower frame foundation, as the main load-bearing member of the hydropower house, is an important node in the vibration-transmission of the house and a key factor for the optimal design of vibration isolation in the hydropower house. 4. On the basis of the signal generated by the vibration response, this paper analyzes the transmission pattern of the hydropower house, which not only identifies the transmission path of vibration in the hydropower house, but also quantitatively describes the transmission feature of the vibration information. The vibration-transmission path based on the CEEMDAN-SVD-TE method can provide a theoretical basis for the identification of vibration-transmission paths in a hydropower house, offer an essential reference for the optimal designing and damping of the house and suggest a new idea for structural vibration monitoring and safety management of hydropower stations. Conceptualization, J.Z. ; methodology, Z.L. and M.C. ; validation, Z.L. and M.C. ; formal analysis, Z.L. and M.C. ; investigation, M.C. and Z.L. ; resources, [PERSON]; data curation, [PERSON] and M.C. ; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON], [PERSON], H.L. and J.H. ; visualization, [PERSON]; supervision, [PERSON], [PERSON] and J.H. All authors have read and agreed to the published version of the manuscript. This work is supported by the National Natural Science Foundation of China (51679091), the Program for Water Conservancy Science and Technology Innovation Project in Guangdong Province (2020-18) and the Innovative Project of North China University of Water Resources and Electric power (YK-2021-30). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Transmission** & **Top Cover\(\rightarrow\)Stator** & **Top Cover\(\rightarrow\)Lower** & **Stator** & **Lower Frame** \\
**Direction** & **Foundation** & **Frame Foundation** & **Foundation\(\rightarrow\)Generator** & **Foundation\(\rightarrow\)Generator** \\  & & & **Floor** & **Floor** \\ \hline Condition 1 & 91.54 & 94.86 & 32.85 & 32.78 \\ Condition 2 & 64.72 & 82.19 & 73.95 & 55.23 \\ Condition 3 & 71.67 & 72.99 & 47.62 & 29.97 \\ \hline \hline \end{tabular}
\end{table}