CHAPTER 4 Preliminary Time, Frequency Domain based Centrifugal
4.3 Phase I Experimentation – Frequency Domain Analysis
monitoring, this classification can help to curb the progression of cavitation right at its inception.
Table 4.4: Percentage prediction accuracy in the binary classification HP and C0 Training and testing
speeds (Hz)
%classification accuracy
C γ
C0 HP Average
40 100 100 100 50 10
45 95.7 98.5 97.1 10 0.5
50 100 98.5 99.2 1 0.05
55 100 100 100 1 0.05
60 100 100 100 1 0.05
65 100 100 100 1 0.005
4.2.5 Conclusions: Phase I Time Domain Results
From the results presented in Tables 4.2 to 4.4, it can be observed that the developed classifiers have a limitation in identifying faults with low severity, especially at lower CP speeds.
Nevertheless, the cavitation inception can be identified with almost 100% accuracy. However, it is essential to accurately detect the low suction restrictions with satisfactory performance to ensure that the fault progression is curbed.
In the subsequent section, the identification of suction blockage faults using frequency- domain based features is studied in order to establish the usefulness and limitations of these features.
4.3.1 Fault Feature Extraction and Selection
Features, such as the entropy, standard deviation, kurtosis, the product of amplitude and corresponding frequency, and root mean square have been considered in the frequency domain. The results for classification accuracy obtained for various features at 40 Hz operating speed is tabulated in Table 4.5. This classification accuracy of each of the features is used as a measure to select the best amongst them. Entropy is found to give the best performance for both binary and multiclass fault classifications, and therefore it would be used for all the further classifications.
Table 4.5: Percentage prediction accuracy of various features for binary and multiclass classifications at 40 Hz
Feature
Fault condition, % classification accuracy C0 SB4 SB3 SB2 SB1 C0, SB4,
SB3
C0, SB4, SB3, SB2
Entropy 98.6 100 99.3 82.9 60 95 88
Standard deviation 100 99.7 98.6 90 60.7 91.8 87.7 Product of amplitude
and corresponding frequency
100 100 100 89.1 57.2 92.4 84.6
RMS 92.9 100 91.4 69.3 54.3 80.4 68
4.3.2 Binary Classifications of Flow Blockages
The binary classification is very crucial to determine the specific characteristics of a fault in comparison to the no-fault condition. Figure 4.2 (a to d) shows the classification accuracy of a specific fault, no-fault for all the experimented speeds. The following observations may be drawn from the results:
i. For SB1 condition, the average classification accuracy over all the speeds has been found to be 73.8%.
ii. The low classification accuracy may be attributed to the close behavior of the fault condition to that of no-fault.
iii. For SB2 condition, the average classification accuracy is found to be 94.3% over the speed range. The classification accuracy just like in the previous case improved gradually with the speed. This may indicate that at higher speeds the effect of the blockage may be prominent.
iv. For SB3 condition, the overall classification accuracy of 99.3% was achieved.
v. For SB4 condition also, a high overall classification accuracy of 99.9% was obtained.
This may indicate that there is a clear distinction of the fault from the no fault condition.
vi. For cavitation inception condition C0, the overall classification accuracy was found to be 99.2%, which is a pretty good estimation of the beginning of cavitation.
Thus, SB3 and SB4 seem to be more serious conditions than SB1 and SB2. Also, it can be observed from the results that the classification accuracy is improving as the blockage increases.
4.3.3 Multiclass Classifications
Though the binary classification gives an overall picture of the fault severity, the multiclass classification has its share of advantages. It gives an understanding of the discreetness of each fault to one another. The following observations may be drawn from the results of the multiclass classification presented in Figure 4.3. The classification accuracies of HP and SB1 are almost comparable.
a
b
c
d
e
Figure 4.2: Binary classification of faults with respect to no fault condition, speed (Hz) versus percentage classification accuracy of, (a) SB1 and HP, (b) SB2 and HP, (c) SB3 and
HP, (d) SB4 and HP and (e) C0 and HP
60.0 77.1 72.1 80.7
70.0 82.9
0 50 100
40 45 50 55 60 65
% classification accuracy
Speed, Hz
SB1 HP % Average classification accuracy
82.9 95.0 91.4 98.6 99.3 98.6
0 50 100
40 45 50 55 60 65
% classification accuracy
Speed, Hz
SB2 HP % Average classification accuracy 99.3
97.1
99.3 100.0 100.0 100.0
94 96 98 100
40 45 50 55 60 65
% classification accuracy
Speed, Hz
SB3 HP % Average classification accuracy
100.0 100.0 100.0 99.3 100.0 100.0
96 98 100
40 45 50 55 60 65
% classification accuracy
Speed, Hz
SB4 HP % Average classification accuracy 98.6
97.1
99.3 100.0 100.0 100.0
94 96 98 100
40 45 50 55 60 65
% classification accuracy
Speed, Hz
C0 HP % Average classification accuracy
Figure 4.3: Multi-class classification of blockage: percentage of classification accuracy versus speed (Hz)
From the binary classification, we may infer that this may be due to the similarity of HP and SB1 vibration signatures.
i. The classification accuracy of SB2 is low at 40 Hz and 60 Hz of pump speeds.
Simultaneously, the classification accuracy of SB3 almost remained 100%
throughout all the speeds.
ii. The classification accuracy of SB4 remained 100% at all the speeds, except for 55 Hz and 60 Hz of pump speeds.
iii. There is a sudden dip in the classification accuracy at 60 Hz pump speed. Hence, the classification of the faults seems to be independent of the operating speed of the pump.
4.3.4 Conclusions: Phase I Frequency Domain Results
Here also like in the time domain study, it can be observed that the classification accuracy is dependent on the amount of suction blockage and the operating CP speed. These developed methodologies need to be worked on further to give better predictability of the classifier. The
71.4
82.3 83.4 88.3
79.4 89.4
0 20 40 60 80 100
40 45 50 55 60 65
% classification accuracy
Speed, Hz
HP SB1 SB2 SB3 SB4 % Average classification accuracy
suction blockage faults and cavitation were addressed until now. However, no mechanical CP faults were considered. In the subsequent section, the Phase II experimentation analysis and results are described. Here, both the blockages and the impeller defects (mechanical faults) and their combinations are considered. Also, the phase II experiments, CP is run from 30 Hz to 65 Hz in steps of 5 Hz.