Chapter 5: Simulation Result and Discussion
5.2 High-Temperature Sensor
Two simulations were performed using the out-of-range, response time, and absent signal algorithm to compare the three suitable methods for the HTS. In the simulations, there are 100 000 data points; each point represents ‘f’ ms.
Because the signal monitored in the algorithms vary, the inserted IEs were of different sorts.
For the out of range and absent signal, random error codes and no signal available were inserted. For the response time, peak values were randomly inserted (random value between ‘h’-UTLHTS(Upper Temperature Limit, HTS)). Regardless of the method used, the IEs were inserted at the same place. The IE inserted was set randomly to have a duration of
‘f’-‘j’ ms. The temperature measured was set to fluctuate between ‘k’-‘l’ C°. For comparison purposes, the simulation had five periods with varying numbers of IEs in each period.
Period 1 had 0.1% IEs, Period 2 had 0.5% IEs, Period 3 had 1% IEs, Period 4 had 2% IEs, and lastly, Period 5 had 5% IEs. See Table 15 for a summary of the simulation.
Table 15. Summarization of the methods used in the simulation.
Sensor High Temperature Sensor
IE Detection Method Out-of-Range, Absent Signal & Response Time IE Inserted Error Codes, No Signal & Peak Values
The results of the simulation are presented in a graph, see Figure 23.
Figure 23. Illustration of the result from the simulation. The five different periods are marked by the black lines.
Figure 23 reveals that the absent signal and out-of-range algorithms could capture all of the inserted IEs. The response time method was far away from capturing all IEs. See Table 16 for the quantification of the IEs detection rate.
Table 16. The total number of IEs introduced and detected by the algorithms for the full simulation.
Number of IEs
Total IEs Introduced 1700
Detected IEs, Response Time Method 270
Detected IEs, Out-of-Range Method 1700
Detected IEs, Absent Signal Method 1700
When observing Figure 23 and Table 16, one might notice that the absent signal and out-of-range method have a 100% detection rate. The reason for the 100% detection rate is because of which signal the algorithms monitor.
It is very straightforward to detect that a signal is missing because the signals are sent with a constant frequency. If there is no signal when there should be, a missing signal is detected.
Consequently, the missing signal method has a 100% detection rate. The out-of-range method (for the HTS) is based on the self-diagnostic of the sensor, as described in 4.1.1.
When an error is active (detected by the self-diagnostics), the sensor will send an error code, communicating to the monitoring algorithm that there is a fault within the sensor, resulting in a 100% detection rate for the out-of-range method.
The reason the response time method only had a detection rate of 16% is the same as already discussed in 5.1, namely the lower limit of the detection threshold (because of the equation used, see Figure 16) and the adjacent sample comparative technique used.
Figure 24. Illustration of the result from the simulation. The five different periods are marked by the black lines.
The lines show the accumulated signal deviance detected during the simulation. The true signal deviance is varying for the different methods because of the self-diagnostics of the sensor.
Figure 24 reveals that the absent signal and out-of-range algorithms could capture all of the signal deviance (with self-diagnostics) because of the inserted IEs. The response time method was far from capturing all the signal deviance (without self-diagnostics) because of the IEs. See Table 17 for the quantification of the signal deviance detection rate.
Table 17. The total signal deviance because of the IEs introduced and signal deviance detected by the algorithms for the full simulation.
Signal Deviance (Without Self-Diagnostics)
Signal Deviance (With Self-Diagnostics)
Total Signal Deviance 1 084 600 30 000
Detected Signal Deviance, Response Time Method
180 600 0
Detected Signal Deviance, Out-of-Range Method
0 30 000
Detected Signal Deviance, Absent Signal Method
0 30 000
Table 17 is split up into signal deviance with and without self-diagnostics. The inserted signal deviance was the same for all IEs. However, for the absent signal and out-of-range method, the self-diagnostics of the sensor detect the errors. When the self-diagnostics of the sensor detect an error, the last fault-free sample is used instead (as described in 2.5.2). Therefore, the accumulated signal deviance was 97% less when the self-diagnostics detects the IEs than when it does not. Consequently, the HTS is much more sensitive towards errors that the sensor's self-diagnostics do not detect.
It is not surprising that the out-of-range and absent signal methods had a 100% signal deviance capture rate considering that those methods detected all IEs. The response time method detects the same signal deviance percentage-wise compared with the number IEs caught, which was expected because there is no moving average or such that affects the signal deviance in the case of the HTS.
Since the signal deviance is not that large for the absent signal and out-of-range IEs (shown in Table 17), the best diagnostic method is the percentage method for those methods, as discussed in 4.3.1. For the response time method, the signal deviance diagnostic method is best. The signal deviance method is recommended because there is nothing that suggests that the signal deviance is a misleading indicator of the impact of IEs, which is the criteria for recommending the percentage method (as discussed in 4.3.2).
For the HTS, if Scania can choose only one IE detection method, the absent signal method is the best detection method. The absent signal method is best because it can capture a low-cost reparable fault, as described in 4.1.5. Moreover, the detection rate is 100% for the number of IEs. The drawbacks of the other methods were also taken into consideration when making this recommendation. The out-of-range method cannot detect a low-cost repairable fault and the response time method drawbacks are the same as discussed in 4.1.2 and 5.1.
5.3 NOx Sensor
Two simulations were performed for the NOx sensor. Since actual data was obtained containing IEs for the NOx sensor, all methods that monitor the sensor's output signal analysed the existing data. The algorithms that monitor other signal parameters were tested on simulated data.
The simulation contained 100 000 data points where each data point represents ‘g’ ms. For the absent signal method, no signal available was inserted into the data. For the signal status method, signal degradations were inserted into the data. Regardless of the method used, the IEs were inserted at the same place. The IE inserted was randomly set to have a duration of ‘m’-‘n’ ms. For comparison purposes, the simulation had five periods with varying numbers of IEs in each period.
Period 1 had 0.1% IEs, Period 2 had 0.5% IEs, Period 3 had 1% IEs, Period 4 had 2% IEs, and lastly, Period 5 had 5% IEs. See Table 11 for a summary of the simulation.
Table 18. Summarization of the methods used in the simulation.
Sensor NOx-sensor
IE detection method Absent Signal & Signal Status
IE inserted Missing Data and Degraded Signal Status The results are presented in a graph, see Figure 25
Figure 25. Illustration of the result from the simulation. The five different periods are marked by the black lines.
The lines show the accumulated signal deviance detected during the simulation.
Figure 25 reveals that the absent signal and out-of-range algorithms was able to capture all of the inserted IEs. See Table 19 for the quantification of the IEs detection rate.
Table 19. The total number of IEs introduced and detected by the algorithms for the full simulation.
Number of IEs
Total IEs introduced 1700
Detected IEs, Response Time Method 1700
Detected IEs, Absent Signal Method 1700
When observing Figure 25 and Table 19, one notices that the absent signal and the signal status method have a 100% detection rate. The reason for the 100% detection rate is the same as discussed in 5.2, namely that these types of IEs are easily detectable.
As stated previously, the algorithms that monitor the output signal of the NOx sensor were tested on actual data from a faulty sensor. Thus the exact amount of IEs is unknown. A logger device recorded the data six hours before a DTC from the already existing
diagnostics triggered. Therefore, this simulation differs from the previous two simulations since this simulation does not have periods. See Table 20 for a summary of the test.
Table 20. The Table below contains the summarization of the methods used in the simulation.
Sensor NOx-sensor
IE detection method Out-of-Range, Response Time and Spectral Analysis
IE inserted None
See the result of the simulation in Figure 26.
Figure 26. The graph above illustrates the result from the simulation.
Figure 26 reveals that none of the algorithms was able to capture all of the signal deviance because of IEs. See Table 21 for the quantification of the signal deviance detection rate.
Table 21. The total number of IEs introduced and detected by the algorithms for the full simulation.
Number of IEs
Detected IEs, Spectral Analysis Method 51 000
Detected IEs, Out-of-Range Method 10 600
Detected IEs, Response Time Method 10 100
Figure 26 and Table 21 show that the spectral analysis method detected the most IEs. The out-of-range method detected the second most IEs. The response time caught the least number of IEs.
The result of the response time method is surprising. According to Figure 15, the response time method should capture all of the IEs out-of-range. Therefore, the response time method should detect more or at least equal amounts of IEs than the out-of-range method. The reason that the response time method captured 500 fewer IEs than the out-of-range method was found in the data used for the simulation. In some cases, the output value went from under the range limit to over the range limit without any samples within range. In those
cases, since values under the range limit are negative, the equation does not capture the values above the range limit. Therefore, those errors are not detected by the response time method, which explains the result.
The high detection rate of the spectral analysis method stems from the fact that 1000
samples are treated simultaneously (as described in 4.1.3). If the resulting frequency content of the 1000 samples is above the detection threshold, the 1000 samples are considered to have been produced while an error is active. When using this approach, it is challenging to calculate signal deviance. Therefore, the percentage method is the recommended diagnostic method for spectral analysis. Moreover, it has to be stated that the spectral analysis method was developed and validated on the same set of data, which could explain the high detection rate. Only one dataset was used because no more data from intermittently fault sensors were available.
Because of the self-diagnostic of the NOx-sensor, as explained in 2.5.3, there is reason to believe that the signal deviance will be significant for the types of errors that are detectable by the self-diagnostic. Therefore, the recommendation is to use the percentage diagnostic method for the absent signal, signal status, and out-of-range methods.
Nothing suggests that the signal deviance detected by the response time method will be a misleading indicator of the impact of the IEs. Therefore, for the response time method, the recommendation is to use the signal deviance diagnostic method.
If Scania can choose only one IE detection method, the recommendation is to use the absent signal or signal status methods. The absent signal method is recommended because it has a 100% detection rate (see Figure 25 and Table 19), and it can detect a low-cost repairable fault, as discussed in 4.1.5. The signal status method is recommended because it has a 100% detection rate (Figure 25 and Table 19). It is easily implementable since no mathematical operations take place - only monitoring the signal status. Moreover, it is not computationally intensive nor poses high memory requirements for the same reason described in the previous sentence.