M.D C Ferreira

W S Venturini
email: venturin@sc.usp.br

F Hild
email: hild@lmt.ens-cachan.fr

M.D W C S Ferreira

F Venturini

Hild

On the analysis of notched concrete beams: From measurement with Digital Image Correlation to identification with Boundary Element Method of a cohesive model

Keywords: boundary elements, cohesive crack, digital image correlation, inverse analysis, parameter identification. Nomenclature

A way of coupling digital image correlation (to measure displacement fields) and boundary element method (to compute displacements and tractions along a crack surface) is presented herein. It allows for the identification of Young's modulus and fracture parameters associated with a cohesive model. This procedure is illustrated to analyze the latter for an ordinary concrete in a three-point bend test on a notched beam. In view of measurement uncertainties, the results are deemed trustworthy thanks to the fact that numerous measurement points are accessible and used as entries to the identification procedure.

vector gathering all unknowns (displacements and tractions)

Introduction

One way of numerically analyzing cracked samples or structures is to resort to cohesive models. Since the pioneering works of Dugdale [START_REF] Dugdale | Yielding of Steel Sheets Containing Slits[END_REF], Barenblatt [2] and Hillerborg et al. [START_REF] Hillerborg | Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[END_REF][START_REF] Petersson | Crack growth and development of fracture zone in plain concrete and similar materials[END_REF],

these models have become very popular [5, 6 , 7, 8 , 9], in particular when dealing with concrete materials. One of the open questions concerns the identification of cohesive laws in a robust way since, in many instances, only strain and load data are available [START_REF] Derewonko | Strength assessment of adhesive-bonded joints[END_REF]. In addition to global data, pictures shot at different scales are also used in a qualitative way [START_REF] Pardoen | Constraint effects in adhesive joint fracture[END_REF][START_REF] Leffler | Shear behaviour of adhesive layers[END_REF][START_REF] Salomonsson | Modeling and parameter calibration of an adhesive layer at the meso level[END_REF][START_REF] Sørensen | Micromechanical model of cross-over fibre bridging -Prediction of mixed mode bridging laws[END_REF] or a more quantitative way by measuring deflections [START_REF] Yang | Elastic-plastic mode-II fracture of adhesive joints[END_REF][START_REF] Su | An elastic-plastic interface constitutive model: Application to adhesive joints[END_REF] and deformed shapes [START_REF] Sargent | Durability studies for aerospace applications using peel and wedge tests[END_REF].

Full-field measurements provide very useful data to identify interface behaviors [START_REF] Abanto-Bueno | Experimental Determination of Cohesive Failure Properties of a Photodegradable Copolymer[END_REF][START_REF] Fedele | Identification of adhesive properties in GLARE assemblies by Digital Image Correlation[END_REF]. In the present paper, it is proposed to use displacement measurements to calibrate the cohesive law. The calibration is performed by resorting to an inverse analysis using the kinematic data as inputs.

Inverse analyses are nowadays a very important tool in many engineering fields. In solid mechanics, the technique is applied mainly to identify, for instance, material properties, boundary conditions, material degradation, crack formation, which are parameters needed to check the structural safety. Identification or inversion procedures are mainly applied by using finite-element-based procedures [START_REF] Bonnet | Inverse problems in elasticity[END_REF] coupled with full-field measurements [START_REF] Avril | Overview of identification methods of mechanical parameters based on full-field measurements[END_REF]. Full-field measurements [START_REF] Rastogi | Photomechanics[END_REF] are generally performed by analyzing the motion and deformation of external surfaces (e.g., by resorting to digital image correlation (DIC) [START_REF] Sutton | Image correlation for shape, motion and deformation measurements: Basic Concepts, Theory and Applications[END_REF]). This specific feature motivates the work presented herein that aims at combining displacement fields measured by DIC and simulations with the boundary element method (BEM) to extract the parameters of a cohesive law describing cracking in concrete.

As for many applications in engineering, the boundary element method (BEM) is a numerical technique very appropriate to perform inverse analyses. The method is recommended when a fine analysis is required only over a small region of the body. The method is also very accurate for problems in which high gradients may occur. These situations are often found in inverse problems (e.g., when dealing with damage and cracks).

There are several works developed so far using boundary element methods for parameter identification in structural analyses [START_REF] Mellings | Flaw identification using the boundary element method[END_REF][START_REF] Alessandri | Crack identification in two-dimensional unilateral contact mechanics with the boundary element method[END_REF][START_REF] Comino | Material constants identification in anisotropic materials using boundary element techniques[END_REF][START_REF] Engelhardt | Crack and flaw identification in elastodynamics using Karman filrter techniques[END_REF][START_REF] Nemitz | Topological sensitivity and FMM-accelerated BEM applied to 3D acoustic inverse scattering[END_REF] in the context of deterministic approaches. There are also several other developed works based on stochastic techniques [START_REF] Burczynski | The identification of cracks using boundary elements and evolutionary algorithms[END_REF][START_REF] Tin-Loi | Identification of cohesive crack fracture parameters by evolutionary search[END_REF][START_REF] Engelhardt | Defect identification in 3-D elastostatics using a genetic algorithm[END_REF]. In all these works, BEM-based procedures are proposed to deal with material property identification in solid mechanics. However, experimental data were only used in the work of Tin-Loi and Que [START_REF] Tin-Loi | Identification of cohesive crack fracture parameters by evolutionary search[END_REF] to show the efficiency of the developed method.

In this work a simple technique based on the BEM singular formulation is used to identify cohesive crack parameters of a concrete beam that is tested up to complete failure.

BEM crack singular formulations [START_REF] Aliabadi | Boundary element formulations in fracture mechanics[END_REF] may also be considered. Three-point bend test is performed on a notched specimen (Section 3). To perform the inverse analysis, only singular equations (i.e., based upon a kinematic formulation [START_REF] Blandford | Two-dimensional Stress Intensify Factor computations using the Boundary Element Method[END_REF][START_REF] Liang | Simulations of non-linear fracture process zone in cementitious material a boundary element approach[END_REF]) are used in the region monitored during the experiment by a camera (Section 2). The latter provides pictures that are used to measure displacement fields by DIC that are entries to the inverse analysis. The BEM algebraic system of equations enables for the computation of crack openings and tractions for which least squares are used to extract Young's modulus and the parameters of a linear cohesive law (Section 4).

Boundary element approach for inverse analyses

For an elastic multi-region body that, for the sake of simplicity, is assumed to be formed of two regions 1 Ω and 2 Ω (Figure 1) separated by an interface (e.g., a crack) the following integral boundary equation expresses equilibrium of each region . The cohesive law will be anlyzed along the interface i Γ .

Γ = Γ + ∫ ∫ Γ Γ d M p M S u d M u M S p S u S C k ik k ik k ik ) ( ) , ( )
For direct analyses, Equation ( 1) is transformed into an algebraic system of equations that is solved directly after taking into account the boundary conditions. To obtain the algebraic representations the boundary and the interface of sub-domains 1 Ω and 2 Ω are discretized by using elements and approximate displacements and tractions along them. For a given sub-region k Ω the following algebraic representations are obtained Similarly, the algebraic relationships written conveniently only for internal points are given by

      =       kj k kj kk kj k kj kk p p G G u u H H ] [ ] [ (2
      ′ ′ +       ′ ′ - = kj k kj kk kj k kj kk i p p G G u u H H u ] [ ] [ } { (3)
Equations ( 2) and ( 3), the equilibrium and displacement compatibility at all interface nodes are needed to solve the problem and to obtain the displacement field inside the solid where required.

In the sequel, the inverse procedure based on a BEM formulation is applied to identify cohesive law parameters. Thus, the sub-region equations given above for the two sub-regions are further simplified. Both sub-regions are assumed to be made of the same (elastic) material described by Lamé's coefficient µ and Poisson's ratio ν . They can be easily found either by using appropriate tests with the uncracked material or by applying, say, the least squares method to load vs. displacement curves during the initial loading process where an elastic phase is assumed. This point is solved differently herein by considering an internal point.

Therefore, to derive the algebraic system of equations for the crack cohesive parameter identification, the elastic parameters of both sub-regions are assumed to be known.

For inverse problems, Equations ( 2 2) and ( 3) Therefore, Equation ( 5) is written only for points where the displacements are known.

yields           =           p k u k p k u k p k u k p k u k p p G G u u H H ] [ ] [ (4)           ′ ′ +           ′ ′ - = p k u k p k u k p k u k p k u k m k p p G G u u H H u ] [ ] [ } { (5)
Depending on the process used to measure these displacements, the number of relationships in Equations ( 4) and ( 5) is very large, leading to a large number of redundant equations that is very important for the minimization process to be applied. Equations ( 4) and ( 5) are joined together to define a system in which the unknowns are moved to the left hand side

          =                   ′ - ′ - - - m p k m p k u k u k u k u k u k u k w v p u G H G H (6) where } { m p k v - and } { m p k w -
contain the contribution of the known values including the measured displacements at internal points.

A similar system of algebraic equations is written for sub-region j Ω . They are joined together after assuming the displacement compatibility and equilibrium conditions along the interface (i.e., given by the chosen cohesive law). The same format as Equation ( 6

          =                   ′ - ′ - - - m p i m p i u i u i u i u i u i u i w v p u G H G H (7) or equivalently } { } { ] [ m p i u i u i b x A - = (8)
Equation ( 8) is a redundant system with a very large number of algebraic relationships usually written for the region of interest where the displacement field is measured. In that case all boundary values are unknown and the redundancy is guaranteed by the large number of internal points where the displacements are known. It is solved using any identification technique to obtain the unknown vector } { u i x . The least squares technique [START_REF] Björck | Numerical Methods for Least Squares Problems[END_REF] is the simplest tool to determine the solution to Equations ( 8

) } { ] [ } { ] [ ] [ m p i t u i u i u i t u i b A x A A - = (9)
Alternative approaches are given by Tikhonov's regularization technique [START_REF] Tikhonov | Solutions of ill-posed problems[END_REF] or the singular value decomposition (SVD) approach [START_REF] Press | Numerical Recipes in Fortran[END_REF]. They are not reported herein, even though they were already used to analyze artificial test cases [START_REF] Ferreira | Inverse analysis for two-dimensional structures using the boundary element mathod[END_REF]. Kalman filters can also be used [START_REF] Bolzon | Parameter identification of a cohesive crack model by Kalman Filter[END_REF].

After obtaining the profiles of tractions } { u i p and crack opening displacements (based upon the interfacial displacements } { u i u ), the parameters of the cohesive model are to be determined. As for any non-linear model, the yield surface F of the cohesive model reads

t F(f , ∆u)= 0 ( 10
)
where t f is tensile (opening) traction in the direction perpendicular to the crack surface, and ∆u the corresponding crack opening displacement.

To identify the cohesive parameters, a "regularized" system of Equations ( 9) for which interpenetration is avoided, i.e. the crack opening displacement is set to zero if a negative value were obtained in the previous iteration. The system given in Equation ( 9) is then reordered accordingly. After obtaining the displacement jump and tractions along the crack line, a regression is used to identify the limit surface using a chosen number of parameters.

Assuming a linear limit surface to describe the cohesive model ( / )

c t t t c F(f , ∆u)= f -f 1 ∆u u 0 - ∆ = (11

Experimental analysis

A three-point flexural test was performed on a regular concrete specimen. The sample size is ca. 150 × 150 × 500 mm 3 , the notch depth is 25 mm and its width 3 mm. The outer span is of the order of 450 mm (Figure 2). The experiment is controlled by using the signal delivered by a clip gauge installed on the lower face of the sample (i.e., the notch opening displacement is regulated). Furthermore, DIC is used to evaluate the displacement fields on one lateral surface of the sample. DIC is an optical technique to measure displacement fields of a surface [START_REF] Sutton | Image correlation for shape, motion and deformation measurements: Basic Concepts, Theory and Applications[END_REF] by registering pictures of the surface for different states, one before loading being the reference state, and the other one when load is applied. In the present case, only one camera is used since the out-of-plane displacements are vanishingly small. By implementing the brightness conservation equation, different displacement kinematics are measurable in a global setting [START_REF] Hild | Digital image correlation: From measurement to identification of elastic properties -A review[END_REF]. In the present case, a so-called Q4-DIC algorithm is used [START_REF] Besnard | Finite-element'' displacement fields analysis from digital images: Application to Portevin-Le Châtelier bands[END_REF]. It consists in decomposing the displacement field into components associated with shape functions identical to those used, for instance, in finite element approaches. The location of the region of interest (ROI) is depicted in Figure 2. A semi-professional camera is used to acquire pictures (Canon EOS 30D, 12-bit RGB CMOS sensor delivering 3,504 × 2,336-pixel images).

The sample surface was prepared by using black and white paint. The texture is obtained by using a mask with an array of holes (Figure 2).

Displacement resolution

For measurement and identification purposes, it is important to assess the accuracy of the experimental results obtained by using a correlation algorithm. The displacement resolution is estimated by considering consecutive pictures when no load is applied, and running correlation analyses. The displacement resolution is estimated when the correlation parameters are modified. In particular, the effect of the element size l expressed in pixels on the displacement resolution is investigated. The quality of the estimate is therefore characterized by the standard displacement resolution, u σ , which is defined as the mean of all the standard displacement resolutions. Figure 3 shows the standard displacement resolution u σ as a function of the element size l . The larger the element size, the smaller the resolution. For the analyzed element sizes, a power law with an exponent α of the order 1 is found

α α σ l 1 + = A u ( 12
)
with A = 0.7 pixel, thereby indicating that the displacement resolution and the corresponding spatial resolution (or element size l ) are the result of a compromise. In the following, 16pixel elements are considered.

A first analysis using displacement measurements consists in comparing the output of the clip gauge to an average displacement jump computed as the horizontal displacement difference between two zones chosen around the notch (Figure 4). The element size is equal to 16 pixels on quarter resolution pictures to perform the analysis on a conventional PC. The analysis is performed for a sequence of 60 pictures. Figure 5a shows the load / notch opening measured by the clip gauge. The points when the pictures were shot are also depicted. With the used concrete sample, a gradual softening occurs.

Figure 5b shows a comparison of the clip gauge data and those obtained by postprocessing the displacement field. Even though the measurement locations are different (Figure 2), a quasi linear trend is observed when the two outputs are compared. In terms of identification residuals, a root mean square value of 2.4 µm (or 0.04 pixel) is found. This result shows that the DIC technique yields results consistent with those obtained by the clip gauge, and constitutes a first validation of DIC to analyze the present test. From the previous resolution analysis, the standard displacement resolution is of the order of 0.03 pixel (or 1.5 µm). The value of the displacement jump remains in the subpixel range (i.e., less than 54 µm) during a significant part of the load history (Figure 5b), yet significantly larger than the measurement resolution. By visual inspection of the picture it is impossible to detect the presence of the crack. Consequently, the present analysis is only made possible by using DIC.

The next step is to analyze the displacement field over the whole ROI (more than 8,900 nodes are used when an element size of 16 pixels is chosen). Figure 6 shows five displacement maps in the softening part of the load vs. notch opening curve. As the notch opening increases the crack propagates. From the displacement contours, it is possible to locate the crack surface.

Last, the crack surface and the corresponding displacement jump are sought. To determine the crack surface, the contour of 0-horizontal displacement is determined (Figure 7b) when the rigid body motion was subtracted from the measured displacement field (Figure 7a). This procedure is applied to a picture after failure for which the horizontal displacement map is shown in Figure 8. To check this evaluation, the actual surface in the deformed picture is compared with the profile obtained when the surface of Figure 7b is translated with the measured displacement field evaluated along the latter. A good agreement is obtained (Figure 8) and gives confidence in the following results. The crack surface is depicted in Figure 6 and the 0-contours. These two quantities allow one to compare the current crack surface and that determined at the very end of the experiment. A good match is observed except for a vertical interval ranging from 1300 to 1500 pixels, and from 200 to 400 pixels. A closer look at Figure 8 in this area shows that there is not a unique crack but two branches that are very close to each other.

The crack opening displacements are obtained when considering the displacement jump of two points located symmetrically from the crack surface. A distance of two element sizes (i.e., 32 pixels) is chosen (see dashed lines of Figure 7b). Figure 9 shows the change of the crack opening displacement for the five pictures analyzed in Figure 6. This plot shows the difficulty of the identification because data are noisy (i.e., the displacement levels are very small), and therefore calls for robust procedures and a large amount of data (here provided by DIC results).

Identification

For the experiment described in the previous section an inverse analysis is carried out to identify the parameters of the cohesive law. First, the elastic properties of the concrete beam are identified. Then, using the model presented in Section 2 the sought parameters are identified.

Elastic properties

Although inserting the elastic modulus as an unknown in Equation ( 7) is very simple, the BEM-based inverse analysis is not used to find the elastic parameters. Instead, the measured displacement at an internal point is used to estimate the elastic modulus. The fine boundary element discretization adopted to construct the applied force vs. displacement curve of the beam is shown in Figure 10. The measured displacements at the chosen internal point are given in Figure 11, where a clear linear relationship is observed after the second load increment. Thus, to evaluate Young's modulus E, the initial part of the curve is discarded and the non-linear part where the crack propagation effects are observed. Comparing this measured slope with the one obtained numerically, an average Young's modulus for this concrete beam is found to be E = 18 GPa. This value is significantly smaller than the Young's modulus measured directly by carrying out standard compression tests on cylindrical specimens cast with this concrete, E = 30 GPa. This may be due to the coarseness of the microstructure of the material studied herein. Poisson's ratio cannot be measured by this procedure because the displacement level is too small in comparison to the displacement resolution. A value of ν = 0.2, obtained using cylindrical specimens is considered in the present analysis. It is important to stress that although the elastic parameters were identified in this part, their influence on the final analysis to identify the cohesive crack parameters is very small.

Cohesive model

Having identified the elastic parameters, the inverse analysis is now carried out for the subdomain of interest indicated in Figure 2. Only a small region around the crack line is considered where the pictures shot during the experiment brought important information regarding displacement fields. This region of interest is discretized by using 81 boundary elements, while the crack line was also approximated by using 104 elements, as shown in and 23 (Figure 15) and nodes 25 and 35 (Figure 16). It is worth noting that when analyzing the data with the error bars (a displacement uncertainty equal to 3σ u = 4.5 µm is considered), all the computed displacement data fall within that zone. When considering these two separate groups of points, the corresponding regressions lead to different cohesive parameters.

Next, the results obtained for all the points are put together. Figure 17 shows the final results and the approximated curve obtained by regression. The gray zone accounts for a measurement uncertainty of ± 3σ u . There is only one point that lies outside this confidence domain. Consequently, it is assumed that the chosen cohesive law describes reasonably the behavior of cracks in that type of concrete. From this approximation, the following cohesive ). The fact that the identified value is close to the upper bound indicates that the aggregates played a role in crack propagation that is not straight (Figure 8).

Summary and perspectives

In this paper it was proposed to couple DIC and BEM to identify mechanical properties. An experimental test on ordinary concrete was performed. In the present case, displacement

fields measured with Q4-DIC were used. It is worth noting that this test is very difficult to analyze since the displacement levels are very small. However it was shown that even with noisy input data, the fact that they were numerous made possible the identification of Young's modulus and the two parameters of a linear cohesive law.

By using the displacement resolution evaluated directly during the experiment, it was shown that the identification results are obtained with a good confidence interval. The fact that parameters identified in the present case lead to a fracture toughness that lies within the bounds associated with ordinary concrete is an additional proof. These two features show that coupling DIC and BEM is a viable route to identify elastic and fracture properties of concrete.

This type of procedure may be applied to other quasi-brittle materials such as composites or other geomaterials.

Last, it is worth remembering that the numerical analyses performed herein were twodimensional. In view of the crack surface, it is likely that 3D analyses are more than desirable for more accurate estimates of the parameters of the cohesive law. However, there is then a need for the identification of the crack surface in addition to the information given by pictures of only one surface of the sample. Two routes can be followed. First, by using two cameras the shape of the crack surface would be known on both sides of the sample. The way they connect would either be assumed or left as an additional unknown to be identified. Second, digital volume correlation [START_REF] Roux | Three dimensional image correlation from X-Ray computed tomography of solid foam[END_REF] could be used as the sample would be imaged in a tomograph.

This technique was shown to be able to extract, for instance, the crack surface and profiles of stress intensity factors [START_REF] Limodin | Crack closure and stress intensity factor measurements in nodular graphite cast iron using 3D correlation of laboratory X ray microtomography images[END_REF], and to compare them with numerical simulations with, say, X-FEM [START_REF] Limodin | Crack closure and stress intensity factor measurements in nodular graphite cast iron using 3D correlation of laboratory X ray microtomography images[END_REF][START_REF] Rannou | Three dimensional experimental and numerical multiscale analysis of a fatigue crack[END_REF]. Analyses with BEM could also be considered. 6). This type of information will be used to identify the cohesive model. The confidence interval (dashed lines) is defined by ± 3σ u .

Figure captions

  obtained by carrying out the integrals over boundary and interface elements for unknown displacements and tractions on the interface [ obtained by carrying out the integrals over boundary and interface elements for prescribed, unknown tractions [ obtained by carrying out the integrals over boundary and interface elements for prescribed, unknown tractions when considering inner points [ kk G ], [ kj G ] matrices obtained by carrying out integrals over boundary and interface elements [ kk G′ ], [ kj G′ ] matrices obtained by carrying out the integrals over boundary and interface elements when considering internal points [ matrices obtained by carrying out the integrals over boundary and interface elements for unknown displacements and tractions on the interface [ p k H ], [ u k H ] matrices obtained by carrying out the integrals over boundary and interface elements for prescribed, unknown displacements [ u k H ′ ], [ p k H ′ ] matrices obtained by carrying out the integrals over boundary and interface elements for prescribed, unknown tractions when considering inner points [ kk H ], [ kj H ] matrices obtained by carrying out the integrals over boundary and interface elements [ kk H ′ ], [ kj H ′ ] matrices obtained by carrying out the integrals over boundary and interface elements when considering internal points K c critical stress intensity factor l element size in the DIC analysis M point on the boundary and in the domain * ik p fundamental Kelvin's solutions for the tractions induced by a unit point load applied to a collocation point S on the external boundary k p boundary traction { k p }, { kj p } vectors containing the boundary and interface tractions } nodal displacements of internal points * ik u fundamental Kelvin's solutions for the displacements induced by a unit point load applied to a collocation point S on the external boundary

  ) and (3) have to be properly modified. Let us consider that the boundary value vector for the sub-region k remaining boundary values and the interface displacement and traction values are unknown and stored in } . All combinations between prescribed and unknown values at boundary nodes are allowed. Thus, a single node may have all boundary values either completely known, or totally unknown, or any other possible combination thereof. Subdividing the matrices in Equations (

  measured during the experiment at a certain number of internal points. It is important to stress that there is no relationship between the numbers of columns defined by the prescribed (p) and unknown (u) boundary values. The size of the boundary displacement unknown vector } { u k u is independent of that of the prescribed traction vector } { u k p . The minimum number of known boundary values is zero.

  ) is obtained but the displacement and traction vectors are modified accordingly to extract the boundary displacements and tractions of the two regions in addition to the interface values } contribution of the prescribed boundary values and the measured displacements are now stored in } { m p i v - and } { m p i w -. Thus, the final system reads

  correspond to the maximum values of the traction and crack opening displacement allowing for load transfer, respectively.

Figure 12 .

 12 Figure 12. The crack surface has been approximated by several straight paths. Therefore, small boundary fluctuations are "ironed out" and only the main corners are conserved to carry out this analysis.

law parameters are found c t f

 t = 860 kN / mm and ∆u c = 0.023 mm. With these values, the toughness becomes G c =

Figure 1 :

 1 Figure 1: Sub-domain discretization and internal points.

Figure 2 :

 2 Figure 2: Schematic view of the test and corresponding reference picture. Lengths are expressed in mm.

Figure 3 :

 3 Figure 3: Standard displacement uncertainty vs. element size. The symbols are data obtained with the a priori analysis, and the dashed line is a power law fit using Equation (12).

Figure 4 :

 4 Figure 4: Location of the two zones (dashed boxes) in the picture used to measure the displacement jump close to the notch.

Figure 5 :

 5 Figure 5: -a-Load versus notch opening. The squares depict when the pictures were shot. -b-Notch opening versus crack opening displacement measured by DIC. The straight line is a linear interpolation.

Figure 6 :

 6 Figure 6: Five horizontal displacement maps corresponding to crack propagation. The analyzed pictures are shown in the load versus notch opening plot. The physical size of one pixel is 54 µm. The picture number is defined in the load vs. notch opening plot.

Figure 7 :

 7 Figure 7: -a-Horizontal displacement of a picture after sample failure. The physical size of one pixel is 54 µm. -b-Crack surface determined from the 0-contour of the horizontal displacement (solid line). The dashed lines show the locations for which the displacement jumps are evaluated.

Figure 8 :

 8 Figure 8: Crack surface superimposed on the deformed picture used to determine the displacement map of Figure 7a. A good match is observed.

Figure 9 :

 9 Figure 9: Displacement jump along the crack surface as a function of picture number (Figure

Figure 10 :

 10 Figure 10: Beam discretization and internal point used to evaluate Young's modulus.

Figure 11 :

 11 Figure 11: Load displacement curve for the considered point (Figure 10) and the linear part used for the identification of Young's modulus.

Figure 12 :

 12 Figure 12: Region of interest. Boundary and crack surface discretizations, and inner nodes.

Figure 13 :

 13 Figure 13: Computed crack opening displacements for a given load level when the nodes are not allowed to interpenetrate.

Figure 14 :

 14 Figure 14: Computed tractions along the crack surface.

Figure 15 :

 15 Figure 15: Identified (solid symbols) and interpolated (solid line) crack opening displacements as a function of the corresponding tractions for the first cracked part

Figure 16 :

 16 Figure 16: Identified (solid symbols) and interpolated (solid line) crack opening displacements as a function of the corresponding tractions for the second cracked

Figure 17 :

 17 Figure 17: Identified (solid symbols) and interpolated (solid line) crack opening displacements as a function of the corresponding tractions for both cracked parts.

Figure 2 . 29 Figure 3 .

 2293 Figure 2.

Figure 4 .

 4 Figure 4.

Figure 11 .

 11 Figure 11.

Figure 12 .

 12 Figure 12.

Figure 17 .

 17 Figure 17.

Acknowledgments

This work was performed with the support of a FAPESP/CNRS project.


Abderazak Guettaf

Ahmed Bettka

Ouafae Bennis

Fateh Benchabane

Yahia Khaled

Arif Ali

Keywords: Wind energy system, Induction generator, Saturation, Induction motor, Direct filed oriented control

Direct field oriented control of induction motor fed by wind turbine generator under saturation effect

I. INTRODUCTION

s a result of increasing environmental concern, more and more electricity is generated from renewable energy. The main advantage of electricity generation from renewable sources is the absence of harmful emission and the infinite availability of the prime mover that is converted to electricity [START_REF] Slootweg | Dynamic modeling of a wind turbine with doubly fed induction generator[END_REF][START_REF] Rahima | Dynamic performance improvement of an isolated wind turbine induction generator[END_REF]. One of the best ways of generating electricity from renewable energy is to use wind turbines. A tendency to erect more and more wind turbines can be observed in power industry. Wind energy technology has developed extremely rapidly and many commercial wind turbines in the market have capacity of 2MW or more. Also the cost of windgeneration electricity has fallen steadily. Wind turbines in USA produce about 1% of total generation [START_REF] Rahima | Dynamic performance improvement of an isolated wind turbine induction generator[END_REF]. Also, wind power meets 3% of the total electricity demand in Europe [START_REF] Seyoum | The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine[END_REF], and this development will continue to grow in coming years. It seems that in the near future wind turbines may start to influence the behavior of electrical power systems. As a result of such developments, extensive research is being carried out on the subject of wind generation.

Self-excited induction generators are good candidates for wind powered electricity generation, especially in remote areas, because they do not need an external supply to produce the excitation magnetic field (emf). It is well known that when capacitors are connected across the stator terminals of an induction machine, driven by an external prime mover, voltage will be induced across its terminals. The induced emf and current in the stator will continue to grow until steady-state condition is reached [START_REF] Rahima | Dynamic performance improvement of an isolated wind turbine induction generator[END_REF][START_REF] Seyoum | The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine[END_REF]. However, self excitation has its own problems and can cause overvoltages, torque and machine speed fluctuations, etc. [START_REF] Seyoum | An insight into the dynamics of loaded and free running isolated self-excited induction generators[END_REF]. The impact of magnetizing inductance, minimum speed and capacitance requirement on self excitation has been examined by Seyoum [START_REF] Seyoum | An insight into the dynamics of loaded and free running isolated self-excited induction generators[END_REF]. The transient and steady state performance of self-excited isolated induction generators for different loading scenarios have been investigated and critical factors identified through various studies [START_REF] Rahima | Dynamic performance improvement of an isolated wind turbine induction generator[END_REF][START_REF] Wang | Dynamic performance of an isolated self-excited induction generator under various loading conditions[END_REF].

In this paper, we present a study of the vector control of an autonomous induction generator taking the saturation effects into account. The output voltage of the induction generator passes by the association rectifier -filterinverter for feeding a three phase induction motor. To use the induction machine in a reliable manner as an autonomous generator that converts wind energy, the machine has to be connected to a rectifier and all the system controlled. The control system is required to keep the DC voltage at a constant value whatever the rotor speed and the load as long as the available power of the wind is sufficient.

We show that the use of the oriented vector control presented in this paper leads us to feed the load with voltage of effective value and frequency fixed whatever the speed of turbine in a given speed range.

In section II, we propose a wind-turbine model. For the induction generator, it's a diphase model obtained by application of the Park transform. Assuming some simplifying hypotheses, the saturation effects is formulataed by a variable magnetizing inductance function of the current that we approximated by a polynomial function of 12th degree. This approach is simple and sufficiently accurate.

The third section concerns the control of the system. To control the flux in the induction machine and the DC voltage at the rectifier output, we use a rotor flux oriented vector control. The vector control algorithm consists of two parallel loops. The first one control the flux and leads to the d axis current reference and, by the same way, the reactive power flow in the system. The second loop control the DC voltage at the rectifier output and leads to the q-axis current reference. This permits the active power to flow from the generator to the DC circuit. In this system control, an additional level of complexity is introduced by the generator saturation. The induction motor (considered as a load of the rectifier) is controlled by a direct field oriented control.

The fourth section presents simulation results of the overall system, using the MATLAB -SIMULINK package.

II. THE TURBINE -GENERATOR SYSTEM MODEL

Fig. 1 shows the wind turbine induction generator system configuration considered in this study. The wind energy generation system consists of a horizontal axis turbine connected to a cage-machine rotor through a gear system. The induction machine is driven at super-synchronous speed and it feeds a constant impedance load at a terminal voltage, V s . The models for the different components of the wind turbine-generator system are given in the following subsections.

A Direct Field Oriented Control Of Induction Motor Fed By Wind Turbine Generator Under Saturation Effect

A. Wind turbine model

The output power of a wind turbine is a complex relationship involving the wind speed (Vw), expressed as [START_REF] Abdin | Control design and dynamic performance analysis of a wind turbine-induction generator unit[END_REF][START_REF] Causebrook | Fault ride-through of large wind farms using dynamic breaking resistors[END_REF]:

3 m p w 1 P A.C .V 2  (1)
 is the air density, A is the swept area by the blades. The power coefficient Cp is a function of the tip speed ratio, , which is the ratio of linear speed at the tip of blades to the speed of wind, expressed as

w R V   (2)
R is the radius,  is the mechanical angular velocity, respectively, of the wind turbine rotor. Expressions of Cp as a function of  employed in [START_REF] Chompoo-Inwai | Reactive compensation techniques to improve the ride-through of induction generators during disturbance[END_REF][START_REF] Karari | Comprehensive control strategy for a variable speed cage machine wind generator unit[END_REF] are:

                    
Typical Cp-- curves for the pitch angle equal zero as shown in Fig. 2. Fig. 3 shows the power-speed characteristics curves of a typical wind turbine for various wind velocities.

B. Induction machine model

The linear model of the induction machine is widely known and used. It leads to relative accurate results when the operating point studied is close to the conditions of the model parameter identification. It's offen the case when studying the motor, operating at rated voltage. As the air gap of induction machines is generally narrow, the saturation effect is not negligible in this structure. So, to improve the accuracy of simulation studies, especially when the voltage is variable, the non-linearity of the iron has to be taken into account in the machine model.

This becomes a necessary condition to study an autonomous induction generator because the linear model is not able to describe the behaviour of the system. Thus, only approaches that take account the saturation effect can be utilised. This effect is not easy to simulate using three phase classical models. So, we adopt diphase approaches to take account globally of the magnetic non-linearity. This needs some simplifying hypotheses. Indeed, the induction is considered homogenous in the whole structure. Moreover, the use of the diphase model supposes that the saturation effect is considered only on the first harmonics and does not affect the sinusoidal behaviour of the variables. In our approach, we adopt the diphase model of the induction machine expressed in the stator frame. The classical electrical equations are written, in the synchronous frame, as follows [START_REF] Idjdarene | Vector control of autonomous induction generator taking saturation effect into account[END_REF][START_REF] Rekioua | An approach for the modeling of an autonomous induction generator taking into account the saturation effect[END_REF]

i V R .l 0 .l i V .l R .l 0 . i R .l R .(l l ) 0 .l R .(l l ) R i 0 i .i i l 0 l l l i i i .i i 0 l l l l i i l 0 l L L                                                   sd sq 2 md m d m q ' ' md m m m mq 2 m d m q ' ' md r m r m m m m di dt di dt . ( 4
) di i .i i l dt i i di i .i i 0 l l l L L dt i i                                                      
Where R s , l s , R r and l r are the stator and rotor phase resistances and leakage inductances, respectively, L m is the magnetizing inductance and  s and  r are the stator and rotor pulsations, respectively. Besides, V sd , i sd ,V sq and i sq are the d-q stator voltages and currents, respectively. i md and i mq are the magnetizing currents, along the d-and q-axis, respectively, given by m d sd rd m q sq rq i i i

i i i        (5)
ird and irq represent the d-q rotor currents.

The saturation effect is taken into account by the expression of the magnetizing inductance Lm with respect to the magnetizing current im defined as

22 m md mq i i i  (6)
To express Lm with respect to im, we use a polynomial approximation of degree 12 [START_REF] Farret | State space modeling of parallel self-excited induction generators for wind farm simulation[END_REF][START_REF] Seyoum | Terminal voltage control of a wind turbine driven isolated induction generator using stator oriented field control[END_REF].

n j m m j m j0 n j1 ' m m m j m mm j0 l f ( i ) a . i dL d l f ( i ) a . i d i d i                 (7)

C. Study of an induction generator connected to a capacitance bank

The stator windings of the induction machine are linked to a capacitance bank connected in parallel to a resistive load (Fig. 1).

As the stator and rotor pulsations are unknown, it is necessary to re-write the electrical equations in the rotor frame where only the mechanical pulsation, known, is considered. In this case, with no load, the diphase stator voltages and currents are linked by the following expression:

sd sd sd sq sq sq 1 0 V i V 0 d c .. V i V 10 dt 0 c                                 (8)
which becomes, when the induction generator is loaded:

sd sd chd sd sq sq chq sq 1 0 V i i V 0 d c .. V i i V 10 dt 0 c                                 (9)

III. THE PROPOSED CONTOL STRATEGY

A. Control strategy of Wind turbine-generator system

To lead to a generated voltage with a constant magnitude and frequency, the induction machine must be connected to a rectifier and an inverter. Both have to be controlled. In this part, we will study the vector control of the system consisting of a wind turbine, an induction generator, a PWM rectifier and a PWM inverter (Fig. 5). The goal of the control is to maintain the DC bus voltage at a constant value when the rotor speed is varying. To control the flux in the generator and the DC voltage at the rectifier output, we use a rotor flux oriented vector control.

The vector control algorithm consists of two loops that operate in parallel (Fig. 6). The first one allows us to control the flux and leads to the d-axis current reference. It controls, by the same way, the reactive power flow in the system. The second loop enables us to control the DC voltage at the rectifier output and then to reach the q-axis current reference. This permits the active power to flow from the generator to the DC circuit. In this system control, an additional level of complexity is introduced by the saturation of the generator. We will show that the control of the flux implies a constant saturation level of the generator and, then, leads to a model of the machine, which becomes linear at an operating point. The flux variations around this point are negligible.

B. Direct Field Oriented Control of Induction Motor

For the induction machine, we adopt the following model, developed in the synchronous reference frame ( , dq ) with rd 0  [START_REF] Yahia | Indirect vector control of induction motor with on line rotor resistance identification[END_REF][START_REF] Rui | Flux and Parameters Identification of Vector-Controlled Induction Motor in the Reference Frame[END_REF] From equations ( 11) to [START_REF] Farret | State space modeling of parallel self-excited induction generators for wind farm simulation[END_REF], and after some steps of calculation, one can find the parameters integral and proportional of the IP controller as [START_REF] Yahia | Indirect vector control of induction motor with on line rotor resistance identification[END_REF][START_REF] Rui | Flux and Parameters Identification of Vector-Controlled Induction Motor in the Reference Frame[END_REF]:

u ( R s L ) I s L I L L u ( R s L ) I L I L L I 1s L I 3p L CI 2L                                      (10) With:
2 n i t n p t J K K (2 J B ) K K            (14)

IV. SIMULATION RESULTS

A. Simulation Results of Wind turbine-generator system

The simulation conditions are given in the appendix. Simulation results using the vector control strategy with different cases are given. Both the inverter and rectifier are modeled in the same way. The switches are considered as ideal, and their states are given by logical functions that take value 1 when the component is closed and 0 when it is open.

First, the rotor speed of the induction machine is increased till the synchronous speed. Once this last is reached, the flux and Vdc reference values are applied. These are: . The DC voltage regulation is obtained using the proposed vector control algorithm. In Fig. 17, we can see the stator voltage waveform. The increase of the rotor speed implies an increase of the voltage. Fig [START_REF] Idjdarene | Vector control of autonomous induction generator taking saturation effect into account[END_REF] presents the a, b, c currents and the DC voltage is presented in fig [START_REF] Rekioua | An approach for the modeling of an autonomous induction generator taking into account the saturation effect[END_REF], we can see that the generated voltage reache the reference one with high precision. The DC voltage is controlled with the torque via the current isq.

B. Simulation Results of Direct Field Oriented Control Of Induction Motor

Simulations using Matlab-Simulink software package have been carried out to verify the effectiveness of the proposed IM indirect field oriented control.

The induction motor used for the simulation studies has the following parameters: Type: three-phase, 0.75kW, 220/380V, squirrel-cage induction motor.

            
The validity of the control scheme is demonstrated through the results shown in figure 12.

Fig 12 shows the step response of speed at 10 sec and with 12 sec a time rating load 5Nm. We can notice the good performances of the control; the real speed converges to the reference one with a high precision. The electromagnetic torque allure is presented, it can concluded that the electromagnetic torque developed by the motor increased at t =12 sec to 5 Nm for compensate the load torque. The d q rotor fluxes, this figure demonstrates the perfect decoupling between the d and q axis. The d stator current conserved a constant value while q stator current followed the increasing and the decreasing of electromagnetic torque. These results demonstrate the good performances of the regulation. V. CONCLUSION

In this paper, the vector control of an induction generator used in an autonomous speed wind system is presented. An analytical model of the autonomous induction generator, taking the saturation effects into account by means of a variable magnetizing inductance has been presented. This magnetizing inductance is expressed, using a polynomial function of degree 12, as a function of the magnetizing current.

The diphase model of the induction machine enabled us to define a vector control for the generator operation of this machine. As the flux is maintained at a constant value, the machine model can be considered linear around an operating point. Then, the adjustment of the torque is independent of the flux. This avoids having a complex algorithm of control when taking into account saturation.

This control enables us to maintain the saturation level of the generator constant and to control the DC voltage through the torque in the same way as it was done for the motor operation. Finally, the use of the control leads us to feed the load with voltage of effective value and frequency fixed whatever the speed of the turbine.

The direct vector control of the induction motor used as charge presents a good performance of regulation of speed. We can say that the associations of the wind turbine and induction generator permits feeding the induction motor with a sufficient voltage and frequency.

Fig. 1 .

 1 Fig.1. Wind turbine-generator system

Fig. 2 .

 2 Fig.2. Typical power coefficienttip speed ratio plot.

Fig. 3 .

 3 Fig.3. Speed Vs. power output characteristics of a wind turbine.

  :

Fig 4 ,

 4 Fig 4, presents magnetizing inductance function of the magnetizing current. This figure demonstrates the non linearity nature of the induction generator.

Fig. 4 .

 4 Fig.4. Lm -magnetising current.

Fig. 5 .

 5 Fig.5. Scheme of the system studied.

Fig. 6 .

 6 Fig.6. Structure of the vector control scheme.

  :

=

   -axis  -axis stator current rr ,   =  -axis  -axis rotor flux ss v , v  =  -axis  -axis stator voltage The block diagram of the direct field-oriented induction motor drive system is shown in fig 7.This can be obviously represented by the control system block shown in fig.8, in witch () =natural frequency.

Fig. 9 .

 9 Fig.9. stator voltage Vabc.

Fig. 10 .

 10 Fig.10. stator current iabc..

Fig. 11 .

 11 Fig.11. DC voltage Vde.

Fig. 7 .

 7 Fig.7. Direct field -oriented control of an induction motor.

Fig. 8 .

 8 Fig.8. Speed control system block with IP controller.

Fig. 12 .

 12 Fig.12. Drive response of induction motor under load disturbanse.

  VI. APPENDIXParameters of the system used in simulation: Parameters of the turbine:

  Parameters of the IM: Type: tree-phase, 4Kw. 220/380V, squirrel-cage induction motor. Parameters of the PWM converter: Supply's voltage and frequency: 220 V(rms), 50 Hz Line's inductor and resistance 0.002 H, 0.08 Ω Output capacitors 0.0025 F PWM carrier frequency 1 kHz

GEB Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria

PRISME Institute, University of Orléans, 21 rue Loigny La Bataille, 28000 Chartres, France

MSE Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria


Virginie ; Dejoux
email: virginie.dejoux@inrets.fr

Jimmy Armoogum
email: jimmy.armoogum@inrets.fr

Inrets -Dest

Cridup

Armoogum Jimmy

Mobility barrier for disabled people

The aim of this paper is to understand why people with disabilities travel less than people with any difficulty and why they use different transport modes. For that, we had a quantitative and qualitative approach. Our research is based on the National Travel Survey (NTS) that was conducted in France in 2007-2008. Secondly, and to provide in-depth elements for the understanding of situations faced by disabled people, we carried out fifty semi-structured interviews with people who may be experienced difficulties when travelling. We will try to detect difficulties that people may face when they are travelling, by observing separately each mode: walking, car, public and specialized transport.

INTRODUCTION

Currently, a situation of handicap is defined as not being able to have a normal life, resulting from the interaction between personal factors and environmental factors [START_REF] Fougeyrollas | Classification québécoise processus de production du handicap[END_REF]OMS, 2001). Previous studies have shown that people with disabilities travel less, make shorter trips, and use different modes than the other [START_REF] Dejoux | The travel practices of disabled travellers in France, 89th Annual meeting of Transportation Research Board[END_REF][START_REF] Bakker | Each trip count. Understanding travel behaviour of people with travel-behaviour of people with travel-impeding handicap[END_REF][START_REF] Hauet | Handicap, gênes ou difficultés ressentis par les personnes dans le cadre de leurs déplacements en dehors du domicile[END_REF][START_REF] Madre | Comment se déplacent les personnes âgées et/ou handicapées ?[END_REF]. This paper should help to understand these differences. For that, we used both a quantitative and qualitative approaches.

The first part of our work is based on the French National Travel Survey (NTS) that was conducted in France in [START_REF] Rocci | Thèse de doctorat : De l'automobilité à la multimodalité ? analyse sociologique des freins et leviers au changement de comportements vers une réduction de l'usage de la voiture[END_REF]-2008[START_REF] Bibliography Armoogum | Préparer la prochaine Enquête Nationale Transport avec un regard international[END_REF]. The Main purpose of this survey is to measure the mobility of people living in France. It allows the study of travel practice and use of personal and public transport modes. With a sample size of about 20,000 respondents households, it consider all trips whatever their purpose, length, duration, transport mode, the period of year or time of day. From this survey, we will detect the difference in term of transport modes for people with and without difficulties when they are travelling. However, the quantitative approach doesn't allow us to detect the specific difficulties encountered by people. Therefore, we have completed our research with a qualitative approach.

The purpose of using a qualitative method is to provide in-depth elements for the understanding of situations faced by disabled people. In the qualitative approach, the individual is seen in its entirety, practices are placed in their context. It is a detailed analysis of individual behaviour, differing, from the quantitative approach that seeks to reduce in groups [START_REF] Blanchet | L'enquête et ses méthodes:l'entretien[END_REF][START_REF] Rocci | Thèse de doctorat : De l'automobilité à la multimodalité ? analyse sociologique des freins et leviers au changement de comportements vers une réduction de l'usage de la voiture[END_REF]. Within our study, we used this qualitative approach with two main objectives: first to improve the knowledge of people with difficulties when they are travelling and to detect environmental factors (physical or social) that make it easier or on the opposite create barriers to mobility of people. We will focus in this paper on the difficulties related to the physical environment encountered by people during their mobility.

We thus carried out about fifty semi-structured interviews with people who may be experiencing difficulties when they make trips, in two French regions: Ile-de-France and Loire Atlantique. The Ile de France, with 11 million of inhabitants with an extensive system of public transport is the highest urbanized area in France; but with significant difference in availability and accessibility by area of residence. In addition, a service transportation on demand (door to door) is available in six of the eight departments. Our second area of study has a population density much lower and public transport or specialized transportation services are infrequent in rural areas. This second field of study enabled us to compare an urbanized and a rural area, with different level of access to public transport or transportation on demand, but also where places of work may be located away from home.

According to the French NTS, in 2007, about 10% of the population over 15 years (i.e. 5.1 million individuals) reported some difficulties when they make trips. In the French NTS we can identify three levels of travel difficulties: simple difficulties, limitations on certain itinerary and limitations on all itineraries. We know that people with difficulties travel less than people without (about 1.8 trips per day per person for people with difficulties against 3.4 for people without any difficulty) and we can see in the table below that their distributions of main transport modes are different (Table 1). We find that about 33% of the trips made by people reporting some difficulties are walking trips or in a wheelchair. For people reporting th WCTR, July 11-15, 2010 -Lisbon, Portugal 3 any difficulty this figure is 19%. Therefore, people with difficulties seem to walk more than those without, this confirm the papers of [START_REF] Hopkin | The Mobility of Old People: A Study in Guildford[END_REF][START_REF] Pieters | Count for pedestrians[END_REF]. Furthermore, even if cars accounted for a smaller share of all the trips made by people reporting some difficulties (58 % compared with 68 %), the share of car passengers was higher. Finally, the share of trips made by public transport is lower, while reasonably those made in specialized transportation are in greater numbers. The objective of this paper is to detect travel difficulties encountered by people, that lead to a lower level of mobility and some preference/reluctance for certain modes. For this, we now present the difficulties encountered for each mode.

1-DIFFICULTIES ENCOUNTERED WHEN WALKING

As we have said, people reporting difficulties make more walking or in wheelchair trips, which concerns 33% of their trips (against 19% for others). Several hypotheses could explain this difference: disabled people makes shorter trips, closer to their home, or the other transport modes are not accessible for them, encouraging them to walk only. Difficulties encountered for other transport modes will be discussed later in this paper.

However, many complains of walking or in a wheelchair trips were cited during the interviews. The obstacles on pavements are the first difficulties of walking or in a wheelchair trips, according to people affected by a motor or visual impairment. Various obstacles on the sidewalks, like garbage cans, poles, mailboxes, billboard, coffee tables, cars, bicycles or motorcycles parked badly...can lead to difficulties when travelling. People with visual impairments do not always identify these obstacles, and can bump into them or have difficulties to get round them. People with motor impairments, also mention the problems of obstacles on the sidewalk, making passage in wheelchairs or with crutches difficult or impossible. George, who is 54 years old and suffering from poliomyelitis, explains: "When I am on the sidewalk, we have all problems that everyone can meet. Cars parked on the curbs, works which are not indicated. So it forces us to skirt around the block, or people who dump th WCTR, July 11-15, 2010 -Lisbon, Portugal 4 cumbersome on the sidewalks… you find oneself with a mattress on the sidewalk and how you go through with a wheelchair".

The other difficulties for walking seem more specific to the type of impairment of the person.

For example, the visually impaired cite the lack of contrast of sidewalks, steps, poles... because it makes their identification difficult or impossible for them. These persons may also experience difficulties to check out a location: either because of difficulty for reading the names and numbers of the streets, or because they are too high and / or written too small, or the writing have not enough contrast with the bottom road sign; but also in intersections or roundabouts complicated, especially because of the noise. Indeed, people with visual impairments can take mark through various noises (cars travelling or stationary, pedestrian crossing, works ...). If these mark are too numerous or too intense, from too many sources, check out may be more difficult.

Those declaring a motor impairment cite other difficulties for their mobility, specially the configuration of the sidewalks (which may be related to design or wear): holes, bumps, slopes, cobblestones, lack of curb… as Eloise, who have the multiple sclerosis states: "with a manual wheelchair it is impossible to travel alone, because of banked sidewalks or there are sometimes no curb to go down the sidewalks. So we arrive at the end of the sidewalk and then we must go look for another curb elsewhere...and sometimes to be on the road".

Apart from the difficulties encountered during the trips on the sidewalk, some other difficulties are mentioned by respondents: the crowd, the rain or breakdown of the electric wheelchair.

Through interviews we can see that the difficulties mentioned by people when walking or using wheelchairs, are strongly linked with obstacles (trash can, badly parked cars ...) and configuration of streets and sidewalks ( slopes, holes, bumps, lack of contrast ...). Indeed, feeling safe is an important point for mobility of people with impairment [START_REF] Carreno | Which aspects are most important for elderly and mobility-impaired pedestrians[END_REF]. The implementation of a new law should reduce the barriers faced by these people (in France, since February 2005 we had the law on equal opportunities, participation and citizenship of people with disabilities). However, its application, which applies only to new roads or upgrading roads, may be long. And a part of learning and civility of the whole population is needed to overcome some obstacles, such as vehicles parked on sidewalks or pedestrian crossings.

2-CAR, SYNONYMOUS WITH FREEDOM

According to NTS in 2007, while 83 % of the French population aged 18 or over have a driver's license it is the case for only 59 % of people reporting difficulties in their mobility.

Several hypotheses can then be formulated:

-People who declare difficulties when they are making trips may have severe impairments; their health does not allow them to pass the driving license. This hypothesis is confirmed through qualitative interviews, where people do not have the driver's license have often cited the inability to pass as a reason for non-possession. th WCTR, July 11-15, 2010 -Lisbon, Portugal

5

-We know that age has an influence on the discomfort, we might wonder if the share of ownership of the driving license is also influenced by a generational effect, to the extent previously, the shares of each generation to get the license was lower especially for women.

-Finally, we can also think that do not own a driving license is a source of embarrassment: Driving a car allows go where you want, when you want. The car is often perceived as a facilitator in terms of mobility. Do not own and therefore do not drive a car can lead to the feeling of embarrassment. This hypothesis has been validated through the speech of people. The car seems to bring freedom, autonomy and ease mobility. Indeed, the loss of freedom and autonomy in the case of stop of driving is mainly cited during the interviews [START_REF] Espinasse | la phase d'étude qualitative approfondie auprès : 1) D'aidants naturels à la mobilité[END_REF],.

If we look only to the owners of driving license, we find that the most limited during their mobility drive less than those reporting a level of discomfort lower (Graph 1). While about 96% of people do not declare themselves embarrassed when driving a car (regularly or occasionally), it is the case for only 62 % of people restricted to certain routes and 21 % of those unable to travel alone. It seems that the reasons for stopping driving a car are therefore more related to a choice among those reporting no discomfort during their mobility. These people, because they do not like to drive, prefer to use another mode of transport but probably not feel penalized in their mobility. Conversely, those forced to stop to drive because they can no longer, could feel a restriction in their mobility.

Whether you use a car as a driver or a passenger, the main problem mentioned in the interviews are the parking spaces reserved for people with disabilities, as Christian explains :

"it is the reserved parking taken by others, it is the lack of parking spaces, these reserved spaces that are not well built or not properly indicated or are unknown".

Apart from the parking spaces, few difficulties concerning the use of the car were cited during the interviews. Thus, people who can not drive or own a car may report some discomfort for their mobility, since a car can be seen as a facilitator of mobility.

3-URBAN TRANSPORT

According to the NTS, in France, during the last 12 months, 42% of people without difficulty used public transport for travels of less than 100km around the home, against only 27% of people with difficulties. According to the same survey, while 67% of people without difficulty do not use public transport because they do not need, this reason is mentioned by less than half of those with difficulties (Table 2). We note then that nearly one quarter of these people to cite their health problem as a reason for not using public transit. Thus it seems that people can not use public transport because of a disparity between their disability in terms of mobility and the accessibility of public transport. The interviews allowed us to go further in the analysis and to detect the problems and barriers that were encountered by them in public transport. The difficulties can be revealed to several sequences of a trip [START_REF] Nicollet | L'accessibilité des transports collectifs aux personnes handicapées ou à mobilité réduite -une approche globale[END_REF]:

-at the level of information required, whether before the trip, to prepare the trip, or during the trip to find its location, delays ... -at the level of booking tickets.

-at the level of access to stations and vehicles, for example, the get on or the get off the vehicle, security inside ... The transport situations involve 3 types of abilities: ambulation, prehension and communication [START_REF] Dejeammes | Personnes à mobilité réduite et transports urbains[END_REF](Dejeammes et al., et 1988)). The disabilities of people being strongly differentiated by type of impairment; it is the same for necessary adaptation to the transport system.

Difficulties of people with visual impairments:

The difficulties cited by people with visual impairments are related to the access to information at stations or in vehicles and the use of booking systems, purchasing tickets. Whether the numbers of bus or tram, the names of stops, schedules and platforms, or signs indicating the direction to take when changing mode, people with impaired vision can not read properly. According to these people, these signs are written either too small or too high or too far away from them or with a colour that do not allow optimal contrast. Paul who is myopic since birth said: "I see the bus number just at the bus stop, I can not read before. And what is annoying, is where there are several lines, I never know the bus which arrive". People, especially the blind also cite the lack of voice announcement.

Another difficulty in the speeches of respondents is the booking and ticket sales, in particular due to the development of ATMs. This difficulty could be offset by the help of staff, but a lack of training and of knowledge seems to limit this help, as Jerome explain to us: he wanted to buy a ticket and the staff said "no, sir we do not no longer issued ticket, you must go to the ATMs"; and when he said that he was visually impaired, the staff of Transportation asked him "to go to the next station".

Difficulties of people with motor impairments:

The main problems cited by people with motor disabilities in public transport concern access to stations and vehicles, and particularly for people in wheelchairs. The problems identified the access to vehicles are:

-the failure of lifts and pallet systems -the lack of knowledge of these systems by drivers

Difficulties of people with hearing impairment

People with hearing impairment reported few difficulties in transportation. However, they wanted more visual signs, especially in case of problems (breakdowns, strikes, the need for evacuation ...). As Marie explain to us, deaf after an illness, "In the subway actually there are problems when there are strikes or accidents because I can't hear any message, so I must ask people to explain to me: what is going on."

The interviews have shown that the difficulties experienced in public transport depend greatly on the type of impairment and disability. Beyond accessibility, knowledge and attitudes of the staff of transport services is important [START_REF] Morris | Attitudes of transit personnel and public transit consumers toward public transportation accessibility[END_REF].

4-SPECIALIZED TRANSPORT

Specialized transport is a door to door service on demand, for people who have difficulty for their displacement. It is reserved for people holding a disability card (but not all regions in France have this service). A large proportion of people affected by a function of locomotion used this transportation system (Dejeammes et al., 1988) During our interviews, the most often complexity mentioned on the special transport services for people with difficulties for their trip, is the booking system. Indeed, the principle of this system is based on the fact that people wishing to go out book their transport by phone a few days before. But the demand seems to be high, this booking period can reach one or several weeks. So people can not decide when they want to go out, there is no spontaneity, everything must be planned well in advance. for example with "PAM3 , you need to plan your trip at least a week in advance. If you want to go to the museum today, it is impossible, you have to wait a week" (according to Julien)

The second difficulty cited by people for the use of specialized transport is the time constraints: for example, it seems to be given priority at certain hours for people going to work. This service manages all trips and the desired schedules are not always possible and may not always be respected, sometimes resulting in some delays or advances. Moreover, it is not always easy for anyone to predict the time at which the activity will end (for example, for a medical appointment). A lack of autonomy may then be again felt : Frédérique who regularly use the service said "the constraint is the time to return back, that's clear. Because having an appointment is easy, but to know at what time it will ends is much more complicated".

In conclusion, the lack of freedom seems to be the greatest difficulty for people who use specialized transport: firstly it is necessary to book several days before we need it, spontaneity is then not being allowed, and secondly according to the purpose of the trips it is very difficult or impossible to get this service at certain periods of the day.

5-CONCLUSION

Quantitative surveys are worthy methodology to have good pictures of the population with difficulties to travel, for instance to have the figures of the share of the population with and without difficulties to travel, etc… The last French National Travel Survey shows that people with difficulties travel less and use different modes of transport than those without difficulty. However, this survey do not give the reason why the mobility is lower for people with difficulties and therefore do not help to understand the difficulties encountered by these people.

With the qualitative approach we have seen: the difficulties encountered are different by modes of transport and depending impairments. During walking and in wheelchair trips people report more difficulties of inaccessibility of pavements, stops, vehicles...While by car and specialized transport, the lack of freedom and autonomy are mentioned.

In this paper we have studied the difficulties in different transport modes, but we should not forgot that access to home, to work or for others activities the social environment plays an important role in the formation or not of a handicap

Graph 1 :

 1 Driving according to the level of reported difficulties

Table 1

 1 Breakdown of the principal transport modes used by people with travel difficulties and those without.

	Main modes of transport	People reporting any difficulty	People reporting some difficulties	Whole population
	Walk	19.2%	33.1%	20.0%
	Including wheelchair	0%	1.4%	0.1%
	Two wheels	4.3%	1.8v	4.1%
	Car	68.3%	57.5%	67.7%
	Including car driver	60.1%	44.0%	59.3%
	Including car passenger	8.2%	13.5%	8.4%
	Urban transport	7.0%	5.2%	6.9%
	Including bus and tramway	3.0%	3.2%	3.0%
	Including subway,RER	3.5%	1.3%	3.4%
	Others	1.2%	2.4%	1.3%
	Including specialized transport	0%	1.9%	0.1%
	Total	100%	100%	100%
	Sources: INSEE -NTS 2007-08

Table 2

 2 Reasons for not using public transport for people reporting difficulties during their mobility and without any difficulty.

	Reasons not to use public transport	People reporting any difficulty (%)	People reporting difficulties (%)	Whole population (%)
	There is none, can not go where you want to	28.5	20.3	27.5
	very infrequent	5.3	3.2	5.0
	Too far	5.7	6.2	5.8
	Too slow or too uncomfortable	2.3	3.1	2.4
	Too expensive	2.7	3.1	2.7
	No usefulness	66.9	49.3	64.7
	Others, including	5.2	31.5	8.4
	health issues	0.3	23.4	3.2
	Sources: INSEE -NTS 2007-08
	Several possible answers

th WCTR, July 11-15, 2010 -Lisbon, Portugal

DEJOUX, Virginie; ARMOOGUM, Jimmy

PAM : Paris Accompagnement Mobilité is the specialized transport service in Ile de France


Roux Sophie
email: sophie.roux@inrets.fr

Armoogum Jimmy
email: jimmy.armoogum@inrets.fr

Analysis of biases due to survey non response in the French National

Keywords: Survey, Nonresponse, bias, Calibration on margins

While nonresponse results in a reduced sample size, a more important concern of researchers is the possible impact of nonresponse bias. Bias is introduced when those that do not respond to the inquiry are systematically different from those that do respond on key estimates. In this circumstance, as the above section describes, the response mechanism is "confounded" with characteristics of the sample units. For example, if nonrespondents tended to take more trips, or longer trips than respondents, the estimates of travel produced from only survey respondents will be too low and not representative of the whole population (only those that responded). Getting the advantage that for the last French National Travel Survey (FNTS) 2007-2008 the sample was drawn directly from the census and the list of new residences built since the census, and therefore we have lots of information about respondent and non-respondent to the different survey instruments in the FNTS. We will quantify these biases by using auxiliary information in different calibration that we will produce.

INTRODUCTION

All surveys are susceptible to a variety of types of error that affect different parts of the survey process, have different implications for data quality and are amenable to different forms of prevention or compensation [START_REF] Groves | Survey Errors and Survey Costs[END_REF][START_REF] Richardson | Survey Methods for Transport Planning[END_REF][START_REF] Zimowski | Nonresponse in Household Travel Surveys[END_REF]. Nonresponse errors are those generally associated with the failure of sample units to participate fully in the survey. It is usual to distinguish two different forms of nonresponse.

 Unit nonresponse refers to the failure of a unit in the sample frame to participate in the survey. In the context of travel diary surveys, unit nonresponse can arise for a number of different reasons including refusal, non-contact, infirmity or temporary absence (see, e.g., Brög andMeyburg, 1980, Kim et al., 1993;[START_REF] Richardson | Non-response effects in mail-back travel surveys[END_REF][START_REF] Stopher | Blow up: Expanding a complex random sample travel survey[END_REF][START_REF] Thakuriah | Non-response bias and trip generation models[END_REF].

 Item nonresponse refers to the failure to obtain complete information from a participating unit. In the context of travel diary surveys, the most significant form of item nonresponse is probably the under reporting of mobility due to respondents" failure to properly recall and/or record all the relevant journeys that they make (see, e.g., [START_REF] Ampt | The validity of self-completion surveys for collecting travel behaviour data[END_REF][START_REF] Brög | Considerations of non-response effects on large scale mobility surveys[END_REF][START_REF] Brög | Problems of non-reported trips in surveys of nonhome activity patterns[END_REF][START_REF] Hassounah | Underreporting of trips in telephone interview surveys[END_REF]. Item nonresponse can be regarded as a particular form of the more general problem of measurement error in survey research [START_REF] Groves | Survey Errors and Survey Costs[END_REF].

There is no justification for assuming that people who respond have the same characteristics as those who do not [START_REF] Forsman | The Impact of Nonresponse and Weighting in a Swedish Travel Survey[END_REF]. Thus, in computing estimates from the available data collected, we may face biases, whose size and direction of error are unknown. In order to show how these non-response problems can be solved, we will take as an example the daily trips in the French National Travel Survey 2007-08. Most of these solutions are rather general, but some aspects are specific to this case as the sample is drawn from the census, which allows the characterization of the households that refused to answer.

THE FRENCH NATIONAL TRAVEL SURVEY2007-08

Once per decade, the Ministry of Transport and the National Institute of Statistics use to conducting a National Household Travel Survey with the scientific support of INRETS. It is the data source providing the most transverse and consistent overview of mobility, whatever the modes and the transport situations of people living in France may be. The aim of the French National Travel survey is the description of short and long distance trips made by households living in France, as well as their access to and use of public and private transport means.

Six survey instruments were used:

1.

During the first visit a CAPI questionnaire is designed to collect at household level (including household members) the socio-demographic variables, characteristics of commuting trips to work, school or kindergarten; driving licenses and car use, traffic accidents; season tickets and discounts in public transport; description of vehicles available in the household and the housing environment; 2.

A 7 days vehicle diary is attributed to one of the household's vehicles (selected with unequal probability distribution to give more chance to be drawn to motor two wheelers, which are particularly interesting on the point of view of road safety) to be filled by the vehicle users; 3.

During the second visit, for one person above 6 years old, selected with unequal probability distribution giving more chance to highly mobile persons (within each households), is asked to describe her/his long distance trips made during the last three months (as recalled from memory); 4.

The same person was asked to describe her/his trips made one weekday before the interview, and one weekend day (either Saturday or Sunday); 5.

A sub-sample of approximately 1 100 individuals was asked to fill a biographical grid in order to describe the transport means used throughout their whole past life; 6.

A sub-sample of approximately 750 volunteers took a GPS receiver. th WCTR, July 11-15, 2010 -Lisbon, Portugal 4 A sample size of about 30,000 dwellings (including 5 regional add-ons) was selected in the 1999 census and the list of new residences built since the census. The sample was spread over six waves covering 12 months, in order to neutralize the seasonal variations which affects mobility (especially for long distance travel). Although the majority of residences in our sample are the main residence of a household, this is not always the case: among the 30 165 dwellings visited, 4 272 (14%) were out of the scope (vacant housing, second or occasional homes). Among the 25 893 selected households in the scope, 7 261 (28%) of them refused to respond to the 2nd visit of the survey.

THE RESPONSE MECHANISM

Among the 22 724 dwellings that were main household dwellings in the 1999 French census, we have some useful information allowing us to find out the probability for a household to respond to the survey, this is usually called the response mechanism. We built a logit model to detect the response mechanism because logit modeling shows the influence of each dimension "everything being equal in other respects". Although the household living in the selected dwelling could be different from those who lived there in 1999 (at the moment of the census), we consider them as equivalent. We compute the following variables for the response mechanism:  Zone of residence (people living in rural areas, people living in conurbation of less than 20 000 inhabitants, people living in conurbation from 20 000 to 100 000; people living in conurbation from 100 000 to Paris region; Paris conurbation);  Building belonging to the municipality with « low rents lodging »(yes; no);  Type of dwelling (house and farm ; others types);  Dwelling with/without interphone (house; apartment with interphone; apartment without interphone);  Number of rooms of the dwelling (0-1 room ; 2-3 rooms ; 4-5 rooms ; 6 rooms and more);  Surface of the dwelling (less than 40m²; from 40 to 70 m²; from 70 to100 m²;from 100 to 150 m² ; more than 150 m²);  Size of the household at the 1999 census (1 person; 2 persons; 3 persons; 4 persons and more);  Age of the head of the household at the 1999 census (from 15 to 34 years old; from 35 to 49 years old; from 50 to 64 years old; from 65 years old and more);  Gender of the head of the household at the 1999 census (male; female);  Household car fleet at the 1999 census (0 car, 1 car ; 2 cars and more);  Wave of survey (May -June 2007;July -August 2007;September -October 2007;November -December 2007;January -February 2008;March -April 2008). We computed a global significance analysis of the variables used in the Logit model, following the methodology in [START_REF] Gourieroux | Econometrics of Qualitative Dependent Variables[END_REF], as the difference -2LogL-(-2LogL0) follows asymptotically a Chi-2 law. Among the variables we had with the census, the zone of residence, the wave of survey, the age of the head of the household at the census, the household car fleet at the census, and the number of rooms of the dwelling play a major role in the response mechanism. The other variables such as the building belonging to the municipality with « low rents lodging », the type of dwelling, the surface of the dwelling, the dwelling with/without interphone, the gender of the head of the household at the 1999 census, and the size of the household at the 1999 census are correlated with the probability to respond or not respond to the survey but adding them in the model do not add significant information (see The odds ratio indicate the probability of the interviewees to be non-respondent by zone of residence, wave of survey, age of the household, household car fleet and number of rooms of the dwelling at the 1999 census.  Failures are more often in densely populated conurbations, indeed households living in densely area have an higher probability to be non-respondent than those living in rural areas;

 Failures are more frequent during summer, a period during which we assume that households are more mobile (holidays,…). The risk to be non-respondent is 1.2 times higher among the households surveyed in July and August 2007 than among those surveyed in March and April 2008.  Failure rates are higher for households whose head is under 35 years and for those whose head is over 65 years. When the heads of households is aged from 35 to 65, we have a reduced risk of nonresponse compared to those aged 65 year old or those younger than 35. Most likely for different reasons, for the first group it emphasizes the difficulty for interviewer to reach these households and for the second group for the reluctance of older people to answer to long and burdensome questionnaire;  Non motorized households are less favorable to accept the survey. Indeed, households without any cars are 1.3 times more likely to be non-respondent in comparison to multiequipped household;  Households living in a single room dwelling are 1.6 times more likely not to respond in comparison to households living in several rooms. Let"s note that this variable is correlated with the number of people living in the household. Thus, a big household size is accompanied with a greater probability to respond;

The variables of the 1999 census which explain the response mechanism to the FNTS, often emphasize the difficulty of the interviewers to reach younger households, who are probably the most actives and the most mobile, and households living in the cities most densely populated, where there are more and more buildings equipped with interphone.

STRATEGIES TO CORRECT NONRESPONSE BIAIS

Calibration on margins is a weight-class method used when the total of each auxiliary information is known. Calibration on margins is an iterative process that adjusts certain sample totals or ratios, to make them match with certain corresponding totals or ratios that are known from the population. The calibration"s methodology was developed by Deming and Stephan in the early 40"s with the raking ratio process. We have used a software of calibration on margins called CALMAR2, which was developed by INSEE [START_REF] Deville | La correction de la non-réponse par calage généralisé[END_REF][START_REF] Le Guennec | La macro Calmar2, manuel d'utilisation[END_REF].

This stage is essential to ensure a representative sample and the comparison with some others statistics sources (for instance, other national surveys). The calibration on margins must be implemented on variables which explain (or are correlated with) transport behavior the variable that explain the nonresponse mechanism, and for which the total is accurately known (Deville, 1999). The population reference is ordinary households known by the rolling census.

When trying to reduce the impact of nonresponse bias by looking at known characteristics of nonrespondents and comparing them with those same characteristics of respondents. If differences in known characteristics are found between respondents and nonrespondents, weights can be developed that will reduce these biases. We had tested nine different calibrations to see the impacts of these weighting methods on the estimation of daily mobility. We choose the following margins from the census, as they are in the response mechanism and/or correlated with mobility: the report day; professions and socioprofessional categories, age and gender, size of the households, wave of survey, motorisation, zone of residence. Let:

-W-ALL be the weight obtain by using a calibration all information (eg: the report day; professions and socioprofessional categories, age and gender, size of the households, wave of survey, motorisation, zone of residence);

-W-UR be the weight obtain by considering a uniform response mechanism (eg: the final weight is obtain by using an equal response rate); -W-DAY be the weight using all available information in the calibration except the report day (eg: professions and socioprofessional categories; age and gender; size of the households; wave of survey; motorisation; zone of residence); -W-PCS be the weight using all available information in the calibration except the professions and socioprofessional categories; -W-AGG be the weight using all available information in the calibration except age and gender; -W-SHH be the weight using all available information in the calibration except the size of the households; -W-WAV be the weight using all available information in the calibration except the wave of the survey -W-CAR be the weight using all available information in the calibration except the motorization; -W-ZON be the weight using all available information in the calibration except the zone of residence

We consider that W-ALL is the best weight we can produce (as we use all auxiliary information we have). Let"s compare the estimates of the number of individuals that the other weights give.

In the Tables 4 to table 10 we show only the estimation of the number of individual for the W-ALL weight, the relative difference with W-UR for all variable in the calibration (where generally we have the deepest gap) and the difference with W-X where X is not in the calibration (it"s not necessary to see the other tables because if the variable is in the calibration then we do not have any gap). The daily mobility is measured with a face to face interview by the description of the mobility made the day before. The protocol does not impose any particular weekday, as the interviewer and the interviewees choose the day of the visit. The relative difference with W-ALL and W-UR confirms that interviewers have difficulties to collect data on households on Mondays and Thursdays. They have therefore more complicatedness to contact households on Tuesday and on Friday. In contrast, Friday is the most describe day, as respondents are more willing to meet interviewers on Saturday. The relative difference with W-ALL and W-UR and W-ALL and W-DAY give similar results for each day. When we remove the "report day" off the calibration, the other variables of the calibration do not adjust properly at the distribution of survey days, e.g 20% for each day. If we use W-DAY we will have some bias in our estimations (the gap W-DAY and W-ALL is not negligible), it is necessary to introduce the reporting day in the calibration.

This is also true for the wave of the survey. As the interviewees are less accessible at their home in summer (probably for holidays), the response rate is lower in July and August. If we use W-WAV we will have some bias in our estimations (the gap W-WAV and W-ALL is not negligible), it is necessary to introduce the wave of the survey in the calibration.

The relative difference with W-ALL and W-AGG shows to us that interviewees are more often woman aged 35 to 65 and less often men aged 6 to 35. When we remove the "age and gender" of the calibration, the other variables of the calibration do not adjust the distribution by age and gender. There is no correlation between the variable "age and gender" and the other variables, it is therefore necessary to introduce the information age and gender in the calibration.

The relative difference with W-ALL and W-UR and W-ALL and W-PCS give different results.

When we remove the "Professions and Socioprofessional Categories" off the calibration, the other variables of the calibration do not compensate properly the distribution of the "Professions and Socioprofessional Categories". The "Professions and Socioprofessional Categories" must be part of the variable calibration. When we look at the number of trips per day for the overall population, the relative difference with W-ALL and all other weights we found similar results except for the "Professions and Socioprofessional Categories", "age and gender" and "zone of residence". For the first, the removal of this variable has the effect of slightly increasing the average number of trips per day. Conversely, the other two variables have the effect of decreasing the mean number of trips per day. The fact that the average number of trips per day is quite similar does not necessarily imply that people who did not respond had the same behaviour in terms of daily mobility. These means are the result of a play of compensation between those who have not responded because they do not perform trips and those who have not responded because they are very mobile.

IN TERM OF MOBILITY

CONCLUSION

The methods presented in this paper depend on the context of the survey. The analysis of the nonresponse mechanism for calibrations depends on the availability of an exhaustive and up to date sampling base. Working with our National Institute of Statistics, we had the opportunity, of drawing the sample from the census. This is not always the case, as in certain countries, drawing samples from the census is forbidden for privacy reasons. We found that the best explanatory factors of total nonresponse are the zone of residence, the survey period, age & gender of the head of the households, the households car fleet and the size of the households.

It is important to minimize the biases due to measurement errors by a calibration on margins using the variables that play a role in the response mechanism.

Figure 1 Figure 1 :

 11 Figure 1: Overview of the French National Travel Survey (FNTS 2007-2008).

Table 1 -

 1 Sample size and response rate

	Number of dwelling drawn in the sample	Number of dwelling out of the scope	Number of Main dwelling	Number of non-respondents (2 nd visit) households	Number of survey performed
	30 165	4 272	25 893	7 261	18 632

Table 2 -

 2 Global significance analysis of the variables used in the Logit model

	Effect	DF	Wald Chi-Square	Pr > ChiSq
	Zone of residence	4	47,65	<0,0001
	Wave of survey	5	41,99	<0,0001
	Age of the head of the household at the 1999 census	3	23,47	<0,0001
	Household car fleet at the 1999 census	2	15,28	0,00
	Number of rooms of the dwelling	3	10,07	0,02
	Building belonging to the municipality with « low rents lodging »	1	2,35	0,13
	Type of dwelling	1	1,68	0,20
	Surface of the dwelling	4	2,44	0,66
	Dwelling with/without interphone	2	0,21	0,90
	Gender of the head of the household at the 1999 census	1	0,02	0,90
	Size of the household at the 1999 census	3	0,59	0,90

Source: INSEE-SOeS-INRETS, French National Travel Survey 2007-08

Table 3 -

 3 Odds ratio on the propensity of nonresponse according to variable that explain the response mechanism

		Variable	Odds Ratio	Probability > CHI 2
	Intercept		0.4	<0,0001
		People living in rural areas	0.7	<0,0001
		people living in conurbation of less than 20000 inhabitants	0.8	0,0013
	Zone of residence	people living in conurbation from 20000 to 100000	0.9	0,0481
		people living in conurbation from 100000 to Paris region	0.9	0,0016
		Paris Conurbation	1.0	Reference
		May -June 2007	0.9	0,0432
		July -August 2007	1.2	0,0021
	Wave of	September -October 2007	0.9	0,1836
	survey	November -December 2007	1.0	0,8560
		January -February 2008	0.9	0,0108
		March -April 2008	1.0	Reference
	Age of the	From 15 to 34 years old	1.0	0,6743
	head of
	the	From 35 to 49 years old	0.9	0,2338
	household
	at the	From 50 to 64 years old	0.8	<0,0001
	1999
	census	From 65 years old and more	1.0	Reference
	Househol	Non motorized household	1.3	<0,0001
	d car fleet
	at the	Household with one car	1.2	<0,0001
	1999
	census	Multi-equiped household	1.0	Reference
	Number of	0-1 room	1.6	<0,0001
	rooms of
	the	2-3 rooms	1.3	<0,0001
	dwelling
	at the	4-5 rooms	1.1	0,0951
	1999
	census	6 rooms and more	1.0	Reference
	Source: INSEE-SOeS-INRETS, French National Travel Survey 2007-08

table 2). th WCTR, July 11-15, 2010 -Lisbon, Portugal 6

Table 4 -

 4 Gap between the estimation of number of individuals with W-ALL, W-UR and W-DAY

		Weight used
	W-ALL	W-UR	W-DAY
	Number of individuals (in thousands)	Relative difference with W-ALL	Relative difference with W-ALL

Table 5 -

 5 Gap between the estimation of number of individuals with W-ALL, W-UR and W-PCS

		Weight used
	W-ALL	W-UR	W-PCS
	Number of	Relative	Relative
	individuals	difference	difference with
	(in thousands)	with W-ALL	W-ALL

Table 6 -

 6 Gap between the estimation of number of individuals with W-ALL, W-UR and W-AGG

		Weight used
	W-ALL	W-UR	W-AGG
	Number of individuals (in thousands)	Relative difference with W-ALL	Relative difference with W-ALL

Table 7 -

 7 Gap between the estimation of number of individuals with W-ALL, W-UR and W-SHH

		Weight used
	W-ALL	W-UR	W-SHH
	Number of individuals (in thousands)	Relative difference with W-ALL	Relative difference with W-ALL

Table 8 -

 8 Gap between the estimation of number of individuals with W-ALL, W-UR and W-WAV

		Weight used
	W-ALL	W-UR	W-WAV
	Number of individuals (in thousands)	Relative difference with W-ALL	Relative difference with W-ALL

Table 9 -

 9 Gap between the estimation of number of individuals with W-ALL, W-UR and W-CAR

		Weight used
	W-ALL	W-UR	W-CAR
	Number of individuals (in thousands)	Relative difference with W-ALL	Relative difference with W-ALL

Table 10 -

 10 Gap between the estimation of number of individuals with W-ALL, W-UR and W-ZON

		Weight used
	W-ALL	W-UR	W-ZON
	Number of individuals (in thousands)	Relative difference with W-ALL	Relative difference with W-ALL

Table 11 -

 11 Gap between the estimation of number of average trips by day with W-ALL, W-X

	Mean of the
	number of trips			Relative difference with W-ALL
	per day
	W-ALL	W-UR	W-DAY	W-PCS	W-AGG W-SHH W-WAV W-CAR W-ZON
	3,21	0,04%	0,05%	0,15%	-0,23%	0,05%	0,04%	-0,05%	-0,30%
	Source: INSEE-SOeS-INRETS, French National Travel Survey 2007-08