Challenges and methodology for pre-processing measured and new rail profiles to efficiently simulate wheel-rail interaction in switches and crossings

This paper describes a methodology developed to systematically pre-process rail profile data from switches and crossings for railway vehicle dynamics simulation. The methodology accepts two data sources, unworn geometries from CAD drawings or worn geometries from digitised track measurements. The method addresses key challenges with the relative positioning and quality improvement of the input data and explains the necessary steps to ensure compatibility with the interpolation schemes used to represent the rail profile in certain multibody software. The case studies presented show how small misalignments in the processed digitised measurements affect simulation results and how simulations can help understand the qualitative evolution of switches and crossings rail profiles in a used track. This paper concludes that one of the most challenging tasks remains the automation of rail pre-processing for measured data because it is difficult to correct vertical and lateral misalignments of the profile cross-sections without a reference system.


Introduction
Switches and crossings (S&C) are critical assets of the railway infrastructure as they allow trains to change routes and consequently, the network to function. The interaction between the vehicle and S&C is characterised by high wheel-rail contact forces due to the wheel load transfer from one rail to another, which leads to faster degradation of the infrastructure when compared to the remaining railway network [1]. Multibody software (MBS) packages have been widely used to predict wheel-rail contact forces, which are of great importance to assess the performance of S&C designs [2,3]. However, more often than not, the process considers unworn rail shapes. In reality, the S&C rails initially wear very quickly until their geometry conforms with the wheels of the local traffic. Thus, the S&C unworn geometry is not really representative of in-service conditions, which is why evaluating measured geometry along-side new designs is necessary.
CONTACT Y. Bezin y.bezin@hud.ac.uk Since MBS software use interpolation techniques to represent the rail surface and assess wheel-rail forces, they require a series of discretely measured rail cross-sections along the track length as input [4][5][6]. The numerical results are highly sensitive to this input. For instance, slight misalignments caused by measurement approximation of the rail profiles can lead to unrealistic wheel-rail contact forces, and discretising the rail with too few profiles can lead to gross geometry approximations. Therefore, modelling the rail surface of S&C is a complex task that requires considering the interpolation techniques used by the MBS package and thoroughly pre-processing the input profiles, whether they are unworn (new) or worn (measured).
Wheel-rail contact models are implemented in MBS to predict the forces resulting from the wheel-rail interaction [7][8][9][10][11][12]. At each time step of the numerical simulation, the MBS determines the interaction between each wheel and rail pair and corresponding contact conditions to compute the normal and tangential contact forces. In multibody simulations with a focus on the wheel-rail contact conditions, associated contact forces are determined based on the penetration between the wheel and rail surfaces [8,[13][14][15]. Due to the very high stiffness associated with the wheel-rail contact, a small penetration of the order of 50 μm can lead to a normal contact force of approximately 25 kN [8]. Therefore, rail surfaces must be carefully represented because tiny geometrical inaccuracies can have disproportional effects on the wheel-rail force evaluation.
In MBS packages, the rail surface of S&C is handled through the interpolation of the discrete profiles that are provided by the user [6,[16][17][18]. In practice, only the top part of the rail where the wheel is expected to contact is considered. Before the numerical simulation, many MBS packages resample the rail profiles to ensure they all have the same number of points and generate longitudinal polynomials that allow interpolating the rail profiles at the wheel's longitudinal position [16,19]. Commercial software, such as VI-Rail or SIMPACK, lack tools to assess the quality of the rail interpolation. The only way to qualitatively assess the quality of the interpolation is to analyse the simulation results.
The inputs that represent S&C need to be properly processed to ensure meaningful numerical results. For unworn S&C, CAD models are convenient because they allow obtaining many profiles at low cost with minimal processing [20]. On the contrary, there are challenges associated with worn S&C. One is the time available to perform the measurements, which is prescribed by the infrastructure manager. Another challenge is the relative alignment of the measured profiles laterally and vertically, which is not tracked by the measurement equipment such as MiniProf [21] or the laser based Calipri [22]. Therefore, the profiles need to be adjusted considering the requirement of MBS tools but without jeopardising the geometry of the rail. Although measured S&Cs have been addressed in a few scientific papers [6,23], there is no discussion in the literature about pre-processing of measured profiles. This paper presents a series of techniques to pre-process S&C rail profile data, which has a variable cross-section, into inputs compatible with the MBS software VI-Rail. Note that the same process should be equally effective for many other software. Different examples of switches and crossings, including unworn and worn cases, are used to demonstrate the proposed pre-processing techniques. The quality of the rail surface parameterisation is analysed using visualisation tools for each set of input profile, so that the quality can be appreciated and iterative corrections made, if necessary, before simulation start. Finally, multibody simulations are performed to show the impact of various pre-processing choices and their effects on the wheel-rail interaction prediction.

Multibody dynamics software (MBS) requirement
MBS software requires a series of consecutive rail profiles as input to represent rails with variable cross-section along the track [16]. These data can be obtained either from a CAD model or digital measurement. The requirements to define a rail with variable cross-section in VI-Rail, which are similar in other MBS (e.g. SIMPACK, Medyna and MUBODyn), are presented hereafter. Figure 1, which schematically represents of a rail with variable crosssection, is used hereafter to illustrate the main steps used by MBS software to model the geometry of the rail surface.
One of the main steps is to identify section break planes, i.e. positions at which two consecutive rail profiles show an abrupt variation in shape. A section break plane delimits two consecutive longitudinal rail segments. At these section break planes, an 'additional profile' is defined by trimming the 'widest profile' so that a perfect match exists with the 'shortest profile' where they overlap as exemplified in Figure 1. Two section breaks define a longitudinal segment in which longitudinal polynomials defined before the multibody simulation allow interpolating the rail cross-sections during run time. VI-Rail resamples the rail profiles at the section break planes so that all profiles contained within each longitudinal segment has the same number of points, which allow defining the longitudinal polynomials shown in Figure 1.
At each integration step, rail profiles are interpolated at the longitudinal position of the wheels, based on the longitudinal polynomials. Non-parameterised polynomials in the y-z plane are determined to fully describe the interpolated profiles. This implies a few constrains. First, input profiles cannot have vertical faces, i.e. multiple points with the same abscissa. Second, the interpolated rail profiles should not comprise series of points forming sharp edges as they can lead to local overshoots that would lead to unrealistically high wheel-rail contact forces. Sharp edges must be smoothed in the input profiles, which is a topic addressed later in this paper.

Methodology for S&C geometry processing
This section describes the methodology developed to process rail data. Although many processes used are similar for both switches and crossings, there are significant differences that justify explaining separately the process for Switches and Crossings in the following two Sections 3.1 and 3.2, respectively, with accompanying diagrams in Figure 2. Where useful, further detailed explanation of each process is given in the following Subsection 3.3.
In both switch and crossing cases, the process starts with either measured data or data derived from a CAD file. In case of measured data, there is an additional process added to clean the profiles, which consist of a number of operations necessary to render the rail surface useable. This is described in Subsection 3.3 in more details. Additionally, the measured data requires specific alignment in the vertical (z) and horizontal (y) direction, which is not required for the CAD data as it already comes aligned. This is also discussed in Section 3.3.

Switches
For switch rails, the processing in Figure 2 (left) applies. A global alignment is performed to move switch toe to the desired position longitudinally (x) and laterally (y) with the gauge point vertically (z) at −14 mm. The profiles are then trimmed to discard non-required edges where wheel is not expected to contact the rail. Sharp edges are avoided by identifying locally high curvature and removing points is necessary to avoid overshoots during resampling and interpolation by the MBS software. The data points are then resampled to the desired resolution using equidistance spacing of points. For the purpose of considering the relative movement between the switch and stock rail [24], the two are separated by creating a smooth artificial groove in between and separating the two profiles at this location. The edges at their interface are trimmed and any remaining sharp edge removed, if present. A final smoothing of all profiles is performed to confirm smooth curvatures and continuity between data points. Finally, the longitudinal interpolation intervals (surface breaks) are defined to form clusters of profiles with similar shapes and width in the final geometry. Switch (left) and crossing (right) geometry processing algorithm flow diagram. Note that certain operation can be interchangeable, this is the case of the 'trim' function that could be placed before or after the cleaning of the profiles.

Crossings
For crossings, the processing in Figure 2 (right) applies. The crossing theoretical Intersection Point (IP) is determined, and translated to an agreed convention of [0, 0, −14] mm in longitudinal (x), lateral (y) and vertical (z) coordinates, respectively. Profiles are trimmed beyond non-necessary lateral and vertical coordinates. The groove between wing rails and crossing rails is recreated using a smooth U-shape, to ease the rail surface interpolation. This was implemented because certain measured profiles do not fully capture the bottom of the groove or their data is discontinuous. Vertical or near-vertical faces are replaced with inclined faces to meet MBS software requirement in terms of maximum slopes (in this case this was set at 1 in 60). A resampling is done at the desired equidistant interval. Smoothing of the profiles is performed to ensure smooth curvatures and continuity between data points. Finally, surface breaks locations are defined to form clusters of profiles with similar shapes and width in the final geometry.

Cleaning of measured data
This process is necessary and includes a few operations as follows. First several rogue points are searched for and removed according to the following criteria: (1) Non-increasing y-coordinates, to avoid point backing on themselves that cannot be described as a function of the independent lateral coordinate. (2) Points that are too close to one another to avoid local spikes in the interpolated spline function later on; default criteria 1 used is 0.2 mm. (3) Consecutive points having an angle steeper than the default criteria 1 of 1 in 100, to avoid high derivative of the profile function.
Then series of monotonically non-increasing data points are searched for and replaced with new data points using a pchip spline interpolation, which is a Matlab shape preserving function. Measured profile generally include general roughness in the data and there can be areas of the profiles in steep faces capturing concave shapes that are undesired, i.e. not compatible with MBS calculation requirements and where no wheel-rail contact is possible.

Resampling profiles and smoothing
The resampling procedure is performed along the arc length of all input profile with equidistance between data points so that the resampling performed by the MBS software, which is described in Section 2, do not modify significantly the input profiles. The resolution of the input profiles is prescribed between 0.4 mm to 1 mm maximum to ensure an adequate representation of the rail profiles while not exceeding the limits of the MBS software, which is 400 points per profile in the case of VI-Rail.

Treating sharp edges
Removing sharp edges has proven challenging because profiles with a locally high slope (ranging from +/− 1 in 100 to 1 in ±∞) between consecutive data points are classed as sharp edges that result in local overshoot of profile shape if not treated. Also, abrupt changes in slope e.g. from vertical to horizontal faces is another manifestation of sharp edges. The challenge at this stage of processing, is in automating the decision-making process to specify which remedy is adopted, in which location. It takes human intervention to decide whether to remove certain points with high slope or introduce a spline to smooth the transitions between vertical and horizontal faces, thus making the step manual and tedious.
In Figure 3, the input profile leads to an overshoot that is obtained with VI-Rail MBS software, which results from the VI-Rail resampling process. The remedy applied in this case is to remove a few data points in the area near the highest curvature and replace with shape preserving interpolation (Matlab pchip function) to slightly smooth the profile in the gauge corner. A user parameter is used to specify the area within which points need to be replaced, defined as a circle of a given diameter around the sharp point. Figure 3 also shows that this process although required to avoid concentrated contact points in the gauge corner, can also lead to removing too much material in that area if not applied carefully. Treating local sharp edges causing overshoot in the MBS process. Note that the modified profile in this case removes nearly as much as 1 mm of material in the gauge corner and this might affect contact conditions and forces. It is therefore required for the user to apply his best engineering judgement in these cases.

Determination of section breaks
To tackle the drastic changes in profile shape and width, more pronounced in crossings, surface interpolation breaks are introduced at key longitudinal positions such as those pictured in Figure 4, identified with different colours for each consecutive section. The reader can observe that these sections are introduced to indicate areas where the width is either constant or where it widens / narrows at a rate that is more or less constant. This allows a better control of 3D rail interpolation at each wheel position within each section. The section breaks are defined by creating a duplicate profile at the end/beginning of each consecutive surface interval as explained in Section 2. The profile with the widest lateral coordinate is usually copied and cut to size to match the width of the previous/next section being narrowest. This ensures continuity and avoidance of contact jumps as the wheel moves from one section to the next. Within each section, the profiles are extended or trimmed to match other profiles of that section, i.e. either with a constant width or with a constantly increasing/decreasing width.

Alignment of switches and crossings data
Because field measurement equipment does not include an absolute referential as series of profiles are measured, there is a need to carry out local alignment of all profiles post measurement. The measured data is aligned laterally (y) by taking a point below the gauge point of each profile where no wear/deformation is expected (−30 mm from top of rail used in this case) and aligning them to the known theoretical running edge for the type of switch considered. Vertical (z) alignment for measured switches is done using absolute height of the switch stock rail in the region where little or no wear and plastic deformation is anticipated, e.g. gauge point at the field side of the stock rail, realigning all at z = 0.
For the case of the crossing, the alignment is more complicated and can be improved using as reference known positions from an equivalent CAD geometry if available or else other theoretical reference (e.g. theoretical machining extrusion path for cutter in nose, wing and throat). This method ideally implies the availability of a suitable 3D CAD model of the original crossing and a judgement on areas of reference which do not show any wear or deformation on the measured data.
The methodology implemented in this paper for the crossing is illustrated using the data of the NR56E1 vertical 1 in 13 crossing measured at the Wooden Gate site on the UK East Coast Main Line [25]. Initially the lateral alignment is performed by taking a point on the gauge face away from any deformation due to contact (e.g. 30 mm from top of rail as for the switch) and all profiles realigned. In the crossing nose, this would generally fail because the nose is machined locally to have narrower dimensions where the running edges meet. Therefore, locally some manual alignment might be required or alignment can be performed using the opposite face on the groove of the wing rail at angle 1 in N (where N is the crossing angle, e.g. 13).
Next, the vertical alignment is performed. In Figure 5, the measured data (a) and the CAD design (b) are shown. The red and green markers show selected reference positions along each set of data that can be used: • Red crosses following the centre line of the nominal rail up to the IP position and then diverging at 1 in N angle. • Green crosses marking the outer position on the field side of the wing rail, away from any possible contact wear/tear, and offering a stable vertical position adjacent to the crossing nose.
• Red crosses following the centreline of the nominal rail on the casting vee, past the point where wing rail reference is no longer present.
At these positions, the vertical coordinate of each profile can be obtained and realigned against either the CAD reference if a good match is possible, or more likely, a linear or other regression is carried out in each section, and all profiles are then offset vertically with respect to this regression function. If selected reference points are either in an area away from contact wear and tear, or on the contrary in the middle of the observable contact band, then a smooth contact condition would be expected.

Data used and site description
In Sections 4.2 and 4.3 data from the UK Wooden Gate site is used. This is for a vertical 56 crossover (NR56 V) which was measured twice three years apart in 2016 and 2019 and installed in 2012 [25]. Both measurement sets were obtained using a MiniProf device [21], capturing ∼ 20 cross-sections in the switch panel and ∼ 80 in the crossing panel. These were measured under intermittent track possession, thus limiting the number of crosssections that could be measured. In Section 4.4, an Italian 60E1-170-0.12 crossing is used. It was measured using the CALIPRI optical measurement device [22] with a higher number of ∼ 140 cross-sections to produce higher potential accuracy in shape representation. The crossing shape was however as newly manufactured before going into track.
The primary aim of the analysis presented is to understand how wear and tear affects the wheel-rail interaction in S&C panels and how it compares to the unworn design. In the comparison process, there are also additional variations that might arise from the measurement that can be attributed to the type of devices used, the skills of the operator and the practical/environmental conditions under which the measurements are taken. The second aim is to understand the influence of the processes and user choices applied to the measured data, as discussed in previous sections. In the following sections, the analysis of the Wooden Gate data for the switch and crossing panels are presented first, followed by the Italian crossing.
In all simulation presented hereafter the Manchester Passenger vehicle model with new S1002 wheel profile has been simulated at a speed of 50 or 100 km/h over the S&C components in the through facing direction. The track properties are the same as defined in the S&C Benchmark [26].

NR56 switch simulations -new, 2016 and 2019 measured
The 2016 and 2019 measurements of the switch components have been processed independently using the process explained in Section 3. They are then compared to the new design dataset as used for the S&C benchmark [27]. The results in Figure 6 (top) show the vertical Q-forces transfer from the stock rail (STR-solid line) onto the switch rail (SWR-dashed line). In all cases, this occurs between 2.5 m and 3.5 m after the start of the switch, with a small reduction of vertical load on the stock rail as it deviates to the right, and a dynamic impact on the switch rail after the load transfers. The bottom plot of Figure 6 shows the contact band for each case as view from the top of the rail, the dash line representing the centre of the equivalent Hertzian ellipse and the solid lines the edge of the contact ellipse. The transfer of contact from stock rail to switch is seen in correspondence with the Q force transfer of the top plot.
The main difference is that for the unworn design, the load transfer occurs at about x = 3.4 m while for both measurements it occurs earlier at about 2.7 m. Both measurements results are in fact very close together and both show that the contact on the main stock rail is wider and closer to the top of the rail, while the new design with unworn gauge corner leads to narrower and slightly closer to the gauge contact band. The load amplification on the switch rail for both measurements are quasi-identical and about 3% lower than the new design. The contact on the worn switch rail components initiates slightly nearer the switch toe, and closer to the interface between switch and stock rail. This tendency seems to be evolutive as the 2019 measurement shows the contact band running closer to that interface in the region 3 to 3.5 m.

NR56 crossing simulations -new, 2016 and 2019 measured
The 2016 and 2019 measurement of the Wooden Gate crossing is also compared to the NR56 V data from the S&C Benchmark [27]. The crossing component is placed so that x-axis zero coordinate corresponds to the crossing IP position. Figure 8 shows the Qforces (top) in correspondence with the contact band (bottom) as viewed from the top of the crossing shape, the dash line representing the centre of the equivalent Hertzian ellipse and the solid line the edges of the contact ellipse (up to three simultaneous contact patches are plotted). Associated with this, the axle kinematic vertical motion can be seen in Figure 9 top and the bottom plot shows the same contact band plotted over the wheel profile circumference.
There are a larger number of variations observed in the crossing as follows.
On the entry to the crossing (around −1 m) the wheels moves from the nominal rail onto the wing rail which shape changes rapidly, including a ramping effect. For the new design, a very drastic change of contact condition occurs, i.e. large jump to the field side, which translates into a large transient vertical load increase followed by unloading. This feature is to some extent an exaggeration of the new design with does not account for any manual grinding post manufacture and installation, combined with initial wear from running traffic, that tends to smooth this transitional shape. The difference is evident on the 2016 measurement with a more gradual lateral deviation of the contact onto the wing rail. For the 2019 measurement, while the initial entry to the crossing also appears smoother, there is a very sudden contact jump associate with impact load and loss of contact at x = −0.75 m, when the contact momentarily jumps to the gauge corner. There is in this area, a rather square shape of the measured profiles, while previous ones are more rounded in the gauge corner. The wheel can be seen to bounce up at that point. It is not clear if this is due to issues remaining with the local profiles alignment and corresponding 3D interpolation deformation where the throat machining start, i.e. wing rail departing at an angle. Evidence from   the site does not show such behaviour, as can be seen in Figure 10 (a) where the contact band rapidly shifts towards the field side of the wing rail before the throat and remains fairly constant after that.
The second area of interest is the load transfer from the wing rail to the nose, occurring between x = 0 m and 1 m. For the unworn design, the wheel briefly contacts on the thin running edge of the diverging wing rail, loses contact (thin contact band and low force), until contact with the nose occurs at 0.4 m (peak force of 230 kN), the wheel rebounds and momentarily loses contact again, until it regains contact at 0.7 m with a lower peak force of 90 kN. In terms of wheel motion, this translates into a very fast drop on the wing rail contact and forced wheel upward motion on the nose topping. In contrast, for the 2016 measurement, the wheel remains in contact with the wing rail slightly longer and on an area further away towards the field side, and as can be seen in Figure 8. This corresponds to a contact on the very edge of the wheel outer rim surface. Once the wheel leaves the wing rail, there is a short loss of contact until contact is made on the nose at 0.56 m with a peak force of 166 kN. For the 2019 measurement, something similar happens with more sudden contact changes towards the outer part of the wing rail, which leads to a first near wheel unloading in correspondence to the IP location. The departure from the wing rail translates in a second longer complete loss of contact to touch the nose at 0.62 m with a peak force of 281 kN, the largest of the three cases 2 (see Table 1 for a summary of the dynamic loads). These values indicate that the four-year-old worn crossing leads to dynamics force reduction of about 30% compared to the new design, however after 7 years of use, this force has increased by about 20% compared to the new design and nearly 80% compared to 2016.
For the remaining contact on the vee of the crossing, each set of data gives a fairly distinctive contact band. The new design initially having a contact in the gauge corner, jumps to the top of vee from x = 1.4 m, returning to a nominal contact from x = 2.7 m, also  Figure 11. IT60E1 crossing measurement (left) and acquired raw data (right).
associated with a transient load. Both measurements, however, show a larger and more constant contact band throughout with much smaller transient effect on return to the nominal rail. It is also seen from the vertical wheel motion that the transition is much smoother.

IT60E1 crossing simulations -new measured
One of the most common crossing in Italy is the 60E1-170-0.12. The crossing is installed on turnouts with radius of 170 m that can be largely found on conventional railways up to 200 km/h. The crossing is straight and made of casted manganese steel and then machined by milling process. The main entry profile from the nominal 60E1 rail vertical profile to the crossing nose is made by a double inclination of 1:20 and 1:10. The solid model of the crossing was not available, and the geometry of a new crossing was scanned using the CALIPRI optical measurement device, recording separated sections with a relatively tight spacing between each profiles measurement. The longitudinal alignment of the different sections has been performed manually using as reference an aluminium bar laid along the crossing. An image of the measuring process and the raw result of the scanning are shown in Figure 11.  (1) The 'initial' measurement (trimmed, smoother etc.) subject to alignment as supplied from the field measurement described above.   (y = + 35 mm) on the early part of the wing and on the flat part of the vee, (d) vertical alignment along the diverging wing rail, (e) automated alignment in the nose area using moving average function along the top coordinate of the nose. The y and z coordinate offset calculated for all these steps are plotted in Figure 12. Both modification-1 and -2 manage to suppress a lot of these transient forces, which are simply due to very small misalignment of the consecutive profiles leading to larger deviation in the calculated 3D profiles along the crossing, i.e. exaggerated roughness of the surfaces. This has a significant effect on force predictions. Note a high transient is also apparent at the end of the crossing while returning to nominal rail.
In Figure 13 as well as Figures 14 and 15, markers are shown on the top to indicate positions of section breaks as introduced for each crossing model, SB-ini stand for 'initial', SB-1 for modified-1 and SB-2 for modified-2. SB-ini only as a section break at the beginning and at the end of the crossing, SB-1 as 11 section break locations and SB-2 has one less. Figure 15 shows the corresponding vertical motion of the wheel, which is much smoother for the modification-2 case.
The simulation at the higher speed of 100 km/h shows a series of loss of contact with the crossing, similar to those observed with the NR56 benchmark geometry, on the leg entry to the crossing, when the contact shifts to the outer part of the diverging wing rail and finally on rebound after first impact with the crossing nose. Figure 16 shows the lateral shift of contact on the entry onto the wing rail, with certain wheels contacting right on the upper edge of the wing rail shape. The contact on the nose appears very near the tip and is initially very thin in comparison to the contact width seen on the wing rail. Overall, the simulation results corroborate very well with these site observations, showing that the MBS simulation process proposed can accurately capture the expected wheel-rail contact behaviour.

Conclusions and contribution
A procedure to pre-process longitudinally varying rail shape in switches and crossings from either new CAD geometry or field measurement has been presented. The achieved process has then been tested in a commercially available railway MBS software, showing evidence for the change in behaviour between new and worn design, but crucially a very high sensitivity of the results on the user-defined pre-processing of the rail input data.
In terms of comparing new and worn design, the proposed methodology has allowed a qualitative assessment of the performance against time to be made for the UK data of the Wooden Gate site. One conclusion is that the switch condition remains a lot more constant than that of the crossing. The crossing measurement indicates an initial 'bedding in' of the wheel-rail interaction in the initial years, through normal wear of the crossing, and then an increase in dynamic forces after several years, which are associated with site evidence of weld repairs on the nose and on the crossing vee, as well as varying contact conditions most likely associated with poor support and voided bearer [25].
The results presented here, also show small discrepancies with site observations, mainly that the shift of the contact band towards the end of the wing rail (field side) is not seen on site (Figure 10), and that the alignment procedure still requires improvement. Current measurement equipment such as MiniProf and Calipri (most widely used for S&C), do not offer a way of ensuring absolute referencing of consecutive profiles in the lateral and vertical planes. This remains a very difficult task dependent on trials and errors and subjective judgements. This is further evidenced by the last analysis on the IT60 crossing showing that even for an unworn measured crossing shape, the process of alignment can lead to significant differences in the resulting dynamic output depending on how the alignment is carried out and how careful the user implements them in a specific software environment.
As further work, the authors will investigate the use of other sources of data such as the laser-based Loccioni Felix [28] measurement system, and develop a more systematic approach to the alignment of measured data.