# A Novel Framework for Online Remaining Useful Life Prediction of an Industrial Slurry Pump
## 2 Methodology
### Data Collection and Its Filtering for Valid Datasets Acquisition  
The vibrational measurement datasets were collected from the application of Smart Asset Management System (SAMS) software developed by the smart engineering asset management Lab. The data acquisition instrument included a National Instrument (NI) DAQ 9172 and a DAQ module NI 9234. The four accelerometers (PCB 352A60), C1, C2, C3, and C4, were mounted on four different locations of the slurry pump, as shown in  
Figure 1: The proposed framework for data filtering, health degradation assessment, automatic selection of HDTs data points, and online _RUL_ prediction of slurry pump. During the above-stated condition monitoring stage, the vibration signals were collected after every one hour. A total of 24 data sets were collected per day. Since the sampling frequency was set to 6000 Hz, consequently, each dataset had a data length of 6000 samples. The total number of datasets or files stored in the system was 4269 sets. During the data collection process, many of the datasets were not collected correctly due to different reasons. For example, many of them were collected when the pump was flushing with water, or sensor cables were loosened or broken, or the pump was interfered by the other nearby machines vibrations, or human errors, etc. Therefore, there was a need to remove those invalid datasets that were not reflecting the true operating conditions of the slurry pump. [PERSON] et al. and his research team worked on a number of faults-related features to select a criteria for distinguishing valid datasets from the raw vibration datasets [13]. Based on their past experience and research efforts, they selected three statistical features i.e., root mean square, kurtosis, and percentage mean difference in the time domain and one statistical feature i.e., kurtosis, again in the frequency domain for separating the valid and invalid datasets. The utilized statistical features are defined as the following:  
\[\text{Root mean square i.e., }RMS=\sqrt{\frac{1}{N}\sum_{n=1}^{N}(X_{n})^{2}} \tag{1}\]  
\[Kurtosis=\frac{\sum_{n=1}^{N}(X_{n}-\mu)^{4}}{(N-1)\sigma^{4}} \tag{2}\]  
\[\text{Percentage mean difference i.e., }PMD=\frac{PM-NM}{(PM+NM)/2}\times 100 \tag{3}\]  
where  
\(N=\) data length of the dataset  
\(n=\) selected length of the considered dataset i.e., \(n=\) 1, 2,..., \(N\)  
\(X_{n}=\) processed vibration signals  
\(\mu=\) mean of the dataset  
\(\sigma=\) standard deviation of the dataset  
\(PM=\) _mean of positive values for one particular vibration signal_  
\(MN=\) _mean of negative values for one particular vibration signal_  
Figure 2: C1 monitored the vibration at the suction/inlet of the pump, while C2 and C3 were responsible for gathering the vibration signals of the rotating vanes. Lastly, C4 monitored the vibration at the discharge/outlet of the pump. The datasets which were utilized in the conducted research were observed from channel 2, i.e., T2G1 C2, and channel 4, i.e., T2G1 C4. To study the statistical features of collected vibration signals, a LabView program was built up that filtered the invalid signals from the raw data. The outcome of the program was two separate pools of data. One contained the valid while the other contained the invalid datasets. The filtering criteria are depicted in Table 1.  
In the LabVIEW program, the values of the four statistical features were calculated automatically, and it scored one point if the values of the statistical features were within the pass range, as shown in Table 2. A signal was determined as valid if it scored 3 points or more. Otherwise, the signal was considered invalid. Figure 3 shows the raw signals before and after the data filtering process. It can be observed that the invalid data signals, which were outliers or with values nearly equal to zero, were filtered out efficiently.