10 Axle Box Accelerometer Signal Identification and Modelling 91 0 50 100 1 1.5 2 Training, red type Validation, red type Training, green type Validation, green type Training, blue type Validation, blue type 0 50 100 1.5 2 2.5 3 3.5 104 0 50 100 -7 -6 -5 -4 -3 104 Fig. 10.4 Selection of the model order of the LPV-AR models (for a fixed functional basis order of 2) 34 36 38 40 42 44 0 20 40 60 80 100 120 140 -100 -50 0 50 Fig. 10.5 LPV-AR model-based PSD of the response time series as a function of the vehicle speed and the track superstructure type (m/s) for a model order 80 and a hermite basis order 2 Standard model order selection is carried out, where range of model orders is calculated, while a plausible value of the functional basis order is selected. Different performance criteria are compared to determine the optimal model order. From Fig. 10.4 it can be observed that a basis order of 80 sufficient to reach less than 1.5% RSS/SSS error, while minimizing the BIC criterion and maximizing the log-likelihood. The dynamics of the identified LPV-AR models is subsequently analysed. Figure 10.5 illustrates the PSD of the LPVAR model as a function of vehicle speed for the different track type segments of Table 10.2. The sleeper passage frequency, evidenciated in Fig. 10.2 is captured by the LPV AR model, and as expected varies in function of the superstructure type. The highlighted in green in particular experiences much larger vibrations compared to the tracks with more elastic superstructures highlighted in red and blue. 10.4 Conclusions The present signal identification emphasizes that vehicle speed, rail condition and track type influence the vehicle axle box response. In the high frequency domain, effects such as the rail condition are not negligible for the detection of defects on the infrastructure type. Encouraging results from parametric identification substantiate future studies, integrating overall infrastructure type and condition into the estimation process. Acknowledgments The authors acknowledge the support of the Swiss Federal Railways (SBB) via the Future Mobility Research Program Grant (ETH Mobility Initiative) on the topic of On Board Monitoring for Integrated Systems Understanding & Management Improvements in Railways.
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