Émilie Masson

Pierre Combeau

Yann Cocheril

Lilian Aveneau

Marion Berbineau

Rodolphe Vauzelle

Ray Launching Modeling in Curved Tunnels with Rectangular or Non Rectangular Section

Introduction

Since several years, digital wireless transmissions are experiencing a significant increase with the development of digital TV, satellite communications, mobile phones, internet, wireless local area networks and automation in various domains. The transportation field as a whole is a major actor of these changes. Technologies and systems for wireless communications are increasingly used in the field of guided transport (underground, conventional trains, high speed trains, tramways, etc.) to ensure communications between trains and between a train and the infrastructure. These systems answer the key operational needs for safety and comfort, such as control and command of the trains, traffic management, maintenance, security and information for passengers and crew members. We can distinguish two main families of systems: low-data rate reliable transmissions, for traffic control and command, and robust high data rate transmissions, for video surveillance, remote diagnostic or embedded multimedia applications. Consequently, the radio coverage prediction of these wireless systems is mandatory to optimize the deployment of the radio access points in order to ensure the robustness and reliability of radio links and to minimize the antennas positioning phase duration. Indeed, minimum field strengths are generally required to ensure Key Performance Indicators (KPI) related to the requirements of dependability and Quality of Service (QoS).

For underground applications, these systems operate in complex environments, such as tunnels, where the usual laws for predicting the propagation in free space are no longer valid. Like the telecommunication operators, railway manufacturers or guided transport operators should invest in planning tools to deploy their radio communication systems. However, to our knowledge, no general model for predicting free propagation in tunnel exists, as easy to use as well known existing models in the world of mobile phones, such as statistical models derived from Okumura-Hata, Cost231, etc. The tunnel case is usually solved with heavy measurement campaigns that are time consuming and costly. Thus, the development of specific and efficient propagation models for tunnels is very relevant for railway industry to allow both fast responses to tenders, and quick deployments of their wireless communication systems in these specific environments. The tunnels can be rectangular, circular or arch-shaped. In addition, they may be straight or curved, with only one or two tracks.

Several methods to model radio wave propagation in tunnels have been published in the literature and will be presented in this chapter with their advantages and drawbacks. Among them, only few works are dedicated to non rectangular cross section and curved tunnels. Hence, we focus on a new method recently developed. The structure of the chapter is as follows. Section 2 presents the context of the works and why deployments of wireless telecommunication systems are needed for transport applications. Existing techniques to model radio wave propagation in tunnel are presented in section 3 with their respective advantages and drawbacks. The fourth and fifth sections are respectively devoted to the design and the evaluation of a propagation prediction model for curved tunnel with a rectangular or a circular cross section. Finally, section 6 concludes and presents some perspectives to these works.

Wireless telecommunication systems needs for transport applications

The growing of wireless networks including cellular (GSM, GPRS, EDGE, UMTS, etc.) saw the arrival on the market of a number of software tools dedicated to radio systems planning, for industrial and telecom operators. These tools allow the identification of sites to set up base stations from the definition of the characteristics of areas to cover, possibly by imposing the location of some sites (favorite sites). Most of these tools are very heavy to handle, dedicated to radio engineers, optimized and enriched by in-house phone operators to take into account the different propagation environments encountered.

Like the general public telecommunications world, the widespread use of wireless communication systems in the field of transport requires the use of software tools for planning and optimization for the efficient deployment of these systems. Some existing tools in the world of telecommunications are specifically adapted, for example for the deployment of GSM-R infrastructures in various European countries. But to our knowledge, no module specifically dedicated to the metro tunnels is currently sold. Thus, in most cases, the industrials perform measurement campaigns that are time consuming and costly. These experimentations require free access to the operational sites, which is a difficult task to achieve:



In the case of a line under construction, site access depends on the progress of the construction that may experiences significant delays. Indeed, the development of a wireless communication system is the final step of the overall transportation system;



In the case of a line already in operation, access to the site has to be done outside the hours of operation of the metro, which leads to very short ranges that occur most often during night.

To limit the measurement campaigns, it is necessary that the railway industrials possess planning tools to determine the field strength regardless of the environment encountered: consideration of tunnels with different cross and longitudinal sections and building materials for example. Propagation models must meet the best compromise between accuracy and computation time and have to be simple to use.

For outdoor areas, predictive models of the radio coverage are the well-known statistical models, such as free space attenuation, Okumura-Hata model or 2-rays model. These models work well because the deployment is in Line-Of-Sight (LOS) and distances between transmitter and receiver are weak. The measurement campaigns are easy to implement and generally there are few constraints for the positioning of access points that are most often located on existing poles (signaling, lighting, etc.).

In tunnel areas, the prediction of radio coverage is currently based on intensive use of feedback on measurements and implementation of engineering rules.

Configurations of complex tunnels, such as curved tunnels of circular cross section are more frequently encountered in the modern metro lines and it becomes necessary to refine the prediction process of the radio coverage for deployment based on more sophisticated tools, such as the method presented in this chapter.

Existing techniques to model radio wave propagation in tunnel

Methods based on simulation and measurement of radio wave propagation in tunnels were presented in the literature. Analyses based on measurements at 900 MHz and 1800 MHz represent the first approach [START_REF] Hwang | Ray-optical prediction of radio-wave propagation characteristics in tunnel environments. 1[END_REF], (Zhang & Hwang, 1998a), (Zhang et. al, 1998), [START_REF] Zhang | Ray-Optical Modeling of Simulcast Radio Propagation Channels in Tunnels[END_REF], in order to characterize propagation in wide rectangular tunnels. In (Zhang & Hwang, 1998b), [START_REF] Lienard | Propagation in wide tunnels at 2 GHz: a statistical analysis[END_REF], statistical characteristics of propagation channel in tunnels are performed from measurement results. However, analyses performed from the measurements presented in these papers are specific to a given shape of tunnel. Radio wave propagation modeling in generic tunnels is thus a major research field.

Some authors have proposed methods based on the modal theory to provide all the modes propagating in tunnel. Approximate and exact solutions have been determined for straight rectangular tunnels and straight circular tunnels respectively (Laakman & Steier, 1976), [START_REF] Emslie | Theory of the propagation of UHF radio waves in coal mine tunnels[END_REF], (Mahmoud, 1974), [START_REF] Dudley | Linear Source in a Circular Tunnel[END_REF], [START_REF] Dudley | Wireless propagation in tunnels[END_REF].

The modal theory considers tunnels as oversized waveguides. It provides good results but it is limited to canonical geometries, which are not the main cases according to the generally encountered tunnels.

Several papers present results based on an exact resolution of Maxwell's equations using numerical techniques such as integral methods or the resolution of the Vector Parabolic Equation [START_REF] Chang | Field Analysis of Dielectric Waveguide Devices based on Coupled Transverse-mode Integral Equation-Numerical Investigation[END_REF], [START_REF] Reutskiy | The methods of external excitation for analysis of arbitrarily-shaped hollow conducting waveguide[END_REF], [START_REF] Popov | Modeling radio wave propagation in tunnels with a vectorial parabolic equation[END_REF], [START_REF] Bernardi | A Numerical Scheme for the Solution of the Vector Parabolic Equation Governing the Radio Wave Propagation in Straight and Curved Rectangular Tunnels[END_REF]. One more time, these kinds of techniques are limited, mostly due to the computational complexity. Indeed, these methods are based on a volume discretization of the propagation environment with a scale that should be smaller than the wavelength. Consequently, the complexity is prohibitive for operational environments.

Finally, frequency asymptotic techniques based on the ray concept, being able to handle complex tunnel geometries in a reasonable computation time, seem to be a good solution. A first simple approach based on a 2-rays model was proposed in [START_REF] Zhang | Novel model for propagation loss prediction in tunnels[END_REF], [START_REF] Ahmed | Comments on the Hybrid Model for Propagation Loss Prediction in Tunnels[END_REF]. This method suffers from lack of accuracy due to approximations on the number of rays considered in the model. In (Mahmoud, 1974), a model based on a Ray Tracing, based on image method, takes into account multiple reflections, but only for the case of straight rectangular tunnels. In [START_REF] Mariage | Theoretical and experimental approach of the propagation of high frequency waves in road tunnels[END_REF], the authors use this method and adds diffraction phenomenon in order to analyze the coupling between indoor and outdoor. In [START_REF] Agunaou | Propagation d'ondes électromagnétiques hyperfréquences à l'intérieur d'un métro -Modélisation numérique de l'influence des changements de section[END_REF], works are purchased by considering changes of tunnel sections, but still only in straight rectangular tunnels. However, tunnels in real environments, such as metro ones, can have non rectangular cross section. Furthermore, they can be curved. Ray Tracing is no longer valid with curved surfaces since the source image is no more unique. Consequently, only a few studies deal with the case of non-rectangular cross sections and curved tunnels.

The first intuitive approach for curved surfaces consists of a tessellation of the curved geometry into multiple planar facets, as proposed in [START_REF] Chen | SBR image approach for radio wave propagation in tunnels with and without traffic[END_REF], [START_REF] Torres | An engineering tool for planning and design of wireless systems in enclosed spaces[END_REF], [START_REF] Baranowski | Optimisation des règles d'ingénierie radiomodélisation de la propagation d'ondes radioélectriques en tunnels courbes[END_REF], [START_REF] Masson | Radio Wave Propagation in Arch-Shaped Tunnels: Measurements and Simulations using Asymptotic Methods[END_REF]. Unfortunately, the surface curvature is not taken into account in this type of techniques. Furthermore, one of the major drawbacks of this approach is the impossibility to identify an optimal number of facets for a given tunnel cross section and a given frequency [START_REF] Masson | Radio Wave Propagation in Arch-Shaped Tunnels: Measurements and Simulations using Asymptotic Methods[END_REF]. In [START_REF] Wang | Simulations and Measurements of Wave Propagations in Curved Road Tunnels for Signals From GSM Base Stations[END_REF], a ray-tube tracing method is used to simulate wave propagating in curved road tunnels. An analytical representation of curved surfaces is proposed. Comparisons with measurement results are performed in straight arch-shaped and curved tunnels. The paper lacks of information. Consequently, we focused on the works presented in [START_REF] Didascalou | Ray-density normalization for ray-optical wave propagation modeling in arbitrarily shaped tunnels[END_REF], [START_REF] Didascalou | Subway tunnel guided electromagnetic wave propagation at mobile communications frequencies[END_REF]. A Ray Launching combined with a ray-density normalization is presented. The surface curvature is taken into account. Comparisons with measurements are performed respectively in a scaled tunnel (with 20 cm reduced diameter dimension, and then higher frequency at 120 GHz for compensating the former), and in curved subway tunnels at 900 MHz and 1800 MHz. The method provides good results but exhibits two main defaults: the geometric shapes of the tunnels are not all flexible, and the computation time is high due to the large number of rays launched at transmission. To overcome these drawbacks, we developed a method to model the electromagnetic propagation in tunnels with curved geometry, either for the cross section or the main direction. The main advantage of this new method is its best compromise between accuracy and computation time for applications at 5.8 GHz. It is presented in the next section.

Design of a propagation prediction model for non rectangular cross section and curved tunnels

The aim of the developed method is to model radio wave propagation in non rectangular cross section and curved tunnels. The problem to be solved consists in taking into account the presence of curved surfaces which induces divergence of rays by reflection on surfaces. An adaptation of the Ray Launching technique and a correction on paths trajectories have to be performed.

The method consists of three main steps. First step consists of an adaptation of a classical Ray Launching technique for the consideration of curved surfaces. Developments on emission, reception and intersection between rays and curved surfaces are performed. Second step is to correct the received paths trajectories after the Ray Launching step. It consists of a minimization of the paths length, a choice of optimized paths and an adapted algorithm for the Identification of Multiple Rays (IMR). Last step consists in taking into account the divergence of rays for the Electric Field calculation in the presence of curved surfaces.

We consider four kinds of tunnel geometry encountered in operational cases, illustrated in Figure 1:

 the straight rectangular tunnel;  the straight circular tunnel;  the curved rectangular tunnel;  the curved circular tunnel.

For tunnels with circular cross section, a floor and/or a roof can be added in the model of the environment to take into account arch-shaped sections for example. All these configurations lead us to consider three kinds of elementary geometry: The plane for the straight rectangular tunnel and the additional floor/roof, the cylinder for the straight circular tunnel and the walls of the curved rectangular one, and finally the torus according to the curved circular tunnel. All these components are quadrics, which is important for the simplicity of intersection computation with rays.

Ray launching for curved surfaces

Emission

Since no a priori information on privileged propagation direction is available, we chose to implement a Ray Launching technique based on a uniform distribution of rays radiated from the transmitter. There are different techniques to obtain a uniform distribution.

We consider a stochastic Monte Carlo method [START_REF] Didascalou | Ray-density normalization for ray-optical wave propagation modeling in arbitrarily shaped tunnels[END_REF] in order not to skew the results. Instead of using random sequences, the method consists in using quasi-random sequences [START_REF] Morokoff | Quasi-monte carlo integration[END_REF] to regularly cover all the space. Indeed, quasi-random sequences allow minimizing the discrepancy, which corresponds to a measure of the gap between a reference situation, generally perfect uniformity, and a given configuration. Figure 2 illustrates the distribution of 512 rays computed from a random sequence compared to ones obtained from two quasi-random sequences, namely Halton [START_REF] Halton | On the efficiency of certain quasi-Monte-Carlo sequences of points in evaluating multi-dimensional integrals[END_REF] and Hammersley [START_REF] Hammersley | Monte Carlo methods[END_REF]. The Hammersley sequence allows us to obtain the best uniform distribution.

In order to prove it, we present in Figure 3 the histogram of the angles between each ray and its nearest neighbor. So, the most uniform sequence is the one which provides the highest peak for a given angle value in its histogram, it will then minimize the discrepancy. It appears again that the best one is the Hammersley sequence. Therefore, we chose to use it to trace the rays radiated from the transmitter.

Reception

The Ray Launching technique requires a reception sphere to determine which rays contribute to the received power. Indeed, the probability that a given ray meets a receiver point is always zero. The reception sphere radius, denoted as rR, depends on the path length r and the transmission angle  [START_REF] Seidl | Site-specific propagation prediction for wireless in-building personal communication system design[END_REF]:

3 R r r   (1)
The main drawback of a reception sphere is that it should receive a collection of rays whereas an only one is predicted by Geometrical Optics. These rays are called multiple rays, as illustrated in Figure 4. If all of them are added together the result will be an overestimation of the received power. Thus, it is necessary to discriminate them. This can be performed with an Identification of Multiple Rays (IMR) algorithm [START_REF] Iskander | Propagation prediction models for wireless communication systems[END_REF]. Classical criteria include the number of reflections, the path length and the transmission angle. In case of curved surfaces, multiple rays are much more scattered and distant from each other. A specific treatment of the rays and an adapted IMR are so needed and proposed in section 4.2.

Intersection ray/curved surface

We have shown that besides planar surfaces, both cylindrical and toroidal surfaces have to be taken into account in the considered tunnel configurations. These geometrical objects belong to the quadrics family and can thus be easily expressed in an analytical form.

In Cartesian coordinates, the equation of a cylinder with the axial direction along the y-axis and centered at the origin is given by:

222 c xzr  (2)
with rc the radius of the cylinder.

In a same way, the equation of a torus around the z-axis and centered at the origin is as follows:

222 22 2 2 22 () 4 ( ) 0 tt t xyzRr R xy      (3)
with Rt and rt the radiuses of the torus.

The definition of a ray being as follows:

xx xd t d i   , yy yd t d i   , ( 4
) zz zd t d i  
with (dx, dy, dz) the origin of the ray and (dix, diy, diz) the direction vector of the ray, the intersection of a ray with a cylinder and a torus leads to the resolution of respectively, a quadratic equation and an equation of degree 4.

Optimized IMR and final choice of corrected rays

The section 4.1.2 has shown that using a reception sphere leads to take multiple rays into account. The multiple rays are determined by classical IMR algorithms based on similarity criterion according to geometrical characteristics of the rays. Then, the choice of the retained ray is randomly realized among the identified multiple rays, without any physical considerations. So, they lead to a bad approximation of the real ray. To enhance this approach, we propose here to add a correction algorithm of the trajectories of multiple rays that makes them converge to the correct geometrical one. The ambiguous choice of the ray for a correct field calculation is thus avoided.

Correction algorithm of the paths trajectories

The general principle is as follows. Once a ray is launched from the transmitter using the Hammersley quasi-random sequence, its propagation is recursively computed, by calculating its intersection with the curved surfaces, until it reaches the reception sphere.

Either it undergoes the fixed maximum number of reflections, or it goes outside the tunnel. So, a contributive ray (a path), i.e. one that has reached the reception sphere, presents some geometrical approximations since it does not go through the exact receiver position, as it has been explained in section 4.1.2. Using the Fermat Principle, indicating that the path followed by a wave between two points is always the shortest one, we propose to reduce the geometrical approximation involved in each path: The correction algorithm consists, for a given path, in minimizing its length assuming that it reaches the center of the reception sphere.

While the path length function is not linear, we propose to use the well-known Levenberg-Marquardt algorithm [START_REF] Marquardt | An algorithm for Least-Squares Estimation of Nonlinear Parameters[END_REF]. Nevertheless, the algorithm is efficient only if the starting point (i.e. the initial ray) is near the solution. By using the Ray Launching, it can be assumed that the paths caught by the reception sphere are close to the real paths existing with a Geometrical Optics meaning, i.e. the shortest. Thus the received rays represent a good initialization of the algorithm. The principle of the Levenberg-Marquardt algorithm consists in finding the best parameters of a function which minimize the mean square error between the curve to approximate and its estimation.

Applied to propagation in tunnels, the objective becomes a path length minimization. The criterion to minimize is then the total path length J given by:

11 2 N kk N k JE P P P P R         (5)
With E the transmitter position, R the receiver position and Pk the k th interaction point position of the considered path, as illustrated in Figure 5.

The vectors defined in (5) depend on the coordinates of the interaction points along the path. The iterative algorithm requires the inversion of a Hessian matrix which contains the partial derivatives of the J criterion to minimize with respect to parameters. To keep computation time and numerical errors reasonable, the matrix dimensions and thus the number of parameters have to be minimized. Local parametric coordinates (u, v) from the given curved surface are used instead of global Cartesian coordinates (x, y, z). The parameters vector can be written as:

11 NN uv u v      (6)
Where (uk,vk) correspond to coordinates of the reflection point Pk.

Validation of corrected trajectories

Since the Levenberg-Marquardt algorithm is a numerical method, its convergence cannot be guaranteed. So, we have to proceed to a validation test on the corrected paths, which can be incoherent in the case of an algorithm divergence.

This test consists in checking if the Geometrical Optics laws are respected, specifically the Snell-Descartes ones. For each reflection point, we verify if the angle of reflection r equals the angle of incidence i, as illustrated in Figure 6. If not, the path is discarded. For instance an unphysical path

Final choice of the correct ray

Section 4.1.2 indicates that the Ray Launching algorithm leads to the existence of multiple rays corresponding to the same contribution according to Geometrical Optics. They must be identified and only one ray has to be kept. However, the correction technique previously presented allows obtaining multiple rays very close to the real path, and consequently very close to each other. Nevertheless, due to numerical errors, they cannot be strictly equal to each other. Thus, the choice of the final ray can be done on the base of the reflection points localization: If the reflection points of two candidate paths are at a given maximal interdistance, the paths are considered to be equal and one of the two is removed, it does not matter which.

Electric field calculation

In the case of a curved surface, Electric Field can be computed after reflection by classical methods of Geometrical Optics as long as the curvature radiuses of surfaces are large compared to the wavelength (Balanis, 1989).

It can be expressed as follows (Figure 7): Unlike the case of planar surfaces, the curvature radiuses of the reflected ray are different from those of the incident ray. Indeed, the following relation holds (Balanis, 1989):

1,2 1,2 1 2 11 11 1 2 ri i f          (8)
With 1 i and 2 i the curvature radiuses of the incident ray and f1,2 a function depending on 1 i , 2 i and the curvature radiuses R1,2 of the curved surface (Balanis, 1989).

Performance analysis in curved tunnels

This section is dedicated to the performance analysis of the method presented in section 4 in tunnels presenting non rectangular cross section and/or curved longitudinal section. This evaluation is performed from measurement results obtained in real tunnel environments. Performances are evaluated in narrow band by using a comparison of received narrow band powers. First part of the section is dedicated to analyses in a straight arch-shaped tunnel.

Second and third parts of the section focus on rectangular and circular curved tunnels. The measurements were performed at 5.8 GHz. The transmitter was located at a fixed position at the center of the section, at a height of 4.8 m. It consists of a horn antenna (10.1 dBi gain at 5.8 GHz), vertically polarized. The receiver was moving along the longitudinal axis of the tunnel thanks to a go-kart allowing a very small and regular velocity, compatible with the acquisition rate. It is illustrated in Figure 9. The receiving antenna was vertically polarized and had the same characteristics than the transmitting one. It was located in the middle of the two tracks, 2.4 m from the sidewall, at a height of 4.1 m. Figure 10 illustrates the antennas configuration of measurements.

Performance analysis in

Comparison between simulation and measurement loss

Figure 11 presents the comparison between measurements and simulations in terms of normalized received power (Pr) with respect to the transmitted one (Pt), versus the distance between transmitter and receiver along the longitudinal tunnel axis in the Tunnel of Roux.

A quite good concordance between simulations and measurements is highlighted. A detailed analysis is performed in the following.

Statistical analysis of results

Statistical analysis of slow and fast fading is performed on simulation and measurement results. The procedure to extract these data is as follows. First step consists in smoothing signals by using a running mean. The window's length is 40  on the first 50 m, and 100  elsewhere, according to the literature [START_REF] Lienard | Propagation in wide tunnels at 2 GHz: a statistical analysis[END_REF].

Then, the analysis of slow fading can be performed by the computation of the mean and standard deviation of the error between measurements and simulations. Results are illustrated in Table 1. The slow fading analysis highlights a good agreement between results both for the mean and the standard deviation. Indeed, the values are in the range of 4/6 dB, which generally, from a practical point of view, illustrates good agreement.

Mean (dB)

Standard deviation (dB) 5.8 GHz 5.35 6.86 All the analysis carried out according to measurement and simulation results leads us to a quite good matching between measurements and simulations in terms of slow and fast fading. The developed method provides good performances in a straight arch-shaped tunnel.

Furthermore, it has to be noticed that results presented in this part do not depend on the location in the tunnel, while the cross section is similar. This kind of results can be found in literature [START_REF] Lienard | Experimental analysis of wave depolarization in arched tunnels[END_REF]. On the other hand, position of antennas in the cross section can have a big impact on the received power.

Performance analysis in curved tunnels

Curved rectangular tunnel

Configuration

Measurements were performed in a curved rectangular tunnel by an ALSTOM-TIS team. The measurement procedure is as follows. The transmitter is located on a side near the tunnel wall. It is connected to the radio modem delivering a signal at the required frequency. Two receivers, separated by almost 3 m, are placed on the train roof. They are connected to a radio modem placed in the train. Tools developed by ALSTOM-TIS allow us to carry out field measurements and to take into account a simple spatial diversity by keeping the maximum level of the two receivers. Measurements were performed at 5.8 GHz. The measurements configuration is depicted in Figure 12. The curved rectangular tunnel has a curvature radius equal to 299 m, a width of 8 m and a height of 5 m.

Comparison between simulations and measurements

Figure 13 presents the comparison between measurements and simulations in the configuration of Figure 12, in terms of normalized received power (Pr) with respect to the transmitted one (Pt), versus the distance between transmitter and receiver along the longitudinal tunnel axis in the curved rectangular tunnel.

One more time, a quite good concordance between simulations and measurements is highlighted. An analysis is presented below.

Statistical analysis of results

For these measurements, analysis of fast fading was not possible because of the lake of measured data (spatial sampling greater than /2). We only present a slow fading analysis, as it was performed in the section 5.1.3. Mean and standard deviation values of the error between simulations and measurements are presented in Measurements were finally performed in a curved circular tunnel. As for the curved rectangular tunnel, the measurements were also realized by an ALSTOM-TIS team. The same measurement procedure was followed. Measurements were performed at 5.8 GHz.

The measurements configuration is depicted in Figure 14. The curved circular tunnel has a curvature radius equal to 1000 m and a radius of 2.6 m.

Comparison between simulations and measurements

Figure 15 presents the comparison between measurements and simulations in terms of normalized received power (Pr) with respect to the transmitted one (Pt), versus the distance between transmitter and receiver along the longitudinal tunnel axis in the curved circular tunnel.

It appears a relative good concordance between simulations and measurements. We analyze these results in the following section.

Statistical analysis of results

As for the curved rectangular tunnel, analysis of fast fading was not performed in this case.

Mean and standard deviation values of the error between simulations and measurements are presented in Table 4. It can be observed values around 6 dB which represents a relative good concordance between measurements and simulations in the case of the curved rectangular tunnel. However, some different behaviors can be observed on few areas, such as between 50 and 100 m or 150 and 200 m. These differences are due to problems that can remain in the correction algorithm and lead to a bad estimation of the received power.

Mean (dB)

Standard deviation (dB) 5.8 GHz 5.35 6.80 A global remark can be added for the case of curved tunnels (with rectangular or circular cross section). As for the case of results presented in section 5.1, results are not dependent of the location in the tunnel while the cross section is similar and also while the curvature radius is the same. In this case also, position of antennas in the cross section can have a big impact on the received power.

Analysis and discussion

Modeling of radio wave propagation in non rectangular and/or curved tunnels was presented. A first part is dedicated to the presentation of the requirements of wireless telecommunication systems for transport applications. These systems lead to the need for industrial of models to predict radio propagation in particular environments such as tunnels. As presented in details in [START_REF] Masson | Etude de la propagation des ondes électromagnétiques dans les tunnels courbes de section non droite pour des applications métro et ferroviaire[END_REF], no such tools are marketed in transport domain and specific tools have to be developed for transport applications in tunnels.

Second part presents the methods to model radio wave propagation in tunnels. Three kinds of models are presented. Methods based on the modal theory provide all the modes propagating in tunnel. These methods provide good results but are limited to canonical geometries, such as rectangular and circular straight tunnels. Some papers are based on the exact resolution of Maxwell's equations. These kinds of techniques are also limited due to the computational complexity. Finally, frequency asymptotic methods based on the ray concept leads to the best compromise between accuracy and computation time. However, tunnels in real environments can have non-rectangular cross section and can also be curved.

Only a few studies deal with these cases.

The developed method is presented in the third part where each step of the method is detailed. This one is based on a Ray Launching technique combined with an optimized IMR technique based on a correction of paths trajectories. It consists in a minimization of the total distance of the considered path in order to make it converge to the real one, existing in Geometrical Optics meaning. The technique is based on the well-known Levenberg-Marquardt algorithm. A validation of computed paths after correction is realized by verifying the angles of incidence and reflection. A new IMR algorithm is also developed leading on comparison of reflection points.

Last part is devoted to the evaluation of the method in three different geometries of tunnels: the straight arch-shaped tunnel, the curved rectangular tunnel and the curved circular tunnel. This evaluation is performed from measurements realized in real environments, at 5.8 GHz. For the case of the straight arch-shaped tunnel, a slow fading study was realized and lead to a mean and standard deviation between measurements and simulations of about 5-6 dB, which represents a quite good agreement between simulations and measurements. A fast fading study was also performed. The data were extracted by a smoothing procedure. The CDF were computed from measured and simulated data and the KS criterion was applied. Comparisons with theoretical distributions of Rayleigh, Rice, Nakagami and Weibull were performed. It appeared that the Weibull distribution better minimizes the KS criterion, for both measurements and simulations. This kind of study is very useful to reproduce statistically fast fading variations in order to realize studies on system performance. For the case of curved rectangular and circular tunnels, similar studies on slow fading were realized and lead to a mean and standard deviation between measurements and simulations of about 3-6 dB, which represents a good agreement of results, validating the method.

There exist many perspectives to this work. As it was seen in the previous section, in some areas, bad estimation of the received power is obtained in the case of a curved circular tunnel. These errors can be due to imperfection of correction algorithm that could be improved to obtain reliable results.

Right now, the method is able to treat empty tunnels. The following step will consist in taking into account the presence of trains in the tunnel. The phenomenon of masking train will also be investigated. In this case, diffraction has to be taken into account in the Ray Launching technique. The diffraction phenomenon would also allow taking into account complex geometries such as station, crossing, etc.

Conclusion

The chapter was dedicated to the radio wave propagation modeling in non rectangular and/or curved tunnels. It was shown that classical methods (modal theory, rigorous methods, asymptotic methods) to model propagation in these kinds of tunnels can not be used. Specific treatments on Ray Launching, based on a correction of paths trajectories, have to be implemented. They were presented, evaluated and discussed.

Figure 1 .

 1 Figure 1. Four kinds of treated tunnels

Figure 2 .Figure 3 .

 23 Figure 2. Comparison of the distribution of 512 rays at transmission between the use of a random sequence and 2 quasi-random sequences: Halton and Hammersley Random Halton Hammersley

Figure 4 .

 4 Figure 4. Illustration of multiple rays by using a reception sphere

Figure 5 .

 5 Figure 5. Principle of optimization of paths

  i = r) is shown in figure6. The path

Figure 6 .

 6 Figure 6. Validation criterion of corrected paths

  1 r and 2 r the curvature radiuses of the reflected ray, r the distance between the considered point P and the reflection point Q, k=2/ with  the wavelength, and R the matrix of dyadic reflection coefficients.

Figure 7 .

 7 Figure 7. Reflection on a curved surface

  a straight arch-shaped tunnel 5.1.1. Configuration Measurements were first performed in a straight arch-shaped tunnel, the tunnel of Roux. It consists of a two-way road tunnel located in Ardèche in France, and is illustrated in Figure 8. The straight section has a length of 3325 m. The arch-shaped cross section has a maximal height and width of 5.8 m and 8.3 m respectively.

Figure 8 .

 8 Figure 8. Illustration of the Tunnel of Roux

Figure 9 .Figure 10 .

 910 Figure 9. Go-kart used at reception

Figure 11 .

 11 Figure 11. Comparison between measurements and simulations loss in the Tunnel of Roux -5.8 GHz

Figure 12 .

 12 Figure 12. Antennas configuration of measurements in the curved rectangular tunnel

Figure 13 .

 13 Figure 13. Comparison between measurements and simulations in the curved rectangular tunnel -5.8 GHz

Figure 14 .

 14 Figure 14. Antennas configuration of measurements in the curved circular tunnel

Figure 15 .

 15 Figure 15. Comparison between measurements and simulations in the curved circular tunnel -5.8 GHz

Table 1 .

 1 Mean and standard deviation (in dB) of the error between simulations and measurements in the Tunnel of Roux -5.8 GHz Second step consists of an analysis of fast fading. The data are extracted by the smoothing procedure as above. The Cumulative Density Functions (CDF) are computed from measured and simulated data and the Kolmogorov-Smirnov (KS) criterion is applied. Comparisons with theoretical distributions of Rayleigh, Rice, Nakagami and Weibull are performed. Results are given in Table2. It appears that the Weibull distribution better minimizes the KS criterion, for both measurements and simulations. This study is very useful to reproduce statistically fast fading variations in order to realize studies on system performance.

		Measurements	Simulations
	Rayleigh	0.22	0.24
	Rice	0.22	0.24
	Nakagami	0.05	0.06
	Weibull	0.03	0.02

Table 2 .

 2 KS criteria of the simulations and measurements compared to theoretical distributions in the Tunnel of Roux -5.8 GHz

Table 3 .

 3 It can be observed values around 2 dB which represents a quite good concordance between measurements and simulations in the case of the curved rectangular tunnel.

		Mean (dB)	Standard deviation (dB)
	5.8 GHz	2.15	2.55

Table 3 .

 3 Mean and standard deviation (in dB) of the error between simulations and measurements in the curved rectangular tunnel -5.8 GHz

	5.2.2. Curved circular tunnel
	5.2.2.1. Configuration

Table 4 .

 4 Mean and standard deviation (in dB) of the error between simulations and measurements in the curved circular tunnel -5.8 GHz

Acknowledgement

The authors would like to thank the ALSTOM-TIS (Transport Information Solution) who supported this work.

Author details


Maria Ferrara

Joseph Virgone
email: joseph.virgone@insa-lyon.fr

Enrico Fabrizio

Frédérik Kuznik

Marco Filippi

Modeling Zero Energy Building: technical and economical optimization

This study was born in the context of new challenges imposed by the recast of Energy Performance of Buildings. The aim of this work is to provide a useful method to deal with a huge number of simulations corresponding to a large number of single-family house configurations in order to optimize a constructive solution from both technical and economical point of view. The method combines the use of TRNSYS, building energy simulation program, with GenOpt, Generic Optimization program. The reference building is a low-consumption house case-study situated in Amberieu-en-Bugey, Rhône-Alpes, France. After a short description of the case-study and of TRNSYS model, the link and the configuration files which have been created between the simulation program and the optimization software are illustrated. A first parametric study is performed in order to evaluate the impact of variation of various parameters of envelope and shading elements on the total annual energy consumption for heating and cooling. As a second study, the global cost method is applied to the case-study, and GenOpt is used to determine the cost optimal level of the reference building. Beyond the result, we think this study shows useful method and tools that could support technical and cost optimal level research, providing an easy and fast way to explore various building configuration with a huge number of simulations, as requested by European Standard.

INTRODUCTION

In the context of the European Union efforts to reduce the growing energy expenditure, it is widely recognized that the building sector has an important role, accounting 40% of the total energy consumption in the European Union [START_REF]Cost Optimality. Discussing methodology and challenges within the recast Energy Performance of Building Directive[END_REF]. The recast of the Directive on the Energy Performance of Building (EPBD) [START_REF]26 octobre 2010 relatif aux caractéristiques thermiques et aux exigences de performance énergétique des bâtiments nouveaux et des parties nouvelles de bâtiments[END_REF] imposes the adoption of measures to improve energy efficiency in buildings in order to reach the objective of all new buildings to be nearly Zero Energy Building (nZEB) by 2020. This practice could lead to greenhouse gas emission reduction in the building sector of 80-90% by 2050. As the results in term of energy efficiency are evaluated at a global (or at least European) scale, it is remarkable that a good nZEB design is strictly related to the local scale, depending on climatic data, available technologies and materials, population lifestyle. Moreover, as usual, measures related to ecological sustainability could not be pursued without taking into account an economical sustainability. It is obvious that the design of a zero-energy building is not yet profitable in terms of costs, and that this will lead to different results depending on the country, the age of the building and its use (commercial buildings, residential, etc.). Consequently, EPBD recast has set out that Member States (MSs) ensure that minimum energy performance requirements are set with a view to achieve the cost optimal level, that is defined as the energy performance level which leads to the lowest cost during the estimated economic lifecycle. Based on Global Cost method, the aim is to define for each MSs the most effective strategies to improve building performance with the lowest global cost. In order to develop general strategies, a huge number of case study should be examined and a common method to compare a large number of simulations has to be established. We have collaborated between France and Italy in order to improve our methodologies and to apply them on the single-family houses, with references buildings, constructive solutions, typical sources of energy accessibility, costs, etc...In the present article we present one carried out with TRNSYS computing environment with a view to establish a procedure for technoeconomic optimization using the tool GenOpt.

The reference building.

The Reference Building (RB) is a new single-family house situated in Amberieu-en-Bugey, Rhône-Alpes, France. It is representative of new construction of single family house in the region. The gross floor area (GFA) of the two floors is equal to 155 m 2 (see plans in figure 2). It's possible to recognize many design features generally used in passive/low consumption houses: the insulated living space is a cubic compact shape (S/V ratio is equal to about 0,68 m -1 , S being the heat losses area and V the heated volume) that minimize the exchange surface between the outside and inside. In order to reduce heat loss due to windows and benefit of solar gains, the maximum of large openings are south-oriented (49% of total glass surface (TGS) on the south external wall, 19% on the south roof slope) while the percentage of openings in east and west orientation is less relevant (respectively 10% and 15% of TGS) and there are only very small north oriented openings (7% of TGS). Window area is approximately 1/5 of the GFA: the minimum imposed by the national regulation [3], which is equal to 1/6 of GFA, is largely exceeded. A roof overhang protects south-oriented windows. RB was modeled using TRNSYS [START_REF]TRANSSOLAR, Centre Scientifique et Technique du Bâtiment, Thermal Energy System Specialists, TRNSYS 16 Documentation[END_REF], dynamic building simulation program [START_REF] Enrico | Introduzione alla simulazione energetica dinamica degli edifici[END_REF]. Each room was modeled as a thermal zone, in order to better evaluate the evolution of temperature and the thermal exchange from one zone to the other, as the HVAC system is considered active only in the main rooms of the house. Set-point temperature for heating (19°C) and cooling (26°C) was set only in the living-room (PP), in the bedrooms (C1, C2, C3) and in the mezzanine (M), while other zones as restrooms (R1, R2), dressing (D) and passages (DGT1, DGT2) are supposed to take heat (or cool) from transmission through internal walls and doors. Garage (G) and laundry(B) are considered non-conditioned zones. The standard meteonorm weather file of Amberieu-74820 were used in the simulation. Lighting and occupancy were modeled using schedules related to a standard 4 people family working life, week-ends are taken in account but holidays are not considered. The sum of infiltration and ventilation rate is fixed equal to 0.7 ach as a medium value for all the zones. Based on these settings, heating needs are estimated to be 48 kWh/m 2 /year, while cooling needs are equal to 12 kWh/m 2 /year.

METHODS -PARAMETRIC STUDY

In order to allow multiple simulation and optimal level research, building simulation software was coupled with the general optimization software GenOpt and configuration files were created [START_REF]GenOpt-Generic Optimization Program[END_REF]. Configuration file contains building simulation software configuration, error indicators and start command, the command file contains parameter list and settings and related functions which were inserted in simulation input files to obtain simulation input template. GenOpt run is based on the initialization file, where location of input files and position of the objective function are specified.

The more a house is energy efficient, the bigger is the influence of envelope design on the final energy demand. In order to estimate the impact of the variation of each element of building envelope and geometry (wall, roof and slab insulation, window type, window and solar protection dimension) on the final total annual energy consumption, a parametric study on the reference building was done. All set parameters and values referred to the house section are shown in the figure below. Note that minimal window dimension corresponds to the limit imposed by French regulation. The initial value (Ini) is the fixed value assumed by parameters during the parametric run. Four Ini scenarios were set: one is referred to the low-cossumption RB, the others are respectively representative of a very less-insulated building, a standard insulated building, and the last is an utopic very strong insulation. Geometric parameters are always equal to RB.

Window Type U [W/m 2 K] g-value [%/100]

RESULTS -PARAMETRIC STUDY

Here below results related to RB scenario are shown. Winter and summer performances are separately evaluated and compared, while percentages are referred to the total annual energy needs. Positive values of percentages indicate energy savings corresponding to decreases in energy demand. It is clear that insulation of opaque envelope takes an important role among energy savings measures. In details, roof insulation accounts the most relevant impact in both summer and winter case. In case of outwall and ground slab an increase of insulation corresponds to an increase of heating energy savings and a decrease of cooling energy savings, while in roof case insulation increase causes energy savings during all the year. This is due to the fact that most of roof surface is south oriented and a major solar absorption is caused by dark color of tiles.

Figure 6. Impact of window type (see table 2) on energy demand gains -RB scenario.

Results related to window type clearly show the impact of g-value and window orientation on transparent envelope performances. A differentiation of window type based on optimization of these parameters could be desirable taking into account also shading devices geometry and window dimensions (see figure 7).

Results based on other scenarios revealed mostly the same curves, but it is clear that the higher performances are set in initial scenarios, the higher is impact of parameter variation in terms of percentage of energy demand.

Figure 7. Impacts of roof window dimension and shading overhang length on total energy demand -RB scenario.

METHODS -ECONOMICAL OPTIMIZATION

In accordance with the EPBD, global cost calculations result in a net present value of costs incurred during a defined calculation period, taking into account the residual values of components with longer lifetimes. Following the procedure described in the European Standard EN 15459 [START_REF]CEN (European Committee for Standardization)[END_REF], global cost is directly linked to the duration of the calculation τ and it can be written as:

(

where C G represents the global cost referred to starting year τ 0 , C I is the initial investment cost, C a,i (j) is the annual cost for component j at the year i (including running costs and periodic or replacements costs), R d (i) is the discount rate for year i, V f,τ is the final value of component j at the end of the calculation period (referred to the starting year τ 0 ). In the context of cost optimal research in this method costs are written as function of parameters p. So the terms of the previous equation become:

Where f j (p) is the cost function of the component j related to parameter p. A typical all-electrical energy system was considered, whose investment cost is 300 €/kW of maximal power installed, with a replacement time of 15 years. Energy price was assumed equal to current prices of major electricity companies based on difference in tariffs for night and day. In details, costs were fixed equal to 0.07952 €/kWh during the night and 0.11442 €/kWh during the day. Market interest rate was assumed to be 4%, calculation period is 30 years.

RESULTS -ECONOMICAL OPTIMIZATION

All combination of parameters value performed by the optimization program can be considered as a package of Energy Efficiency Measures, according to the European Guidelines [START_REF][END_REF]. Note that in (1) only variable cost related to variation of parameters were considered. So the objective function of optimization represents the global cost for each EEM. Particle Swarm Optimization algorithm for discrete variables was used. The first optimization run was performed only with parameters related to opaque and transparent envelope resistance as variables. Geometric parameters (window dimensions and shading overhang length) were fixed equal to RB values.

Here below cost values are shown referred to primary energy consumption (primary energy conversion factor for electricity in France is equal to 2.58). Values are normalized to GFA.

DISCUSSION

As cost of electricity is quite high, it is clear that considering global cost for 30 years an initial high investment cost in high-performances of envelope is recommended also from economical point of view. This is only an example, as this work attempted to establish a fast and precise procedure for optimization which could be applied to different case-studies. It is known that the use of more efficient energy system could lead to different solution. Moreover, further studies have to be performed in terms of sensitivity analysis based on variation of financial data and product costs.

Figure 1 .

 1 Figure 1. Facades of reference building. a) South, b) North, c) West, d) East.

Figure 2 .

 2 Figure 2. Plans of reference building, 1:200. a) First floor, b) Second Floor.

Figure 3 .

 3 Figure 3. Simulation-optimization framework.

Figure 4 .

 4 Figure 4. Parameter list.Table1. Parameter settings Table2. Window Types

  hr -Roof window height [m] 0 4.72 0.3 Roof window area ResR -Roof insul. [m 2 Kh/KJ] 0.25 5 0.25 -S -Overhang projection [m] 0.2 3.6 0.2 Overhang height bm -mezzanine south window width [m] 2

Figure 5 .

 5 Figure 5. Impact of opaque envelope insulation in term of resistance (m 2 Kh/kJ) on energy demand gains -RB scenario.

Figure 8 .Figure 9 .

 89 Figure 8. Cost optimal curve for RB geometry Cost Optimal level corresponds to 343 €/m 2 for a primary energy consumption of 120 kWh ep /m 2 /year. In details, ResO is 1.75 m 2 Kh/kJ, ResR is 2.5 m 2 Kh/kJ, ResS is 2 m 2 Kh/kJ and window type is 5. The maximal investment cost corresponds to the minimal energy consumption and leads to a global cost of 353 €/m 2 , while the minimal investment cost corresponds to the maximal energy consumption which leads to a global cost of 431 €/m 2 .A second optimization run was performed in order to estimate the variation of global cost with variation of window dimension. In this case cost optimal corresponds to 297 €/m 2 for a primary energy consumption of 120 kWh ep /m 2 year. In details, ResO is 1.75 m 2 Kh/kJ, ResR is 3 m 2 Kh/kJ, ResS is 3 m 2 Kh/kJ. South oriented window area is half of RB windows area and WTS is 3. Roof window area is equal to 0 and window type of other windows is 5. Talking about window dimension, internal comfort and natural light should be considered before taking decision to reduce window area.

Table 1 .

 1 Parameter settings

Table 2 .

 2 Window Types

Table 3 .

 3 Initial value scenarios

Table 4 .

 4 Cost function of parameters.Cost functions were determined combining French price lists [8] and quotations of local construction companies, all costs are comprehensive of human work and installation costs. Cost analysis revealed that insulation cost functions are exponential functions, while window cost were simplified in linear function.

	Investment Cost	Parameter	Unit	Unit cost function (€/unit)
	Outwall internal insulation	ResO	m 2	37.639*exp(0.351*ln(ResO))
	Slab insulation	ResS	m 2	38.115*exp(0.186*ln(ResS))
	Roof insulation	ResR	m 2	43.478*exp(0.309*ln(ResR))
	Window Type 1	Area	m 2	349.35x+28.17
	Window Type 3	Area	m 2	390.85x+29.37
	Window Type 4	Area	m 2	454.16x+36.62
	Window Type 5	Area	m 2	460.45x+34.45

ACKNOWLEDGEMENT

This work has been supported by the Région Rhône Alpes COOPERA-2012 project "Modélisation des bâtiments zéro-énergie : optimisation technico-économique".


Patrick Sondi
email: patrick.sondi@lisic.univ-littoral.fr

Marion Berbineau

Mohamed Kassab

Martine Wahl

Christophe Gransart

Etienne Lemaire

Georges Mariano

Mohamed Ghazel

Vincent Benard

Walter Schön

Virtual lab based on co-simulation to include impairments of wireless telecommunication such as GSM-R in the evaluation of ERTMS

Keywords: Co-simulation, European Rail Traffic Management System, European Train Control System, GSM-R

The deployment of the European Rail Traffic Management System (ERTMS) is mandatory along European railway corridors, but it will follow a long and expensive process. Thus, there is a need for faster roll-out and reduction in cost for the certification and authorization necessary to put equipment into service. One of the solutions to accelerate the process relies on making intensive use of lab-testing before real deployment. The ANR VEGAS project, labeled by i-Trans will design, develop and evaluate a virtual laboratory based on cosimulation by connecting an ERTMS functional simulator with a simulator dedicated to telecommunication technologies evaluation. In this way, the co-simulation will allow evaluating the functional subsystem behavior while taking into account the impairments related to the telecommunication subsystem (radio propagation impairments such as bad radio links and cuts, electromagnetic interferences or attacks). This paper presents the ongoing work on this virtual laboratory, the preliminary results and interesting prospective work in this context.

Résumé

Le déploiement du système européen de gestion du trafic ferroviaire (ERTMS) est obligatoire sur les principales lignes européennes, mais ce processus sera long et coûteux. Dans ce contexte, if faut trouver des solutions permettant d'accélérer et de réduire les coûts liés à la certification et à la mise en service de nouveaux équipements. L'une d'elles repose sur l'utilisation de laboratoires virtuels pour évaluer les technologies avant de coûteux prototypages et tests réels sur voies. Le projet VEGAS, financé par l'ANR et labélisé par le pôle de compétitivité i-Trans, conçoit, développe et évalue un laboratoire virtuel basé sur la co-simulation. L'idée est de connecter un simulateur de la composante fonctionnelle de l'ERTMS avec un simulateur de réseau modélisant la composante télécommunication afin de réaliser des évaluations qui prennent en compte les aléas liés aux communications (mauvaise liaison radio, coupures, interférences électromagnétiques, charge sur le réseau, etc). Cet article présente les travaux en cours sur le laboratoire virtuel, les résultats préliminaires et les perspectives.

Mots

Introduction

In order to harmonize the different train control systems deployed in Europe and to optimize traffic efficiency by dynamic train control, the International Union of Railways introduced the European Rail Traffic Management System (ERTMS). This system relies on two major components which are the GSM-R (GSM-Railway) subsystem that ensures wireless communications between the train and the control center, and the functional subsystem, identified as the European Train Control System (ETCS), that ensures train control by defining the signaling exchanged with the control center via the GSM-R. The deployment of ERTMS is mandatory along European railway corridors, but it will follow a long and expensive process. Thus, there is a need for faster rollout and reduction in cost for the certification and authorization necessary to put equipment into service. One of the solutions to accelerate the process relies on making intensive use of lab-testing before real deployment.

The ANR VEGAS project, labeled by the competitive cluster i-Trans will design, develop and evaluate a virtual laboratory based on co-simulation. Indeed, while existing ERTMS simulators usually model only the behavior of the functional subsystem, this project aims at connecting an ERTMS simulator with a simulator dedicated to the evaluation of telecommunication technologies. In this way, the co-simulation will allow us evaluating the functional subsystem performance while taking into account the impairments related to the telecommunication subsystem (radio propagation impairments such as bad radio links and cuts, electromagnetic interferences or attacks and also network load).

One key target of VEGAS is to evaluate an evolution of the ERTMS telecommunication subsystem from the GSM-R towards a 4G technology such as LTE in order to prepare the future of railway communications. Such a virtual lab will allow railway industry to anticipate the consequences of various scenarios and will contribute to increase quality, reliability and safety of railway transport while maintaining a high productivity by reducing the trial costs. The originality of the VEGAS project relies on three main points. Firstly, VEGAS is the first proposal that will design a co-simulation approach in order to develop a simulation-based testbed for ERTMS evaluation. Secondly, VEGAS will be the first initiative that integrates a complete model of the telecommunication subsystem from the physical to the application layer in a platform dedicated to ERTMS evaluation. Finally, instead of building a new tool from scratch, VEGAS will rely on a validated industrial tool, the ERTMS simulator by ERSA, and will connect it to the network simulator OPNET. After a brief presentation of the ERTMS and related work on the evaluation of its major components in section 2, we describe our approach to co-simulation in section 3. In section 4, we present the ongoing developments in both simulators in order to realize the virtual laboratory, and section 5 concludes the paper.

ERTMS overview

The International Union of Railway (UIC) introduced the European Rail Traffic Management System (ERTMS) in order to harmonize the different train control systems in use in Europe and optimize the railway traffic and infrastructure usage by dynamic train control. The European Union (EU), which coordinates ERTMS development and legally and financially supports its implantation, decided that its deployment is mandatory on the major European corridors in case of new installations or of an upgrade of the train control or radio communication systems. An overview on railway signaling systems, including the description of all the components of ERTMS, is proposed by [START_REF] Midya | An overview of electromagnetic compatibility challenges in European Rail Traffic Management System[END_REF]. We will focus on two major components which are the European Train Control System (ETCS) and the radio telecommunication subsystem (GSM-R).

The ERTMS functional subsystem

The European Train Control System (ETCS) is dedicated for train signaling and control, while achieving three objectives [START_REF] Levêque | ETCS Implementation Handbook[END_REF]:  Improved safety by train driving supervision: during its movement, the train receives information about running limitations (speed, distance, etc) in the form of a Movement Authority (MA) that defines a place on the track (End of Authority -EOA), which it must not pass.  Higher performance by increasing speed and capacity: the driver obtains movement information directly through displays and follows safely the speed limitation until the EOA without look at trackside signals.  Interoperability: contrary to trackside signaling systems based on colors depending on national rules, ETCS is the appropriate train control system for the lines belonging to different railway administrations.

Fig. 1. ETCS operational levels (adopted from [START_REF] Levêque | ETCS Implementation Handbook[END_REF].

To achieve these goals progressively on the different railroads, ETCS specifications define different ETCS implementation levels for the lines in relation with trackside equipment. Among all the configurations, including those specifying the interactions with non ETCS equipment, we focus on the next three configurations (Fig. 1):

 ETCS level 1: train equipped with ETCS operating on a line equipped with Eurobalises, and optionally Euroloop or Radio in-fill to exchange messages between the train and the trackside. The train obtains its position and movement data set from the balises and it calculates the braking curves for its movement.  ETCS level 2: train equipped with ETCS operating on a line controlled by a Radio Block Center (RBC) and equipped with Eurobalises and GSM-R. The train is permanently connected to the RBC using GSM-R infrastructure. In this way, the control center can update the information about trains movement in real-time and supervise them more dynamically. Therefore, Eurobalises mainly serve as a reference location. However, the train detection and train integrity supervision are still performed by trackside equipment.  ETCS level 3: similar to level 2, except that the train location and the train integrity supervision are performed by onboard equipment inside the train, and no longer by trackside equipment. Eurobalises only serve as a reference location. In the future, this information could be obtained from systems such as GPS or Galileo.

The ETCS applications play a key-role in safety and efficient supervision of railway traffic. For this reason, their conception and evolution follow a stringent validation process. In this context, testbeds are particularly useful in order to perform fast and low-cost preliminary evaluations. Some simulators dedicated to ERTMS evaluation are presented in [START_REF] Mera | ERTMS/ETCS test simulation bench[END_REF] and [START_REF] Müller | ERTMS: on track for success[END_REF]. The ERTMS simulator used in this work has been implemented following the subset 026 specifications (UNISIG, 2010), and the resulting simulation platform is compliant with the requirements for ERTMS testbeds. Though such ERTMS simulators usually include a GSM-R interface, the functioning of their telecommunication subsystem is idealized. Therefore, it is not possible to evaluate accurately the values of telecommunication-related metrics such as end-to-end delay, loss rate, network load, throughput, retransmission count per message, etc. Moreover, the impact of a dysfunction in the telecommunication subsystem on the behavior of the whole system cannot be simulated with these tools. As a result, in their current state, such simulators cannot be used in order to evaluate accurately other prospective telecommunication technologies than the GSM-R in the context of ERTMS scenarios.

The ERTMS telecommunication subsystem

The telecommunication subsystem is actually the second major component of the ERTMS. In the ERTMS level 2, its main part is currently implemented using the GSM-R (Fig. 2). This technology is based on the classical GSM architecture, but it uses specific frequency bands dedicated to railway communications. The Base Transceiver Stations (BTS) are placed every 3 to 7 kilometers along the railway in order to ensure high redundancy and to support high speeds up to 500 km/h. The telecommunication subsystem plays a key-role in the ERTMS since it ensures the communications between the control center and the train for the traffic related to both the signaling and the applications. For these reasons, stringent requirements have been specified for the telecommunication technologies candidate that could be adopted in ERTMS. Since the adoption of GSM-R, many evolutions have occurred in transportation. Indeed, the development of Intelligent Transport Systems (ITS) have brought new applications for safety and monitoring of transport systems, and also new services for customers and user-friendly applications.

In this context, the GSM-R may not still be the appropriate technology [START_REF] Sniady | An Overview of GSM-R Technology and its shortcomings[END_REF][START_REF] Sondi | Toward a Common Platform for Simulation-Based Evaluation of Both Functional and Telecommunication Subsystems of the ERTMS[END_REF]. In addition, mobile telephony operators in Europe have moved to 3G technologies and they are even planning to evolve towards 4G technologies such as LTE. Moreover, the industrials announced in 2009 the end of maintenance operations on GSM equipment for ending 2015 before they commit recently to ensure them until 2025. This situation will oblige railroad operators to resort to specialized services for manufacturing and maintaining GSM equipment in order to keep GSM-R operational. Consequently, GSM-R may still not be the least expensive technology for ERTMS wireless communications in a few years.

For these reasons mentioned above, several researchers have proposed to investigate other telecommunication technologies for the ERTMS, such as GPRS [START_REF] Ruesche | Increase of Efficiency in Wireless Train Control Systems (ETCS level 2) by the Use of Actual Packet-Oriented Transmission Concepts[END_REF], WIMAX [START_REF] Aguado | Wimax Role on CBTC Systems[END_REF] and recently LTE [START_REF] Sniady | An Overview of GSM-R Technology and its shortcomings[END_REF]. Some analytical and simulation based evaluations on these telecommunication technologies are proposed in the literature regarding various telecommunication metrics. However, most of the related experiments concern only the behavior of the telecommunication subsystem and are disconnected from the functional part of the ERTMS. The ETCS applications evaluated are modeled approximately in terms of the messages that they generate during the simulation scenarios, but the behavior of the functional component of ERTMS is not actually modeled in these scenarios. Consequently, it is possible to evaluate the value of the telecommunication metrics for some particular messages exchanged during the scenario, but it is not possible to actually observe the behavior of the functional component of ERTMS when a dysfunction occur in the telecommunication component simulated.

These observations emphasize the need of an evaluation tool for the ERTMS in which both the functional and the telecommunication subsystems can be simulated, and in which the impact of the behavior of one component on the functioning of the other component can be studied accurately.

Our co-simulation approach to ERTMS evaluation

We propose a new approach based on a co-simulation platform that will connect the ERTMS simulator with a simulator especially designed for telecommunication technologies, namely OPNET, in order to design a simulation tool dedicated to joint evaluation of both functional and telecommunication subsystems of ERTMS.

The co-simulation platform

In any ERTMS level 2 scenario, each train moves on a specific track as described in figure 2. The train sends to the control center via the RBC various information on its movement through GSM-R and it receives specific instructions (MA) by the same way. Therefore, under the assumption that all the communications occurring in the scenario between the train and the RBC meet the requirements imposed by ERTMS at the GSM-R interface, the behavior of the functional subsystem can be accurately evaluated using the ERTMS simulator.

Following the same reasoning, let us consider a scenario simulated on the ERTMS simulator where the movement (successive positions, instant velocities, etc) of the train in the time is completely stored, as well as all the sequence of the messages exchanged in the time with the RBC during this movement. Under the assumption that we are able to reproduce precisely the same movement in OPNET and the same sequence of messages following the same chronology, it is possible to obtain precisely the value of the end-to-end delay for each message exchanged. Other telecommunication related metrics can be studied in the same way. Based on these observations, we can state that an ERTMS simulation session can be regarded either:  as a simulation of the functional subsystem based on a set of assumptions on the functioning of the telecommunication subsystem;  as a simulation of the telecommunication subsystem where the inputs are based on a realistic functioning of the functional subsystem. Following these ideas, the co-simulation platform architecture can be described as in fig. 3.a. The functional subsystem is simulated using the ERTMS simulator, and the telecommunication subsystem is simulated using OPNET. The key-elements that synchronize both simulators are the movement of the train and the messages exchanged with the control center during this movement.

Co-simulation concepts

Any ERTMS scenario can be partially modeled inside each one of both simulators in order to evaluate the related components. To ensure the coherency of each partial scenario modeled inside a simulator with the original ERTMS scenario, the following concepts are introduced:  the Track: this concept represents the physical and static elements that materialize the railroad, the network infrastructure, the localization and signaling systems components. Each particular point j of a Track T i can be fully described by a T ij =(L ij ,P ij ) where L ij is its location (e.g latitude, longitude and altitude) and P ij is a description of its properties (e.g color, size, type,…). The precise definitions should follow railway standards.  The Trajectory: refers to the movement of one train during a specific scenario S k on a set of Tracks T 1 , …, T i , …, T p . Each step j of the Trajectory TS can be fully described by TS j =(T ij , D ij , V ij ) where T ij is the element of the Track T i that the train passes at the date D ij while moving with a speed V ij . In this way, the movement of any train during an ERTMS scenario can be reproduced faithfully inside any of the simulators.  The Transmissions: refer to the set of messages exchanged between each train and the control center during a scenario S k . Each message j sent at a moment MS j of the scenario S k can be fully described either in a: spatial reference domain by MS j =(T ij , M j ) where T ij is the point of a Track T i at which the message j was sent, and M j is a full description of the message j; temporal reference domain by MS j =(D j ,M j ) where D j is the date at which the message j was sent in the scenario S k , and M j is a description of the message j; spatio-temporal reference domain by MS j =(T ij , D j , M j ) when TS j .T ij =MS j .T ij in the spatial reference domain and TS j .D ij =MS j .D j in the temporal one. In this case, the scenario partial model is perfectly synchronized with the original scenario.

Even when a Trajectory is perfectly reproduced in both simulators, the transmission and the reception of the messages performed when the train is located between two elements of the Trajectory may not occur exactly and simultaneously at the same date and the same intermediate location in both the original scenario and the partial scenario of each simulator. For these reasons, we distinguished the spatial and the temporal domains for the Transmissions, and this will be very useful in the design of our co-simulation protocol.  the Metrics: refer to the indicators that are evaluated during a scenario S k . In an ERTMS functional simulator, one can mainly evaluate the conformity of the train behavior with the ERTMS safety specifications. In a telecommunication simulator, one can evaluate the metrics such as end-to-end delays, loss rate, handover duration, etc. For any scenario S k , we state that: the ordered set ES k of the instructions given to the train by the control constitutes the Metrics for this scenario S k in the ERTMS simulator.

the Metrics in OPNET is the set ES k formed by the values of the metrics for each message j and that are stored in the message description M j (e.g end-to-end delay, retransmission count), and by the values of the metrics attached to each specific element of the Track T i located at the point h and that are stored in its properties description P ih (e.g for a RBC: the number of trains connected simultaneously, lost messages per train, average queuing delay, duration of connection loss per train, etc).

When generating the partial view of an ERTMS scenario for a specific simulator, a specific view must be generated for each one of these four concepts (see Fig. 3b). According to the component evaluated by one specific simulator and the related metrics considered, the related view will contain more or less details. However, online co-simulation suits better in a context where all the models are at a release stage, and when all the problems related to the synchronization of both simulators are solved. During the development process, offline co-simulation is necessary; especially when some parts of the models are still being refined. In this mode, the scenario is first simulated with the ERTMS simulator and the information about the Track, Trajectory, Transmissions and Metrics are backed up. In this way, it is possible to check that the scenario is valid from a functional point of view. This scenario is then replayed in OPNET to evaluate the behavior of the telecommunication subsystem under realistic functional constraints. The debugging process is easier in this mode since it is possible to determine quickly which simulator is concerned with a specific error and use its built-in debugger to fix it.

Co-simulation modes

Offline co-simulation protocol

Online co-simulation mode implies live exchange of data between both the ERTMS simulator and OPNET. The co-simulation process is directly under the control of the functional subsystem simulated by the ERTMS simulator which is already validated as compliant with ERTMS specification (UNISIG, 2010). Therefore, any abnormal situation occurring either due to the telecommunication subsystem or to the functional one will lead to an immediate reaction of the control system. In this way, it is obvious to validate a co-simulation and analyze the results obtained for both subsystems and for the entire system.

However, in the offline mode, a scenario previously evaluated on the ERTMS simulator is replayed in OPNET.

Though we are sure that this scenario is valid from a functional point of view, while it will be running in OPNET we will have no functional warning if the telecommunication subsystem behaves abnormally. In these conditions, we need some formalized mechanisms that will allow us determining if an offline co-simulation is valid based on the partial simulation performed in OPNET during the replay phase. We also need accurate methods that will allow us analyzing the results obtained through OPNET concerning each subsystem and the entire system.

Notations, assumptions and definitions

In order to describe clearly the offline co-simulation protocol that we propose to tackle these problems, we introduce the following notations and assumptions:  When the values of all the telecommunication metrics observed on a scenario S k during a simulation SO n in OPNET meet the constraints imposed by ERTMS specifications on the GSM-R, we can write it as follows:

 We denote by SO n (S k , T k [], TS k [], MS k [], ES k []) and SE n (S k , T k [], TS k [], MS k [], ES k [])
. ⊂

Offline co-simulation protocol overview

Using the notations and definitions presented in section 3.4.1, the main procedure of the protocol for offline cosimulation can be described as follows: However, SO 1 (S k , T k , TS k , MS k , ES k ) may introduce some variations on the dates at which some messages are received, or cause loss of some important messages which could cause a different behavior of the functional subsystem. For this reason, the entire co-simulation can be validated only if the scenario based on SO 1 (S k , T k , TS k , MS k , ES k ) is valid from a functional point of view and leads to the same ordered set of instructions than SE 0 (S k , T k , TS k , MS k , ES k ) (step 3). In addition, if the condition SO 1 ⊂QOS is verified, it can be concluded that a valid co-simulation in which both functional and telecommunication subsystems meet ERTMS constraints has been performed.

In case the condition SO 1 ⊂QOS is not verified, the result SE n+1 = SE n only establishes that the co-simulation is valid. However, the telecommunication subsystem architecture needs improvement in order to meet ERTMS requirements. The operator can make the necessary improvements and repeat the co-simulation process until he gets a satisfactory configuration. When the validation test fails, this means that the scenario has changed from a functional point of view and that it makes no sense to continue iterating based on the resulting data. In this case, the co-simulation cannot be validated for the related scenario.

The mechanisms proposed in this section 3 are voluntary intuitive and constitute an attempt to formalize the description of the operations in the context of co-simulation, especially in order to evolve toward automatic operations at all levels (generation of test scenarios, evaluation by co-simulation, validation and interpretation of the results). Naturally, these mechanisms can be refined. For example, it is possible to define additional validation conditions such as the difference between the dates of transmissions of any message j in both simulators can be slightly different without exceeding a given threshold (e.g |SE n .S k .MS j -SO n .S k .MS j |<ε). Other similar conditions can be specified considering spatial properties.

Preliminary results

The co-simulation approach proposed in this paper is part of the work dedicated to the development of a virtual laboratory for ERTMS components evaluation (VEGAS). The ERTMS simulator is a complete and operational commercial tool compliant with the specifications for ERTMS testbeds. The related models for track and scenario design and evaluation are available and ready for use, and it also supports interactions with external tools through a CORBA interface, thus allowing online co-simulation. The main remaining implementations concerning this tool are related to automatic data input in the context of an offline co-simulation, and to the integration of the telecommunication subsystem model being implemented in OPNET.

A complete model of the telecommunication subsystem, especially a model of the GSM-R in OPNET is still needed. The OPNET Modeler provides a model for the UMTS, WIMAX and LTE technologies, but not for the GSM. Several custom GSM models have been proposed for the OPNET simulator, but they all present severe limitations that impede their straightforward use in ERTMS context. One of these models is a GPRS model [START_REF] Ruesche | Increase of Efficiency in Wireless Train Control Systems (ETCS level 2) by the Use of Actual Packet-Oriented Transmission Concepts[END_REF] that focuses on data transmission and does not implement completely GSM signaling, thus impeding the study of situation such as handover which is a critical operation in ERTMS. The physical layer of the model is also very simplified, thus impeding deep analysis of the impairments which is one of the main motivations of our work. Another custom GSM model is available in the OPNET contributed models repository.

Originally designed in order to study the GSM technology from the point of view of signaling, it implements almost all the features including signaling messages, measures procedures, different handover procedures, user actions, SIM operations, interconnection with other networks and all the components of a GSM network (MS, BTS, BSC, MSC, SS7, GMSC, HLR, PSTN). However, the model misses some important features: the Link layer and the TDMA frames are not modelled, the transmission of Voice and Data are not modelled. We are currently improving this model in order to complete all the features and adapt it to obtain a GSM-R model.

We assumed that a co-simulation always start with a valid scenario from a functional point of view. It may appear that such scenario can be obtained only after a first simulation using the ERTMS simulator. However, if we consider the traces of a train that moved on real-world ERTMS level 2 lines while being controlled by ETCS, the scenario resulting from these traces is a valid scenario from a functional point of view. Considering that such a scenario is our scenario S k , we can use it to generate the related views for both OPNET and ERTMS simulator. Therefore, it is obvious that simulating S k using the ERTMS simulator will result in SE 0 (S k , T k , TS k , MS k , ES k ) which will be valid from a functional point of view since S k is. As a result, provided that there exist real-world traces of ERTMS scenarios that are recognized as valid from a functional point of view and that provide sufficient information to build data input that have the same structure than SE 0 (S k , T k , TS k , MS k , ES k ), these data can be used directly to perform SO 1 (S k ,…) and obtain the behavior of the telecommunication subsystem under a realistic functioning of a valid functional ERTMS scenario. Some industrials such as ALSTOM and RFF already provide such real-world traces for research purposes. In a recent work [START_REF] Sondi | Generating Test Scenarios Based on Real-World Traces for ERTMS Telecommunication Subsystem Evaluation[END_REF], we used the traces provided by ALSTOM in order to validate the preliminary GSM-R models developed in OPNET.

Conclusion

In this paper, we described the co-simulation approach that we have developed in order to design a virtual laboratory for ERTMS functional and telecommunication subsystems evaluation. The models of the GSM-R in OPNET are still being developed, and they will be evaluated using real-world traces of trains moving on ERTMS lines. In our future work, we will perform the evaluations of several ERTMS scenarios using the virtual lab, and we will introduce new models in order to evaluate other prospective technologies such as LTE.

Fig. 2 .

 2 Fig. 2. GSM-R infrastructure with redundant Base Transceiver Stations in each cell.

Fig. 3 .

 3 Fig. 3. Co-simulation architecture and concepts.

Fig. 4 .

 4 Fig. 4. Co-simulation modes: offline and onlineIn order to perform a co-simulation, the ERTMS simulator and OPNET can be connected in live for an online simulation or it can done offline by replaying a scenario previously run in one simulator into the other. Online simulation presents the advantage of running both functional and telecommunication subsystems simultaneously, thus allowing a more realistic evaluation of the entire ERTMS scenario. In this mode, the model of the telecommunication subsystem implemented in OPNET replaces the Radio Network Simulator of the ERTMS simulator (Fig.4). The Trajectory information of the train is transmitted in live to OPNET so that the train follows the same movement in both simulators. The messages generated by the train in the ERTMS simulator go without delay through the OPNET train model where they are sent to the OPNET RBC model through BTS1 or BTS2, under realistic conditions of mobility, propagation and network transmissions. They are then routed without delay from the OPNET RBC model to the RBC Simulator inside the ERTMS simulator for functional processing. The messages generated by the RBC Simulator to the train follow the inverse process.

  the n th simulation session in OPNET and in ERTMS simulator, respectively, of the scenario S k , and where: T k [] is the set containing all the tracks involved in S k , and that can be referenced as T 1 , T 2 , …, T p . A reference to the simulation session can be given by denoting SO 1 .S 2 .T 3 the third track used in the first simulation session in OPNET of the scenario S 2 , for example; TS k [] is the ordered set of the steps encountered on the trajectory TS during the simulation of the scenario S k . A reference to the simulation can be given as well, for example by using the notation SE 3 .S 1 .TS 6 for the sixth step on the trajectory of the scenario S 1 during its third simulation in the ERTMS simulator MS k [] is the ordered set of the messages sent during the simulation of the scenario S k . For example, SO 1 .S 4 .MS 1024 is the 1024 th message sent during the first simulation of scenario 4 in OPNET; ES k [] is the ordered set of the instructions received by the train in the ERTMS simulator or the set of Metrics observed in OPNET, respectively.  We assume that each co-simulation process of one scenario S k must start with a valid functional view of this scenario. In other word, only SE 0 (S k , …) exists, but not SO 0 (S k , …).  We assume that the (n+1) th simulation of a scenario S k in one simulator depends on the simulations SO n (S k ,…) and SE n (S k ,…) of this scenario S k . Of course, SO 1 (S k , …) depends only on SE 0 (S k , …) since SO 0 (S k , …) does not exist.  We define an equivalence relation between two successive simulations of a scenario S k in the ERTMS simulator as follows: . [] = +1 . [] . = +1 . , ∀ → = +1

Fig. 5 .

 5 Fig. 5. Offline co-simulation protocol

  validation and interpretation of the resultsAn offline co-simulation is currently an interactive process controlled by a human user. Yet at step 1, we get through SE 0 (S k , T k , TS k , MS k , ES k ) a valid simulation of the scenario S k from a functional point of view. At step 2, we obtain through SO 1 (S k , T k , TS k , MS k , ES k ) the functioning of the telecommunication subsystem under a realistic functional behavior SE 0 (S k , T k , TS k , MS k , ES k ). Particularly SO 1 .ES k provides the values of all the telecommunication metrics that were considered as of interest in the study of the considered scenario.

  -clé: Co-simulation ; ERTMS ; ETCS ; GSM-R

	Nomenclature
	ERTMS European Rail Traffic Management System
	ETCS European Train Control System
	OPNET Optimum Network Performance
	GSM-R Global System for Mobile Communications-Railway
	UIC	International Union of Railway
	MA	Movement Authority
	EOA	End Of Authority
	RBC	Radio Block Center
	MS	Mobile Station
	BTS	Base Transceiver Station
	ITS	Intelligent Transport Systems
	GPRS General Packet Radio Service
	WIMAX Worldwide Interoperability for Microwave Access
	RBC	Radio Block Center
	MAC/RLC Medium Access Control/Radio Link Control
	UMTS Universal Mobile Telecommunication System
	TDMA Time Division Multiple Access
	BSC	Base Station Controller
	MSC	Mobile Switching Center
	SS7	Signalling System 7
	GMSC Gateway Mobile Switching Center
	HLR	Home Location Register
	PSTN Public Switched Telephone Network

  1. Consider the scenario S k , generate a view for the ERTMS simulator and run SE 0 (S k ,…).2. Based on SE0 (S k , T k , TS k , MS k , ES k ), generate the view for OPNET and run SO 1 (S k ,…) 3. Based on SE n (S k ,T k , TS k , MS k , ES k ) and SO n+1 (S k ,T k , TS k , MS k , ES k ),generate a view for ERTMS simulator and run SE n+1 (S k ,…) /* initially n=0 */ IF SE n+1 = SE n THEN IF SO n+1 ⊂ QOS THEN STOP ON SUCCESS ELSE THEN Based on SE n+1 (S k ,T k , TS k , MS k , ES k ), generate OPNET view and run SO n+2 (S k ,…)

	SET n=n+1 AND GOTO STEP 3 /* The operator decides when to abandon */
	END IF
	ELSE STOP ON FAIL
	END IF

Acknowledgements

The present research work is supported the VEGAS project (http://vegas.ifsttar.fr) funded by ANR (ANR-12-VPTT-0004) and labelled by i-Trans, the CISIT, the FEDER, and the Region Nord -Pas de Calais. The authors gratefully acknowledge the support of these Institutions.