Experiment Results

Yaw Sensor Failures

The results for the yaw rate sensor fault detection time are presented in Table 4.6.

Generally, large magnitude faults are quicker to detect than small magnitude faults.

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The greater the magnitude of the fault, the sooner the residual generated using equation (4.6) will cross the threshold τ . This observation is reflected in the results presented in Table 4.6, which compares the results for a sudden step fault of large and small magnitude. On average, the step fault of large magnitude is detected instantaneously compared to an average of 0.8 sec in sample time for the small magnitude step fault.

Similar results can be observed with the hard additive type faults with a ramp duration of TR= 1 sec (see Section 4.6.2). Although the detection time is affected by the magnitude of the fault, it is also affected by the transient phase (ramp duration TR) of the developing fault. Due to this, the detection time for hard faults is greater than that for step type additive faults.

In comparison to the step and hard additive type faults, soft faults have the longest detection time. These faults have the highest ramp duration (TR = 4 sec) amongst the three types of additive fault. On average, the detection time for soft faults of large magnitude is 2.6 sec, in comparison to an average of 4 sec (sample time) for small magnitude fault. In the case of the constant bias fault, the average detection time is 1.6 sec.

In Figure 4.12, the signals associated with the yaw rate sensor during the oc-currence of a hard fault are presented. Figure 4.12a shows the response of various signals during the occurrence of a hard fault of large magnitude in scenario 1. In Figure 4.12b, the responses of various signals during a hard fault of small magnitude in scenario 4 are shown. Notice the response of the fault signal FA in both cases after the occurrence of the fault. The time of fault is marked by the vertical green line running across the three plots.

Pitch Sensor Failures

The results for the pitch rate sensor fault detection time are presented in Table 4.7.

The results reflect the observations made in the yaw rate sensor results. Large mag-nitude faults are quick to detect and additive faults with a ramp duration TR> 0 sec take a longer time to detect. On average, the hard additive faults with small

mag-390 392 394 396 398 400 402 404 406 408 410

390 392 394 396 398 400 402 404 406 408 410

-0.5 0 0.5 1

Norm. Yaw Rate

390 392 394 396 398 400 402 404 406 408 410

-0.5

(a) Scenario: 1, Magnitude: Large, Fault Occurrence: 400 sec

425 430 435 440 445 450 455 460

-0.4

425 430 435 440 445 450 455 460

0 0.5 1

Residual

425 430 435 440 445 450 455 460

-0.5

(b) Scenario: 4, Magnitude: Small, Fault Occurrence: 430 sec Figure 4.12: Yaw sensor hard fault simulations.

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Table 4.6: Yaw FDI Results

Detection Time for Fault Types in Sample Time (sec)

Scenario Const.Bias Hard Step Soft

- - L S L S L S

nitude are detected in 3 sec. In comparison, the hard faults with small magnitude are detected in an average of 1.4 sec.

Compared to the hard faults, the soft additive faults take on average 3 sec and 5.2 sec in sample time, for large and small magnitude respectively. Notice that the average detection time of soft faults is longer than that of hard faults. This is because the ramp duration is greater for soft faults, which is set at TR = 4 sec, instead of TR = 1 sec for hard faults. The step fault type has the lowest average of the additive fault types due to the ramp duration of TR = 0 sec. Step faults with small and large magnitude have an average of 0.8 sec and 2.6 sec respectively. The constant bias fault type has an average of 0.8 sec.

Comparing Table 4.6 and Table 4.7 shows how the average detection time for the pitch rate sensor is greater than that of the yaw rate sensor, especially for the additive fault types. This is due to the higher fault residual threshold τ used for the pitch rate sensor. In comparison to the yaw rate sensor, the pitch rate estimator has a higher modelling error, as discussed in Section 4.5, therefore requiring a higher value for τ . The threshold τ is set to 0.8 for the pitch sensor whereas for the yaw sensor, τ = 0.2. The modelling errors are reflected on the average SSE of the pitch and yaw rate estimators presented in Table 4.3 and Table 4.2 respectively.

In Figure 4.13, the signals associated with the pitch rate sensor during the

occur-of various signals during the occurrence occur-of a step failure occur-of large and small magni-tude respectively. Note that Figure 4.13a presents the response of various signals in scenario 3 during a step fault. This is the scenario in which the pitch rate anomaly is significant. Although the anomaly between the sensor and estimator is significant, there is no false fault detection.

Table 4.7: Pitch FDI Reults

Detection Time for Fault Types in Sample Time (sec)

Scenario Const.Bias Hard Step Soft

- - L S L S L S

In Table 4.8, the results for the roll rate sensor fault detection are presented. Similar to the pitch rate sensors, τ is set at a higher value: τ = 0.8. This is to accommodate the difference between the estimator value and the sensor value. The least detection time is taken by the constant bias fault type with an average of 1 sec in sample time.

For hard fault types the average is 2 sec and 4.6 sec in sample time for large and small magnitude. As expected, due to higher residual threshold, the fault detection time is longer.

The soft fault types take the most amount of time to be detected. For large magnitude soft faults, the average detection time is 4 sec in sample time. The average detection time is even higher for small magnitude soft failures, standing at an average of 7 sec in sample time. These results are considerably higher than the detection time in the yaw rate sensor. The longer detection time is caused by the higher residual threshold.

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370 380 390 400 410 420 430

370 380 390 400 410 420 430

0 2 4 6

Residual

370 380 390 400 410 420 430

-0.5

(a) Scenario: 3, Magnitude: Large, Fault Occurrence: 400 sec

270 280 290 300 310 320 330

-0.1

270 280 290 300 310 320 330

0 0.5 1

Residual

270 280 290 300 310 320 330

-0.5

(b) Scenario: 1, Magnitude: Small, Fault Occurrence: 300 sec Figure 4.13: Pitch sensor step fault simulations.

In the case of the step type failures, the average is at 1.2 sec in sample time for large magnitude. However for the small magnitude, the average is at 3.75 sec with a fault going undetected in scenario 1. This is quite possible in scenarios where the magnitude of the fault is relatively small. The fault went undetected because the residual failed to trigger the threshold. This could be solved by reducing the threshold τ , but this risks false fault detection. Future work would consider additional inputs to the roll rate estimator to improve the estimate, and therefore improve the chances for detection.

In Figure 4.14, the signals associated with the roll rate sensor during the oc-currence of a soft failure are presented. Figure 4.14a and Figure 4.14b, shows the response of various signals during the occurrence of soft failures of large and small magnitude respectively. Notice how the residual signal slowly rises over the thresh-old. This causes a delay in fault detection, as is evident from the fault signal response.

Table 4.8: Roll FDI Results

Detection Time for Fault Types in Sample Time (sec)

Scenario Const.Bias Hard Step Soft

- - L S L S L S