# Wheel load estimation for autonomous vehicle by using a fiber optical sensor

Alex Coiret, Martin Fontaine, Julien Cesbron, David Bétaille

► To cite this version:

Alex Coiret, Martin Fontaine, Julien Cesbron, David Bétaille. Wheel load estimation for autonomous vehicle by using a fiber optical sensor. Transportation Research Procedia, 2023, 69, pp.131-138. 10.1016/j.trpro.2023.02.154. hal-04441814

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<figure><img src="image_1.png" /></figure>
AIIT 3rd International Conference on Transport Infrastructure and Systems (TIS ROMA 2022),
15th-16th September 2022, Rome, Italy

Wheel load estimation for autonomous vehicle by using a fiber
optical sensor

Alex Coiret<sup>a,*</sup>, Martin Fontaine<sup>a</sup>, Julien Cesbron<sup>b</sup>, David Betaille<sup>a</sup>

<sup>a</sup>Univ Gustave Eiffel, COSYS-SII, F-44344 Bouguenais, France

<sup>b</sup>Univ Gustave Eiffel, CEREMA, UMRAE, F-44344 Bouguenais, France

Abstract

In order to ensure safe driving without human supervision the autonomous vehicles are using a wide range of sensors as cameras, lasers, lidar to evaluate the road scene and to measure the vehicle trajectory. The vehicle weight is of critical importance since it affects both braking dynamics and stability in curves. This total weight depends on the number of occupants and goods or luggage, so it has to be dynamically estimated, at least at each traveling start. The literature review indicates that some infrastructure-based sensors exist but tire related systems are preferable if the vehicles can start routes at indefinite points. In this work an experimental system is developed to estimated the load applied to a non rolling tire with several concurrent sensors. First the elongation of the tire to road contact patch is estimated by the means of an internal optical fiber sensor based on Rayleigh scattering interferometry, since this elongation is related to the applied load according to literature results. A laser sensor situated inside the tire is giving the tire sidewalls deflection which is related to applied load too. At last tire to road contact patch length and width are estimated by using Fuji pressure sensible paper. As a results for loads of 2.8 to 4.8 kN the optical sensor and the laser sensor are leading to load estimation error lower than 3%. Moreover the estimated tire contact patch is confirming the tire belt elongation estimated by the optical fiber sensor. In perspective the two measurements from optical fiber and laser could be used by autonomous vehicles in order to have a redundant load estimation for one or several wheel, under vehicle symmetry hypothesis.

© 2023 The Authors. Published by Elsevier B.V.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Peer-review under responsibility of the scientific committee of the Transport Infrastructure and Systems (TIS ROMA 2022).

Keywords: autonomous vehicle; load estimation; road safety; in-tire sensors

**1. Introduction**

Vehicle load estimation has always been a major road transportation concern, either for billing process and carrying
limits in case of bulk goods trucks or for road usage enforcement, particularly in winter periods when road surfaces are
prone to unfreeze related wear. Autonomous vehicles are bringing a new requirement: without driver the autonomous
vehicle should achieve a load estimation in order to verify the load limit compliance and to adapt its dynamics like

<footnote>* Corresponding author:</footnote>

<footnote>E-mail address: alex.coiret@univ-eiffel.fr</footnote>
braking and curve trajectory adaptation. This is of first importance in case of autonomous shuttle buses, where there
is not a physical person responsible of the loading, and for which over-loading can occur at rush hours.

From the road infrastructure, weighting platforms are widely used (Captels, 2022), and some systems are able to estimate tangential forces too in an attempt to detect the grip potential used by vehicles (Coiret and Orfila, 2008; De Beer, 1996). Contrary to the weighting platforms, these two latter systems are able to estimate tridimensional forces on a given location of the road infrastructure.

For vehicles like autonomous delivery vehicles, the load may vary over an itinerary at any stop site and so the load evaluation should be realized from the vehicle itself. Sensors can be situated on dampers (Van Raden, July 18, 1967), on suspension (Tarter and Gerstbauer, Apr. 25, 1995; Hagedorn and DeForrest, Aug. 5, 1980), on axles (O'Dea, dec. 26, 1995) or on vehicle junction if existing (Fredrickson, aug. 11, 2016). The knowledge of the static load is an important information for an autonomous vehicle in order to verify the load capacity limit, but moreover the effect on this load is important to estimate the dynamic performances of the vehicle in terms of handling in curves or braking distances. So this work is centered on an in-vehicle load estimation method.

Facing the large variety of vehicles suspensions, as in geometry as for component sets, this work aims at estimating the load directly in the tires, since they represent the most standardized part of the vehicle-to-road subsystem. In the next section an experimental setup is presented in that aim, for a non rolling vehicle, but perspectives are drawn for rolling tires in the conclusion.

## 2. Experimental Set-Up

In order to be able to estimate wheel load for a static vehicle, before starting a road trip, a tire sensor should be efficient for each angular position of the wheel.

Tire deflection can be used to estimate the wheel load with quite a good confidence and laser sensors can be used in that aim, but a laser sensor should be fixed on a stationary bracket, outside the tire, in order to be used for a static vehicle. A laser sensor mounted inside the tire will give the deflection estimation for only one tire angle position.

So a fiber optical sensor was chosen since it is able to estimate the tire belt elongation at each point of the tire circumference. In this work and for validation purpose a laser sensor is positioned at the bottom end of the internal rim with a focus point at the lower point of the internal surface of the tire, despite the fact that in a general use this perfect positioning should not be easily realizable for each vehicle stop. For our experiments the tire is fixed on a press arm in order to apply various wheel loads (Fig. 3). An air pressure sensor is mounted on the rim too. The detail of the optical fiber is given in Fig. 1 and the mounting of the 3 sensors is visible on Fig. 2.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Optical fiber (yellow fiber bounding with glue) on the inner tire liner.</figcaption></figure>

Vertical forces are applied by the hydro-static press and are measured by a loading cell (sensitivity of 0.2 mV/kN).
An optical fiber is glued in the center of the inner tire belt, over the full circumference and it is linked to the Luna
acquisition system. A laser sensor is screwed on the rim to measure the vertical tire deflection to the lowest inner
<figure><img src="image_3.png" /><figcaption>Fig. 2. Sensors mounting: fiber to the left, pressure at bottom and laser to the right.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 3. General view of the tire in the hydraulic force cage and with sensor cables.</figcaption></figure>

belt point (sensitivity 0.2 V/mm). A pressure sensor is screwed on the rim too (sensitivity 2.9 V/bar) and sheets of pressure-sensitive paper are placed between the tire and the ground surface (Fuji paper).

The tire is new, its characteristics are: 185/65R15 88T, radial type construction, 1 polyester ply in sidewall, 1 polyester/2 steel/1 polyamide plies in tire belt. Tire inflation is set at 2.1 bars. This relatively small tire was chosen in order to evaluate the fiber sensor in the context of small autonomous vehicles such as airport or urban shuttles, with aleatory loading. This work should be adaptable to heavier vehicles.
The optical fiber and its acquisition system are allowing a strain measurement of about 10,000 με. In our experiments the higher loads are leading to a maximum strain of 4000 με, so within the optical fiber sensor strain scale. This Distributed Optical Fiber sensor (DOF sensor) allows the measurement of the distributed strain over the whole tire circumference at a sampling frequency of 10 Hz.

DOF sensors are based on reflectometry by involving swept-wavelength interferometry (Froggatt and Moore, 1998). Their ability to monitor strain all over an element are justifying their use for Structural Health Monitoring (SHM) (Bassil et al., 2019).

Technically the fiber index of refraction is locally altered by the strain and temperature variations, and this phenomenon induces signal losses by back scattering and it is evaluated by the fiber interrogating system. The frequency shift can be expressed as a function of temperature and strain variations:

$$ \frac{\Delta v}{v} = K_T \Delta T + K_\epsilon \Delta \epsilon, \qquad (1) $$

with $\frac{\Delta v}{v}$ the frequency shift, $\Delta T$ and $\Delta \epsilon$ the temperature and strain variations, and $K_T$ and $K_\epsilon$ are constants.

By carefully maintaining the experiment at a constant temperature the strain can be computed from the frequency shift. Spatial resolution of the DOF sensor is of 0.65 mm, with 1500 strain values over 1 meter long fiber.

In this experiment the elongation of the tire contact patch is evaluated by the DOF sensor since it is reported to be in relation to the tire loading. The vertical deflection is evaluated by the laser sensor since it is the most common indicator of tire loading too. Moreover, sheets of pressure sensitive Fuji paper are placed between the tire and the ground in order to evaluate both the load value and the tire contact path elongation.

Experiments are realized by applying several vertical loads on the tire, from 2000N to 5000N by 500N intervals. Each load is maintained 30 seconds and three types of transition are experimented between these loading steps: $L_{50}$, $L_{100}$ and $L_{500}$. The load variation speeds for these transitions are respectively of 50 N/s, 100 N/s and 500N/s.

## 3. Results

Figure 4 presents the comparison between actual applied load and load estimation from the laser sensor and the DOF sensor, for a loading range between 2800 to 4800 N, on 5 loading steps. Intended loading range was of 3000 to 5000 N but the actuator presented a shift, without sensible consequences on this preliminary comparison test.

The laser sensor is providing a very good load estimation for the full loading range. The DOF sensor is providing a good evaluation of the load for the 3000 to 4400 N range, but the evaluation error reaches up to 5% for low and high load cases. The laser sensor precision is higher than the DOF precision but it should be recalled that the laser remains dependent to a unique angular position of the tire, with the laser beam pointed vertically to the center of the contact patch.

Figure 5 presents the internal contact patch length estimation from the DOF sensor for a 2000 to 5000 N loading range with 30 seconds stationary step at each 500 N increment and with the three speed transition values $L_{50}$, $L_{100}$ and $L_{500}$. High speed transitions are showing non-linear variations of the contact length, but stationary values are still the same as the $L_{50}$ low speed transition value. For each transition case the load/length relation is quite linear above a 2500 N load level. DOF sensor appears to be an adequate mean of wheel load estimation, through internal contact patch length evaluation.
<figure><img src="image_5.png" /><figcaption>Fig. 4. Load estimation from laser and DOF sensor.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 5. Contact patch length for three test cases estimated by fiber optical sensor over the loading range.</figcaption></figure>
Figures 6 and 7 are giving the tire to ground footprints for the 2000, 3000, 4000 and 5000 N loading cases by using sheets of pressure sensitive Fuji paper.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Tire footprint on Fuji pressure sensitive paper: vertical load of 2000 N (a) and 3000 N (b).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. Tire footprint on Fuji pressure sensitive paper: vertical load of 4000 N (a) and 5000 N (b).</figcaption></figure>

As a first interpretation it appears that the longitudinal length is stretching out more than the transverse width with the load increasing. Table 1 gives the dimensions of the tire footprint in pixels for a 600 dots per inch scanning of the Fuji paper sheets, and the total pixel count, for each loading case concerned by paper footprints. Lengths are deduced from the flatbed scanner resolution and DOF length determined from Figure 5 are also given in Table 1.

Pixel count is realized by means of a linux script on 8 bits converted footprint pictures (softwares: imagemagic, convert, histogram). This pixel count appears to be in direct relation to the loading, with a $R^2$ regression coefficient of 0.9986 (Figure 8). Theoretically the load is equal to the integral of the normal pressure over the contact patch area. Each dot on the picture correspond to the reach of the local activation pressure for which the local ink capsule is broken. Moreover the tire inflation pressure and the rubber elasticity are leading to a common pressure over the contact patch area, so each dot correspond to a common pressure of a value over the paper activation pressure, so that the relation between load and dot numbers should be linear. This means that the load depends linearly on the size of the actual contact area within the loading range considered in this study. The very high value of the regression coefficient is showing the good quality and the appropriate usage range of the Fuji paper.

The pixel count can be converted in contact patch surface, or more precisely in the equivalent surface with a pressure higher than the paper activation pressure. Considering the 600 dots per inch of the scanning, equivalent contact surfaces for 2, 3, 4 and 5kN are respectively 10,822 14,883 18,241 and 21,870 mm².
From the data set presented on Table 1, contact patch length from DOF sensor and Fuji footprints are plotted in function of the loading in Figure 9. Length are differing for several reasons. The most important one is that DOF is used to estimate the internal contact patch length whereas Fuji paper is related to external tire footprint. Second the Fuji length is greater on tire sides, probably due to sidewalls loading, whereas the DOF sensor is estimating the tire central length.

Despite Fuji papers are a good mean to evaluate the loading directly by surface estimation, length comparison to DOF is obviously not relevant for structural reasons (inside/outside and lateral/central).

<table><caption>Table 1. Fuji paper footprint analysis (600 dpi scanning).</caption><thead><tr><th>Wheel load (kN)</th><th>Width (pixels)</th><th>Length (pixels)</th><th>Pixel count</th><th>Length (mm)</th><th>DOF internal length (mm)</th></tr></thead><tbody><tr><td>2</td><td>2672</td><td>2260</td><td>6,038,720</td><td>95.7</td><td>127</td></tr><tr><td>3</td><td>2996</td><td>2772</td><td>8,304,912</td><td>117.3</td><td>157</td></tr><tr><td>4</td><td>3096</td><td>3292</td><td>10,178,864</td><td>139.4</td><td>168</td></tr><tr><td>5</td><td>3188</td><td>3828</td><td>12,203,664</td><td>162.1</td><td>176</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Fuji tire footprint pixel count in function of wheel loads.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 9. Fuji tire footprint length and DOF internal contact patch length.</figcaption></figure>
## 4. Conclusion

Among other many sensors, autonomous vehicles would take advantage of having a loading information, globally or for each wheel. Indeed the vehicle weight affects both braking dynamics and stability in curves and a knowledge of wheel loads at least at each vehicle start is part of the vehicle safety process, in the absence of a driver. The literature review indicates that infrastructure-based sensors exist but tire related systems are preferable if the vehicles can start routes at indefinite points. In this work an experimental system has been developed to estimate the load applied to a non rolling tire. The elongation of the tire to road contact patch is estimated by means of an internal optical fiber sensor based on Rayleigh scattering interferometry. A laser sensor situated inside the tire and sheets of pressure sensitive Fuji papers have been used as comparison systems. As a result for loads of 2.8 to 4.8 kN the optical sensor and the laser sensor are leading to load estimation error lower than 3%. Moreover the estimated tire contact patch is confirming the tire belt elongation estimated by the optical fiber sensor, with differences attributable to different locations of the systems, one inside the tire belt, the other outside, and one more focused on the central part of the tire, the other on the external parts of the contact patch. Nevertheless the Fuji paper has allowed a precise estimation of the total load via the surface integration of the contact patch. In perspective the two measurements from optical fiber and laser could be used by autonomous vehicles in order to have a redundant load estimation for one or several wheel, the new optical fiber solution having the advantage to deliver a load estimation independently to the wheel angle position, at any vehicle start. A more advanced development of this prototype could allow the continuous load estimation for a rolling vehicle but issues such as tire temperature elevation or tire rigidity alteration would have to be addressed. In a first attempt such a development could give access to the standing wheels loads, while resisting to rolling constraints in a full tire life. Manufacturers could use optical fiber embedded in the tire belt, associated to low-cost fiber interrogators.

## Acknowledgements

This work is part of a research collaboration involving Université Gustave Eiffel and Captels Society (see reference bellow).

## References

Bassil, A., Wang, X., Chapeleau, X., Niederleithinger, E., Abraham, O., Leduc, D., 2019. Distributed Fiber Optics Sensing and Coda Wave Interferometry Techniques for Damage Monitoring in Concrete Structures. Sensors 19, 356. URL: http://www.mdpi.com/1424-8220/19/2/356, doi:10.3390/s19020356.

Captels, 2022. CAPTELS Society, france, http://www.pesage-captels.com/.

Coiret, A., Orfila, O., 2008. Concurrent evaluation of the tire/pavement contact torsor by means of both a dynamometer wheel and a road infrastructure-integrated system. Bulletin des Laboratoires des Ponts et Chaussées, pp 133-145 URL: https://www.researchgate.net/publication/294145091_Concurrent_evalution_of_the_tirepavementContact_torsor_by_mean_of BOTH_a_dynamometer_wheel_and_a_road_infrastructure-integrated_system.

De Beer, M., 1996. Measurement of tyre/pavement interface stresses under moving wheel loads. Int. J. of Heavy Vehicle Systems 3, 97-115. doi:10.1504/IJHVS.1996.054553.

Fredrickson, D., aug. 11, 2016. Weight sensing vehicle hitch. URL: https://patents.google.com/patent/WO2016127058A1/en.

Froggatt, M., Moore, J., 1998. High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter. Applied Optics 37, 1735. URL: https://www.osapublishing.org/abstract.cfm?URI=ao-37-10-1735, doi:10.1364/AO.37.001735.

Hagedorn, T.H., DeForrest, A.L., Aug. 5, 1980. Load measuring system for leaf spring suspensions.

O'Dea, J.O., dec. 26, 1995. On-board vehicle weighting system.

Tarter, R.E., Gerstbauer, T.M., Apr. 25, 1995. Vehicle on-board weighting system and method.

Van Raden, F., July 18, 1967. Pneumatic Weighing System for Load Carrying Vehicles.