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Markov Chain Modelling of Duty Cycle

4.3 Data Processing

4.3.4 Analysis of Identified Trips

The logged data can now be analysed with regard to input into the Markov model genera-tion. It is important that the Markov model accurately represents the typical usage pattern for the Microcab with regards to the expected load on the powertrain. Analysis of the trips identified for the Microcab Mail Delivery route and the Loughborough Grounds & Gardens route are shown in Figure 4.5 and Figure 4.6 respectively. The results for the other duty cycles are shown in Appendix A. The left-hand side of each figure shows histograms of important aspects of the drive-cycles, the right-hand side shows the SAFD analysis of the complete dataset.

Figure 4.5: Microcab Mail Room Trip Analysis

Unfortunately, due to the fact that limited data are available for the Microcab, only 3 trips were identified for mail delivery, 2 for teaching support and 6 for testing. For the mail delivery and teaching support, the trips varied between 3.5km and 3.9km. The testing data had trips up to 20km although this is not likely representative of normal usage. As a result, the data are not sufficient to describe every circumstance that the vehicle is likely to encounter and therefore not ideal for SDP optimisation.

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Figure 4.6: Loughborough Grounds & Gardens Trip Analysis

An alternative is to use some of the data collected at Loughborough. Initial inspection identified that the Grounds and Gardens data are the most likely to represent the usage that the Microcab is likely to encounter. It can be seen in the analysis of the trips identified in Figure 4.6 that the trips varied in distance from 1km up to approximately 13km, although the vast majority were below 5km, the modal speeds for these trips varied from 2km/h to 7km/h, the same range as the Microcab, suggesting that similar speed limits were observed by the drivers. It is very important that the Microcab is able to complete the trips in regard to speed and acceleration limits. If the vehicle is unable to achieve the maximum speed or peak acceleration, this will severely affect the optimisation results. The Microcab saw a maximum speed of 11ms−1in normal usage and 15ms−1during testing, a peak acceleration of 2ms−2was reached although 1ms−2peak was more common for the teaching and testing trips. The grounds and gardens vehicles saw a maximum speed of 10ms−1 in one trip, however maximum speeds of around 7.5ms−1were more common, and a peak acceleration of 2ms−2, but again 1ms−2 was the modal peak acceleration across all trips.

Of the other duty cycles logged at Loughborough, the electrical (Figure A.1) and security (Figure A.3) vehicle trips were least appropriate due to much higher maximum speeds and peak accelerations of more than 3ms−2, which the Microcab would be unable to achieve.

Typical trip lengths for the security vehicles were also much too long. This is largely due to the fact that these vehicles often leave campus and drive on local roads, and that secu-rity vehicles are occasionally used to patrol the area for extended periods rather than for point to point journeys. The mail room (Figure A.2) and teaching support (Figure A.4) vehi-cles showed a fairly good correlation with the Microcab data, however maximum speeds of higher than 15ms−1were observed occasionally. Detailed examination of these trips shows that they are most likely due to re-fuelling at a nearby service station which requires driv-ing down a 40mph dual carriageway (Figure 4.7). As the Microcab would be refuelled on campus, this type journey is not required. Therefore, by removing any trips which exceed the 15ms−1, the correlation to the Microcab data can be improved, see Figure 4.8.

Figure 4.7: Loughborough Mail Room Vehicle Refuelling

Figure 4.8: Loughborough Mail Room Data with Refuelling Journeys Removed

4.3.4.1 SAFD Comparison

SAFD analysis can be used to compare the agreement of the various usage patterns nu-merically. The comparisons between each type of driving are shown in Table 4.2. It can be seen that the Loughborough University mail room vehicles most accurately match the real-world Microcab data. As was mentioned in the previous section, these cycles included re-fuelling journeys which exceeded the Microcab’s maximum speed. The Grounds and Gardens trips were all achievable by the Microcab, but showed comparatively poor agree-ment. Therefore, the SAFD agreement has been recalculated without journeys that exceed 15ms−1, the results of which are shown in Table 4.3.

Ele

Electrical 100 47.5 77.1 71.4 86.6 67.8 70.3 81.8 Grounds & Gardens 47.5 100 64.4 72.6 60.3 68.9 56.3 61.1 Mail Room 77.1 64.4 100 78.5 88.2 83 77.7 77.1 Security 71.4 72.6 78.5 100 81.3 77.5 63.3 76.8 Teaching Support 86.6 60.3 88.2 81.3 100 78 74.4 85.8 Microcab Mail Room 67.8 68.9 83 77.5 78 100 66.1 77.5 Microcab Teaching 70.3 56.3 77.7 63.3 74.4 66.1 100 64.8 Microcab Testing 81.8 61.1 77.1 76.8 85.8 77.5 64.8 100

Table 4.2: SAFD Agreement Between Duty Cycle Types (%)

Ele

Electrical 100 48.1 77.1 71 87.3 68 71.2 82 Grounds & Gardens 48.1 100 65.2 76.5 60.3 68.9 56.3 61.1

Mail Room 77.1 65.2 100 80.6 87.7 82.8 78.9 76.5 Security 71 76.5 80.6 100 82.7 79.1 66.9 78 Teaching Support 87.3 60.3 87.7 82.7 100 78 74.4 85.8 Microcab Mail Room 68 68.9 82.8 79.1 78 100 66.1 77.5 Microcab Teaching 71.2 56.3 78.9 66.9 74.4 66.1 100 64.8 Microcab Testing 82 61.1 76.5 78 85.8 77.5 64.8 100 Table 4.3: SAFD Agreement Between Duty Cycle Types with Limited Speed (%)

Removing any trips that exceed 15ms−1only affects the journeys made outside campus which, aside from the security data, were mainly for re-fuelling the vehicles. Therefore, this should not affect the validity of the remaining data. Firstly, it can be seen that the grounds and gardens and teaching support agreement is unchanged. This is to be expected as none of the trips exceeded 15ms−1. The electrical, mail room and security SAFD agreements have changed slightly, but more importantly all included trips now remain below the Microcab’s maximum speed. The electrical and security vehicles did still exceed the maximum accel-eration limit of the Microcab. Although these journeys could theoretically be filtered out in an equivalent way, there is no real-world justification for this. Therefore, the validity of the data would be compromised and the SAFD would no longer be representative of real-world driving patterns.

4.3.4.2 Summary

The data obtained from the Microcab’s usage in Birmingham are the most accurate repre-sentation of the duty cycle that the vehicle is likely to see. This is because it represents the actual usage of the vehicles whilst they were used for teaching support and mail delivery on the University of Birmingham campus. Because this is logged data from the actual vehicles, it is unlikely to show any speeds or accelerations that the vehicle is unable to achieve, how-ever it must be noted that the gradient data have been neglected and therefore it is possible that the vehicles could have exceeded their maximum acceleration or speed if assisted by gravity during testing. Unfortunately, only limited data from actual use are available and therefore it may be preferable to use alternative data available from the vehicles logged on Loughborough University campus.

Initial analysis of the data from Loughborough highlighted the Grounds and Gardens vehicles as the most likely candidate for an alternative. This is because these vehicles are similar in performance to the Microcab and rarely leave campus. As a result, the maximum speeds and acceleration seen in the data do not exceed the capability of the Microcab. How-ever, after some simple data processing, SAFD analysis shows a better correlation between the mail room cycle and the Microcab data. Unfortunately, the mail room vehicles occa-sionally exceeded the capability of the Microcab. On closer inspection of the data, it has been observed that these trips were made in order to re-fuel the vehicle at a nearby service station. This would not be required for the Microcab as hydrogen would be available on campus, and therefore they can be removed without affecting the validity of the recorded data.