Sensor Selection and Placement for Track Switch Condition Monitoring through Validated Structural Digital Twin Models of Train–Track Interactions

: Railway track switches experience high failure rates, which can be reduced by monitoring their structural health. The results obtained from a validated Finite Element (FE) model for train– track switch interaction have been introduced to support sensor selection and placement. For the FE models with nominal and damaged rail proﬁles, virtual strain sensor measurements have been obtained after converting the true strains to engineering strains. Comparisons for the strains before and after the introduction of the fault have demonstrated greater amplitude for the strains after fault introduction. The highest difference in strain amplitude is in the vertical direction, followed by the longitudinal and lateral directions.


Introduction
Switches and Crossings (S&Cs) are components of the track infrastructure that facilitate trains to change track lines. Due to varying cross-sections and the discontinuous rail profiles, S&Cs are subject to a higher failure rate than continuously running rails [1]. The existing approaches for detecting S&C rail failure include visual inspection and condition monitoring. Traditional inspection methods have involved the use of visual judgement and measurement equipment, which are now being complemented with measurement trains fitted with sensors as well as unmanned aerial vehicles.
Continuous condition monitoring of S&Cs is currently carried out to a limited extent and involves the measurement of signals from the Points Operating Equipment (POE) to detect a limited number of failure modes. This has been reviewed by Hamadache et al. [2], where various examples in literature for fault detection and diagnosis for S&Cs were included. Recent research has investigated the installation of sensors on the rails to obtain reliable signals that can be used in fault detection and diagnosis algorithms. In previous research, site measurements were carried out by installing strain gauges and accelerometers at various locations along the length of S&Cs, where a more linear trend was obtained from strain gauges than accelerometers for the measurement of the wheel-rail contact forces for different rolling stock [3]. The appropriate placement of such sensors is of vital importance for successfully detecting faults without redundancy. Numerical simulation approaches have traditionally been used for failure mechanism prediction for S&Cs [4]. They present an efficient alternative to field experimentation for carrying out preliminary studies to support predictive maintenance. Therefore, a novel numerical simulation approach for train S&C track interaction has been implemented to obtain virtual signals from the rail that have been post-processed to determine the orientation and placement of sensors.

Methodology
A combined numerical simulation approach based on Multi-Body Simulation (MBS) and Finite Element (FE) analysis was utilised to obtain the outputs necessary to predict the fault locations and determine sensor placement [5]. A holistic MBS model was developed to simulate the dynamic train-track interaction between a Manchester benchmarks passenger vehicle [6] and a 60E1-760-1:14 railway switch [7]. The results from the wheel-rail contact interaction were used to determine the Wear number, Tγ, which has been correlated to the risk of damage occurrence on the rail surface [8]. The detailed 3D FE model shown in Figure 1 was developed for the location with high damage susceptibility. Unlike the MBS model, which is limited to the prediction of forces and stresses at the wheel-rail contact surface, the FE model is able to obtain dynamic response outputs for the subsurface. studies to support predictive maintenance. Therefore, a novel numerical simulation approach for train S&C track interaction has been implemented to obtain virtual signals from the rail that have been post-processed to determine the orientation and placement of sensors.

Methodology
A combined numerical simulation approach based on Multi-Body Simulation (MBS) and Finite Element (FE) analysis was utilised to obtain the outputs necessary to predict the fault locations and determine sensor placement [5]. A holistic MBS model was developed to simulate the dynamic train-track interaction between a Manchester benchmarks passenger vehicle [6] and a 60E1-760-1:14 railway switch [7]. The results from the wheelrail contact interaction were used to determine the Wear number, Tγ, which has been correlated to the risk of damage occurrence on the rail surface [8]. The detailed 3D FE model shown in Figure 1 was developed for the location with high damage susceptibility. Unlike the MBS model, which is limited to the prediction of forces and stresses at the wheel-rail contact surface, the FE model is able to obtain dynamic response outputs for the subsurface. The dynamic behaviour of the track model and the wheel-rail interaction results were validated by comparing the rail receptance and contact force, respectively, against the reference results, as published in [5]. At present, a railhead surface fault has been introduced to this model in the form of a discontinuity on the railhead, as demonstrated in Figure 2a, the geometry of which is influenced by a large "squat" modelled by Bogdański et al. [9]. As shown in Figure 2b, Squats take the form of indentations on the railhead and occur where changes in the track stiffness are observed, such as S&C and rail joints [10,11]. The dynamic train-track interaction simulation has been carried out using FE for the passage of the train at 160 km/hr, both before and after the introduction of the surface The dynamic behaviour of the track model and the wheel-rail interaction results were validated by comparing the rail receptance and contact force, respectively, against the reference results, as published in [5]. At present, a railhead surface fault has been introduced to this model in the form of a discontinuity on the railhead, as demonstrated in Figure 2a, the geometry of which is influenced by a large "squat" modelled by Bogdański et al. [9]. As shown in Figure 2b, Squats take the form of indentations on the railhead and occur where changes in the track stiffness are observed, such as S&C and rail joints [10,11]. simulation approach for train S&C track interaction has been implemented to obtain virtual signals from the rail that have been post-processed to determine the orientation and placement of sensors.

Methodology
A combined numerical simulation approach based on Multi-Body Simulation (MBS) and Finite Element (FE) analysis was utilised to obtain the outputs necessary to predict the fault locations and determine sensor placement [5]. A holistic MBS model was developed to simulate the dynamic train-track interaction between a Manchester benchmarks passenger vehicle [6] and a 60E1-760-1:14 railway switch [7]. The results from the wheel-rail contact interaction were used to determine the Wear number, Tγ, which has been correlated to the risk of damage occurrence on the rail surface [8]. The detailed 3D FE model shown in Figure 1 was developed for the location with high damage susceptibility. Unlike the MBS model, which is limited to the prediction of forces and stresses at the wheel-rail contact surface, the FE model is able to obtain dynamic response outputs for the subsurface. The dynamic behaviour of the track model and the wheel-rail interaction results were validated by comparing the rail receptance and contact force, respectively, against the reference results, as published in [5]. At present, a railhead surface fault has been introduced to this model in the form of a discontinuity on the railhead, as demonstrated in Figure 2a, the geometry of which is influenced by a large "squat" modelled by Bogdański et al. [9]. As shown in Figure 2b, Squats take the form of indentations on the railhead and occur where changes in the track stiffness are observed, such as S&C and rail joints [10,11]. The dynamic train-track interaction simulation has been carried out using FE for the passage of the train at 160 km/hr, both before and after the introduction of the surface The dynamic train-track interaction simulation has been carried out using FE for the passage of the train at 160 km/hr, both before and after the introduction of the surface fault. Virtual strain sensor measurements were obtained for all rail elements by converting the true strain (ε t ) obtained from FE simulations to the engineering strain (ε e ), which is the actual parameter measured by strain sensors by using the relationship in (1). The virtual strain measurements before and after introducing the fault were compared and the change in strain due to fault introduction was calculated. The results can help inform the required resolution for the sensors as well as the best locations to install them for fault detection. Similarly, the results for the Von Mises stress, which can help determine the fatigue life of the rail at the potential sensor installation locations have been compared for the models with the nominal and damaged rail profiles.

Discussion of Results
The results for the rail strain and stress outputs obtained from the dynamic train-track interaction carried out in FE have been discussed with respect to their utilisation to inform sensor placement.
The surface fault shown in Figure 2 was introduced at a distance of 9.44 m from the beginning of the switch toe. Results have been obtained from the frame at which the wheel passes over the railhead discontinuity and exerts a high impact load on the rail. The results from the same time frame have been obtained for the models with both the nominal and damaged rail profiles. In Figure 3a,b, the Von Mises stress (SMises) on the railhead has been plotted. A higher concentration of stresses on the rail gauge corner at a longitudinal distance of 9.44 to 9.46 m is observed due to the wheel-rail contact patch. Also, higher amplitude of stresses is observed in Figure 3b due to the high impact force resulting from the rail discontinuity. Similarly, in Figure 3c,d, higher amplitude of vertical strains (E22) is observed for the model with the fault. Negative values for the strains denote compression, whilst positive values denote tension. As the wheel, impact force results in high compressive stresses and strains on the railhead; the strain amplitude is mostly negative.
fault. Virtual strain sensor measurements were obtained for all rail elements by converting the true strain obtained from FE simulations to the engineering strain , which is the actual parameter measured by strain sensors by using the relationship in (1).

ln 1
(1) The virtual strain measurements before and after introducing the fault were compared and the change in strain due to fault introduction was calculated. The results can help inform the required resolution for the sensors as well as the best locations to install them for fault detection. Similarly, the results for the Von Mises stress, which can help determine the fatigue life of the rail at the potential sensor installation locations have been compared for the models with the nominal and damaged rail profiles.

Discussion of Results
The results for the rail strain and stress outputs obtained from the dynamic traintrack interaction carried out in FE have been discussed with respect to their utilisation to inform sensor placement.
The surface fault shown in Figure 2 was introduced at a distance of 9.44 m from the beginning of the switch toe. Results have been obtained from the frame at which the wheel passes over the railhead discontinuity and exerts a high impact load on the rail. The results from the same time frame have been obtained for the models with both the nominal and damaged rail profiles. In Figure 3a,b, the Von Mises stress (SMises) on the railhead has been plotted. A higher concentration of stresses on the rail gauge corner at a longitudinal distance of 9.44 to 9.46 m is observed due to the wheel-rail contact patch. Also, higher amplitude of stresses is observed in Figure 3b due to the high impact force resulting from the rail discontinuity. Similarly, in Figure 3c,d, higher amplitude of vertical strains (E22) is observed for the model with the fault. Negative values for the strains denote compression, whilst positive values denote tension. As the wheel, impact force results in high compressive stresses and strains on the railhead; the strain amplitude is mostly negative. As the railhead experiences high stresses and fault initiation, it is more plausible to install sensors away from this region. The results for the strains from the lower portion of the railhead, rail web and foot have been plotted in Figure 4. Strains in the lateral Eng. Proc. 2021, 10, 49 4 of 6 direction (E11) for the nominal and damaged rail profiles have been plotted in Figure 4a,b, respectively, where high compressive lateral strains are observed at the lower corner of the rail web due to bending. In Figure 4c,d, high compressive strains are observed on the rail web due to the vertical wheel impact load. In Figure 4e,f high compressive longitudinal strains are observed closer to the railhead, whereas tensile strains are observed at the rail foot, demonstrating the expected flexural behaviour. As expected, the strain amplitude is higher for the model with the damage than the nominal rail profile. As the railhead experiences high stresses and fault initiation, it is more plausible to install sensors away from this region. The results for the strains from the lower portion of the railhead, rail web and foot have been plotted in Figure 4. Strains in the lateral direction (E11) for the nominal and damaged rail profiles have been plotted in Figure 4a,b, respectively, where high compressive lateral strains are observed at the lower corner of the rail web due to bending. In Figure 4c,d, high compressive strains are observed on the rail web due to the vertical wheel impact load. In Figure 4e,f high compressive longitudinal strains are observed closer to the railhead, whereas tensile strains are observed at the rail foot, demonstrating the expected flexural behaviour. As expected, the strain amplitude is higher for the model with the damage than the nominal rail profile.  The strain amplitude in the rail web and foot in Figure 4 are large enough to be detected using strain sensors. However, the detection of fault would require the determination of adequate sensor resolution to measure the change in strain resulting from the fault occurrence. Therefore, the change in strain amplitude due to fault introduction have been plotted in Figure 5. The highest change in strain is observed in the vertical direction since it is also the amplitude of strains in the vertical direction that is the highest. The second Eng. Proc. 2021, 10, 49 5 of 6 highest change is observed for the longitudinal strains followed by the lateral strains. Hence, the placement of sensors on the YZ plane or the sides of the rail would help sense a higher difference in strain amplitudes on fault occurrence. The placement of sensors in the XZ plane or the rail bottom will also help capture an adequate difference in strains, with improved fatigue life of the sensor.
The strain amplitude in the rail web and foot in Figure 4 are large enough to be detected using strain sensors. However, the detection of fault would require the determination of adequate sensor resolution to measure the change in strain resulting from the fault occurrence. Therefore, the change in strain amplitude due to fault introduction have been plotted in Figure 5. The highest change in strain is observed in the vertical direction since it is also the amplitude of strains in the vertical direction that is the highest. The second highest change is observed for the longitudinal strains followed by the lateral strains. Hence, the placement of sensors on the YZ plane or the sides of the rail would help sense a higher difference in strain amplitudes on fault occurrence. The placement of sensors in the XZ plane or the rail bottom will also help capture an adequate difference in strains, with improved fatigue life of the sensor.

Conclusions and Future Work
Validated simulations of train-track switch interactions have been used to inform strain sensor placement for predictive maintenance. The FE simulations were carried out for a switch model with nominal rail profiles and after introducing surface damage. Higher strain and stress outputs have been obtained after introducing surface rail damage. The overall amplitude for the rail strains as well as its change on fault introduction is the highest in the vertical direction, followed by the longitudinal and lateral directions. Further analysis of the modelling results will be carried out to determine detailed positioning of sensors based on the rail fatigue life, risk of fault occurrence and measurement redundancy. Similarly, parametric simulation studies for different railway traffic conditions will be input to inform sensor placement. As the present work is limited to modelling a specific surface defect, future work will involve introducing worn rail profiles and change in track stiffness into the model for determining sensor placement to detect multiple faults. Additional complexities can be introduced into the models and a bigger dataset can be statistically analysed for determining sensor placement. With the availability of data for live traffic, Digital Twin models of different routes could enable intelligent decisions for supporting condition monitoring and risk-informed predictive maintenance.