domain: spi info math

text:
Jianshun Wu

Lihong Qiao
email: lhqiao@buaa.edu.cn

Zuowei Zhu

Nabil Anwer

A novel representation method of non-ideal surface morphologies and its application in shafthole sealing simulation analysis

Keywords: Non-ideal surface morphology representation, Deviation coordinate system, Hermite-Fourier polynomials, Parametric matrix, Sealing simulation, Manufacturing errors

Assembly process simulation has been recognized as an effective tool for design verification. The representation of actual part surfaces produced by manufacturing processes is an important issue for assembly simulation. Manufactured part surfaces can also be regarded as non-ideal surface morphologies caused by manufacturing errors. This paper presents a new approach to describe non-ideal cylindrical surface morphologies. A deviation coordinate system is developed by adding a new deviation dimension along the normal direction of the nominal surface modelled in the cylindrical surface curvilinear coordinate system. Considering characteristics of the cylindrical surface machining process, a unified expression of combined Hermite polynomials and Fourier series is used to demonstrate variations that commonly appear on manufactured non-ideal cylindrical surfaces. The Hermite-Fourier polynomials constitute multimorphologies resulting from different manufacturing errors. In the proposed method, a parametric matrix is created from the expansion of the Hermite-Fourier polynomials. Each morphology can be represented by a corresponding matrix. The total deviation of a non-ideal part surface is the sum of deviations caused by each manufacturing error source through a linear combination of various matrices. The effectiveness of the proposed method is verified by a simulation of the sealing function of shaft-hole assemblies.

Introduction

In the assembly process, the performance of two mating components depends largely on the contact status and clearance between their mating surfaces. As a critical part of product design, assembly simulation provides important information for evaluation of product performance. However, at present, most available simulation systems for assembly analysis are based on the ideal part geometry, while ignoring the possible deviations on part surfaces that may cause assembly failure. Therefore, it is necessary to incorporate the manufactured part surfaces in the assembly simulation model to consider actual product geometry.. With this regard, efficient methods to model practical manufactured geometry of cylindrical surfaces should be developed. With the help of such methods, the impact of various manufacturing errors on the cylindrical surfaces The modeling of manufactured surface has received much research attention. Some previous studies lack of considering form deviations in the modeling of the non-ideal surfaces. Louhichi et al. modelled the position and orientation defects of components based on the shape of the tolerance zone, the toleranced feature type and the tolerance type [START_REF] Louhichi | An algorithm for CAD tolerancing integration: Generation of assembly configurations according to dimensional and geometrical tolerances[END_REF] . Dantan and Qureshi utilized convex hulls defined in the parametric space to simulate the influences of geometric deviations on the geometrical behavior of the mechanism [START_REF] Dantan | Worst-case and statistical tolerance analysis based on quantified constraint satisfaction problems and Monte Carlo simulation[END_REF] . However, these studies are lacking in the consideration of form deviations, which have a great impact on the functional and performance of products and should be modelled. Anwer et al. investigated the fundamentals of skin models at a conceptual, geometric and computational level to address the geometrical variations [START_REF] Anwer | The skin model, a comprehensive geometric model for engineering design[END_REF][START_REF] Zhang | Discrete shape modeling for skin model representation[END_REF] . Schleich and Anwer proposed the skin model shapes paradigm by the superposition of the nominal surface and geometric deviations that are divided into systematic deviations and random deviations [START_REF] Schleich | Skin model shapes: A new paradigm shift for geometric variations modelling in mechanical engineering[END_REF][START_REF] Schleich | Approaches for the assembly simulation of skin model shapes[END_REF] . This paradigm provides a method for the modeling, representation and analysis of geometric deviations. A method proposed by Zhu et al. improved the pre-processing stage to prepare the skin model shapes to be used for tolerance analysis [START_REF] Zhu | An Improved Tolerance Analysis Method Based on Skin Model Shapes of Planar Parts[END_REF] . Samper proposed to parameterize form deviations by building a geometrical model based on the natural modal shapes of the ideal surface, which simplifies the consideration of surfaces with form defects in assembly simulation [START_REF] Samper | Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces[END_REF] . With the application of the discrete modal decomposition, a surface with multi-scale deviations was simulated and evaluated with respect to tolerance specification by Cao et al [START_REF] Cao | Geometrical Simulation of Multiscale Toleranced Surface With Consideration of the Tolerancing Principle[END_REF] . Huang et al. developed a modebased method to characterize part geometric error using Discrete Cosine Transform (DCT) [START_REF] Huang | Mode-based Decomposition of Part Form Error by Discrete-Cosine-Transform with Implementation to J Engineering Manufacture 0(0) Assembly and Stamping System with Compliant Parts[END_REF] , in which the modes related to the manufacturing process error could be identified. Based on the measurement data, a manufacturing signature model was established by XXX to facilitate the representation of the actual profiles of manufactured surfaces [START_REF] Colosimo | Manufacturing signature of turned circular profiles[END_REF][START_REF] Wilma | Manufacturing Signature for Tolerance Analysis[END_REF] . With the manufacturing signature and the assembly conditions, Corrado, Polini and Moroni proposed a geometric model to simulate the assembly of parts with geometric deviations, based on which a new CAT (Computer Aided Tolerancing) tool was developed [START_REF] Corrado | Manufacturing signature and operating conditions in a variational model for tolerance analysis of rigid assemblies[END_REF] . To generate consistent skin model shapes, two deviation combination methods were proposed to preserve the deviations of surfaces by Yan and Ballu 14 . Cai studied the rigid and compliant variation modeling of sheet metal assembly [START_REF] Cai | Rigid-Compliant Hybrid Variation Modeling of Sheet Metal Assembly with 3D Generic Free Surface[END_REF][START_REF] Cai | Unified variation modeling of sheet metal assembly considering rigid and compliant variations[END_REF] . The assembly sequence planning research are also be studied [START_REF] Bahubalendruni | A novel concatenation method for generating optimal robotic assembly sequences[END_REF][START_REF] Bahubalendruni | A review on assembly sequence generation and its automation[END_REF][START_REF] Ghandi | Assembly sequence planning of rigid and flexible parts[END_REF] .

Meanwhile, the modeling of cylindrical surface deviations has also drawn research interest. A typical method is the combination of the Fourier series and Chebyshev or Legendre polynomials, which has been employed to model cylindricity errors. Zhang et al. introduced a unified functional tolerancing approach involving Legendre and Fourier polynomials for modeling and characterizing typical geometrical errors commonly found in machined cylindrical parts [START_REF] Zhang | Unified functional tolerancing approach for precision cylindrical components[END_REF] . Additionally, Ni and Yao attempted to model the cylindricity errors with Legendre/Fourier polynominals and the effects of the cylindricity error on position accuracy are analyzed [START_REF] Ni | Cylindricity modeling and tolerance analysis for cylindrical components[END_REF] [START_REF] Henke | Methods for evaluation of systematic geometric deviations in machined parts and their relationships to process variables[END_REF] .

Since cylindrical features are basic geometric features that have been widely used in assembly, we will put our focus on cylindrical features in the paper. The effects of different manufacturing errors on the cylindrical features are studied. Zhang et al. studied the typical manufacturing errors, such as errors caused by spindle rotation, fixture distortion, misalignment of spindles and work centers, workpiece deflection et al. The effects of these errors on manufactured surfaces are also investigated [START_REF] Zhang | Unified functional tolerancing approach for precision cylindrical components[END_REF] . Muhummad et al. described a concurrent measurement of radial, axial and angular motions of spindle using concentric circle grating and phase modulation interferometers in order to depict the deviation of the manufactured surface from the nominal surface [START_REF] Madden | Concurrent measurement method of spindle radial, axial and angular motions using concentric circle grating and phase modulation interferometers[END_REF] . Chien expanded the approximated harmonic model by adding the knowledge of machining process [START_REF] Chien | Approximate harmonic models for roundness profiles with equivalent energy mean square values[END_REF] . It was also concluded that the number of lobes on manufactured surface is related to the number of jaws on the chuck which holds the workpiece [START_REF] Sawabe | Influence of radial motion on form error of workpiece in turning[END_REF][START_REF] Rahman | Effect of clamping conditions on chatter stability and machining accuracy[END_REF] . A cutting force model was built to analyze the workpiece deflection caused by the cutting force [START_REF] Rao | A comprehensive dynamic cutting force model for chatter prediction in turning[END_REF][START_REF] Sadílek | Cutting forces during turning with variable depth of cut[END_REF] . The research of XXX also established a relationship between cutting time and tool wear and found it linear in the nominal wear stage [START_REF] Stavropoulos | Tool wear predictability estimation in milling based on multi-sensorial data[END_REF] . A relationship between the actual and nominal depth of cut was also revealed [START_REF] Schindler | Thermo-elastic deformations of the workpiece when dry turning aluminum alloys-A finite element model to predict thermal effects in the workpiece[END_REF] .

Many of the proposed models represent the manufactured surface either by discrete surface points or by the whole surface shape. A model that can represent the deviated surface with respect to its ideal design remains to be developed. It is Wu et al. necessary to develop a precise non-ideal surface morphology representation method for highfidelity simulation modeling. The representation should consider the manufacturing errors that affect the final manufactured surface morphology. This paper proposes a deviation coordinate system and Hermite-Fourier combination polynomials to express manufactured cylindrical part surface morphologies. The deviations of multiple morphologies of a manufactured cylindrical surface can be easily calculated by the parametric matrices resulting from the expansion of the polynomials. The effectiveness of the method is verified through simulation and analysis of the sealing function of shaft-hole assemblies.

Coordinate representation and formation of the non-ideal cylindrical surface

The nominal cylindrical surface in cylindrical coordinate system Due to the extensive application of cylindrical surfaces in product design, it is significant to establish an effective coordinate representation for cylindrical surfaces. For cylindrical surfaces, a cylindrical coordinate system ( ) , , r z q is commonly used to describe the ideal (i.e. designed and intended) geometry, namely the nominal surface. In this coordinate system, the nominal surface can be expressed as:

( ) 0 , 0 z ,0 2 n r f z r z q q p = = £ £ £ £ (1)
The function represents a nominal cylindrical surface in a 3D coordinate system, where 0 r is the radius of the nominal cylinder and n z is the height of the cylinder. Fig. 1 shows the nominal cylindrical surface in the cylindrical coordinate system.

Figure 1 A nominal cylindrical surface in cylindrical coordinate system

Point P could be expressed as:

0 ,z , i i r r z q q = = = (2)
Where i=1,2,3 n , i z is the height of point P , and i q is the circumferential position of P .

Any point on the nominal surface can be represented by 0 r , i z and i q . With the definition of the cylindrical coordinate, the non-ideal cylindrical surface can be easily described.

Relationship between non-ideal cylindrical surfaces and nominal surfaces

The performance of an assembled product is associated with the shape of mating component surfaces in the assembly. It is important to consider the effects of the manufactured shape in the simulation analysis to achieve more practical and accurate understanding of the assembly performance.

For example, Fig. 2 illustrates different nonideal shaft-hole assemblies. In this figure, the hole is nominal, while the shaft is non-ideal and three non-ideal surface shapes are included in the assemblies. It should be noted that various nonideal surface shapes that comply with the same tolerance zone Tz may have different effects on the sealing performance of the assembly.

Figure 2 Illustration of the effect of different surface morphologies on product performance

It is obvious from Fig. 2 that, the product performance varies significantly when the shape of the manufactured surface changes. Therefore, in order to capture this variability, the relationship between the non-ideal manufactured surface and the nominal surface should be studied.

The manufactured non-ideal surface can be considered as a deviated state of its nominal geometry or ideal surface. Any point on the nonideal surface can be corresponded to a point on the nominal surface, and be defined as a "deviation" of that point from its theoretical position. As shown in Fig. 3, the non-ideal surface resembles a blanket that wraps the nominal surface, with the thickness at each point of the blanket as the corresponding deviation of With this relationship, the non-ideal cylindrical surface can also be represented in the cylindrical coordinate system ( )

, , r z q , and three definitions are proposed as follows to describe the relationship.

Definition 1: According to the definition of the nominal surface in the cylindrical coordinate system, a two-dimensional system -cylindrical surface curvilinear coordinate system ( ) , z q is defined [START_REF] Qiao | Approach to the Deviation Representation of Non-ideal Cylindrical Surfaces Based on the Curvilinear Coordinate System[END_REF] . The entire nominal surface could be mapped onto this coordinate system.

In fact, the non-ideal surfaces could still be represented using cylindrical coordinate system ( )

, , r z q . Which is similar to the representation of an object (such as a satellite) in the geodetic coordinate system ( )

, ,h j l 32 , where j , l and h

show the values of geodetic latitude, geodetic longitude, and geodetic height, respectively. The radius vector i r of a point P¢ on the non-ideal surface is the function of two coordinates i z and i q .

And it can actually be expressed in terms of ( )

, , r z q , that is: ( )

, i i i r f z q = (3)
Definition 2: A variable d can be defined as "deviation variable", and expressed as:

( )

, i i 0 i i r r z d j q = -= ( ) 0 , r r f z d q = -= (4)
Equation ( 4), termed as "deviation function", is a function in the cylindrical surface curvilinear coordinate system.

According to Definition 1, the deviation variable i d represents the deviation of the non- ideal surface points when i z z = and i q q = . The deviation variable i d can also be regarded as an attribute of the point on the non-ideal surface in the cylindrical surface curvilinear coordinate system ( )

, z q .
Definition 3: Based on the cylindrical surface curvilinear coordinate system ( ) , z q , by adding a deviation dimension, a novel 3D coordinate system -deviation coordinate system is defined as ( )

, , z d q .
It is known from Definition 2 that the non-ideal surface can be represented by one function in the deviation coordinate system. Therefore, it can be treated as a surface in the deviation coordinate system.

The non-ideal cylindrical surface in deviation coordinate system

According to Definition 2 and 3, the deviation d could be regarded as a vector: the direction of d is the radial direction of the cylindrical surface; and the value of d is the distance between the point on the nominal surface and its corresponding point on the non-ideal surface.

Since directions of d , z and q are orthogonal, the 3D deviation coordinate system ( )

, , z d q
constructed by d , z and q is an orthogonal coordinate system. In the deviation coordinate system, the origin of the deviation dimension is no longer the same for each point. For point P¢ on the non-ideal surface, the origin of the corresponding deviation coordinate is point P on the nominal surface, as shown in Fig. 4. The figure gives a cross-section of the cylinder when i z z = . In the figure, O is the center of the nominal profile. The cylindrical surface curvilinear coordinate system is established on the nominal surface and O¢ is the origin of the q coordinate. According to the definition of the deviation coordinate system, every point can be represented by the deviation coordinates in this coordinate system. And the deviation function established in this coordinate system has the following characteristics: a) If 0 d º for all the points, the non-ideal cylindrical surface yields to its nominal and there is no deviation; then the non-ideal cylindrical surface has the same geometrical shape as the nominal surface thus only a dimensional deviation exists; c) The distribution of the deviations can be plotted by the deviation function. Such a definition of the deviation coordinate system provides a clear and easy representation of non-ideal surfaces. The non-ideal surface could be cast into a standard and unified form by the deviation function, which leads to simplified modeling and calculation of the non-ideal surfaces in computer-aided systems.

Formation of the non-ideal surface morphology

In a manufacturing process, the manufactured surface of the workpiece is not consistent with the nominal surface due to manufacturing errors. Under the influence of some typical errors caused by cutting force, tool wear, thermal factors, spindle motion error and fixture error, surface morphologies are introduced. Table 1 provides a description of the manufacturing errors as well as their corresponding non-ideal surface morphology and mathematical formulation. The workpiece fixed at one end and hanging at the other end can be regarded as a cantilever beam. With the increase of the distance from the spindle end, the diameter of the manufactured surface increases with the third power of the distance.

Deviation modeling and parametric representation of the non-ideal cylindrical surface

Deviation modeling of the non-ideal surface

Two motions exist in a cylindrical turning process, namely main motion and feed motion as depicted in Fig. 5. The main motion is a rotational motion of the spindle. The variations of spindle will result in the variation of the relative position between the workpiece and tool. The deviation on the manufactured surface resulting from the main motion is only related to the angle of rotation, and is therefore periodic.

Feed motion is the translation of the tool along the axis of the spindle. Deviations may occur due to force deformation caused by the equipment and cutting force and the variation of the tool tip geometry caused by heat and/or tool wear. Such deviations are generally dependent on the axial position, while unaffected by the rotation of the workpiece. The deviations of the manufactured surface during feed motion can be expressed by a function of the distance between the cutting location and the spindle end.

Figure 5 Two motions in cylindrical turning process

A manufactured cylindrical surface is composed of multiple non-ideal surface morphologies, each corresponding to a certain manufacturing error. Each morphology includes deviations both in the axial direction and along the circumferential direction, the former can be represented by polynomials and the latter is periodic.

Chebyshev and Legendre polynomials 20, 22 were adopted to demonstrate the deviations along the axial directions. Since the range of Chebyshev and Legendre polynomials is [ ]

1, 1 -+ , the axial coordinate should be mapped to [ ] 1, 1 -+ first
when representing the cylindrical surface. Different from the aforementioned polynomials, the range of a Hermite polynomial is ( ) , -¥ +¥ , which makes it easier to describe the cylindrical surface with this polynomial.

Thus, Hermite polynomials and Fourier series can be used respectively to express the deviations along these two directions. The comprehensive expression of the cylindrical non-ideal surface deviations caused by multiple errors can be expressed by the combination of the Hermite polynomials and Fourier series, as shown in Eq. 5.

( ) ( ) ( )

0 0 0 cos sin u v v i i j i j i j j H z a j b j d q q = = = é ù = + ê ú ë û å å å ( 5
)
Where d is the deviation of the non-ideal surface, 0 r is the nominal radius of the cylinder, u is the order of the Hermite polynomials, v is the order of Fourier series,

The first five Hermite polynomials are:

( ) ( ) ( ) ( ) ( )
H z H z z H z z H z z z H z z z = = = - = - = - + (7)
Each morphology is a linear combination of several Hermite polynomials.

The selection of these two orthogonal functions conforms to the motion characteristics of the turning or grinding process. The orthogonality of these two polynomials facilitates the expression of the non-ideal surface.

From the above analysis, the Hermite-Fourier polynomials of typical non-ideal surface morphologies can be concluded in Table 2.

Feed

Wu et al.

i i i j j ij ij j j H z a k b k d q q =¥ = =¥ =¥ = = = é ù × + ê ú ë û å å å 6 Fixture error ( ) 0 1 ( ) ( ) cos3 AH z BH z d q = +
In Table 2, A, B, C, D and E are constants. Therefore, the non-ideal surface morphology generated by each manufacturing error can be represented by Hermite-Fourier polynomials, which allows the unified expression of various deviation functions. Different non-ideal surface morphologies have their characteristic parameters, and these parameters can be conveniently expressed by a parametric matrix.

Parametric representation of the non-ideal surface

Establishment of the parametric matrix for non-ideal surface Considering the differences between manufacturing conditions, the expression of the manufactured surface should combine multiple morphologies resulting from different manufacturing errors. By analyzing the non-ideal cylindrical surface morphology and the characteristics of the Hermite-Fourier polynomials, a parametric matrix can be created from the expansion of the Hermite-Fourier polynomials. Using the polynomials in Eq. 5, the deviation function can be represented as a multiplication of three matrices:

[ ] ( ) ( ) 0,0 0,1 0,1 0,2 0, 2 0, 0, 1,0 1,1 1,1 1,2 1,2 1, 1, 0 1 2 1,0 1,1 1,1 1,2 1,2 , , 1 cos
sin cos 2 sin 2 cos sin

J J J J k I i i i i i IJ IJ a a b a b a b a a b a b a b H H H H a a b a b a b J J q q q d q q q - - - - - é ù ê ú ê ú ê ú é ù ê ú ê ú ê ú ê ú = ê ú ê ú ê ú ê ú ê ú ë û ê ú ê ú ê ú ë û (8)
The matrix in the middle is the parametric matrix of the Hermite-Fourier polynomials. In J Engineering Manufacture 0(0) this matrix, i=1,2,3 I , j=1,2,3 J , which represent items of the Hermite polynomial and Fourier series respectively. The k in k d represents a certain manufacturing error. High order terms of the Hermite-Fourier polynomials have less impact on the non-ideal surface and can be omitted when studying the large-scale deviations of the manufactured surface. Thus the parametric matrix in the deviation function can be simplified as a 5*7 matrix shown in Eq. 9.

[ ] 0,0 0,1 0,1 0,2 0,2 0,3

q q d q q q é ù ê ú ê ú ê ú = ê ú ê ú ê ú ë û 3q é ù ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú ë û (9)
The parameters in the matrix are relevant to a certain morphology and are determined by the corresponding manufacturing error. The parameter values reflect the extent of variation of the morphology. Take the first manufacturing error in Table 3 as an example, according to the non-ideal surface morphology formulation defined in Table 1 and Table 2, the deviation of the manufactured surface is only related to the third power of the distance between the cutting location and the spindle end. The parameter 3,0 a is the coefficient of Hermite polynomial ( )

H z contains not only the cubic polynomial but also a linear polynomial. In order to compensate for the effects of the linear polynomial, ( )

1
H z is introduced with a coefficient 1,0 a , the rest of the parameters in the matrix are 0. The other parametric matrices in Table 3 are calculated in a similar way. Table 3 summarizes the parametric matrix of each morphology caused by a certain manufacturing error. The total deviations of the non-ideal surfaces are the consequence of various manufacturing errors. Each error plays a definite role in the manufacturing process.

Considering the independence of the manufacturing errors during the manufacturing process, the total deviations of the manufactured surface can be regarded as the composition of the deviations caused by each error. With the unified expression of each nonideal surface morphology, the superposition of multiple Hermite-Fourier polynomials is still a Hermite-Fourier polynomial. The total deviations of the manufactured surface can be considered as the superposition of corresponding parametric matrices. The expression of total deviations of a manufactured surface is given in Fig. 6. On account of the unified representation of each non-ideal surface morphology and the different levels of the impact caused by manufacturing errors, the manufactured surface can be modeled by the linear combination of the non-ideal surface morphologies by parametric matrices.

Verification of the representation method of non-ideal cylindrical surface

To verify the effectiveness of the representation method, a shaft-hole assembly is selected in the following case study. Using the Herimite-Fourier polynomials, several types of shaft-hole assembly are modeled, then, sealing simulations and subsequent analysis are performed. Three typical non-ideal long shaft cylindrical surfaces (taper, convex, concave) affected by three different primary manufacturing errors are chosen for sealing simulation. For taper surface, tool wear is the dominant error during manufacturing. For a low-rigidity workpiece clamped with a chuck and work center, the convex shape will appear under the effect of the cutting force, and the concave surface will be resulted from the vertical misalignment of chuck and work piece center. Models of these three features are shown in Fig. 7. With these three non-ideal shaft surfaces, the assembly structures of non-ideal long shafts and nominal holes are constructed. And the clearance fit is applied to these assemblies. Exemplary shaft-hole assemblies for sealing simulation analysis are given in Fig. 8.

é ù ê ú ê ú ê ú ê ú ê ú ê ú ë û 0,0 0,1 0,1 0,2 0,2 0,3 0,3 1,0 1,1 1,1 1,2 1,2 1,3 1,3 2,0 2,1 2,1 2,2 2,

Figure 8 Example shaft-hole assemblies

In the figure, c denotes the clearance of the hole and shaft, x is the form variation of the non- ideal surface shape. The values of x vary during the simulation. With these two parameters, the influence of geometrical tolerances on the sealing requirement of the mating structure will be estimated, which facilitates the improvement and optimization of the product design.

The long shaft-hole examples used in the sealing simulation and analysis consist of several non-ideal surface morphologies. The tapered shaft is affected mainly by cutting tool wear error, along with other two non-ideal cylindrical surface morphologies caused by cutting force and thermal effect. According to the mathematical formulations and parametric matrices listed in Table 1, Table 2 and Table 3, when 0.0004

x = mm, the parameters 0,0 a and 1,0 a in the third matrix listed in Table 3 ´, the parameters 0,0 a and 1,0 a in the fourth matrix ´. Similarly, the other surfaces applied to sealing simulations are modeled following the same principle.

The preconditions are set for the simulation, in which the maximum dimension of shaft is 4.995 mm and 0.0025 c mm = . The instances in Fig. 8 are applied to the sealing simulation analyses and the simulation is implemented in Fluent 6.3 following the general process of fluid analysis in the system. The parameter settings of the fluid in the simulation are listed in Table 4. The inlet pressure is 0.12MPa, and the outlet pressure is barometric pressure. The leakage results are depicted in Fig. 9. From Fig. 9, it should be noted that the leakage variation increases along with the increase of the form variation. The leakage variations are multitudinous because of the differences between surface shapes. By comparing the leakage of different surface shapes, it can be concluded that the leakage of convex shaft is minimum, the leakage of taper shaft is larger than convex shaft, and the leakage of concave shaft is maximum. The results also indicate that different non-ideal surface shapes that conform to the same tolerance zone have various effects on the functionality and performance of the product. Through this analysis, the validity of the representation method is verified by comparing the differences between

J

  Engineering Manufacture 0(0) that point. Thus the non-ideal surface can be represented mathematically by the superposition of the nominal surface and deviations.

Figure 3

 3 Figure 3 Relationship between non-ideal and nominal cylindrical surfaces

Figure 4

 4 Figure 4 Representation of non-ideal surface in deviation coordinate system

  d d = for all the points and d is a constant,

Table 1

 1 Description of typical manufacturing errors in the turning process and mathematical formulation of corresponding non-ideal surface morphologies Manufacturing errors Illustration Description Non-ideal surface morphology Formulation Cutting force error with work piece in a chuck

  The workpiece fixed in a chuck and supported by a work center of the tail stock can be regarded as a simply supported beam; and the diameter of the work piece is related to the 2nd, 3rd and 4th power of the distance between the cutting location and the fixed end.

  The cutting edge gradually deviates from the theoretical cutting path. As the cutting process continues, the actual cutting material decreases and the actual radius of the work piece increases gradually. The expansion of the workpiece and removed material increases gradually, meanwhile, the radius of the work piece decreases gradually.Radial error motion results in the deviation in the circumferential direction, and the angular error motion is relative to the variation coaxial to the axis of the workpiece.

  low rigidity, a main deviation of shape is caused by the clamping force. The number of lobes on the actual profile conforms to the number of jaws of chuck.

  Computing the total deviations for the non-ideal surface

Figure 6

 6 Figure 6 Expression of total deviations of a manufactured surface

Figure 7

 7 Figure 7 Three typical non-ideal surfaces in turning process

Table 4 Figure 9

 49 Figure 9 Comparison of leakage of different surface shapes

Table 2

 2 Hermite-Fourier polynomials of each non-ideal surface morphology generated by a certain error

	No.	Manufacturing errors	Non-ideal surface morphology	Mathematical formulation
	1	Cutting force error with workpiece in a chuck

Table 3

 3 Hermite-Fourier parametric matrix of each non-ideal surface morphology caused by a certain error

	No.	Manufacturing errors	Non-ideal surface morphology	H-F parametric matrix	Notes
	1	Cutting force error with work piece in a chuck

Department of Industrial and Manufacturing Systems Engineering, Beihang University, China

Laboratoire Universitaire de Recherche en Production Automatisee, Ecole Normale Superieure de Paris Saclay, France

Funding

This work is supported by the National Science Foundation of China (Grant 51575031) and National High-Tech. R&D Program of China (No.2015AA043702). The authors would also like to thank Beijing Municipal Education Commission (Build a Project) for its support.

these shafts applied in the sealing simulation.

When implanting multiple simulations, the non-ideal cylindrical surfaces need to be added in the simulation model continually, therefore, they should be sustained and generated rapidly. Since the non-ideal surfaces are caused by multiple manufacturing errors, the parametric matrices proposed in this paper make it possible to consider each of the errors in the simulation. Moreover, the non-ideal surface can be easily obtained by changing the parameters in the parametric matrices when errors vary during manufacturing processes. The parameters in the matrix also represent different levels of effects of each error on the manufactured surface.

Unlike previous models established for analysis of product performance, the models developed by this representation method are based on non-ideal assemblies. To a large extent, the analysis results approximate the real conditions of the manufactured product. The representation method also facilitates the generation and application of non-ideal surfaces.

Conclusions

In this paper, a novel representation method for non-ideal surfaces is proposed and verified by the sealing simulation analysis of shaft-hole assemblies. A deviation coordinate system has been developed to describe the deviations of the non-ideal cylindrical surface. The system is established by adding a deviation dimension along the normal vector of the nominal surface expressed by a cylindrical surface curvilinear coordinate system, which makes the description of deviations more simplified and effective.

A unified formula is selected to express the deviations of the non-ideal cylindrical surfaces. The formula combines Hermite polynomials and Fourier series, representing deviations in the axial direction and the circumferential direction respectively. The parametric matrices created from the expansion of the Hermite-Fourier polynomials are utilized to represent the corresponding morphologies generated by the manufacturing errors. The parameters in each matrix correspond to the effects of one particular manufacturing error. The total deviations of the manufactured surface can be considered as the superposition of corresponding parametric matrices. The proposed representation method facilitates modeling of the non-ideal cylindrical surfaces for simulation process, and other application cases.

Declaration of conflicting interests

The authors declare that there is no conflict of interest.


text:
Lihong Qiao

Yifan Qie

Zuowei Zhu

Yixin Zhu

Uzair Khaleeq

Uz Zaman

Nabil Anwer

Uzair Khaleeq Uz Zaman

An ontology-based modelling and reasoning framework for assembly sequence planning

Keywords: assembly sequence planning, geometry, ontology, reasoning

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The assembly process is an important manufacturing activity, in which a product is created combining the processes of design, engineering, manufacturing, and logistics in an efficient and cost-effective manner. Assembly refers to a product which comprises a set of components and their relationships, or the process the product is created. According to Samy and ElMaraghy [START_REF] Samy | A Model for Measuring Complexity of Automated and Hybrid Assembly Systems[END_REF], assembly consumes up to 50% of total production time and accounts for more than 20% of total manufacturing cost.

Product modelling and assembly process planning have become active research topics since the early 1980s. The product model has emerged as a comprehensive concept for capturing geometric data and semantic information during the product lifecycle [START_REF] Krause | Product Modelling[END_REF]. The assembly process is the result of Assembly Sequence Planning (ASP), which takes into account available assembly resources to improve design, simplify maintenance, and reduce the cost of production [START_REF] Hadj | Toward an Integrated CAD Assembly Sequence Planning Solution[END_REF][START_REF] Perrard | A Priori Checking Inconsistencies Among Strategic Constraints for Assembly Plan Generation[END_REF]. Over the past decades, many researchers have developed various models and software solutions regarding to assembly process. The development of Computer-Aided Process Planning (CAPP) techniques has facilitated ASP by deriving the best sequence of assembly operations given the geometrical representation of the assembly [START_REF] Xu | Computer-aided Process Planning -A Critical Review of Recent Developments and Future Trends[END_REF].

Although these models and techniques have been extensively investigated, inherent limitations in the existing work still exist when it comes to the knowledge sharing between the product model and assembly process planning. Effective reasoning of such knowledge also remains to be addressed. Product design relies on geometric information of the product, whereas assembly process planning is based on both the process information and the underlying geometric information in product models. Shape, posi-tion, contact and mobility of parts are main factors that must be considered in an assembly process. ASP needs to incorporate such information to enrich the semantics in model representation and enhance the decision-making capabilities. Moreover, ontology modelling, as one of the commonly used modelling methods in data management, can express unified, structural and semantic information and it allows for reasoning capabilities due to the formal and logic-based specifications underlying in the information model. In other words, it makes the implicit information explicit [START_REF] Huang | Ontology Model for Assembly Process Planning Knowledge[END_REF].

In this context, a geometry enhanced ontology modelling and reasoning framework for ASP is proposed in this paper. In the framework, the ontology model of assembly operations is established considering product geometry. A reasoning mechanism is also proposed to infer the sequence of assembly operations based on predefined rules and the ontology model. The overall paper is structured as follows: Section 2 highlights the research background of the ontology-based modelling, representation and reasoning framework in the context of ASP; Section 3 explains the proposed ontology modelling and reasoning framework for ASP along with the discussion of construction of rules and RUs; a case study is given in Section 4 to validate the framework and the conclusion is drawn in Section 5.

Literature Review

Ontology is a formal way to represent knowledge within a given domain. As it enables concept elicitation and generalization, and offers more explicitness to define properties and relationships between the concepts, multiple ontologies and data models have been developed to represent each stage of product life cycle over the past decade. Moreover, it supports inference through deductive reasoning, thus has been applied in many domains such as medical information science, geographic information system, enterprise modelling, organization learning, and software engineering [START_REF] Alexander | Methods in Biomedical Ontology[END_REF][START_REF] Morbach | OntoCAPE-A (re)usable Ontology for Computer-aided Process Engineering[END_REF][START_REF] Valaski | Ontologies Application in Organizational Learning: A Literature Review[END_REF][START_REF] Huang | Ontology-based Enterprise Knowledge Integration[END_REF][START_REF] Agustina | Ontology-driven Geographic Information Integration: A Survey of Current Approaches[END_REF][START_REF] Almeida Biolchini | Scientific Research Ontology to Support Systematic Review in Software Engineering[END_REF].

The traditional approaches for assembly modelling and ASP mainly focused on the relations among parts of a product. The concept of assembly precedence relations (APRs) was proposed to express the precedence relations among parts in an assembly by answering a series of structured questions [START_REF] Bourjault | Contributionune approche methodologique de l'assemblage automatise: Elaboration automatique dessequences operatiores[END_REF]. Graph-based methodologies, such as liaison sequence graph (LSG) and AND/OR graph [START_REF] Fazio | Simplified generation of all mechanical assembly sequences[END_REF][START_REF] Homem De Mello | A Correct and Complete Algorithm for the Generation of Mechanical Assembly Sequences[END_REF], have also been proposed to deduce feasible assembly sequences in a graphical way. In order to integrate knowledge in the decision-making of ASP, Zha et al. [START_REF] Zha | Integrated Knowledge-based Assembly Sequence Planning[END_REF] proposed a novel approach for the automatic generation, selection and evaluation of assembly plans, but the approach was inefficient due to limitations in modelling techniques. It is therefore highly imperative that knowledge is integrated in ASP via an efficient reasoning mechanism to better support decision-making in later design stages.

However, few researches can be found on knowledge representation of assembly process planning and the inference of assembly process planning information from geometrical product model. Therefore, ontologies that enable the description of more de-tailed information are drawing increased research attention. As one of the pillars for semantic web, ontology enriches knowledge representation [START_REF] Liu | Using Ontology for Design Information and Knowledge Management: A Critical Review[END_REF]. It enhances a comprehensive information model or knowledge model thereby reducing ambiguity [START_REF] Lee | OWL-Based Hybrid Product Knowledge Model for Collaborative Engineering Environment[END_REF]. Ontology also gains its application in the manufacturing domain to formalize domain concepts and processes. NIST (National Institute of Standards and Technology) proposed PSL (Process Specification Language), which is an interexchange format designed to help exchange process information automatically among a wide variety of manufacturing applications such as process modelling, process planning, scheduling, simulation, workflow, project management, and business process re-engineering tools [START_REF] Schlenoff | The Process Specification Language (PSL) Overview and Version 1.0 Specification[END_REF]. A STEP-based ontology named OntoSTEP was proposed to translate the product geometric information in STEP file into ontology [START_REF] Raphael | OntoSTEP: Enriching Product Model Data Using Ontologies[END_REF]. Panetto et al. [START_REF] Panetto | ONTO-PDM: Product-driven ONTOlogy for Product Data Management Interoperability within Manufacturing Process Environment[END_REF] proposed a productdriven ontology, ONTO-PDM, for product data management interoperability within manufacturing environment. In engineering product design, Chang et al. [START_REF] Chang | An Ontology-based Support for Product Conceptual Design[END_REF] proposed a graphical modelling tool to support conceptual design. Kitamura et al. [START_REF] Kitamura | A Functional Concept Ontology and Its Application to Automatic Identification of Functional Structures[END_REF][START_REF] Kitamura | Deployment of an Ontological Framework of Functional Design Knowledge[END_REF][START_REF] Kitamura | Ontology-based Systematization of Functional Knowledge[END_REF] proposed an ontology-based framework that can represent product functional design, functional design knowledge and functional structure recognition. While in the domain of process planning, Bock and Gruninger [START_REF] Bock | Inputs and Outputs in the Process Specification Language[END_REF] showed how manufacturing knowledge can be expressed by the PSL ontology. Cochrane et al. [START_REF] Cochrane | Manufacturing Knowledge Verification in Design Support Systems[END_REF] proposed a PSL-based ontology to indicate process planning knowledge.

As the decision-making process is highly related to knowledge modelling, there have been many researches on the knowledge modelling for assembly process planning. Holland et al. [START_REF] Holland | Assembly Features in Modeling and Planning[END_REF] established feature models for single-part and assemblies and discussed their application in assembly process planning. Zhao and Liu [START_REF] Zhao | OWL/SWRL Representation Methodology for EXPRESS-driven Product Information Model: Part I. Implementation Methodology[END_REF][START_REF] Zhao | OWL/SWRL Representation Methodology for EXPRESS-driven Product Information Model: Part II: Practice[END_REF] proposed an Ontology Web Language (OWL) representation methodology for an Express-driven product information model. Rachuri et al. [START_REF] Rachuri | A Model for Capturing Product Assembly Information[END_REF] established the Open Assembly Model (OAM), which is an assembly model based on the NIST Core Product Model (NIST -CPM). Defined with an object-oriented representation, it covers assembly function, form and behaviour. With an open structure, it could be applied in a collaborative environment. Although the model is relatively complete for representing the geometric assembly information, some implicit geometric information underlying in the product model is not well considered. Gruhier et al. [START_REF] Gruhier | A formal ontology-based spatiotemporal mereotopology for integrated product design and assembly sequence planning[END_REF] introduced a formal ontology-based on spatiotemporal mereotopology in the context of integrated assembly design and sequence planning. Yu et al. [START_REF] Yu | Assembly Ontology for Assembly Sequence Planning[END_REF] also worked on assembly ontology for ASP of a ball valve assembly.

An obvious limitation of the above mentioned researches is their lack of support for reasoning and inference mechanisms. Therefore, some researchers from NIST proposed to transform existing assembly model-CPM and OAM, from UML model to ontology model, and to develop reasoning techniques based on the ontology model [START_REF] Fiorentini | An Ontology for Assembly Representation[END_REF]. Kim et al. [START_REF] Kim | Design Formalism for Collaborative Assembly Design[END_REF] proposed the Assembly Relation Model (ARM) to represent the assembly information based on spatial relations between parts and features, thus a reasoning mechanism is developed through ontology representation of the ARM [START_REF] Kim | Ontology-based Assembly Design and Information Sharing for Collaborative Product Development[END_REF]. Noh et al. [START_REF] Noh | Hybrid Knowledge Representation and Reasoning with Ontology and Rules for Product Engineering[END_REF] proposed a framework for collaborative product engineering environments by combining a product information model with a rule-based model using Description Frame Logic. Samer et al. [START_REF] Samer | Collaborative Product and Service Life Cycle Management for a Sustainable World[END_REF] enhanced the collaboration among designers by defining feature-based ontology model and Semantic Web Rule Language (SWRL). Zhu et al. [START_REF] Zhu | Semantic Applications Enabling Reasoning in Product Assembly Ontologies-Moving Past Modeling[END_REF] proposed an ontology reasoning mechanism to infer the implicit information in the product model and implemented a layered semantic application architecture for the reasoning unit to query and reason assembly information from CAD systems. However, the description of the geometric information is not deep enough in the reviewed works.

Geometry Enhanced Ontology Modelling and Reasoning Framework for ASP

In order to enrich the semantics in ASP and to improve reasoning of the implicit knowledge underlying in the existing data, a geometry enhanced ontology modelling and reasoning framework is proposed in this paper, which takes advantage of the geometric information and shape representation to better specify product assemblability. The framework is composed of two main parts:

(1)

An ontology model that depicts the terminology and data structure for ASP; (2)

A reasoning mechanism that infers the underlying relations among the existing data. These contents will be discussed in the following sections.

As illustrated in Figure 1, in the proposed framework, the information from product model is parsed, imported and stored as the ontology data, which contains many implicit relations between product structure, product geometry and the assembly sequence. Based on predefined rules and reasoning units established according to the assembly process knowledge, new relations will be inferred from the implicit relations to support efficient decision-making for ASP. {Please insert Fig. 1

about here}

As the foundation of the modelling and reasoning framework for ASP, the ontology model contains the key concepts of assembly operations and the relations between them. These concepts and relations should be clarified and well organized within the ontology model in order to ensure the completeness. OWL-DL is applied in this paper as the modelling language for building up the ontology model. As one of the most widely used ontology modelling languages proposed by World Wide Web Consortium (W3C), OWL-DL ensures the universality of the model. The Directed Graph is also utilized to graphically represent the OWL-DL model [START_REF] Allemang | Semantic Web for the Working Ontologist: Effective Modeling in RDFS and OWL[END_REF]. Figure 2 What distinguishes the OWL-DL model from object oriented model is the ability to describe properties and their restrictions. Property descriptions describe properties in a global context while property restrictions describe properties within the context of a specific class.

Property description and property restriction together enrich the semantics within the relationships between concepts. In later stages, through the processing and reasoning of inference engines, some underlying relationships will inferred to support decisionmaking.

OWL-DL Representation of the Ontology Model for ASP

In order to represent the ontology model for ASP, some concepts should be clarified. Classes representing these concepts can be sorted as: (a) assembly structure; (b) assembly process; (c) assembly position and orientation; and (d) assembly entity geometry, with each class having its subclasses, as shown in the class hierarchy in Figure 3.

{Please insert Fig. 3

about here}

Assembly Structure

Assembly structure conveys the structure information of the assembly from product design to assembly process planning. A product is generally composed of parts and components, while components can be further decomposed into parts or lower-level components. The relative position and orientation of parts and components are defined by geometric constraints. Table 1 illustrates the properties defined in the OWL-DL ontology model of assembly structure as well as the classes linked by them. According to the hierarchy of the assembly structure, the relations between classes like Product, Part and Component are established through properties like isComposedOf and compose. Constraints are defined between these classes by specifying a hasConstraint or constrains property. isComposedOf and compose are defined as inverse properties by imposing the property description owl:inverseOf between them, so it is with hasConstraint and constrains. {Please insert Tab. 1 about here}

Assembly Process

Assembly process conveys the information that connects assembly structure, assembly resources and other information together in a logical and time-sequenced way. It consists of a series of basic elements, namely assembly operations. In an assembly operation, a specific part or component is assembled using certain resources. Each assem-bly operation has logical relations (before, after) and time relations (start time, end time) with another.

Table 2 illustrates the properties defined in the OWL-DL ontology model of assembly process, together with the classes linked by them. Figure 4 further represents the OWL-DL model of assembly process using directed graph. The start and end time of an assembly operation is indicated by data properties-beginAt and endAt that belong to a dateTime data type. Before and after, as two object properties that connect two assembly operations, define the sequence of operations. The assembly structure to be assembled in each operation is defined with the assembling property, while the assembly resource to be used is defined with the use property. Property descriptions and restrictions are added to fully represent the relations between different assembly operations, as well as the corresponding assembly structure and assembly resource used in them. {Please insert Tab. 2 about here} {Please insert Fig. 4 about here}

Assembly Position and Orientation

Many aspects of assembly process planning, such as relative positioning of parts and assembly path planning, depend on the position and orientation of parts or components. In order to express the position and orientation of a rigid body geometrical entity, two coordinate systems (CS) are defined: an absolute CS in 3D environment and a relative CS fixed on the entity. The coordinate of the relative CS origin in the absolute CS defines the position of the entity while its orientation is defined by the yaw, pitch and roll angles of the relative CS.

Hence the position and orientation ontology in OWL-DL could be built, as shown in Table 3. {Please insert Tab. 3 about here}

Assembly Entity Geometry

Assembly Entity Geometry contains detailed geometric information of the product, part or component. Based on STEP AP 203, assembly entity geometry is represented by some basic geometric elements such as closed shell, face bound, edge loop and so on. The OWL-DL model of assembly entity geometry can be indicated by the properties and classed as shown in Table 4. The geometric information can be obtained from a STEP file, which is supported by most mainstream CAD software packages, and then organized as such in ontology models. {Please insert Tab. 4 about here}

Ontology Reasoning for ASP

Apart from the explicit relations established in the ontology model, there remains substantial implicit relations within the model, especially those underlying between the geometric elements. These relations could be inferred through a reasoning mechanism to support decision-making in assembly process planning. The ontology and assembly sequence reasoning mechanism will be discussed in the following sections.

The Ontology Reasoning Mechanism

The ontology model based on OWL-DL is composed of a set of triples, with each triple represented as (x,R,y) or R(x,y), in which x and y denote two individuals related to property R. Thus, the reasoning process of implicit relations can be described by the mathematical model as explained in Equation 1.

               1 1 2 2 2 1 1 ( , ) ( , ) ... ( , ) ( , )
        (1)
In Eq. 1, Rt(x,y) is the outcome of reasoning. OntIndividuals represent the collection of all individuals. FactBase is a collection of all the explicit individuals and properties, while InferBase denotes the collection of properties that has been inferred. Each line in the equation represents a constraint, in which Pij(xij,yij) is the jth premise in ith constraint, and Ri is the inferred result of the ith constraint. In each constraint, all premises shall be true to ensure the correct result of inference.

To elaborate, the reasoning mechanism can be depicted with the following steps:

Step 1: Instantiate all the explicit individuals and the properties between them in the existing information, since these individuals and properties compose the facts for reasoning, as denoted by FactBase in the mathematical model.

Step 2: Define the semantic web rules according to the assembly knowledge. The assembly knowledge can be expressed as constraint equations in Eq. 1, which serve as semantic web rules and can be interpreted with the Semantic Web Rule Language (SWRL). SWRL can be recognized by a rule-based reasoning engine such as Pellet [START_REF] Sirin | Pellet: A practical OWL-DL reasoner[END_REF]. Based on the rules defined in SWRL, the engine can infer the implicit relations between individuals, thus creating new triples to compose the InferBase as defined in Eq. 1. For instance, a rule in SWRL defines that if there exist a relation between two individuals A and B, and another relation between individuals B and C, a new triple will be formed inferring a relationship between A and C.

Step3: Query the result by defining an objective function as shown in Eq. 1. Then the Semantic Query-Enhanced Web Rule Language (SQWRL) could be utilized to query the triples that satisfy the objective function. Based on this ontology reasoning mechanism, this paper will discuss the reasoning strategies in the planning of assembly sequence.

Enhanced Reasoning with RU

Traditional SWRL can represent simple rules and logic, while the reasoning of relations between geometric information of product and its assembly process calls for complex computational and decision-making efforts. Therefore, in this paper, the concept of geometry enhanced RU is proposed to enhance the knowledge representation and reasoning capabilities of the ontology-based mechanism.

RU is an extension of rules. As shown previously in Eq. 1, rules are defined based on the judgment of several premises. Each premise has input and output parameters, returning a Boolean value to signify whether the premise is true. Similar to the structure of a premise, an RU also has these parameters and returns a value. Taking advantage of the Custom Built-in Mechanism of SWRL, RU encapsulates complex algorithms, equations and logical judgments through computer programs, which greatly reinforces the reasoning capabilities of SWRL and simplifies the representation. According to their functionalities, the geometry enhanced RUs can be classified into complex algorithms (e.g. calculation of bounding boxes), complex logical judgments (e.g. identification of assembly constraints, in which a series of judgments are made according to the given conditions to decide whether certain constraints exist between two assembly components), and complex equations (e.g. equations for the calculation of relative position of assembly components, in which the distance between the bounding boxes of the components are calculated to decide their relative position).

The RU applied in this paper utilizes the geometric information extracted from STEP files as input parameters, while the computation and logical judgment with the built-in programs, inferred results such as assembly constraints, bounding boxes, relative position of parts and components are output to support the decision-making in ASP.

Assembly Sequence reasoning

Assembly sequence, as a fundamental information in assembly process planning, specifies the logical and time sequence of assembly operations. The design of assembly sequence should be carried out under comprehensive consideration of assembly structure, assembly geometry and relative position of assembly components.

For the proposed framework, the inference engine infers all the implicit relations between individuals according to the rules and existing information. Some of the rules are listed in Table 5. Thereafter, an objective function defined by SQWRL queries the inferred sequence between assembly operations. Since the sequence relations between AssemblyOperation individuals are identified according to their before properties, the individual that owns the largest number of before properties should be assembled first. Thus, the sequence can be determined by sorting the individuals in a descending order of the number of before properties that they have. Accordingly, the objective function can be written in SQWRL as: AssemblyOperation (?x) ∧ before (?x,?y)  sqwrl:select (?x) ∧ sqwrl:count (?y)

By executing Eq. 2, a list of assembly operation instances will be returned showing all the AssemblyOperation individuals and the number of before properties that each individual owns in descending order. Thus, the assembly sequence could be identified from the list. {Please insert Tab. 5 about here}

Case Study

The ASP of a transmission is shown as an example to illustrate how the geometry enhanced ontology modelling and reasoning framework works. The structure of the transmission is shown in Figure 5. {Please insert Fig. 5 about here} First, the existing data, including the product structure and geometry information extracted from the STEP files are imported and stored into the ontology model as the facts for reasoning. Thereafter, rules are defined according to the available knowledge and related RUs are developed for the processing of product geometry information. In addition to the common rules illustrated in Table 5, some specific rules applied in this case study are defined in Table 6. Based on the existing data, rules and reasoning units, the inference engine Pellet is used to infer the implicit sequence relations between assembly operations and the inferred the results are queried through SQWRL.

{Please insert Tab. 6 about here}

The inferred assembly sequence of the product is as follows:

Shaft  right and left bearing right cover screws for the right cover  key for the driving wheel driving wheel left cover  screws for the left cover  key for the gear gear

The sequence is then validated by an assembly process simulation software-DELMIA. The simulation result shows that the inferred sequence is acceptable without causing any clash or interference during the assembly process, thus proving the effectiveness of the proposed framework.

Conclusion

In this paper, a geometry enhanced ontology modelling and reasoning framework is proposed for ASP, which includes an ontology model for assembly operation and an ontology reasoning mechanism for the inference of assembly sequence based on established rules and RUs. The ontology model is highly flexible and customized, due to its extendibility. Main concepts and relations in the domain of product modelling and assembly process planning, such as product structure and assembly process, are described in this framework. Information, such as assembly entity geometry, assembly position and orientation information, is also included in this model, which enhances its ability for geometric representation.

An ontology reasoning mechanism is further proposed using SWRL as a rule description language to make the implicit knowledge explicit. The RUs are also incorporated in this mechanism to enhance its ability in the processing of geometric information. Thus, the implicit relations underlying in the geometric information can be inferred from the ontology data to support automatic decision-making in ASP. A case study is provided to implement the models and methods proposed in this framework in the ASP of a transmission. The result proves the validity of the proposed framework. Moreover, the proposed framework overcomes some inherent limitations in existing models by taking into consideration of geometric information. However, more efforts are needed to complete the representation of assembly process and to incorporate more practical knowledge for ASP.

Structure of the transmission

  is an example of the directed graph. {Please insert Fig. 2 about here} As depicted in Figure 2, the ontology structure is organized with class, property and individual. Concept is represented by class, while individual is an instance of a class. Property includes object property and data property. It founds relationships be-tween two resources.The object property links two individuals and the data property links an individual with a specific type of data.

1

 1

  Figure 1.Ontology-based modelling and reasoning framework

Figure 2 .Figure 3 .

 23 Figure 2. An example of the directed graph representation for OWL-DL model

Figure 4 .

 4 Figure 4. The OWL-DL model of Assembly Process in directed graph representation

1

  If components exist in a product, components should be assembled before single parts Component (?x) ∧ AssemblyOperation (?y) ∧ assemble(?y, ?x) ∧ Part (?z) ∧ AssemblyOperation (?a) ∧ assemble (?a, ?z)  before (?y, ?a) 2 Base part is assembled first Base (?x) ∧ AssemblyOperation (?y) ∧ assemble (?y, ?x) ∧ AssemblyOperation (?z)  before (?y, ?z) 3 The part having the most contact with other parts is the base part Assembly (?x) ∧ enhancedOnto:isBase (?x)  Base(?x) 4 Internal parts are assembled Assembly (?x) ∧ AssemblyOperation (?y) ∧ assemble before external parts (Judging from the distance between the part bounding box and the product bounding box) (?y, ?x) ∧ enhancedOnto:hasDistance (?x, ?u) ∧ Assembly (?z) ∧ AssemblyOperation (?a) ∧ assemble(?a, ?z) ∧ en-hancedOnto:hasDistance (?z, ?v) ∧ greaterThan (?u, ?v)  before (?y, ?a) Table 6. Part of the case study-specific rules for ASP Sr. Implicit relation description Rule description in SWRL 1 The Base part needs to be assembled first. Base (?x) ∧ AssemblyOperation (?y) ∧ assemble (?y, ?x) ∧ AssemblyOperation (?z)  before (?y, ?z) 2 For the screw fastening, assemble the part to be fasten first, then assemble the bolt Screw (?x) ∧ AssemblyOperation (?y) ∧ assemble (?y, ?x) ∧ Component (?z) ∧ hasPart (?z, ?x) ∧ hasPart (?z, ?a) ∧ hasPart (?z, ?b) ∧ AssemblyOperation (?c) ∧ assemble (?c, ?a) ∧ AssemblyOperation (?d) ∧ assemble (?d, ?b)  before (?y, ?c) ∧ before (?y, ?d) 3 For the key connection, assemble key into the key hole first, then assemble the other part Slot (?x) ∧ AssemblyOperation (?y) ∧ assemble (?y, ?x) ∧ Component (?z) ∧ hasPart (?z, ?x) ∧ hasPart (?z, ?a) ∧ hasPart (?z, ?b) ∧ AssemblyOperation (?c) ∧ assemble (?c, ?a) ∧ AssemblyOperation (?d) ∧ assemble (?d, ?b)  before (?y, ?c) ∧ before (?y, ?d)

  ...

	Objective
	Rt x y x y OntIndividuls Rt FactBase InferBase
	ST
	P x y	P x y	n P x y n	n		r x y R x y r r	r
	P x y	P x y	n P x y n	n	r x y R x y r r	r
	m P

Table 1 .

 1 Properties defined in Assembly Structure

	Property	Domain	Range
	isComposedOf #1	Product	Part/Component
	compose #1	Part/Component	Product
	hasConstraint #2	AssemblyStructure	Constraint
	constrains #2	Constraint	AssemblyStructure
	Note: Properties marked with #1 and #2 are two pairs of inverse properties

Table 2 .

 2 Properties defined in Assembly Process

	Property	Domain	Range
	assembleBefore #1 *1	AssemblyOperation	AssemblyOperation
	assembleAfter #1 *1	AssemblyOperation	AssemblyOperation
	assembling *1	AssemblyOperation	AssemblingStructure
	assembled *1	AssemblyOperation	AssembledStructure
	beginAt	AssemblyOperation	xsd:dateTime
	endAt	AssemblyOperation	xsd:dateTime
	use *2	AssemblyOperation	Resource

Note: Properties marked with #1 are a pair of inverse properties. Properties marked with *1 have cardinality restriction with the cardinality as 1, while those with *2 have someValuesFrom restriction

Table 3 .

 3 Properties defined in Assembly Position and Orientation : Properties marked with *1 have cardinality restriction with the cardinality as 1

	Property	Domain	Range
	hasLocation	AssemblyStructure	Location
	hasAxis	Location	Axis
	hasPosition *1	Axis	Position

Note

Table 4 .

 4 A portion of the properties defined in Assembly Geometry Entity

	Property	Domain	Range
	haGeometry	Part	AdvancedBrepRepresentation
	hasManifoldSolidBrep AdvancedBrepRepresenta-	ManifoldSolidBrep
		tion
	hasClosedShell	ManifoldSolidBrep	ClosedShell
	hasAdvancedFace	ClosedShell	AdvancedFace

Table 5 .

 5 Part of the common rules for ASP

	Sr. Rules	Rule description in SWRL

Acknowledgement

This work is supported by the National Natural Science Foundation of China (Grant 51575031), the National Hi-Tech R&D Program (863 Program) (Grant 2015AA043702), and the Graduate Student Innovation Fund of Beihang University. The authors would like to express their appreciation to the agency.


Élise Garrot

Sébastien George

Patrick Prévôt

A SYSTEM TO SUPPORT TUTORS IN ADAPTING DISTANCE LEARNING SITUATIONS TO STUDENTS

Keywords: Computer based environments for human learning, tutors' role and instrumentation, ontology, expert system

Currently, tutor's roles in distance learning are not clearly defined and few tools support him/her in his/her functions. Some tools help tutors to monitor learners and interact with them, but no tools assist them in the setting-up of learning sessions. Activities are created by instructional designers who envisage standard scenarios without knowing the learners. Thus, the aim of our research project is to create a system to help tutors to adapt learning situations to learners' needs and characteristics. The first phase of our work consists in determine tutor's roles in collaborative distance learning, in order to identify his/her needs. Then, we implement an assistance system based on an ontology containing learners' characteristics and parameters of learning situations. An inference engine creates links between these characteristics by reasoning on the ontology. Finally, some rules deduce relations between ontology elements in order to give the tutor advice.

INTRODUCTION

Over the last thirty years, distance learning moved from postal to an on-line teaching in which information and communication technologies (ICT) play a prominent part. In particular, it involved a new definition of teacher roles, even if up to now these are rather badly defined and vary from one educational institution to the other.

Our research is in the area of the computer-based environments for human learning, using partnership between man and machine, particularly through ICT. Internet generalization makes this dimension currently central.

On the one hand, we identify tutor's roles, especially in collaborative learning situations; on the other hand, we design a system aiming at helping the tutor to take up all roles which are assigned to him. More particularly, this tool assists tutor in the setting-up of learning sessions adapted to learners' needs and characteristics.

In this paper, we first determine distance learning functions of tutors, compared with traditional teacher roles. The next section explains why we supply an assistance tool to the tutor. The following sections show system design with an example of implementation in the form of rules which advice the tutor. The final section presents an overview of our work in progress.

TEACHER'S ROLES: FROM PRESENCE TO DISTANCE

Our work is based on a literature survey on teacher's roles in traditional education and distance learning. We first want to determine the effects of distance on teachers' roles and the differences on the actors' interactions and relations due to distance, specifically in collaborative learning. The aim of this study is to determine the roles of the different actors of the course, especially the role of "tutor". [START_REF] Houssaye | Théorie et pratiques de l'éducation scolaire (Tome 1-Le triangle pédagogique)[END_REF] represents relations between learner, teacher and knowledge, under the shape of the "educational triangle". This triangle brings out three educational styles [START_REF] Faerber | Le groupe d'apprentissage en formation à distance : ses caractéristiques dans un environnement virtuel. La place des TICE en formation initiale et continue à l'enseignement : Bilan et perspectives[END_REF]. The teacher-knowledge relation corresponds to the traditional education with transmission of knowledge, the teacher-learner relation defines the emotional and psychological relation between these two actors and learner-knowledge relation represents the appropriation phase of knowledge by the learner.

In traditional education, teacher often has a role of "transmitter of knowledge" and learners absorb a quantity of information, among which little will be transformed into knowledge. School has still an approach to education which tends to inculcate a set of knowledge and capacities which will not be reusable in another context than the one in which they were learnt [START_REF] Perrenoud | L'approche par compétences, une réponse à l'échec scolaire ?[END_REF]. [START_REF] Perrenoud | L'approche par compétences, une réponse à l'échec scolaire ?[END_REF] suggests setting learners in true situations, steps of project, open problems, and incites teachers to offer learners activities in which they will be the actors of their learning. It joins to it the constructivist theories [START_REF] Doise | The Social Development of the Intellect[END_REF] which consider learning as a personal experience towards knowledge, influenced by the social context in which it takes place.

According to the socio-constructivist approach, interactions between learners play a dynamic role in individual learning. In this way, collaborative learning activities are more and more used in distance education. This kind of activity, as projectbased learning [START_REF] George | Project-Based Learning as a Basis for a CSCL Environment: An Example in Educational Robotics[END_REF], business game, case solving, has already proved to be useful When we transpose the "educational triangle" to collaborative and distance learning, other poles and relations appear. In a specific collaborative learning, another element appears: learning group [START_REF] Faerber | Le groupe d'apprentissage en formation à distance : ses caractéristiques dans un environnement virtuel. La place des TICE en formation initiale et continue à l'enseignement : Bilan et perspectives[END_REF]. By introducing this new element, we take into account interactions and relations between learner, teacher and learning group, each learner being a member of a group. These relations and interactions are more complex in the context of our study due to distance. So it is very important to consider the learning group in order to identify teachers' roles and to help the different actors to interact in a positive way.

In distance learning, the function of teacher is then divided into two distinct roles: the instructional designer of courses supports and contents, and the tutor who helps learners to build knowledge and competencies and assess them. A one single person can play both roles, but each role does not intervene in the same moment of the course.

Figure 2 represents new relations between that appear between the learning elements. The relations between items have to be defined: both between the pedagogical team (instructional designer and tutor) and other elements (group, learner and knowledge), and between instructional designer and tutor. Are these both in relation with knowledge? Are they both in relation with learners? A lot of questions appear and our research tends to answer them. We want to determine relations between learner, learning group and pedagogical team and with the knowledge to be acquired by the learner. With this in mind, we consider the tutor as the centre of the learning and try to identify his/her role in specific collaborative distance learning.

TUTOR'S ROLES

In literature, distance tutors are named differently, according to the functions that one assigns to them: moderator, facilitator, online tutor, online moderator, e-moderator, coach, distance education tutor, e-tutor… Reviewing the literature on the tutor's role in distance learning, we were surprised by all the roles that are assigned to only one person and the differences according to distance courses.

Tutors' roles are generally classified into four parts: pedagogical, organisational, relational and technical. [START_REF] Denis | Roles and Competencies of the e-Tutor (Learn Nett project)[END_REF], inside the Learn-Nett project, assign seven different roles to the tutor. For them, the tutor is a content, metacognition and process facilitator, an advisor/counsellor, an assessor, a technologist and a resource provider. According to Lentell (2003, p. 74), "They [tutors] have to be effective listeners and communicators, to be a coach, facilitator, mentor, supporter and resource. They have to listen, to shape, to give feedback, to motivate, to direct, to appreciatebroadly to be developmental and problem solving." According to [START_REF] Dillenbourg | What do you mean by 'collaborative learning'? Collaborative-learning: Cognitive and Computational Approaches[END_REF], the tutor is a "facilitator" because he/she has to assure a minimal educational intervention to guide the learning group in a productive way or to follow which members are except the interaction.

Learner Tutor Designer

Learning Group

Knowledge

Pedagogical team

We based our view of tutors' roles on those who are assigned to them by the platform ACOLAD [START_REF] Faerber | Groupements, processus pédagogiques et quelques contraintes liés à un environnement virtuel d'apprentissage[END_REF] and on the view of [START_REF] Daele | Le tuteur en ligne, quelles conditions d'efficacité dans un dispositif d'apprentissage collaboratif à distance ? In 19ème colloque de l'AIPU[END_REF]. Tutors, in the ACOLAD environment, decide which learning situations to propose to learners, in order to adapt them to their needs. For a given situation, tutors can bring documents and personal references. We agree with this view of tutors' roles because we think that it is very important for them to have the possibility to adapt the activities to learners' needs and characteristics.

It is necessary to differentiate the activities and the interactions so that each learner is in his/her proximal zone of development [START_REF] Vygotsky | Thought and Language[END_REF], so that he/she is constantly or at least very often confronted with the most fertile didactics situations for him/her. Tutors, thanks to their psychological and emotional role, are the ones who are best placed to choose the activities which are appropriated to learners and the resources which they need. [START_REF] Daele | Le tuteur en ligne, quelles conditions d'efficacité dans un dispositif d'apprentissage collaboratif à distance ? In 19ème colloque de l'AIPU[END_REF] are interested in collaborative distance learning based on a pedagogical model centred on the learner and on interactions. In this context, they distinguish two levels of intervention: with the learning group and with the learner. Tutors help the group to define a common project, to find adapted resources, to organize and regulate exchanges, to respect the instructions and deadlines, and to structure itself. They help the learner to express his/her personal project, to articulate it to the project of the group, to think about his/her own approach of learning and collaboration at distance. We also think it is essential to distinguish these two levels of intervention in order not to lose the learner into the learning group. [START_REF] Dillenbourg | What do you mean by 'collaborative learning'? Collaborative-learning: Cognitive and Computational Approaches[END_REF] gives four means to try to develop interactions. These means are the following: to carefully set up the situation of learning (group size, selection of group members, suited tasks…), to specify the "contract of collaboration" with a scenario based on roles (to give different viewpoint to subjects, asking subjects to play a specific role in an argumentation,…), to specify interaction rules for the computer-mediated interactions in collaboration, to monitor and regulate the interactions. This advice corresponds with many roles tutors have to perform in collaborative learning.

In order to be able to play all their roles, tutors must have experience and competencies to base on, so as to be credible towards learners. The tutor may have experience as a teacher or in a local point of expertise in the field of the contents. It is necessary that the tutor has a minimum of competencies in these two fields (pedagogy and in the subject area), so as to have capacities to build himself/herself as an expert. He/she is a witness of his/her personal experience; he/she must be able to bring out the sense of the contents to learners, for example by giving them anecdotes and personal references.

Regarding the works previously described, we synthesize tutors' roles. For the learning group, the tutor is:

A group assessor: he/she assess the learning group's productions and activities.

A resource provider: for a given learning situation, he/she can provide documents or advise adapted resources in order to guide learners in a good way.

A moderator: he/she has to set up the dynamic of the group and to develop interactions within all possible means [START_REF] Dillenbourg | What do you mean by 'collaborative learning'? Collaborative-learning: Cognitive and Computational Approaches[END_REF].

A pedagogical architect [START_REF] George | Complexité des situations pédagogiques e-learning dans un contexte multi-culturel, collaboratif et synchrone[END_REF]: he/she has degrees of freedom to adapt the learning situations created by the instructional designer to learners' needs and characteristics, provided that the designer foresaw that one needs to furnish the training [START_REF] Faerber | Groupements, processus pédagogiques et quelques contraintes liés à un environnement virtuel d'apprentissage[END_REF].

Tutors also have different roles to help the learner. For a learner in particular, the tutor is:

A learner assessor: he/she evaluates the knowledge and competencies that the learner has acquired during the course.

A psychological and emotional support: he/she is a human mediator to motivate the learner, to encourage, stimulate and boost him [START_REF] Lentell | The Importance of the Tutor in Open and Distance Learning[END_REF].

A regulator: he/she has to regulate the learning, to adapt learning situation difficulties for each learner, and to give him/her feedback on the assessment.

A guide and facilitator so that the learner acquires the competencies necessary to autonomy in a specific context of distance and collaborative learning [START_REF] George | Complexité des situations pédagogiques e-learning dans un contexte multi-culturel, collaboratif et synchrone[END_REF]. He/she helps the learner to take part to the learning group interactions and activities.

AN ASSISTANCE TOOL FOR THE TUTOR

As [START_REF] Dufresne | Vers un modèle générique d'assistance aux acteurs du téléapprentissage[END_REF] emphasize, the instrumentation of tutors' activity in distance learning environments is still little developed. Research was rather centred on the characterization and the standardization of learning activities in order to assist authors in the designing of scenarios, and also centred on tutors to support them to monitor learner's activities and interact to solve difficulties [START_REF] Després | Synchronous Tutoring in Distance Learning[END_REF].

As we assert in the previous section, tutors have several roles which do not only consist in monitoring and interacting with learners. We want tutors to be resource providers and pedagogical architects, to set-up the dynamic of the group, to regulate the learning and to adapt situations to learning groups and to each learner in particular. We think that it is impossible for tutors to assume all these roles without a tool to assist them. As suggested by [START_REF] Bennett | Are We Expecting Online Tutors to Run Before They Can Walk[END_REF] tutors are being asked "to run before they can walk".

Generally, the instructional designer prepares scenarios without knowing learners. We prefer the concept of "learning situation" to "scenario". A scenario anticipates a learning process and interactions during learning sessions [START_REF] Faerber | Caractérisation des situations d'apprentissage en groupe[END_REF]. It generally defines a progress through contents, resources, and it anticipates behaviour, tasks sequencing. But is it possible to provide a scenario for all possible cases? We prefer the term "learning situation" which is more general and shows all the possibilities offered to the tutor to adapt learning sessions during the course, according to learners' needs and progress, not defined a priori.

The system we developed assists tutors in the instantiation of generic learning situations provided by instructional designers. Learning situations consist of a set of activities carried-out by a learners group engaged in a same objective. Project, case study, problems resolution… are examples of learning situations. The designer defines parameters for each situation, in order to give degrees of freedom to the tutor to adapt them to learners. The system assists and advises tutors in the setting-up of learning sessions, by creating links between learners' characteristics and the parameters of activities.

Figure 3 highlights the role of the assistance system for tutors to help them to set-up learning sessions. In this configuration, the instructional designer has to envisage a variety of activities and possible situations of learning with parameters (number of students, group size…). Then the tutor can prepare specific learning situations from existing generic situations.

DESIGN OF THE ASSISTANCE TOOL

Development choices

The assistance system must be able to adapt to learning situations which vary according to the type of online courses and the tutoring model applied.

That's why we chose to separate knowledge and reasoning. The system is based on an ontology which represents the different concepts (like actors or activities), their properties and the relations existing between them. Ontology has the advantage to make explicit what is regarded as implicit in the field (Kasai et al., 2004), to use a vocabulary comprehensible by all actors, to re-use and make this vocabulary evolve.

Concerning the implementation, we chose the software Protege20001 , a tool for modelling and knowledge acquisition developed by the University of Stanford, in the United States. The plug-in JessTab2 , integrated into Protege2000, makes it possible to introduce the knowledge stored by Protege2000 into a data base, in order to be inferred by some rules written in the inference engine Jess3 , an expert system independent of Protege2000.

Ontological model

The developed ontology identifies and describes several concepts: the actors of the learning (learner, tutor, designer…), learning situations (project, case-study…), resources, knowledge, behaviour and an historic of the learning. For example, we created two different concepts: Actor and Actors' characteristics. These two concepts correspond to classes which each contains subclasses (figure 4). The class Actor has for subclasses Learner, Tutor, Instructional Designer and Computer Designer. To each subclass of the class Actors'-characteristics correspond general characteristics (like identity) and the subclass Learner has specific characteristics. For the moment, we have especially developed learner characteristics but tutor characteristics can be added later. Both concepts are connected by properties of the class Actor which are instances of the class Actors'characteristics.

For the learner, we identified five general characteristics: learner's knowledge and behaviour, his/her experience, identity profile (curriculumvitae, cultural origins, interests and habits), needs and objectives, and cognitive capacities (figure 4). To give a structure and describe learning situations, we referred to the granularity levels of the standard IMS-LD (IMS Learning Design) 4 . This model, based on the EML standard [START_REF] Koper | Modeling Units of study from a pedagogical perspective -The pedagogical metamodel behind EML[END_REF], describes a formal way to represent the structure of a Unit of Learning and the concept of a pedagogical method specifying roles and activities that learners and support persons can play using learning objects.

In the ontology, activities are decomposed in the following way: Course -> Learning situation -> Activity -> Resources and communication tool -> Media (figure 5). The course corresponds to a unit of learning described in IMS-LD and, as we said in the previous section, the concept of "learning situation" is preferred to "scenario". 4 http://www.imsglobal.org/learningdesign/index.html We consider that learners carry out a set of activities within a same learning situation. In a case study-based learning, an activity can be the problem formalization, searching for causes or solutions. Some resources (documents…) and means of communication (chat, forum, e-mail…) are offered to actors before and during learning sessions. They represent the learning environment. A resource is composed of media (picture, video, sound…).

We have brought out two important concepts: knowledge and behaviour [START_REF] Paquette | Modélisation des connaissances et des compétences[END_REF], because these two concepts are linked to other concepts of the ontology: activity, learning situation and learner. On the one hand, activities and learning situations have properties which define pre-required knowledge and behaviours, and knowledge and behaviours to be acquired. On the other hand, learners have initial behaviours and knowledge, and some to acquire during the course. It is important for the tutor to have the possibility to note and to have access to data concerning learners. We give tutor the possibility to keep for each learner and learning group a chronological record of learning. With this chronological record tutors can indicate learners' achievements, interactions and carried-out activities. Tutors can also note their perceptions about learners, on their level of initiative, motivation, stress, autonomy or interactions, at some point of the course.

IMPLEMENTATION OF RULES TO ADVICE THE TUTOR

The implementation of the system consists in writing different types of inference rules. These types are the following ones:

Rules which create links between learners' characteristics.

Rules which deduct advice to give to the tutor concerning the type of pedagogy to be applied for each learner, according to some of his/her characteristics.

Rules which create links between activities' parameters and learners' characteristics by advising the tutor an activity to attribute to a learner according to some variables.

Rules can help tutors to play all the roles we assigned in a previous section. For example, tutors are moderators who have to develop interactions. To play this role, [START_REF] Dillenbourg | What do you mean by 'collaborative learning'? Collaborative-learning: Cognitive and Computational Approaches[END_REF] gives recommendations: set up the situation, specify interaction rules and roles inside the learning group. These recommendations can be implemented in the system in the form of rules, which infer advice to tutors, according to the characteristics of a given activity defined in the ontology, in the form of an instance of the class Activity.

For example, let us consider a learner who has just validated an activity. We have developed a rule which advises the tutor an activity to attribute to the learner and the modality associated (individual or collective), according to the need for autonomy declared by this learner. The rule so created looks for activities which need the pre-required activities validated by the learner. Then, in the case of an activity which can be indifferently done in an individual or collective way, we look at the need in autonomy declared by the learner and we advise an activity with the associated modality. We present a part of the code which enables this rule to be followed: (if (and (eq ?pre_required_activities ?validated_activities_object) (eq (slot-get ?activity modality) individual-or-collaborative)) then (foreach ?need (slot-get ?learner has-as-needs-and-objectives) (if (eq (slot-get ?need autonomy) TRUE) then (printout t "Propose to learner "?name" to do the actvity "?activity_name "individually."crlf))

The rules have no ambition to be totally educationally valid at this time of the project; they only show the feasibility of the system. To validate the rules, we will work with specialists of education sciences.

We also want to give the possibility to tutors to modify and create the instructional rules themselves, so as to ensure a good appropriation of the tool by tutors. We do not want either to replace the tutor by a system, or to automate its work. We want to assist him/her in his/her functions with a system which gives advice. This research is based on the partnership between man and machine.

WORK IN PROGRESS

In the next weeks, we will validate our view of tutors' roles and needs by interviewing some of them. We are in relation with several tutors of various backgrounds who are interested in working in collaboration on this subject. We will present to tutors a model of our assistance tool, so as to make its functionalities progress.

We developed a system to assist the tutor before learning sessions in the setting-up of learning situations. Tutors also monitor and manage learning sessions. Beyond the learners monitoring necessary in a pedagogical way, we are more particularly interested in recovering information about learners' activities and interactions which will guide tutors in the setting-up of sessions to come. This iterative functioning is the heart of our future research work (figure 7). The aim is to develop specific monitoring tools in order to trace learner activities to determine or get more precise learners' characteristics. The monitoring tools will have to be configurable by the tutor. DIRECTION A result of this research concerns tutors' roles in collaborative distance learning. We assigned four roles in regard to the learning group and four roles in regard to each learner individually. This work led to the implementation of a system to help tutors to adapt learning sessions to learners, taking into account their characteristics and needs during the course.

The system is based on an ontology which integrates all the learning concepts (actors, learning situations, activities, resources) by specifying their properties and relations. Finally, the development of the system containing rules, which apply on the classes instances of the ontology, showed the feasibility of our assistance system to set-up learning situations. Moreover, the diversity of rules shows the flexibility of the system and the many prospects offered. Future research will be directed towards two axes: the validation of our view of tutors' roles and needs and the complete implementation of the system. We are in relation with several tutors of various specialities who are interested in working in collaboration on this subject. It will be as many possible grounds for our future experiments.

Concerning the tutor's assistance system to configure learning activities, we want to conceive various interfaces for learning actors, in order to guide them to insert data in the ontology. In addition, it will be interesting to give the tutor the possibility to modify and create learning rules himself, thus ensuring a feed-back on uses and a good appropriation of the tool. We also have in prospect to associate an interactions analysis agent to automatically feed the system with data concerning interactions between learners.

Figure 2 :

 2 Figure 2: Relations between actors of learning and knowledge

Figure 3 :

 3 Figure 3: The functioning and the place of our assistance tool to help tutors

Figure 4 :

 4 Figure 4: Properties associating to learners characteristics in Protege2000

Figure 5 :

 5 Figure 5: Activities description in Protege2000

Figure 7 :

 7 Figure 7: Iterative functioning of the system

http://protege.stanford.edu/

http://www.ida.liu.se/~her/JessTab/

http://herzberg.ca.sandia.gov/jess/