Development of a Novel Methodology for Remaining Useful Life Prediction of Industrial Slurry Pumps in the Absence of Run to Failure Data

The data length of degradation trends from their start to the most heightened point (threshold point) was considered for modeling since the pump’s impellers typically started degradation after this point. The developed model was working in two steps. In the first step, the NAR network was utilized for obtaining a few prediction points in a correct direction, i.e., towards the threshold line. In the second step, the LSTM-BiLSTM model considered the NAR prediction results as the “path to be followed” for a few iterations (seven prediction points of the NAR model were picked up randomly in under-considered cases) for getting the correct direction for its prediction points, and then by taking the benefit of its own long-term memory, it produced outstanding regression prediction results for obtaining the overall RUL and short-term RULs, as shown in Figure 6 and Figure 7

For obtaining the overall RUL, the LSTM-BiLSTM model’s prediction points follow the path created by the NAR model’s predictions and then iterate many times until the prediction points do not reach the threshold line. For obtaining the short-term RUL, the LSTM-BiLSTM model’s prediction points follow the path created by the NAR model’s predictions and then iterate for three more prediction points (since the short-term RUL was calculated for the next ten hours and every single iteration was producing one prediction point which was referred as the one hour). Figure 8 is showing the working mechanism of the developed approach for obtaining the overall RUL.

”, is showing the prediction points which were obtained by the LSTM-BiLSTM model by following the NAR model’s prediction points. “”, is showing the LSTM-BiLSTM model’s prediction points which were obtained by further extending “”. While working for Slurry Pump having dataset of the year 2014, the developed model was predicting an overall RUL of 28.08 days against an actual RUL of 35.62 days, as shown in Figure 6 a. These RULs were obtained by dividing x-coordinates values, i.e., 674 and 856, by 24. Hence it was found that via utilizing 75% data of degradation trend for training, the developed hybrid NAR-LSTM-BiLSTM model is generating its outcomes with an accuracy of 78.83%. In order to estimate the short-term RUL of a slurry pump having 2014 datasets, the developed hybrid NAR-LSTM model was fed with 50% and 25% data for its training. The model was run for ten iterations, or in other words, the RUL prediction results were drawn out for the next ten operating hours. In return, the developed hybrid NAR-LSTM model successfully revealed its results as a predicted RUL of 18.29 days and 10.83 days with an accuracy of 99.78% and 89.28%, respectively, as shown in Figure 7 a,b. Similarly, when working for the slurry pump having datasets of the year 2017, the developed model was predicting an overall RUL of 19.33 days against actual RUL of 22.91 days, as shown in Figure 6 b. Again, for predicting the short-term RUL of this slurry pump, the developed model was fed with 50 and 25% data of degradation trends for determining the RULs in the next ten operating hours., as shown in Figure 7 c,d. It can be observed that the developed model’s average accuracy of the overall RUL prediction for both the slurry pumps was 81.60%, while the average accuracy for the short-term RUL prediction was 95.76%. Table 1 is showing the actual RULs, predicted RULs by the proposed model and Nonlinear Autoregressive Exogenous (NARX) model, and the accuracy of the obtained predicted RULs.

The dynamics of an expressive performance degradation trend have already been discussed in Section 2.2 of the paper. Therefore, unlike before, the degradation trend built-up by the feature STD was selected for dataset 2017, for further simulation. Figure 10 Figure 11 and Table 2 show the overall and short-term predicted RULs obtained by the developed hybrid NAR-LSTM-BiLSTM model. It was noticed that the developed model was predicting its overall RUL with an average accuracy of 82.94%, while short-term RUL with an average accuracy of 98.19%.

In order to verify the applicability of the developed strategy, it was also applied on the data which was obtained from sensor 4 of both the slurry pumps. As earlier, the obtained data was first cleaned, then was utilized for making the performance degradation trends via the proposed FFT method. It can be observed in Figure 9 d that feature RMS has established a suitable degradation trend for dataset 2014, but for the dataset 2017, feature STD has created a more significant degradation trend, as shown in Figure 9 g.

3.2. Validation of the Developed Methodology Using C-MAPSS Dataset

In order to verify the working mechanism of the developed methodology, it was also applied on the publically available NASA Commercial Modular Aero Propulsion System Simulation (C-MAPSS) dataset. It was employed for estimating the RUL of two individual turbofan jet engines in a novel way, i.e., without using their available run to failure datasets as per the concept explained in Section 1 . The C-MAPSS dataset consists of four sub-datasets named as FD001, FD002, FD003, and FD004 with the different or same number of train/test trajectories and operation/fault modes. Each sub-dataset comprises multiple multivariate time series. There are 26 columns which correspond to, (i) engine number, (ii) time (cycles), (iii) operation specifications 1, (iv) operation specifications 2, (v) operation specifications 3, (vi) to (xxvi) Data obtained by sensor 1, to data obtained by sensor 21.

Each row is a snapshot of data taken for a single operational cycle, while each time series is from a different engine. It means that the data can be considered from a fleet of identical engines. Each engine has started with different manufacturing variations and initial wear that is not known to the user. However, this variation and wear is normal, and it is not considered as the fault condition. At the start of each time series, the engines are operating normally, and then they get a fault at some point during their operations. In the training trajectories, there is data where the fault grows in magnitude until it makes the system fail, i.e., run to failure data. In the test trajectories, there is the time-series data that ends sometime prior to the system failure, i.e., run to prior failure data. The dataset has also provided the true values of remaining operational cycles, i.e., actual RUL of the engines. However, the time-series data for the actual remaining operational cycles is not given. Traditionally, researchers utilized the run to failure data for the development of their RUL prediction models and then test their developed model’s results with the provided run to prior failure dataset. In the world of research, this methodology is acceptable, and a lot of research papers can be found on this topic from the literature. However, as discussed earlier, in the real world, it is impossible to have a huge amount of run to failure data from a fleet of identical rotary machines (just like in the case of the C-MAPSS dataset). In industry, operating machines are never run until their failure since they are typically provided with the TBM. Keeping the situation in view, the RUL of two individual engines of the CMAPSS dataset by only utilizing their run to prior failure data has been predicted in this study.

Engine No. 140 from sub-dataset FD002 and engine No. 25 from sub-dataset FD004, were selected for predicting their RULs. Engine 140 has 306 rows of time series from 26 sensors in the package of the run to prior failure data. Since only a constant value of final RUL, i.e., 55 cycles, is given in the dataset, and no time-series data has been provided for these 55 cycles. Therefore, the 306 rows of sensor data were extrapolated to a further 55 rows, which gave a sum of 361 rows. It implies that the total life of particularly this engine is 361 cycles. Via applying the proposed FFT method on these 361 rows (which are actually 361 operational cycles of this engine) of data, four different performance degradation trends using the time-based indicators, i.e., kurtosis, skewness, standard deviation, and root mean square were developed, as shown in Figure 12 a–d.

Similarly, engine No. 25 has 486 rows of time series data (i.e., 486 number of cycles before failure), while its provided actual RUL value is 39 cycles in the dataset. Same like earlier, the given time series data, i.e., 486 rows of data, were extrapolated to 39 more rows, which gave a sum of 525 rows. It implies that the total life of particularly this engine is 525 cycles. By applying the proposed FFT method on these 525 operational cycles, four degradation trends were also developed for this engine, as shown in Figure 12 e,f. Degradation trends that were obtained by using the RMS indicator were selected for predicting the overall and short-term RULs. The threshold line was drawn with reference to the last value of the degradation trend since it was the given threshold point in the dataset. Later on, the developed NAR-LSTM-BiLSTM model was utilized for predicting the overall and short-term RULs for both the engines in the same way as for the slurry pumps. In the case of engine 140, an overall RUL of 288 cycles was predicted against its total real life of 361 cycles, as shown in Figure 13 a.

Similarly, in the case of engine No. 25, an overall RUL of 427 cycles was predicted while its total actual life was 525 cycles, as shown in Figure 13 b. Collectively the accuracy for both the overall RUL predictions was found to be 80.55%. The developed model was again utilized for predicting the short-term RUL of the under-considered engines. RUL for the next 10 cycles was predicted using 50 and 25% data of their degradation trends, and the results were obtained with an averaged accuracy of 98.11% for short-term RULs, as shown in Figure 14