Romain Carletto
email: romain.carletto@univ-tours.fr

Hubert Cardot
email: hubert.cardot@univ-tours.fr

Nicolas Ragot
email: nicolas.ragot@univ-tours.fr

Deep Learning for Document Layout Generation: A First Reproducible Quantitative Evaluation and a Baseline Model

Keywords: Document Layout Generation, Quantitative Evaluation, Generative Adversarial Network

Deep generative models have been recently experimented in automated document layout generation, which led to significant qualitative results, assessed through user studies and displayed visuals. However, no reproducible quantitative evaluation has been settled in these works, which prevents scientific comparison of upcoming models with previous models. In this context, we propose a fully reproducible evaluation method and an original and efficient baseline model. Our evaluation protocol is meticulously defined in this work, and backed with an open source code available on this link :

Introduction

Document Layout Generation

For decades, developments in information and communication technologies leveraged interest in automated document layout generation. This application usually consists in automatically laying out elements on a canvas of given dimensions. It can take as inputs a random vector and additional optional features such as elements categories, reading order of the elements, element contents (texts or images) and geometric constraints such as aspect ratios or areas of the elements. While the outputs can take many forms, it is usually a list of bounding boxes, one for each element, with for each of these boxes its category, its dimensions and positions on the canvas. While former automated attempts in this field faced lack of both functionality and flexibility, recent solutions based on deep generative models reached interesting possibilities and provided encouraging visual and user study results. However, quantitative evaluations of these later solutions show important deficiencies, which prevents any scientific comparison with upcoming works.

A Tricky Quantitative Evaluation

Quantitative evaluation of generative models has always been a delicate matter, and is even more complicated in the specialized field of document layout generation. Real world layout guidelines are mainly implicit, even to layout designers themselves, and while metrics from image generation field are still being adapted, standard metrics from document layout community do not apply. As an example, the IoU score which is commonly used in layout analysis has limited utility in layout generation, where different positions for a same element can be of similar quality.

While in related works interesting quantitative evaluation methods have emerged and are progressively converging to a common standard, none of these works, after a meticulous study, have provided a reproducible and reliable definition of a quantitative evaluation method. In this context, the comparison between a new model and previous works relies mainly on subjective interpretations of visual results, which are of high interest but not sufficient to match hard sciences principles. Therefore, this paper aims to propose, on main document layout datasets, a first reproducible quantitative evaluation of any document layout generation model, as well as an original baseline model.

2 Related Works

From Explicit Methods to Deep Learning Methods

Former works in automated document layout generation focused on turning layout guidelines into explicit and static quantitative rules. Earliest works were based on templates [START_REF] Myers | User Interface Software Tools[END_REF][START_REF] Lok | Evaluation of visual balance for automated layout[END_REF] or on interactive tools combining basic layout rules [START_REF] Feiner | An Experimental System for Creating and Presenting Interactive Graphical Documents[END_REF] and showed poor possibilities. Later works were based on geometrical objective functions to be optimized [START_REF] Merell | Interactive Furniture Layout Using Interior Design Guidelines[END_REF][START_REF] Lin | Active Layout Engine: Algorithms and Applications in Variable Data Printing[END_REF][START_REF] Purvis | Creating Personalized Documents: An Optimization Approach[END_REF] faced qualitative biases and a strong lack of flexibility. To tackle these various shortcomings, recent researches focused on learning methods where guidelines are turned in a dynamic and data-driven way into implicit quantitative rules projected in a multidimensional feature space. More specifically, most recent researches have been based on deep learning generative models, which can learn very complex rules from simple objective functions, and are already successful in other generative tasks such as image or video generation.

In [START_REF] Li | LayoutGAN: Generating Graphic Layouts with Wireframe Discriminators[END_REF], a Generative Adversarial Network (GAN) generates layouts from only a random vector as input. It can generate layouts of documents, layouts of pixels subset (extracted from MNIST handwritten digits images), clipart scenes and geometric tangrams. In [START_REF] Li | Attribute-conditioned Layout GAN for Automatic Graphic Design[END_REF], authors extend [START_REF] Li | LayoutGAN: Generating Graphic Layouts with Wireframe Discriminators[END_REF] previous work to propose two main applications : layout generation and layout adjustment. Layout generation is split into three sub-applications. Image layout generation takes geometric constraints as input and generates several layouts propositions containing only the product image. Attribute-guided layout generation takes these first layout propositions as input and add additional elements, according to these elements attributes, to produce different propositions of complete layouts. Finally, grouping and ranking application allows to select the best layout among different layout propositions, through overlap, alignment and discriminator scores.

The model presented in [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF] is based on graph neural network and Variational Auto-Encoders (VAE) and generates a layout iteratively, element after element. It takes as inputs a set of elements, the order of elements to be iteratively laid out, and optional user-specified constraints. They experimented their models on generating application page layouts, magazine page layouts and private web advertising layouts.

In [START_REF] Zheng | Content-aware Generative Modeling of Graphic Design Layouts[END_REF], authors merge GAN and VAE architectures to propose a model that encodes element attributes at different steps : when encoding a real layout into a latent vector, when generating a layout from a latent vector and when classifying a layout to be real or generated. These attributes can thus be learned in association with real training layouts during the training step and added as inputs, aside with a random vector, when using the model. They contain particularly rich and diversified information, such as image contents, text and label values than can be both continuous (such as aspect ratios) or discrete. Author architecture also allows the users to add optional soft constraints as inputs, such as reserved area for specific types of elements. Experiments are focused on generating magazine page layouts.

While not exactly focusing on document layout generation, [START_REF] Jyothi | LayoutVAE: Stochastic Scene Layout Generation From a Label Set[END_REF] proposes a model based on VAE to generate real scene layouts. Generation steps are divided into several sub-steps : a first VAE generates a list of elements, then another VAE generates bounding boxes from it. The model is applied on a dataset adapted from MNIST, where handwritten digits are laid out on a black screen, and is also applied on COCO dataset, containing real life scenes with for each scene a labeled bounding box for every important object and person in the scene. Other moderately related but yet interesting works, [START_REF] Nauata | House-GAN: Relational Generative Adversarial Networks for Graph-constrained House Layout Generation[END_REF] and [START_REF] Schroeder | Triplet-Aware Scene Graph Embeddings[END_REF], consider a potential sub-task of layout generation and generate bounding boxes from graphs in which strong relational and geometrical constraints are already indicated, e.g. which element must be at the right of which element, or which element has to be bigger than which element.

Deficiencies in Existing Quantitative Evaluation Methods

Previous works usually display visual results and often provide user studies of their experiments, but while this information can draw attention on the presented models, it can't allow any objective comparison with upcoming methods. In parallel, quantitative evaluation methods are also presented in the course of these works, but are not defined in a valid and reproducible way.

While some authors [START_REF] Zheng | Content-aware Generative Modeling of Graphic Design Layouts[END_REF] do not provide any quantitative evaluation at all, others laid incomplete groundwork to define a valid quantitative metric. In [START_REF] Li | LayoutGAN: Generating Graphic Layouts with Wireframe Discriminators[END_REF], absolute alignment and overlap scores are provided for generated document layouts but the dataset on which these scores have been obtained, referred only as "the document layout dataset", has not been made available. The exact same problem is found in [START_REF] Li | Attribute-conditioned Layout GAN for Automatic Graphic Design[END_REF] where alignment and overlap scores are given for a private advertising layout dataset, not available to the scientific community.

In [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF], authors propose an alignment evaluation on two public datasets but while our understanding of their alignment evaluation method has been confirmed by the authors, our results differ from theirs by orders of magnitude when we apply this method on the ground truth layouts of both evaluated datasets. Aside from the alignment evaluation method, [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF] proposes an evaluation based on the Fréchet Inception Distance (FID). As described in their works, this method relies on the feature distribution of the penultimate layer of the discriminator : the distribution obtained on real layouts is compared with the distribution obtained on generated layouts and produces a score ranging from zero to positive infinity, with lower values indicating better performances. Given a fixed discriminator architecture with fixed feature parameters and fixed hyperparameters, this evaluation method allows for a quantitative comparison between two different generative models. But in [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF], these parameters are missing.

3 Experimental Protocol Synthetic Dataset As explained in introduction, real world layout guidelines are mainly implicit which makes it difficult to quantitatively evaluate the quality of a layout. In this context, [START_REF] Carletto | Automatic Generation of Web Advertising Layouts:A Synthetic Dataset and a Deep Learning Baseline Model[END_REF] proposes two synthetic datasets. The first dataset contains 100,000 synthetic document layouts, in which elements have fictitious semantic categories and are laid out following a combination of arbitrary and fictitious layout rules, that are both hard to learn and easy to quantitatively evaluate. A second dataset contains 100,000 other synthetic document layouts, in which elements have this time similar categories as in the web advertising industry : Product Image, Text, Call-To-Action (CTA) and Logo. In this second dataset, elements are laid out according to basic rules and distributions of the web advertising industry (e.g. logos are always on the top or on the bottom of the layout, in a majority of layouts images are bigger than CTAs and logos, ...). These layout rules are thus both realistic and easy to quantitatively evaluate. Any learning document generation model can thus be trained on these two synthetic datasets and then be evaluated in an exact and quantitative way, through reusing the explicit rules that were used in the first place to produce each of these datasets.

In the first dataset, while general rules alone have been used to create the majority of the layouts, additional specific rules have been used when creating certain layouts, as seen in Fig. 1. The use of these additional rules and their precedence on general rules is triggered by specific sequences of categories within the list of elements in each layout to be generated. Furthermore, some of the specific rules are deliberately in contradiction with the general layout rules to challenge the ability of a layout generation model to discern patterns within a complex and implicit combination of layout rules, similarly to what is expected from the model in a real case document generation application. The datasets are available at the following link : https://github.com/romain-rsr/synth_ datasets_for_web_advertising_layout/tree/master RICO This public dataset [START_REF] Deka | Rico: A Mobile App Dataset for Building Data-Driven Design Applications[END_REF] contains 65,538 ground truth layouts extracted from various application pages. Numerous works have experimented on this dataset for its quality and for the high quantity of layouts it contains. Elements within the layouts can be nested and can present very different sizes and aspect ratios. RICO dataset can be found at this link : http://interactionmining. org/rico Magazine Magazine dataset [START_REF] Zheng | Content-aware Generative Modeling of Graphic Design Layouts[END_REF] contains 3,919 magazine page layouts, that can be more similar to advertising layouts than RICO application page layouts. This is of great interest since there is no public dataset available for advertising layouts but high industrial application in this field for sophisticated automated layout. The dataset is available at this link : https://xtqiao.com/projects/ content_aware_layout/

Baseline Model

Architecture Our model is a GAN with both generator and discriminator based on a fully connected residual block architectures. Instead of the usual residual block containing two layers, residual blocks within our model are tangled and contain one layer each. As seen in Fig. 2, both generator and discriminator contain 5 layers assembled in tangled residual blocks, each containing 100 neurons except the last layer. In the generator, the number of neurons in the last layer is equal to the product of the number of elements to be laid out and the number of feature for each element. In discriminator, the last layer contain only one neuron to output the cagory of the input layout : real or fake. In both generator and discriminator, each layer is activated by a ReLU activation function except the last layer activated by a sigmoid function. Training Our experimental protocol can be applied on layouts of any number of elements. Yet, layouts have first to be grouped according to the number of elements they contain so the experiments are run on each group separately, with the number of elements per layout being given as an input parameter of our model and evaluation process. For greater simplicity in the analysis of our experiments, the presented results focus on layouts with three elements.

Model's performance is monitored through the binary cross-entropy loss function during training, and the model is trained through Adam optimizer, which extends rmsprop optimizer on one hand, by adapting its learning rate to each parameter, and extends adagrad optimizer on an other hand, by adapting its learning rate to first and second moment (respectively mean and uncentered variance) of recent gradient magnitudes. In each experiment, we select a subset of the complete dataset and split it in train, validation and test sets, respectively of 60%, 20% and 20% of the subset.

Quantitative Evaluation Metrics

Our quantitative evaluation is based on four metrics : the Fréchet Inception Distance (FID), the Comparative Alignment Score, the Comparative Overlap Score and the Comparative Diversity Score. Some of them are inspired and revised version of incomplete yet interesting quantitative evaluations described in related works. Both pseudo-code and ready-to-use code of these evaluations are publicly available in our git, aside with real and generated evaluated samples.

Fréchet Inception Distance This metric, initially defined in [START_REF] Dowson | The Fréchet distance between multivariate normal distributions[END_REF], is applied as specified in [START_REF] Heusel | GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium[END_REF] to the output feature distribution within the discriminator penultimate layer. The mean and the covariance matrix of these features are first computed when applying the discriminator on generated layouts, then the same operation is carried out with real layouts. Finally, mean µ X and covariance matrix X , obtained on generated layouts, are compared with mean µ Y and covariance matrix Y , obtained on real layouts, following equation :

d 2 (F, G) = |µ X -µ Y |+tr( X + Y -2( X Y ) 1/2 ) (1)
The resulting score is an absolute value which must be as low as possible. As specified earlier, this evaluation is of interest only if fixed architecture, feature parameters and hyperparameters are settled for the discriminator used in the evaluation, so that when comparing two models, the shift in the FID score comes only from the shift in the similarity between real and generated layouts. Also, using a discriminator of a specific existing work in layout generation would give an unfair advantage to this work when comparing new models with it, so a standard and non specialised discriminator architecture has to be used instead. Therefore, we used the pre-classification layers of the open source inception v3 discriminator, whom fixed parameters are indicated in our git.

Absolute Alignment Score In related works, alignment score is often mentioned, as an absolute measure applied on generated layouts only, and measures the closest possible alignment of elements on each layout, according to one of the possible vertical alignment axes (element lefts, centers or rights). Here is the [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF] definition of this absolute alignment score :

alignment gen = 1 N k i min j,i =j {min(l(e k i , e k j ), m(e k i , e k j ), r(e k i , e k j )}) (2)
Where N is the total number of generated layouts, e k i and e k j are the i th and j th elements of the k th generated layout and where l,m and r are respectively the distances between lefts, centers and rights of two considered elements.

Comparative Metric Absolute score can be interpreted very differently according to the type of evaluated documents. On RICO application pages, for example, lower alignment score could be preferred by designers while on advertising layouts, greater misalignment can be a quality factor so absolute alignment score has no general objective value. Therefore, our evaluation goes further and compares the absolute alignment score obtained on generated layouts with the absolute alignment score obtained on real layouts. While simply computing the ratio between two absolute scores would have been a straightforward comparison, it is not adapted if the score used as the divider is equal to zero. To overcome this problem and obtain similar score scales as in the FID evaluation, the following comparative metric has been defined to compare absolute scores score gen and score real , obtained respectively on generated and real layouts :

comp(score gen , score real ) = |log score gen + 1e-10 score real + 1e-10 | (3)
Comparative Alignment Score We apply the comparative metric on the couple of absolute alignment scores obtained on real and generated layouts to get the comparative alignment score, which is finally a robust and objective indication of how similar generated layouts are to the real layouts, independently of the subjective interpretation of what is a good absolute alignment value within each dataset :

alignment comp = comp(alignment gen , alignment real ) (4)
Absolute Overlap Score In parallel to the alignment measure, absolute overlap score is used in several related works and measures the ratio of overlapping areas over the total canvas area :

overlap gen = 1 N k i j,j<i intersection(area k i , area k j ) area k c (5)
Where N is the number of generated layouts, where area k c is the total canvas area of the k th generated layout (in most datasets this value is constant) and where area k i and area k j are the respective areas of i th and j th elements of the k th generated layout Comparative Overlap Score Absolute overlap score encounters the same interpretation concerns as the absolute alignment score : RICO layouts, for example, present nested elements, which are fully overlapping, while in other types of document layouts, overlaps are unacceptable. Therefore, as for the alignment evaluation, our final overlap score is obtained by applying the comparative metric to the absolute overlap scores obtained on generated and real layouts, and hence benefits of the same objectiveness and generalisation as our alignment comparative score :

overlap comp = comp(overlap gen , overlap real ) (6)
Comparative Diversity Score Our evaluation method additionally incorporates the comparative diversity score, which compares standard deviations of real and generated layouts features. As an example, a standard deviation is computed for the left position of the first element, over all generated layouts, and one standard deviation is computed for each pair of element rank -element feature. The minimum value of these standard deviations is then computed for the generated layouts. The same operation is applied on real layouts, then real and generated obtained minimums are compared through the comparative metric.

diversity comp = comp(min i,j {σ ij gen )}, min i,j {σ ij real }) (7)
Where σ ij gen (respectively σ ij real ) is the standard deviation of the j th feature of the i th element over all generated layouts (respectively over all real layouts).

Applying a same comparative metric on different datasets Note that comparative alignment score is neither penalizing or rewarding alignment, it is only penalizing differences between the absolute alignment score obtained on generated layouts, and the one obtained on real layouts. The same reasoning applies for comparative overlap score and for comparative diversity score. Therefore these comparative scores can be easily compared from different datasets, even with high variation of any given property between and within those datasets (such as the number of layout elements).

Independence between training metrics and comparative metrics

Comparative metrics are used only during evaluation and are not used at all during training, so that evaluation scores remain independent of the training process. The only metric used during training is the binary cross-entropy loss function, which is agnostic to our evaluation metrics.

Baseline Evaluation Results

As specified earlier in the related work section, there is no reproducible quantitative baseline for document layout generation, which make impossible for us to compare our model to previous work. As an example, [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF] unconstrained document layout generator achieves an FID score of 143.51 on RICO dataset while our model achieves an FID score of 66.96 on the same dataset. While these results could show that our model allow a significant performance gain, this actually cannot be asserted since the discriminator architecture and parameters used for the FID computation in [START_REF] Lee | Neural Design Network: Graphic Layout Generation with Constraints[END_REF] is not available. Therefore, we propose our own quantitative baseline results, indicated in Table 1. These results are also available in our git along with the evaluation functions and the real and generated layouts that have been used to obtain them. While scores are globally of the same order of magnitude from one dataset to another, some score discrepancies remain noteworthy. FID is particularly lower on synthetic dataset, where size and location ranges are smaller and where there is no nested element. On this dataset, diversity score is also much higher, which is due to first element top position being constant on each real layout. Therefore, even a short deviation in generated layouts corresponding feature is highly penalized. Finally, due to a high number of nested elements, real layouts overlap score is not as tight in Magazine as in the other datasets. Therefore, the absolute difference in overlap score between generated and real layouts is less sensitive and penalized in this dataset, which explains such a low comparative overlap score for Magazine Dataset.

In order to put into perspective these quantitative results, generated layout representations have been randomly selected and are displayed along with real layout representations in Fig. 3. We can see on results obtained on synthetic dataset that only one layout, among all displayed generated layouts, contains an overlapping error. On results obtained on RICO dataset, we see strong similarity between generated and real layout patterns, e.g. a very large bounding box covering the majority of the canvas with much smaller, horizontally aligned bounding boxes above it. We see in both generated and real RICO layouts that elements are generally extremely close to each other without overlapping, which shows that our model matches industrial precision standards. In order to assert the resilience and the versatility of our quantitative evaluation metrics, an additional set of experiments focused on more particular examples. More specifically, these experiments aim to verify that the accuracy and the consistency of our metrics remain proportional to the level of training of the evaluated model and remain independent of datasets properties such as the number of element per layout or the degree of alignment, overlap and diversity within each dataset.

Additional results : application of the quantitative evaluation metrics on specific examples

Evaluation scores after intensive training and after poor training

We evaluated the consistency of our metrics with respect to the level of training by comparing the obtained results after 100 and 10.000 training epochs. This protocol was first ran on the second synthetic dataset, then ran again on Rico dataset. Results of Table 2 show that on both datasets and on each property (alignment, overlap and diversity), better training leads to better comparative scores. As expected, the consistency of these comparative scores is contrasting with the divergence of some absolute scores. As an example, on the second synthetic dataset, more training leads to a higher absolute overlap score while on Rico, more training leads to a lower absolute overlap score. While the interpretation of these two absolute scores relies on the subjective understanding of their related datasets, a lower comparative score systematically implies a better performance, on any dataset.

Evaluating datasets with high differences in terms of alignment, overlap and diversity . The results in Table 3 have been obtained by experimenting the same model on specifically selected layouts of a same dataset, showing opposite values on a given property (alignment, overlap or diversity). As seen in the section focusing on highly and poorly diversified layouts, we see that comparative diversity scores for both data subsets are in the same order of magnitude, which is consistent with the fact that the same model has been experimented on both subsets of layouts, leading to similar performances. Additionally, the sections focusing on highly aligned and poorly overlapping layouts present very high comparative scores (which implies lower performance). These scores show the ability of the comparative metric to encompass the critical difference between a property equal to zero in real layouts (reflecting a hard constraint) and a very low non-zero value for the same property in generated layouts (which are then missing the hard constraint), by heavily penalizing the relative comparative scores.

Evaluating layouts with different numbers of elements Table 4 shows that the comparative metrics are consistent over layouts of different number of elements. Except the sections where generated layouts do not comply with hard constraints, comparative scores remain in the same order of magnitude, independently of the number of elements. Moreover, in the last section of the table we show that one comparative score can easily be applied to two set of layouts, each containing layouts with a distinct number of elements.

Conclusion

Contributions

In a context where recent publications on automated document layout generation show off impressive model architectures and promising user studies, we aimed at setting a sorely missing quantitative basis for scientific comparison and cooperation in the field of document layout generation. We thus propose a first baseline and made our quantitative evaluation method fully reproducible, backing it with a turn-key git containing both data and evaluation metrics that led to the presented results. The model we propose is based on an original yet easy to implement adaptation of the residual block concept and shows satisfying results, in both quantitative and visual aspects.

Future Works

Now that a first reproducible quantitative evaluation is settled, it would be interesting to monitor quantitative performance shifts when adding related work modules to our baseline model, or when adding functionalities such as attributeguided and constrained layout generation.

Another interesting approach would be to add a background image processing module to our layout generation model, since background and foreground graphical balance are a central problem when generating sophisticated graphical layouts.

Finally, a critical step to achieve in automated document layout generation would be to go beyond the bounding box model and consider generating layouts in a pixel-wise dimension. This could also have very interesting applications for image generation, allowing users to add specific constraints or attributes on reserved areas of an image to be generated.

Fig. 1 .

 1 Fig. 1. Layouts from the first synthetic dataset. (a) layouts have been produced through general rules only, while (b) and (c) layouts have been produced by two different specific rules.

Fig. 2 .

 2 Fig. 2. Our generator and discriminator architectures.

Fig. 3 .

 3 Fig. 3. Generated (a) and real (b) layouts from different datasets. First row layouts are from the first synthetic dataset, second row layouts are from RICO dataset and third row layouts are from Magazine dataset.

Fig. 4 .

 4 Fig. 4. Poorly diversified (a) and highly diversified real layouts (b) from the second synthetic dataset

Fig. 5 .

 5 Fig. 5. Generated (a) and real layouts (b) with seven elements, from the second synthetic dataset

Table 1 .

 1 Quantitative evaluation results

	Quantitative Metric	Synthetic dataset I RICO dataset Magazine dataset
	Fréchet inception distance 33.86	66.96	90.15
	comparative alignment score 0.25	0.29	0.32
	comparative overlap score	12.32	17.69	3.59e -4
	comparative diversity score 19.83	0.65	1.37
	(a)			(b)

Table 2 .

 2 Intensive training vs. poor training

	Intensive training on Synth II Alignment Overlap Diversity
	Absolute score on real layouts	0.112	0	0
	Absolute score on generated layouts 0.116	0	0.003
	Comparative score	0.031	0	17.166
	Poor training on Synth II	Alignment Overlap Diversity
	Absolute score on real layouts	0.112	0	0
	Absolute score on generated layouts 0.088	1.15e-05 0.022
	Comparative score	0.238	11.653	19.230
	Intensive training on Rico	Alignment Overlap Diversity
	Absolute score on real layouts	0.120	0.274	0.234
	Absolute score on generated layouts 0.095	0.317	0.174
	Comparative score	0.236	0.146	0.293
	Poor training on Rico	Alignment Overlap Diversity
	Absolute score on real layouts	0.120	0.274	0.234
	Absolute score on generated layouts 0.019	0.157	0.014
	Comparative score	1.830	0.558	2.843

Table 3 .

 3 Results on datasets with high differences in terms of alignment, overlap and diversity

	Highly aligned real layouts (from Rico)	metric Score
	Absolute score on real layouts	alignment 0.0
	Absolute score on generated layouts	alignment 0.00023
	Comparative score	alignment 14.657
	Poorly aligned real layouts (from Rico)	metric Score
	Absolute score on real layouts	alignment 0.365
	Absolute score on generated layouts	alignment 0.340
	Comparative score	alignment 0.070
	Highly overlapping real layouts (from Rico)	metric Score
	Absolute score on real layouts	overlap	0.414
	Absolute score on generated layouts	overlap	0.696
	Comparative score	overlap	0.518
	Poorly overlapping real layouts (from Rico)	metric Score
	Absolute score on real layouts	overlap	0
	Absolute score on generated layouts	overlap	0.001
	Comparative score	overlap	16.228
	Highly diversified real layouts (from Synth II) metric Score
	Absolute score on real layouts	diversity 0.005
	Absolute score on generated layouts	diversity 4.39e-04
	Comparative score	diversity 2.396
	Poorly diversified real layouts (from Synth II) metric Score
	Absolute score on real layouts	diversity 0.002
	Absolute score on generated layouts	diversity 2e-04
	Comparative score	diversity 2.516

Table 4 .

 4 Evaluating layouts with different numbers of elements

	Layouts with 3 elements (from Synth II) Alignment Overlap Diversity
	Absolute score on real layouts	0.023	0	0
	Absolute score on generated layouts	0.024	0	0.001
	Comparative score	0.031	0	15.715
	Layouts with 5 elements (from Synth II) Alignment Overlap Diversity
	Absolute score on real layouts	0.043	0	0
	Absolute score on generated layouts	0.042	1.56e-05 2.14e-05
	Comparative score	0.017	11.960	12.272
	Layouts with 7 elements (from Synth II) Alignment Overlap Diversity
	Absolute score on real layouts	0.043	0	0
	Absolute score on generated layouts	0.048	2.85e-05 2.38e-04
	Comparative score	0.115	12.562	14.686
	3-elements versus 7-elements layouts	Alignment Overlap Diversity
	Absolute score on real layouts (3 elements)	0.023	0	0
	Absolute score on real layouts (7 elements)	0.041	0	0
	Comparative score	0.575	0	0

Acknowledgements

This work is financed by Centre Val de Loire Region, in France, and by Madmix Digital, a creative studio based in Paris and New-York, who helped us to identify and scientifically match the major challenges of document layout generation.

https://github.com/romain-rsr/ quant_eval_for_document_layout_generation


Martin Fontaine
email: martin.fontaine@protonmail.com

Alex Coiret
email: alex.coiret@univ-eiffel.fr

Julien Cesbron
email: julien.cesbron@univ-eiffel.fr

Vincent Baltazart
email: vincent.baltazart@univ-eiffel.fr

David Bétaille
email: david.betaille@univ-eiffel.fr

In-Tire Distributed Optical Fiber (DOF) Sensor for the Load Assessment of Light Vehicles in Static Conditions

Keywords: wheel load, intelligent tire, fiber optical, load evaluation, tire contact patch length

Modern vehicles are using control and safety driving algorithms fed by various evaluations such as wheel speeds or road environmental conditions. Wheel load evaluation could be useful for such algorithms, particularly for extreme vehicle loading or uneven loads. For now, smart tires are only equipped by tire pressure monitoring systems (TPMS) and temperature sensors. Manufacturers are still working on in-tire sensors, such as load sensors, to create the next generation of smart tires. The present work aims at demonstrating that a static tire instrumented with an internal optical fiber allows the wheel load estimation for every wheel angular position. Experiments have been carried out with a static tire loaded with a hydraulic press and instrumented with both an internal optical fiber and an embedded laser. Load estimation is performed both from tire deflection and contact patch length evaluations. For several applied loads from 2800 to 4800 N, optical fiber load estimation is realized with a relative error of 1% to 3%, almost as precisely as that with the embedded laser, but with the advantage of the load estimation regardless of the wheel angular position. In perspective, the developed methodology based on an in-tire optical fiber could be used for continuous wheel load estimation for moving vehicles, benefiting control and on-board safety systems.

Introduction Context and General Aim

Vehicle load measurement is a key technological issue, especially in automotive and road freight fields. The health of roads and infrastructures, fuel consumption and driving safety are all linked to the vehicle load. Actually, infrastructure sustainability is highly related to wheel loading, especially for extreme temperature situations, since rutting or frost issues are amplified by high loads. Fuel consumption, as well as tire wear and wearing of automotive parts, are also load dependent. Finally, driving safety, according to all previous assertions, is mainly based on vehicle control. From a load point of view, a specified weight distribution on axles is mandatory to ensure a good equilibrium of forces at the tire-to-road contact patches. Until now, the driver's ability is required to evaluate his/her vehicle load distribution.

Reflections on new transport solutions, such as autonomous vehicles or truck platooning and energy savings, enforce us to think about load monitoring, especially for autonomous vehicles, without a driver. To measure this load, the vehicle tires appear to be suitable because of their high deformation behavior under loading, and the avoidance of intermediate behavior in the case of the instrumentation of axles or dampers. For now, in-tire load sensors in the state-of-the-art are not designed to sense load in a non-rolling condition for any wheel angular position.

The present work aims at introducing a new embedded load sensor for a non-rolling vehicle whatever the wheel angular position. Indeed, it is of importance for an autonomous or driven vehicle that the load and its distribution could be checked before taking the risk of starting travel with inadequate load conditions. The proposed sensor is based on an optical fiber bonded along the tire inner liner circumference. This new sensor makes it possible that the spatial circumferential strain profile measurement for a non-rolling vehicle. From this profile, the vertical load applied onto the tire is computed.

This paper is organized as follows: a state-of-the-art on main measurable quantities for the load measurement, namely deflection first, and second the circumferential strain and contact patch length (CPL), is exposed. Models and equations to compute the load from these quantities are also exposed in that section. This showcases the novelty of the proposed sensor, especially for the static vehicle load sensing. Then, in the next section, the Distributed Optical Fiber Sensor (DOFS) specification and the instrumented test bed are introduced. Finally, the load estimation method is exposed and the results are discussed.

2. Literature Review/State-of-the-Art 2.1. Load Sensing: From Commercial Use to Autonomous Vehicles Historically, load sensing has mainly been used in transportation for enforcement purposes, to control axles' weight limits applied on roads, or for billing purposes, to establish the value of raw materials loaded on a given heavy carrier.

Large weighting platforms, or scales, are still widely used by manufacturers in those aims [1]. These platforms can either be embedded in roads or be portable. Studies have also been worked out to extend investigations on 3D forces, for discrete matrix forces arrays in low speed cases [START_REF] De Beer | Measurement of tyre/pavement interface stresses under moving wheel loads[END_REF] or aggregate forces in high speed cases [START_REF] Coiret | Concurrent evaluation of the tire/pavement contact torsor by means of both a dynamometer wheel and a road infrastructure-integrated system[END_REF]. Vehicle manufacturers and vehicle fleet managers have developed embedded load sensing systems. Such systems involve sensors located on arms, dampers [START_REF] Van Raden | Pneumatic Weighing System for Load Carrying Vehicles[END_REF] or on suspension blades [START_REF] Tarter | Vehicle On-Board Weighting System and Method[END_REF][START_REF] Hagedorn | Load Measuring System for Leaf Spring Suspensions[END_REF], on axles [START_REF] O'dea | On-Board Vehcle Weighting System[END_REF] or even, indirectly, at the truck to trailer hitch [START_REF] Fredrickson | Weight Sensing Vehicle Hitch[END_REF]. Even if new vehicle-based systems have appeared, the main aim was still related to weight enforcement and goods billing.

Nowadays, the emergence of autonomous vehicles is bringing a new need related to vehicle loading: without driver, the knowledge of an autonomous vehicle load is of great importance to adapt braking strategies and to enhance stability models in curves. Further than the total load, the knowledge of each wheel loading can provide information on loading distribution and alert an operator about stability issues (or limit the allowed speed).

Simultaneously, research on in-tire sensors has been expanding for years. Manufacturer's concepts are also emerging and suggest that intelligent tires are going to be a reality in few years. Small sensors can be used inside tires without impacting the tire behavior and safety too much, and low-power, wireless sensors are usable without impact tire sealing. Micro Electro Mechanical Systems (MEMS) have been used in [START_REF] Erdogan | Tire Sensors for the Measurement of Slip Angle and Friction Coefficient and Their Use in Stability Control Systems[END_REF] in order to measure accelerations at a point inside a tire and to estimate load, pressure and even friction coefficients. Nevertheless, estimation models as a brush model are subjected to fine tuning.

A large literature review of the MEMS use in transportation is part of research on heavy vehicle safety [START_REF] Gnap | Application of MEMS Sensors for Evaluation of the Dynamics for Cargo Securing on Road Vehicles[END_REF]. This experimental work is focused on critical accelerations monitored by MEMS on road cargo. The preliminary literature review shows that MEMS can be used for the measurement of actual roadways' states, or to estimate mutual influence of roads and vehicles, or to be used to feed automatic warnings in the case of an accident, or for smart tire measurements, or for the indication of cargo dommage [START_REF] Gnap | Application of MEMS Sensors for Evaluation of the Dynamics for Cargo Securing on Road Vehicles[END_REF]. The common advantage of MEMS for all these application is to monitor forces with a small device at any location. In fact, vehicle dynamic and static contact features, such as vertical load, can be described by the tire behavior, but measurement and estimations could be more precise by using larger measurement scales, as was chosen in this present work. Among measurable quantities that described this behavior, circumferential strain, deflection and contact patch size are mainly studied to evaluate these features and more specifically the load. The following subsections provide an overview of the state-of-the-art on these measurable quantities and of the background to understand the load sensing method proposed in this work, which involves an instrumented tire in order to address the loading knowledge issue from the vehicle.

Deflection Measurement and Load Relationship

The tire deflection is the vertical displacement of the wheel axis due to the wheel loading [START_REF] Rodgers | The Science and Technology of Rubber[END_REF]. The deflection value is obtained by sensing the distance between the wheel axis and the ground. It is also called the static loaded radius and can be measured by in-tire sensors from the rim to the inner liner. Tire deflection is mainly used by standards organizations, such as ETRTO (European Tyre and Rim Technical Organization), to control and set the load capacity of each tire.

In the literature, several studies aim to sense the deflection from a wheel-embedded sensor. Some examples are presented in Table 1.

Reference

Sensor Type Aim [START_REF] Magori | On-line determination of tyre deformation, a novel sensor principle[END_REF] Ultrasonic sensor Proof of concept, radial displacement profile sensing and deflection-load relationship identification [START_REF] Longoria | An in-wheel sensor for monitoring tire-terrain interaction: Development and laboratory testing[END_REF] Three aligned ultrasonic sensors Deflection sensing, identification of CPL and speed, load and pressure influence, radial stiffness estimation [START_REF] Tuononen | Laser triangulation to measure the carcass deflections of a rolling tire[END_REF] Laser Proof of concept, radial displacement profile sensing, influence quantities identification [START_REF] Xiong | A laser-based sensor system for tire tread deformation measurement[END_REF] Laser CPL identification and behavior through different pressure, speed and load [16] IR -PSD Deflection sensing, deflection-load relationship

The most common sensors used are the ultrasonic sensors [START_REF] Magori | On-line determination of tyre deformation, a novel sensor principle[END_REF][START_REF] Longoria | An in-wheel sensor for monitoring tire-terrain interaction: Development and laboratory testing[END_REF] and the laser sensors [START_REF] Tuononen | Laser triangulation to measure the carcass deflections of a rolling tire[END_REF][START_REF] Tuononen | On-board estimation of dynamic tyre forces from optically measured tyre carcass deflections[END_REF]. Besides the well known tire main deflection, occurring at the bottom part of the tire, there exists a little known counter deflection which occurs at the upper part of the tire, as a repercussion of the main deflection and at a much lower amplitude of typically one to ten. As an illustration, tire deflections and counter deflections are plotted in Figure 1a from experimental data [START_REF] Rhyne | Development of a Vertical Stiffness Relationship for Belted Radial Tires[END_REF], which have been simplified by linearization. In [16], a position sensitive diode (PSD) is used with an infrared diode glued on the inner side of the tire to measure the deflection over the tire circumference and for various loads (Figure 1b). This profile has been obtained by rotating the tire during the sampling for a set of vertical load values. The maximum displacement value at the center corresponds to the tire main deflection.

According to Figure 1, static flattening induced by loading is subjected to a maximum deflection value that varies according to internal pressure conditions. It also highlights that a counter deflection exists at the topside of the tire and is around one tenth of the tire deflection. The deformation principle involved by the generation of this counter deflection is presented in [START_REF] Coppo | A Multisensing Setup for the Intelligent Tire Monitoring[END_REF][START_REF] Lee | Estimation of Tire-Road Contact Features Using Strain-Based Intelligent Tire[END_REF][START_REF] Yang | Finite Element Analysis and Experimental Investigation of Tyre Characteristics for Developing Strain-Based Intelligent Tyre System[END_REF] and it is drawn here in Figure 2. In this figure it can be seen that the deformation of the curved wheel base into a flat surface results in a tension over the contact patch (blue dot), surrounded by compression areas (red dots); these compressions of the tire belt secondarily result in a counter deflection of the tire topside, by belt wire traction. A linear load-deflection relationship is clearly identified in the literature. From a mechanical point of view, it is currently assimilated to a spring model [START_REF] Ballo | A Semi-Analytical Tyre Model for the Study of Tyre/Rim Interaction on a Road Vehicle[END_REF], with a vertical stiffness K z . The vertical load is thus expressed as follows:

F z = K z * d, (1)
with F z (in N) the vertical load and d (in mm) the deflection of the tire. The stiffness value K z is expressed in N/mm or kg/mm and is affected by the vertical structural stiffness of the tire sidewalls and the inflation pressure.

Several ways can lead to the vertical stiffness estimation such as flexible ring models, semi-empirical relationships or load capacity formulas from standards. The formula (2) of the vertical stiffness, expressed in N/mm, was obtained empirically from load/deflection measurements over a wide range of tire sizes in [START_REF] Rhyne | Development of a Vertical Stiffness Relationship for Belted Radial Tires[END_REF].

K z = 0.00028Pg * √ W * OD + K zsw , (2)
with the internal pressure P (in kPa) , the tire footprint W (in mm) width, outside diameter (OD, in mm) and g = 9.81 m/s -2 the acceleration of gravity. The K zsw constant represents the structural stiffness, that is, the tire stiffness value for a deflated tire. The K zsw equals 33.84 N/mm (3.45 kg/mm) in [START_REF] Rhyne | Development of a Vertical Stiffness Relationship for Belted Radial Tires[END_REF]. In [START_REF] Padula | The Pneumatic Tire, Chapter 5 Load Capacity[END_REF], Equation ( 2) is modified to express the tire footprint width only with tire geometric values as follows:

K z = 0.00028Pg * (-0.004a r + 1.03)S N * OD + K zsw , (3)
with a r as the aspect ratio and S N the nominal section width of the tire. In this study, Equation ( 3) is used to compute the load from the measured deflection in Section 5.

Strain Measurement and Load Relationship

Material strain is defined as the elongation ratio along a direction. Some of the main studies on the tire strain measurement are listed in Table 2. It provides an overview on methods and sensors used. Strain-load relationships or observations in each article are also exposed. According to this table, sensing the tire strain from the inner liner in the circumferential direction provides a more sensitive strain value than the other directions [START_REF] Yang | Finite Element Analysis and Experimental Investigation of Tyre Characteristics for Developing Strain-Based Intelligent Tyre System[END_REF][START_REF] Breglio | Fiber Bragg Gratings for Strain and Temperature Measurements in a Smart Tire[END_REF][START_REF] Matsuzaki | Analysis of Applied Load Estimation Using Strain for Intelligent Tires[END_REF]. In-tire strain transducers are usually dependent of the angular position of the tire. In fact, to establish the tire strain along the circumference, tire rotation is mandatory. This leads to dynamic perturbations such as braking, acceleration or dynamic forces, which cause fluctuations in the strain value.

A typical circumferential strain profile is schematized in Figure 2.

The strain time signature can be split into three distinct parts. In the central part, the elongation caused by a tension of the inner liner is observed as explained in [START_REF] Matsuzaki | Analysis of Applied Load Estimation Using Strain for Intelligent Tires[END_REF]. Compression is then observed at both sides of the central part. The third part corresponds to the upper part of the tire which is not influenced by the load. In theory, this profile is symmetric about the center of the contact patch length where the maximum strain value is observed. However, in practice, driving conditions, braking, acceleration or dynamic forces can generate an asymmetric profile [START_REF] Coppo | A Multisensing Setup for the Intelligent Tire Monitoring[END_REF]. As shown in Table 2, the time derivative of this strain profile, the so-called strain rate, is mostly used to assess the contact patch length (CPL). The length corresponds to the distance between the peaks of the strain rate according to Figure 2. This method is based on the Morinaga assumption [START_REF] Hiroshi | Method for Estimating Tire Wear and Apparatus for Estimating Tire Wear[END_REF] which defines the CPL measured from the inner liner as the distance between the points where the force variation in the radial direction is the greatest, which corresponds to peaks in the strain rate profile. According to Tables 2 and3, the CPL knowledge is suitable to compute the vertical load through models.

Acceleration Measurement and Load Relationship

Inner liner acceleration sensing during rolling is also a suitable way for estimation of the contact patch length and associated forces. Studies on this aspect are listed in Table 3. Measurement of acceleration can be performed in several directions (radial, circumferential or transversal) and realized by accelerometers placed on the inner liner of the tire. As for strain sensing, the contact patch length is estimated from the acceleration profile. According to Table 3, the method for contact patch length computing (i.e., peak to peak or zero-crossing) depends of the sensor direction (i.e., radial or circumferential).

Radial displacement can also be estimated and used in a flexible ring model [START_REF] Jeong | Load Estimation of Intelligent Tires Equipped with Acceleration Sensors[END_REF] or recursive least square fitting [START_REF] Singh | Accelerometer Based Method for Tire Load and Slip Angle Estimation[END_REF] to compute the vertical load.

Experimental Setup

Whether with laser, accelerometers, strain gauges or ultrasonic sensors, for load evaluation means investigated up to now in the literature, the static measurement requires turning the considered wheel at a given angular position. An immediate measurement on a vehicle, before each journey, is therefore not easy, especially if the measurement involves several tires. To solve this, a distributed strain sensor made by an optical fiber along the tire inner liner circumference is proposed in this work, with the advantage of delivering the strain all along the belt at each measurement step. Preliminary results can also be found in [START_REF] Fontaine | Static in-tire circumferential strain signature using Rayleigh scattering fiber optic technology: Preliminary results[END_REF].

This work, as a proof of concept, is focused on a static tire. The DOF sensor gives the opportunity to evaluate the tire load independently to the tire rotation angle. Therefore the experimental setup is built around a non rotating tire. However, there exist extension perspectives of this work on the rotating tire while surpassing current limitations. Firstly, the fiber bonding has to be studied more precisely in order to stand up to the tire dynamic forces which could cause damages on the bonding and the fiber sensor. Secondly, the sensor interrogator should be miniaturized to be embedded in the wheel or a rotary coupler should be used [START_REF] Roveri | OPTYRE-A new technology for tire monitoring: Evidence of contact patch phenomena[END_REF]. In an intermediate way, we can imagine a smart tire, equipped with a circumferential optical fiber sensor, which can be plugged to an external interrogator, at the start of a journey; for example, in order to provide the vehicle load.

Vertical Loading Device

The experimental setup consists of a test wheel submitted to a vertical load applied by an hydro-static piston, both being constrained in displacement by a loading cage composed of top and bottom plates interlocked by a four columns cage (force press; Figures 3 and4).

Vertical forces are applied by the hydro-static piston and are controlled via a loading cell (sensitivity of 0.2 mV/kN, displacement range of 150 mm).

Tested Wheel

The wheel is instrumented with the following sensors:

• a laser beam for the measurement of the deflection (Wenglor, sensitivity 0.2 V/mm).

The laser head is screwed on the tire rim and points radially to a white target painted on the center of the inner side on the tire contact patch; • a pressure sensor for the measurement of the tire inflation pressure (Stellar Technology, sensitivity 2.9 V/bar); • an optical fiber glued in the middle of the inner tire belt over the full tire circumference (Luna system).

The tire used during the tests was new. Its dimensions, loading index and speed rating are 185/65R15 88T. It is manufactured by GoodYear, with a radial type construction, 1 polyester ply in the sidewall, and 1 polyester/2 steel/1 polyamide plies in the tire belt. The tire inflation pressure is set at 2.1 bar.

Two acquisition systems are simultaneously used to record the data. The general conditioning and analog to digital converter system (Spider8) is used to acquire the data of all the sensors except the optical fiber sensor, at a common sampling frequency of 400 Hz.

The optical fiber has its own acquisition system, manufactured by Luna, the ODISI-B interrogator. According to the manufacturer, the chosen optical fiber and the ODISI-B interrogator allow a maximum strain measurement of about 10,000 µ (1%). Our experiments, with a large loading scale, lead to a maximum of 4000 µ , so the tire maximum strain is within the DOF sensor strain scale. The DOF sensor acquisition is made at a sample frequency of 10 Hz.

A low frequency generator allows the synchronization of the two acquisition systems. A general view of the experimental system is provided in Figure 4.

In-Tire Dof Sensor

DOF sensors allow the continuous determination of deformations all along a single optical fiber. These sensors are based on reflectometry such as Rayleigh scattering by involving swept-wavelength interferometry [START_REF] Froggatt | High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter[END_REF]. They are widely used for Structural Health Monitoring (SHM) for deformations checking all along a monitored element (e.g., [START_REF] Bassil | Distributed Fiber Optics Sensing and Coda Wave Interferometry Techniques for Damage Monitoring in Concrete Structures[END_REF]).

The fiber index of refraction is locally altered by the surrounding strain and temperature variations. Fluctuation of this index induces signal losses by back scattering, namely, the Rayleigh scattering phenomenon. Practically the local strain or temperature variations are determined by comparing the stressful scatter frequency profile to the stressless scatter frequency profile, or the reference profile. The spectrum frequency shift can be expressed as a function of the temperature and strain variations:

∆ν ν = K T ∆T + K ∆ , (4)
with ∆ν ν as the frequency shift, ∆T and ∆ respectively the temperature and strain variations, and K T and K constants of proportionality.

If the tests are performed at a constant temperature, the strain can be directly computed. The DOFS method allows to locally evaluate the strain at each spatial pitch of the optical fiber, down to pitches of 0.65 mm. Up to 1500 strain values can be recorded all along a 1 meter long fiber. The optical fiber is bonded along the inner liner perimeter of the tire as shown in Figure 5. The optical fiber is going through the rim by a cable gland to ensure the pressure sealing. The chosen paste is a bi-component epoxy paste (Araldite 2011) well adapted for rubber bonding. Agreement between measured strain values (Section 5) and state-of-the-art results confirms this choice. Moreover, before each loading experiment, the operator performed a calibration of the fiber response beforehand to cancel any potential offset. Sometimes successive loading may have alter the fiber response at some locations, because of rare loss of adhesion of fiber to tire, either due to fiber-epoxy or epoxy-tire contact. These points are easily detected on the circumferential fiber signatures and filtered out of the around 3000 other measurement points.

Data Processing for Load Assessment

Through this section the data processing methodology for load assessment is exposed. Firstly, the strain profile measured from the DOF sensor is presented. Then the processing of data is presented and applied on a loading case in order to calibrate the prediction formula. In the same way, the deflection measurement is exposed and the data processing to compute the load is applied.

Loading Cases

As described in Section 3, the instrumented wheel has been loaded by means of an hydraulic press. Three loading cases have been considered for the tests as shown in Figure 6. Each test consists in a 6-steps loading between 2000 N and 4750 N. The step duration is the same for each test and roughly equal to 30 s. The difference between the three tests is the loading speed between each step. Thus, Figures 6a, 6b and6c respectively correspond to a slow, intermediate and fast loading speed. Loading speed is respectively equal to 50 N/s, 100 N/s and 500 N/s for the slow, intermediate and fast loading speed tests. In the following these loading cases will be referred to as L 50 , L 100 and L 500 . The static load estimation from the DOF sensor and the laser sensor is based on load formulas, exposed in Sections 4.2 and 4.3. The L 50 loading case is used as a calibration test in order to estimate formula constants. Only measured values on loading steps are selected to proceed to the calibration. The loading steps are defined using the 'findchangepts' Matlab function. The selected loading steps values are exposed in the Figure 7.

Load Computation from Deflection Data

For the sake of comparison, the load computation from a deflection measurement is processed.

Once the deflection is sensed, a linear relationship is used to compute the load. As exposed in the Section 2.2, establishing load-deflection relationship requires vertical stiffness knowledge. In this article, the stiffness formula defined in [START_REF] Rhyne | Development of a Vertical Stiffness Relationship for Belted Radial Tires[END_REF] and precised in [START_REF] Padula | The Pneumatic Tire, Chapter 5 Load Capacity[END_REF] is applied to compute the vertical load.

It relies on Equation (1) which is written as follows:

F z = (K zP + K zsw )(d laser -d 0 ), (5)
with K zP = 0.00028Pg (-0.004a r + 1.03)S N * OD the tangent stiffness part is expressed in N/mm, due to tire inflation and g = 9.81 m/s -2 the acceleration of gravity. For the tested tire, the aspect ratio a N = 0.65 and nominal section width S N = 185 mm. Term K zsw is the tangent stiffness part (in N/mm) due to the sidewalls of the tire, while d laser is the displacement measured by the laser sensor (in mm) and d 0 is a correction factor (in mm) due to possible alignment error of the laser sensor. Thus, the deflection d is given by:

d = d laser -d 0 . ( 6
)
As the K zsw constant value is defined in [START_REF] Rhyne | Development of a Vertical Stiffness Relationship for Belted Radial Tires[END_REF] for a large range of tires, its value is evaluated for the tested tire in order to better fit to the real structural stiffness of the sidewalls. In order to estimate parameters K zsw and d 0 for the tested tire, the L 50 loading case deflection mean value on step are fitted with a linear fitting curve. The deflection and its fitted curve as a function of the vertical load are shown in Figure 8a. The error between the measured deflection and the fitted curve is represented in Figure 8b. The absolute fitting error is less than 1% and the highest values are mainly observed during load-step transitions. The coefficients estimated from the fitting are d 0 = 1.27 mm et K zsw = 18.01 N/mm (=1.83 kg/mm). These coefficients are used in the following in Section 5.

Load Computation from Dof Strain Data

The typical strain profile obtained from the DOF sensor is represented in Figure 9 for four vertical loads for the L 50 loading case. The strain profile should be symmetrical relatively to a central vertical axis but some perturbations are observed, mainly due to local rigidity such as tire wear indicators and tread pattern or tire unevenness. The measured strain profile has been filtered with a numerical moving Savitsky-Golay filter to reduce the noise induced on the derivative profile. The filter is defined as smoothing filter of polynomial order 2 and a frame length of 30. The filtered profile and its angular derivative are shown respectively in Figure 10a,b for a 3000 N vertical load. As can be seen in Figure 11, once the circumferential strain profile is measured, estimation of the load is based on three main steps.

CPL Computation from DOF Strain Data

The first and second steps aim to estimate the length correlated to the contact patch length from the circumferential strain profile. In the following section, the term "contact patch length" will be used to refer to this length. According to the literature, the peak to peak strain rate method is the most usual way to obtain the contact patch length value. In [START_REF] Matsuzaki | Analysis of Applied Load Estimation Using Strain for Intelligent Tires[END_REF], this method, initiated by Morinaga [START_REF] Hiroshi | Method for Estimating Tire Wear and Apparatus for Estimating Tire Wear[END_REF], allows to remove the friction based strain which is combined with the circumferential strain during rolling. Because of a lack of knowledge on friction strain distribution in the case of non-rolling loaded wheel, the peak to peak method is used. The estimated CPL from the strain profile derivative, using the peak to peak distance method, is plotted as a function of the vertical load in Figure 12 for the three loading cases, in the 2000-4800 N load range. For each cases the observations are the following:

• During the step transition from 2000 N to 2400 N the CPL is highly increasing when reaching and maintaining the 2400 N value, for the three loading cases. This increase of around 10% may be linked to the relaxation of the tire tread rubber, with an applied exceeding the frictional grip force, and resulting to a tread sliding.

•

In the following transition step another drifting with a lower magnitude is observed at the beginning of the 2800 N step. It also may be caused by a tread sliding.

•

The four loadings from 2800 N to 4800 N are presenting quasi linear relations of the length to the load, for the three loading speeds. CPL is no longer increasing for the periods of steady load; tread sliding seems to not occur again.

•

For the higher loading speed L 500 , the CPL values on step transitions adopted a curvilinear motion; increasing and decreasing motion. It is linked to the viscoelastic properties of the rubber/steel structure of the tire.

So we have to distinguish three domains of behavior, below 2400 N, between 2400 N and 2800 N and over 2800 N. Because of these three domains, in order to simplify the relationship between the static CPL and the applied load, the studied load range is fixed between 2800 N and 4800 N. This range usually corresponds to the nominal range of loading on a vehicle wheel.

Load Computation from CPL Data

The third step aims at estimating the vertical load F z from the inner contact patch length L c . Based on the previous section observations and from the contact mechanics theory [START_REF] Johnson | Contact Mechanics[END_REF], the estimated CPL has a non linear relationship with the vertical load. In this study, it is thus estimated empirically by a power law of the form:

F z = αL β c (7)
As explained previously, the studied data range is set between 2800 N and 4800 N. Therefore, the fitting is based on the following equation, including initial values:

F z -F zi = α(L c -L ci ) β (8)
with F zi and L ci the initial value of the load and the initial value of contact patch length. The values of parameter α and exponent β are constant and depend on the geometry of the tire and its mechanical behavior. In order to estimate parameters α and β, a logarithmic regression is computed. In the aim of computing the static load, only data recorded during the steps are selected, as highlighted in Figure 13. Finally, the logarithmic regression is done on the mean values of CPL during steps, for the L 50 loading test, and provides the values of parameters α and β.

Load Estimation from DOFs and Comparison to Laser Estimation

This section presents the load estimation results from the contact patch length. The load estimation based on the contact patch length is involving power law method as detailed in the previous section. The load estimation based on the deflection from the laser measurement is given as a comparison basis for the newly proposed estimation by an optical fiber. Results are presented through three different angles. Firstly, a time-load representation is made on the L 100 loading case. Then, the load is estimated from the DOF sensor on the three loading cases and compared to the deflection based load estimation. Finally, a focus is made on the on-step estimated values in order to estimate the accuracy of the experimental in-tire DOF sensor.

Load Estimation for the L 100 Loading Case

Figure 15a represents the applied load and the DOF sensor load estimation as a function of time for the L 100 loading case. Estimated load by laser is represented as well.

Relative errors for these two estimation methods are given in percents in Figure 15b. The relative error is classically computed as the measured value/estimated value difference over the measured value. As can be seen on Figure 15a,b, the load estimation by optical fiber presents a higher error (up to 6%) on the first loading step (2800 N). The DOF estimation is exhibiting high error levels around 2% for the two higher loading cases. In the middle range, fluctuations of the load caused by PID servo control on step induce error variations. This error is around 1% for the second and third step. Each loading transition induces an overestimation of the load value around 2 and 3%. Comparatively the laser estimation error is around 1% for each step. A relaxation is observable on each step and can be assigned to the loading setpoint overrun at the beginning of the step and the visco-elasticity effect caused by the sidewalls.

Load Estimation from Dof Sensor and Comparison to the Laser Sensor Estimation

In order to better compare the load estimation for each sensor and each loading case, the estimated load is plotted as a function of the applied load in Figures 161718. Estimation by the laser sensor appears to be quite insensitive to the loading case, i.e., to the speed of load variations (Figures 16b, 17b and18b).

Estimation by the DOFS appears to be altered with increasing loading speed (Figures 17a and18a). Higher errors are visible at load transitions between load steps on Figure 17a and even more on Figure 18a. Nonetheless, DOFS estimation values remain very close to the first bisector line during the load steps.

Higher errors by optical fiber sensor observed during load transitions are due to the tire damping, whose contact length is stretching and then relaxing with the application of a rapid load.

As a confirmation of these graphical observations, the mean absolute percentage error values and the root mean square percentage error (RMSPE) values, computed on steps, are given in Tables 456. The RMSPE is defined as the square root of the average of squared differences between computed load and measured value. RMSPE induces higher errors than mean absolute error when large errors are encountered. • RMSPE and mean absolute percentage error value shows that both methods are close but with a higher dispersion for DOF sensor based method.

Conclusions

This work is motivated by the fact that wheel load estimation is of importance both for infrastructure resilience and for vehicle safety concerns. The bibliography indicates that for a still vehicle existing methods as laser impose a wheel rotation until the sensors points towards the tire contact patch. Moreover on-rolling load estimation remains hard due to impact forces.

The novelty of this research is to investigate a distributed sensor, able to estimate the static wheel load, whatever the wheel angle position.

Experiments have been carried out with a static tire loaded by a hydraulic press. The proposed new estimation mean of the load, a Distributed Optical Fiber Sensor, is used for these experiments in addition to an embedded laser sensor as a comparison basis. These two estimation means are respectively involving contact patch length and tire deflection evaluations.

For several applied loads from 2800 N to 4800 N that corresponds to the tire load working range, DOF sensor load estimation is realized with a mean absolute percentage error on the range of 1.13%, but with punctual errors up to 3.09% in conditions of low or high loads in the experimented range.

Loading speed increasing induces more errors of the load estimation. Indeed three loading speeds have been investigated in order to estimate the impact of the tire characteristics like viscoelasticity on the measurements. However this work is focusing on a static tire, as the load knowledge for a still vehicle, before starting a journey, is already a useful information. So a perspective for a moving vehicle exists but should require dynamic corrections as well as technical adaptations like resistant fiber bonding to tire dynamics and sensor interrogator embedded in the wheel or linked to the sensor by a rotary coupler.

The laser-based estimation of the vertical load is realized with a mean absolute error of 0.29%, with much less dispersion, the maximum error being of only 0.76%.

Load processing from DOF sensor is less accurate than the laser sensor. The higher number of in the DOF sensor based load estimation, may induce more errors. Moreover, the DOF sensor is more sensitive to the speed of loading transitions than the laser. Nevertheless load estimation from the DOF sensor remains close to the applied load in each case.

From a technical point of view, optical fiber sensor offers great performances and is spaced-saving. Nevertheless, it remains fragile even if more robust optical fiber, used for structure health monitoring can be more robust than the used one. In-tire integration involves an efficient bonding. The current issue of optical fiber in tire is the acquisition system which has to be miniaturized to be embedded in a vehicle.

As a conclusion, the new estimation mean, involving a Distributed Optical Fiber Sensor, has the advantage of the load estimation regardless of the wheel angular position. In perspective, the developed methodology based on that mean could be used for continuous wheel load estimation for moving vehicles, benefiting to control and safety vehicle systems.

Figure 1 .

 1 Figure 1. (a) Deflection and counter deflection of a tire for 0-12,000 N loadings. (b) Tire deflection measurement over tire circumference, adapted from [16].

Figure 2 .

 2 Figure 2. Schematization: tire tension and compression zones (left) and typical dynamic circumferential strain measurement (right, up) and strain rate (right, down), adapted from [19].

Figure 3 .

 3 Figure 3. Experimental setup with the instrumented tire and the hydraulic press.

Figure 4 .

 4 Figure 4. Synchronized data sampling for optical fiber (Luna system) and other sensors (Spider8 Digital Analog Converter).

Figure 5 .

 5 Figure 5. Optical fiber (in yellow) bonding on the tire inner liner (left) and schematic view of the optical fiber implementation in the tire (right).

Figure 6 .

 6 Figure 6. Step loading cases considered in the study: slow (a), intermediate (b) and fast (c) loading speed, respectively denoted L 50 , L 100 and L 500 .

Figure 7 .Figure 8 .

 78 Figure 7. Identified load step values on the L 50 loading case.

Figure 9 .

 9 Figure 9. Strain circumferential static profiles, for four vertical loads (L 50 case).

Figure 10 .

 10 Figure 10. Filtered strain profile (a) and its angular derivative (b) for a 3000 N vertical load.

Figure 11 .

 11 Figure 11. Estimation steps of the load from the circumferential strain measured by DOF.

Figure 12 .

 12 Figure 12. Contact patch length for the three test cases estimated by the peak to peak method from the strain profile derivative.

Figure 13 .

 13 Figure 13. Measured contact patch length (blue); the selected values on steps (red) and the centered mean values of CPL on each step (black cross) used as fitting points.The calculated constant values of α and β are α = 1.20 × 10 -6 and β = 4.27. The contact patch length and the power law fitting curve for the L 50 are shown in the Figure14. Mean values on steps are represented by black crosses on the estimated CPL in blue. The power law fitting curve is plotted in red. It is close to the mean step values. Gaps between the fitting curve and CPL data are observable during step transitions due to dynamic forces.

Figure 14 .

 14 Figure 14. Power law fitting on the L 50 loading case with α = 1.1998 × 10 -6 and β = 4.2756.

Figure 15 .

 15 Figure 15. (a) Load measurement and estimations from laser and DOF sensors for the L 100 test case; (b) Corresponding relative errors on the load.

Figure 16 .Figure 17 .

 1617 Figure 16. Load estimation for the L 50 test case: (a) DOF sensor (b) Laser sensor.

Figure 18 .

 18 Figure 18. Load estimation for the L 500 test case: (a) DOF sensor (b) Laser sensor.

Table 1 .

 1 Wheel-embedded sensor type and aim of some tire deflection studies.

Table 2 .

 2 Major literature references on the strain/wheel load relationship.

	Reference	Strain Direction Circumferential (C), Transversal (T)	Estimated Characteristic	Method/Model	Sensor or Evaluation Mean	Vertical Load Relationship
	[19,24]	C	CPL	Differentiation and peak to peak	FBG	Not defined
	[20]	C	CPL	Differentiation and peak to peak	Gauges	Not defined
			Radial	Flexible ring model
	[25]	C	displacement and	(displacement) and	Strain gauges	Linear relationship
			CPL	peak to peak
	[26]	C/ T	Strain value and CPL	Differentiation and identification) peak to peak (CPL	FBG	Not defined
				Flexible ring model
	[27]	C	Displacement	on viscous	Gauges	Flexible ring model
				foundation
	[28]	C	CPL and strain value	Differentiation peak to peak	FEM (simulation)	Integral of circumferential strain

Table 3 .

 3 Major literature references on acceleration measurements/wheel load relationship.

	Reference	Acceleration Direction: Radial (R), Circumferential (C)	Estimated Characteristic	Method	Sensor	Vertical Load Relationship
	[30]	C	CPL	Peak to peak	Tri-axial	Flexible ring model
	[31]	R	CPL and Radial max displacement (Comparison)	Zero cross-ing(CPL)/Double integration	Tri-axial	Recursive least square fitting
	[32]	R	CPL	Zero crossing acceleration profile	One axis accelerometer	Identification of correlation between CPL and load
	[33]	R/C	CPL	R.: Zero crossing/C.: Peak to peak	Tri-axial accelerometer	Identification of linear relationship (load vs CPL)
	[34]	C	CPL	Peak to peak	Tri-axial	Calibration

Table 4 .

 4 Loading case with low speed force variation between steps (L 50 ).

	Step Load Applied (N)	Mean Absolute Percentage Error (Laser Sensor)	Mean Absolute Percentage Error (DOFs)	RMSPE (Laser Sensor)	RMSPE (DOFs)
	1	2850	0.28	1.14	0.35	1.41
	2	3330	0.21	1.16	0.26	1.30
	3	3810	0.25	0.40	0.30	0.50
	4	4290	0.15	0.83	0.19	0.91
	5	4770	0.19	0.80	0.26	0.95

Table 5 .

 5 Loading case with medium speed force variation between steps (L 100 ).

	Step Load Applied (N)	Mean Absolute Percentage Error (Laser Sensor)	Mean Absolute Percentage Error (DOFs)	RMSPE (Laser Sensor)	RMSPE (DOFs)
	1	2840	0.27	3.09	0.32	3.34
	2	3320	0.36	0.63	0.41	0.80
	3	3810	0.46	0.48	0.51	0.60
	4	4280	0.25	1.48	0.30	1.60
	5	4770	0.18	1.77	0.21	1.89

Table 6 .

 6 Loading case with high speed force variation between steps (L 500 ). Its RMSPE follows the same behavior with closed values lower than 0.81% which confirms stability of the load estimation from a deflection measurement. • DOFS mean absolute percentage error on steps reaches three high values of 3.09% (L 100 first step), 2.05 (L 500 first step) and 2.76% (L 500 second step), but other values are lower than 2%.

	Step	Applied	Mean Absolute Percentage	Mean Absolute	RMS Percentage	RMS Percentage
	Load	(N)	Error (Laser Sensor)	Percentage Error (DOFs)	Error (Laser Sensor)	Error (DOFs)
	1	2850		0.43	2.05	0.50	2.45
	2	3330		0.66	2.76	0.72	3.20
	3	3810		0.76	1.64	0.81	1.87
	4	4290		0.46	0.67	0.51	1.16
	5	4770		0.30	1.51	0.35	1.80
				It is observed that:
			•	Laser mean relative error has always a value lower than 0.76% and is stable through
				loading increasing.

Acknowledgments:

The authors gratefully thank CAPTELS Society for their financial and scientifical support (namely M. Etienne Lea and Denis Coudouel). Sincere thanks are adressed to Xavier Chapeleau, Louis-Marie Cottineau, Ivan Guéguen, Fabrice Blaineau and Jean-Philippe Gourdon for their technical contribution to this work and experimental resources.

Data Availability Statement: Not available.

Conflicts of Interest:

The authors declare no conflict of interest.