# A Novel Framework for Online Remaining Useful Life Prediction of an Industrial Slurry Pump
## 4 Conclusions  
In the literature, many studies are available for estimating the \(RUL\) of different equipment by utilizing the deep learning neural networks. Researchers have applied a huge amount of available simulation or empirical run-to-failure (training data) and run-to-prior failure (testing data) datasets for estimating the \(RULs\). However, in the real world, only run-to-prior failure data of an operating machine is available, since the machine is never allowed to work until its failure. There is very limited research available where only run-to-prior failure data has been utilized for \(RUL\) prediction. In such studies, researchers have applied curve-fitting methods for their \(RUL\) prediction. Furthermore, the presented HDTs in these studies were very smooth while progressing in a very calm manner towards the threshold line, as in, for instance, [13; 17]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{5}{c}{**Weighted Average Accuracy of Prediction**} \\ \hline  & **Channel 2 Datasets** & & **Channel 4 Datasets** \\ \hline Proposed method & Curve-fitting Method & NARX & Proposed method & Curve-fitting Method & NARX \\ \hline
**42.15\%** & Not Applicable & Not Applicable & **22.01\%** & **7.29\%** & Not Applicable \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The weighted average accuracy of prediction for channel 2 and channel 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Operation Hours**} & \multirow{2}{*}{**Actual \(RUL_{A}\left(x_{j}\right)\)**} & \(\widehat{RUL}\left(x_{j}\right)\) **Using** & \(\widehat{RUL}\left(x_{j}\right)\) **Using** & \(\widehat{RUL}\left(x_{j}\right)\) **Using** \\  & & **Proposed Method** & **Curve-Fitizing Method** & \(\widehat{RUL}\left(x_{j}\right)\)**Using NARX** \\ \hline  & & & **Channel 2 Datasets** & \\ \hline
258 & 9.58 & 4.58 & Not Applicable & Not Applicable \\
288 & 8.33 & 4.2 & Not Applicable & Not Applicable \\
312 & 7.33 & 3.25 & Not Applicable & Not Applicable \\
364 & 5.17 & 1.25 & Not Applicable & Not Applicable \\
416 & 3 & 1.17 & Not Applicable & Not Applicable \\
456 & 1.33 & 0.66 & Not Applicable & Not Applicable \\ \hline  & & & **Channel 4 Datasets** & \\ \hline
456 & 17.33 & 1.45 & 1.76 & Not Applicable \\
496 & 15.67 & 1.34 & 1.77 & Not Applicable \\
565 & 12.79 & 0.62 & 0.84 & Not Applicable \\
655 & 9.04 & 2.5 & 0.99 & Not Applicable \\
720 & 6.33 & 1.91 & 1.07 & Not Applicable \\
824 & 2 & 0.62 & \(-\)0.75 & 0.33 \\
834 & 1.58 & 0.45 & \(-\)0.61 & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Actual and predicted \(RULs\) in terms of Weights. However, the curve-fitting methods cannot be trusted for HDTs that have deep crest- and trough-like structures, due to their issues of under- and over-fittings. In the presented study, only run-to-prior failure vibration datasets of an in-operation industrial slurry pump were available for online _RUL_ estimation. The involved HDTs were very difficult to simulate since there were many deep up and down peaks that were progressing towards the threshold line. To deal with such complicated HDTs of the slurry pump, a hybrid deep LSTM model embedded with a smart learning rate mechanism, was developed in this research work. The _RUL_ prediction results obtained by the developed model outperformed those of other existing methods. The major findings of the conducted research work are below. * It is recommended that the iteration process for prediction should start from particular points of an HDT, which have consecutively increasing slopes. As per [17], it was a research gap that has been attempted to be filled up in this study. * The developed smart learning rate mechanism incorporated into the hybrid deep LSTM model has worked as a \"catalyst\" for obtaining the acceptable prediction points. This feature of the proposed method is saving a large extent of time for estimating the online _RUL_.