Study on Performance Evaluation and Prediction of Francis Turbine Units Considering Low-Quality Data and Variable Operating Conditions  
Ran Duan  
School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology,  
Wuhan 430074, China; [EMAIL_ADDRESS] (R.D. ); [EMAIL_ADDRESS] (J.L. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (P.W. ); [EMAIL_ADDRESS] (X.N.) [PERSON]  
Correspondence: [EMAIL_ADDRESS]  
Yi Liu  
School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology,  
Wuhan 430074, China; [EMAIL_ADDRESS] (R.D. ); [PERSON]AIL_ADDRESS] (J.L. ); [EMAIL_ADDRESS] (Y.L. ); [EMAIL_ADDRESS] (P.  
data. (2) The drastic variation in operating conditions makes it difficult to evaluate and predict the performance of FTU accurately. The working environment of the FTU is hostile, including external interferences such as moisture, dust, vibration and electromagnetic disturbance. The supporting monitoring and data acquisition system of the FTU often involves multiple distributed modules with complex data transmission link structures and long physical distances. Hence, there are often many anomaly samples and missing values in the on-site raw data of FTUs, caused by sensor failure, short-term router failure or electromagnetic interference [7]. Meanwhile, the storage space of the data acquisition system is limited, and the short-term variation trend of each monitored quantity is not evident during the long-term working period of the FTU, so the storage frequency of the on-site data is often relatively low. Some studies about the performance evaluation and the remaining useful life prediction of rotating machinery have achieved excellent results in laboratory environments. However, these approaches often rely on high-quality data and are difficult to directly apply to the engineering practice of the FTU [8; 9; 10]. Focusing on the anomaly data, some current research has adopted denoising methods based on frequency domain analysis or energy spectrum analysis, which are effective while the sampling frequency is high and consistent [11; 12; 13]. However, the missing values and the variable condition significantly affect their effectiveness. The clustering method has been proved to have significant performance in the recognition of outliers of high-dimensional data [14; 15; 16]. As a density-based clustering method, the density-based spatial clustering of applications with noise (DBSCAN) algorithm is widely used in anomaly data detection due to its simple structure and good adaptability to high-dimensional data [17; 18; 19; 20]. Hence, the DBSCAN is adopted to clean the raw monitoring data in this paper. Except for the missing samples in the raw data set, data cleaning also increases the amount of missing data. If these missing values were simply deleted, the potentially important information might be discarded. In order to evaluate and predict the performance of the FTU more effectively, it is necessary to fill in the missing data appropriately. Traditional filling methods based on statistics, such as mean filling and median filling, mostly ignore the time sequence information between data. With the rapid development of machine learning theory and technology, more and more studies are processing sequences with missing values based on improved recurrent neural networks (RNN) [21; 22; 23]. [PERSON] et al. introduced a decay mechanism to the typical gate recurrent unit model (GRU) to construct the GRUD model. It was proved that the decay mechanism enables GRUD to effectively learn potential patterns in sequences with missing values [24]. GRUD has achieved good results in the prediction of incomplete sequences. However, these supervised regression methods cannot be directly used to generate complete sequences because the training targets cannot be set for the missing values.