## 5 Conclusions  
Focusing on the practical problems of low-quality data and the frequently changing operating conditions of the fields of engineering applications of the FTU, an approach to the performance evaluation and prediction of the FTU considering low-quality data and variable operating conditions is proposed in this study. First, the on-site data set is constructed by the operating parameters and the vibration amplitude, and the DBSCAN algorithm is adopted to clean the anomaly data under variable operating conditions. Second, combining the incomplete sequence information mining ability of the GRUD and the hidden pattern learning ability of the WGAN, the GRUD-WGAN based missing value imputation model is proposed to improve the low-quality data utilization value. Third, the probability healthy-state model of the FTU is constructed based on the GPR to reduce the impact of data randomness. Additionally, the NLLP is calculated as the PDI of the FTU. Fourth, the degradation trend prediction model of the FTU is established based on the TPA-LSTM. Finally, a set of comparison experiments were carried out. The verification results demonstrate that the proposed data imputation method enhances the stability and the smoothness of the obtained PDI curve. Among the compared methods, the proposed GRUD-WGAN for data imputation has the highest accuracy at each experimental rate of missing data, \(r\). In addition, when \(r=0.1\), the accuracy of GRUD-WGAN rises with the increase in the input length \(l\). When \(r\geq 0.3\), the imputation accuracy reaches the maximum while \(l=20\). In addition, the constructed prediction model based on TPA-LSTM achieves the lowest RMSE and MAE, and the highest \(R^{2}\) on both the training set and test set, indicating that the model has good accuracy and generalization performance.  
The relative trend of the current state of the FTU against the healthy standard state is identified in this study. In the next phase of our research, if the long-term maintenance records can be obtained, the PDI curve can be correlated with the actual state of the FTU. Furthermore, a multistage degradation alarm model based on the PDI values can be constructed, so as to lay the foundation for state-based maintenance.  
Conceptualization, R.D.; Data curation, Y.L.; Formal analysis, J.L.; Funding acquisition, J.Z.; Investigation, P.W.; Methodology, R.D.; Project administration, J.Z.; Resources, J.Z.; Validation, J.L., P.W. and X.N.; Visualization, Y.L.; Writing--original draft, R.D.; Writing--review and editing, J.L., J.Z. and X.N. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the key project of the Natural Science Foundation of China (U1865202) and the Fundamental Research Funds for the Central Universities (HUST: 2020 JYCXJJ046).  
The study does not require ethical approval.  
The study does not involve humans.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Train Set**} & \multicolumn{3}{c}{**Test Set**} & \multicolumn{1}{c}{**Time Cost**} \\ \cline{2-7}  & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & \(\mathbf{R^{2}}\) & **(s)** \\ \hline TPA–LSTM & 0.094 & 0.064 & 0.999 & 0.104 & 0.068 & 0.999 & 108.36 \\ RNN & 0.111 & 0.080 & 0.999 & 0.133 & 0.097 & 0.997 & 48.36 \\ LSTM & 0.099 & 0.067 & 0.998 & 0.284 & 0.214 & 0.998 & 49.82 \\ GRU & 0.096 & 0.066 & 0.999 & 0.136 & 0.082 & 0.997 & 48.07 \\ SVR & 0.098 & 0.065 & 0.999 & 2.589 & 1.703 & 0.908 & 2.3 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Criteria of different prediction models.