Comparing these results, with the results of the analysis where only the electrical mea-surements and the pressure sensor are considered, it is seen that no addition information is added using the flow sensor. This is in fact true when only logical combinations are considered. But, as it will be shown in Chapter 6, The flow sensor can be used for dis-turbance decoubling, when model-based methods are used. Hereby, it becomes possible to detect the faultfh3corresponding to increased leakage flow inside the pump.
Electrical, pressure difference, flow and impeller eye pressure measurements As the last analysis a pressure sensor measuring the impeller eye pressure is added. This means that effect in the electrical quantities, the pressure difference, the volume flow, and the impeller eye pressure are assumed known. These are given by (4.18), (4.19), (4.20) and (4.21) respectively. The result of this analysis is shown below,
Rr=¡
0 1 1 0 1 1 1¢
. (4.26)
Here it is seen that only the faultsfe1andfh1corresponding to inter-turn short circuit and leakage flow are undetectable. To check the possibilities for identification of the the 5 detectable faults, the effects not corrupted by disturbing events are analysed using Theorem 4.2.3. The logical expression of the faults is given by the following expression.
eem,i4
eem,v1
edh3
edh4
edh6
eq3
eeh2
eeh3
←
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1
·¡ f¢
.
In this expression the effects, which can be corrupted by disturbing events, are removed.
The result of the detectability analysis is shown below, Ri=¡
x 0 0 x 0 1 0¢
(4.27) wherexcorresponds to the fault not robust detectable. Here it is seen that only one fault is distinguishable from the other faults, when all the effects corrupted by disturbing events are removed.
4.4.1 Decision Logic
In the analysis presented in the previous section the system was assumed to be disturbed by 8 different disturbing events, see Section 4.3.3. If this assumption is relaxed by removing the disturbing eventde1the robust detection properbilities are increased. Re-moving this disturbing event is the same as assuming that the supply voltage is balanced at all times. Now consider the sensor configuration including the following sensors,
• Current sensors.
• Voltage sensors.
• Low bandwide pressure difference sensor.
With this sensor configuration the result of the FPA is the following, Rr=¡
1 1 0 0 1 1 0¢
Ri =¡
1 0 x x 0 1 x¢ where thex’s inRiindicates that the given fault is not robust detectable (the interpreta-tion ofRrandRiis described in Section 4.3.5). FromRrit is seen that four faults are logical robust detectable. This means that the following fault vector is detectable using the considered sensor configuration,
f =¡
fe1 fh1 fm1 fin1
¢ .
The connection between the measurable effects, and the faults and disturbing events is in this particular case given by the following logical equation,
eem,i3
edh3
edh4
←
1 1 1 0 0 0 0 1 0 1 1 0
fe1
fh1
fm1
fin1
, (4.28)
where the measurable effects not in use are removed. From (4.28) it is easy to see that the faultsfh1 andfm1are indistinguishable as they affect the same measurable effect.
This is also shown inRi. Likewise it is seen inRithat the faultsfe1andfin1 can be distinguished from the remaining two faults. This is confirmed by examination of (4.28).
The detection logic is very simple in this case, and is given by, eem,i3→fe1
eem,i3∨edh4→fh1
eem,i3∨edh4→fm1
edh3→fin1.
(4.29)
In this expressioneem,i3indicates frequency components of the length of the Park trans-formed motor currents, where the length of the Park current vector is given by,
kisdqk=kTdqisabck.
In this expression the same notation as in Chapter 3 is used. The effectedh3corresponds to zero difference pressure, when the pump is running. Finally, the effectedh4 corre-sponds to low freqency harmonic oscillations in the pressure measurements. Here low frequency components correspond to frequencies larger than 0 [Hz] and up to 2-4 times the supply voltage frequency.
4.4.2 Test Results
To test the validity of the decision logic, derived in the previous subsection, data sets ob-tained by simulating faults on a centrifugal pump is analysed. These data are obob-tained by running tests on a test-bench particular developed for testing fault detection algorithms in this project. A sketch of the test-bench is shown in Fig. 4.10. The pump used in the test-bench is a Grundfos 1.5(KW)CR5-10 pump.
V1 V2
Vc pipe
pump
M motor shaft
Te Hp tank
V3 Vl
Qp
Figure 4.10: Sketch of the test-bench. The measurements are the electrical quantities, the pressure differenceHpdelivered by the pump and the volume flow through the pump Qp.
In the tank and pipe system, connected to this pump, the valveV1is used to model disturbances in the system. The inter-turn short circuit is simulated by shorting windings in phaseain the costimized designed stator particular developed for this purpose. Dry running is simulated by closingV2 and opening V3, and rub impact is simulated by adding an extra force on the shaft. During the test, presented here, this is done by mounting twist on the shaft, which rubs against the mechanical connection between the pump and motor. Hereby an oscilating force, similar to the one expected in a pump during faultfm1, is added. Finally, clogging inside the pump can be simulated by the closing valveVc. However, this valve simulates clogging of for example an inlet filter,
Table 4.5: Summing of the test results. Here, the faults denoted inter-turn, Dry-running, and rub-impact corresponds tofe1,fm1, andfin1respectively. Likewise, and increase in σis, andσhcorresponds toeem,i3, andedh4respectively. Finally, whenµhapproximate zero it corresponds toedh3.
Normal Inter-turn Rub-impact Dry-running
µis 2.7366 5.2066 4.6263 2.0450
σis 0.0037 0.4954 0.0141 0.0041
µh 2.2178 2.2561 1.6402 0.1054
σh 0.0003 0.0006 0.0067 0.0010
and not clogging in one of the channels in the impeller, which was assumed in the logical analysis. Therefore, results from this test are not considered here.
The measurable effects considered in these tests are affecting the current and the pressure measurements, therefore only these will be analysed in the following test re-sults. To evaluate the robustness of the approach, signals obtained on the pump at con-stant speed and at different positions of valveV1 are analysed. The different valve po-sitions simulates the no fault condition at different hydraulic loads. Results from this test are shown in Fig. 4.11. From these test results it is obvious that the DC-level of the considered signals are not usable for fault detection. This was also predicted by the FPA-analysis performed in Section 4.4.1.
Figs. 4.12, 4.13, and 4.14 depitch the current and pressure signals when the pump is exposed to the three faultsfe1,fm1, andfin1 denoting inter-trun short circuit, rub impact, and dry running respectively. The results of these tests are summarized in Table 4.5. In the evaluation of the resultsσisandσh are used as measurements of the end-effects eem,i1 and eh4 respectively. The end-effect edh3 is assumed triggered when µh≈0.
Considering the results presented in Table 4.5 it is seen thatσisis increased consid-erably in the case of the inter-turn faultfe1 and the rub-impact faultfm1. Comparing these results with the decision logic in (4.29), and rembering thatσisis a measure of the end-effecteem,i1 it fits perfectly. Likewise, by usingσh as a measure of theedh4
it is seen that the rub-impact faultsfm1is the only fault which increasesσh. This also fits the results of (4.29) perfectly. Finally, the only fault forcingµhclose to zero is the dry-running faultfin1. As µh ≈ 0 is considered a measure ofedh1 this also fits the results of (4.29).