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Experimental Results

Here, we present the results of applying our diagnosis and prognosis experiments on the simulation model of the WRS. We selected eight different faults for our experiments, namely R-Filt1, R-Filt2, A-FO, A-RO, q(b;20)Filt1 , q(d;0:1)Filt1, p(b;2)Prod, and q(d;0:01)ROPump.

Comprehensive results can be found in the related publications.

In the following we present a detailed integrated diagnosis and prognosis scenario of R-Filt2 fault. In this scenario, Filter 2 clogging begins at t = 0 min with wear rate δRFilt2 = -5x10-12. A fault is detected at 309 min, via an increase in the differential Filter 2 pressure, pFilt2 (see Fig. 6).

pFilt2Block
Figure 6: Estimated and observed values of sensor pFilt2.

Table 1 provides the fault signature table for the selected faults and measurements of the WRS. Note that sensor faults affect only the signature for the faulty sensor. Parametric faults such as the clogging of filters and membranes cause more than one sensor to deviate from nominal.

table1
Table 1: Fault Signatures for Selected WRS Faults and Measurements

As shown in Table 1, only fault R-Filt2 has a 0+ signature for pFilt2, indicating that the fault R-Filt2 would cause the pressure pFilt2 to increase. Since this is the only fault consistent with the observed deviation, a singleton fault candidate set, R-Filt2, is generated, and the fault is detected and isolated at the same time.

Fault identification is initiated once the true fault is isolated. For the Filter 2 Clogging fault, the wear rate ΔRFilt2 was estimated to ΔRFilt2 = -5.11759x10-12 (see Fig. 7).

DeltaRFilt2ID
Figure 7: Estimated ΔRFilt2 values.

For the purposes of prognosis, the EOL of the WRS is defined by when the filters need to be replaced. This is indicated by when the differential pressures across the individual filters, pFilt1 or pFilt2, cross a predefined pressure threshold. The corresponding RUL predictions, made at an interval of 10 min from the time the fault identifier converges to a solution are shown in Fig. 8 which plots the predicted RUL of the WRS under R-Filt2 from t = 540 min at 10 min intervals. At each prediction point, Fig. 8 shows true RUL, RUL*, and a probability density function of the predicted RUL represented using its median value and the 5-25% and 75-95% ranges. The plot also shows a cone of α = 10% accuracy around RUL predictions.

Filt2BlockAlpLamb.
Figure 8: Predicted RUL of the WRS under R-Filt2 fault.

In Fig. 8, from the first prediction point, at t = 540 min, the algorithm has converged and the median RUL predictions remain within the accuracy window of 10% except at t = 610 min, t = 620 min, and t = 640 min. In order to make predictions, we assume that the future inputs are known. Hence, the uncertainty in the predictions is due solely to that resulting from the identification stage, and explains why all RUL predictions did not fall within the accuracy cone.

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