P A Fall

Al Papa

Abdoulaye Fall

Françoise Leroi

Frédérique Chevalier

Camille Guérin

Marie-France Pilet

Protective Effect of a Non-Bacteriocinogenic Lactococcus piscium CNCM I-4031 Strain Against Listeria monocytogenes in Sterilized Tropical Cooked Peeled Shrimp Inhibition of Listeria monocytogenes by Lactococcus piscium

Keywords: inhibition, biopreservation, challenge-test, lactic acid, nutritional competition P

The protective activity of a non-bacteriocinogenic Lactococcus piscium CNCM I-4031 strain against Listeria monocytogenes was investigated in tropical cooked peeled shrimp stored at 8°C in modified atmosphere packaging (50% N 2 -50% CO 2 ). When inoculated alone (L. piscium 10 7 CFU g -1 and L. monocytogenes 10 4 CFU g -1 ), protective culture and target strain grew very well on shrimp reaching a maximum cell number of 10 9 CFU g -1 after 7 and 14 days, respectively. In the presence of L. piscium, growth of L. monocytogenes was totally prevented after 3 days of storage. The count was 3.4 log CFU g -1 lower than in the control after 10 days and until the end of storage (31 days). Using the Seafood Spoilage and Safety Predictor Software (http://sssp.dtuaqua.dk), it was shown that pH decrease from 6.58 to 5.94 and lactic acid concentration of 89.65 mM measured in the co-inoculated batch did not fully explain the inhibition observed.

Introduction

Shrimp is one of the most marketed seafood products in the world. In France, shrimp is the second most imported seafood (after salmon) with 105,300 tons and 536 million euros in value during 2008 (http://www.ofimer.fr/Pages/filiere/bilans_annuels_ofimer). Convenience preparation such as cooked and peeled shrimp packed under modified atmosphere is gaining more and more importance in Europe. These products are very sensitive to microbial growth due to their neutral pH, weak salinity, and presence of nitrogenous compounds with weak molecular weight. Growth of pathogenic microorganisms such as Listeria monocytogenes constitutes a major problem in such refrigerated ready-to-eat (RTE) food products. L. monocytogenes is a human pathogenic bacteria that is responsible for foodborne listeriosis generally associated with a high mortality rate: 20-40% among the high risk group of people (pregnant women, immuno-compromised patients, etc.). The presence of L. monocytogenes was detected in 26.5% of cooked peeled shrimp analyzed by [START_REF] Valdimarsson | Microbiological quality of Icelandic cooked-peeled shrimp (Pandalus borealis)[END_REF] and in 11.2% of semi-final products according to the survey Address correspondence to Marie-France Pilet, ONIRIS, UMR INRA 1014 Secalim, Rue de la Géraudière, BP 82225, F-44322 Nantes, France. E-mail: marie-france.pilet@oniris-nantes.fr of [START_REF] Gudmundsdottir | Contamination of cooked peeled shrimp (Pandalus borealis) by Listeria monocytogenes during processing at two processing plants[END_REF], confirming the safety risk when good hygienic practices are not respected. Growth of this undesirable bacteria is usually delayed, but not totally stopped, by the use of classical techniques such as salting, low storage temperature, or modification of the atmosphere packaging [START_REF] Rutherford | Combined effect of packaging atmosphere and storage temperature on growth of Listeria monocytogenes on ready-to-eat shrimp[END_REF][START_REF] Tsigarida | Behaviour of Listeria monocytogenes and autochthonous flora on meat stored under aerobic, vacuum and modified atmosphere packaging conditions with or without the presence of oregano essential oil at 5 degrees C[END_REF]. Preservatives-mainly organic acids that are not always well-accepted by the consumerare often added with more or less success [START_REF] Heavin | Inhibition of Listeria monocytogenes by acetate, benzoate and sorbate: Weak acid tolerance is not influenced by the glutamate decarboxylase system[END_REF][START_REF] Mejlholm | Antimicrobial effect of essential oils on the seafood spoilage micro-organism Photobacterium phosphoreum in liquid media and fish products[END_REF][START_REF] Tokarskyy | Mechanism of synergistic inhibition of Listeria monocytogenes growth by lactic acid, monolaurin, and nisin[END_REF][START_REF] Mejlholm | Microbial changes and growth of Listeria monocytogenes during chilled storage of brined shrimp (Pandalus borealis)[END_REF]. All of these results pointed out that L. monocytogenes can constitute a major safety risk for consumers in such products.

Therefore, the research of new natural hurdles which limit the growth of pathogenic bacteria in shrimp is important. Biopreservation-a technology consisting of using protective living microorganisms to inhibit the growth of pathogenic and spoiling bacteria-has gained increasing attention to ensure the safety of RTE food. Many studies reported the usefulness of some bacteriocin-producing lactic acid bacteria (LAB) to limit the growth of L. monocytogenes in seafood, especially in cold-smoked salmon [START_REF] Brillet | Biodiversity of Listeria monocytogenes sensitivity to bacteriocin-producing Carnobacterium strains and application in sterile cold-smoked salmon[END_REF][START_REF] Tomé | Growth control of Listeria innocua 2030c on vacuum-packaged cold-smoked salmon by lactic acid bacteria[END_REF][START_REF] Vescovo | Inhibition of Listeria innocua growth by antimirobial-producing lactic acid cultures in vacuum-packed cold-smoked salmon[END_REF][START_REF] Weiss | Lactic acid bacteria as protective cultures against Listeria spp. on cold-smoked salmon[END_REF]. However, the Quality Presumption of Safety status that is a required measure for a food application in Europe may be more difficult to obtain for bacteriocinogenic bacteria, enhancing the interest for protective cultures that do not produce bacteriocin-like compounds. Selection of such bacteria that inhibit L. monocytogenes without changing the delicate flavor of shrimp is still a challenge and has so far been explored only in a few studies [START_REF] Nilsson | Growth control of Listeria monocytogenes on coldsmoked salmon using a competitive lactic acid bacteria flora[END_REF][START_REF] Nilsson | Growth inhibition of Listeria monocytogenes by a non-bacteriocinogenic Carnobacterium piscicola[END_REF][START_REF] Yamazaki | Inhibition of Listeria monocytogenes in cold-smoked salmon by Carnobacterium piscicola CS526 isolated from frozen surimi[END_REF].

In a recent study, a strain of Lactococcus piscium has been isolated from raw salmon and has shown capacities to enhance the sensory shelf-life of naturally contaminated cooked/peeled shrimps and cold-smoked salmon (Matamoros et al., 2009a). This strain also showed inhibition of L. monocytogenes without bacteriocin production. The aim of this study was to confirm the specific antimicrobial activity of this strain against L. monocytogenes in tropical shrimp packed under modified atmosphere and to investigate the inhibitory mechanisms that could be involved in this inhibition. For that purpose, a sterilized shrimp model was used to avoid the background flora. Physicochemical parameters related to the growth of the protective and the target strains were also determined in order to tentatively explain the inhibition.

Materials and Methods

Strains and Culture Conditions

The strains of Lactococcus piscium CNCM I-4031 (formerly, Lactococcus piscium EU2241) and Listeria monocytogenes RF191 used in this study were isolated from fresh salmon steak packed under modified atmosphere (Matamoros et al., 2009b) and from tropical cooked peeled shrimp, respectively (CEVPM, Boulogne-sur-mer, France). Bacterial strains were stored at -80°C in their growth medium containing 10% glycerol. For challenge tests, L. monocytogenes RF191 and L. piscium CNCM I-4031 were subcultured twice successively in Brain Heart Infusion and Elliker broth (Biokar Diagnostics, Beauvais, France), respectively, for 24 h at 26°C. Cultures were then diluted in physiological solution (0.85% NaCl, 0.1% peptone) to obtain appropriate cell concentrations.

Shrimp Preparation

Farmed tropical shrimp (Penaeus vannamei) from Colombia were supplied by MITI (Nantes, France) in frozen, beheaded, and peeled conditions, without sulphite added. They were cooked in our laboratory at 100°C for 2.5 min in 3% salted water. After cooking, shrimp were immediately immersed in melting ice and frozen at -80°C. They were transported to IONISOS (Pouzauges, France) for ionization at 3.75 kGy, under frozen conditions (-80°C).

Challenge Tests

Cooked shrimp were inoculated at 10% (v/w) by spraying diluted cultures to obtain an estimated final level of 7 log CFU g -1 and 4 log CFU g -1 for L. piscium and L. monocytogenes, respectively.

Four batches were prepared: (1) sterility control;

(2) inoculation with L. piscium CNCM I-4031; (3) inoculation with L. monocytogenes RF191; and (4) co-inoculation with L. piscium + L. monocytogenes. After inoculation, portions of 125 g of shrimp were packed in punnets under modified atmosphere 50% N 2 -50% CO 2 (Multivac T250, Wolfertschwenden, Germany) with a ratio shrimp:gas of approximately 2:1. The samples were stored at 8°C for 31 days and regularly sampled for microbiological and physicochemical analyses. All the analyses were done in triplicate.

Microbial Enumeration

Each day of analysis, three punnets per batch were opened, and 20 g of shrimp were mixed with 80 mL of physiological solution in sterile plastic bags and blended with a stomacher 400 (Seward Medical, London, UK) for 2 min. Total microbial flora was determined in uninoculated batch by pour plating (26°C, 48-72 h) on Plate Count Agar (Biokar Diagnostics). L. piscium was enumerated by spread plating onto Elliker agar plates incubated at 26°C for 48 h under anaerobiosis for batch 2 and at 8°C for 7 days for batch 4. L. monocytogenes was enumerated on spread plate of Palcam with selective supplement (Biokar Diagnostics) after 24 h at 37°C.

Physicochemical Parameters

The pH was measured immediately after microbiological analyses into the stomacher bag by immersing the electrode of the pH-meter (Mettler Delta 320, Halstead, UK). L-lactic and acetic acid determination was performed using enzymatic kits with NADH 2 detection at 340 nm (acetic acid 021 and L-lactic acid kit 022, Biosentec, Toulouse, France). D-lactic acid was not monitored as we had previously confirmed that L. piscium and L. monocytogenes did not produce this isoform. Fifty grams of flesh per punnet were homogenized in a Waring Blender (Waring, New Hartford, CT, USA), and 3 g of homogenate were mixed with 20 mL of water. The mixture was centrifuged at 10000 g for 10 min. The supernatant was transferred into a new tube and used as sample solution in the assays by following the instruction of the enzymatic test kit supplier. Sugar content was measured by a modified colorimetric method of [START_REF] Dubois | Method for determination of sugars and related substances[END_REF]. The nature of the sugar was identified by gas chromatography using the method of [START_REF] Kamerling | Chatacterization by gas-liquid chromatography mass spectrometry and proton-magnetic resonance spectrospcopy of pertrimethylsilyl methyl glycosides obtained in methanolysis of glycoproteins and glycopeptides[END_REF], modified by [START_REF] Montreuil | Carbohydrate Analysis: A Practical Approach[END_REF]. The injection of compounds derived from glycoside residues was performed on an AT 6890N chromatograph (Agilent Technologies, Santa Clara, CA, USA) equipped with an automatic sample loader, a Factorfour capillary column VF-1MS (Varian Inc., Lake Forest, CA, USA) with helium as carrier gas and a flame ionization detector. The temperature profile was programmed as follows: 50°C for 1 min, from 50°C to 120°C at 20°C min -1 , from 120°C to 240°C at 2°C min -1 , from 240°C to 280°C at 10°C min -1 , and 280°C for 10 min. Prior to inoculation, shrimp characteristics (pH, water phase salt content, proteins, lipids, and dry matter) were analyzed in triplicate from 125 g of crushed flesh. For water content, 8 g of sample were dried at 105°C overnight. The Kjeldahl method [START_REF] Crooke | Determination of ammonium in Kjeldhal digests of crops by an automated procedure[END_REF]) was used to determine total proteins. Salt content in shrimp meat was determined using a chlorine analyser (Sherwood MK II analyser 926, Grosseron, Nantes, France). Total fat content was extracted by using the Folch method [START_REF] Folch | A simple method for isolation and purification of total lipids from animals tissues[END_REF].

Listeria monocytogenes Growth Prediction

The Seafood Spoilage and Safety Predictor software V3.1 (SSSP V. 3.1) proposed by Mejlholm and Dalgaard (2007b) and developed to predict the growth of L. monocytogenes in seafood product was used (http://sssp.dtuaqua.dk, retrieved September 3, 2009). This software takes into account different product characteristics such as pH; water phase NaCl; lactic, acetic/diacetate, benzoic, citric, and sorbic acids; phenolique content; storage temperature; % CO 2 in headspace gas at equilibrium; and naturally occurring lactic acid bacterial count.

Results and Discussion

After cooking, shrimp were composed of 73 ± 0.5% of water, 22.1 ± 0.0% of proteins, 0.49 ± 0.0% of total lipid, 0.47 ± 0.04% of glucose, and 1.24 ± 0.02% of NaCl, and had an initial pH of 6.54 ± 0.02. In uninoculated batches, no colony was detected on the Petri dishes within the 31 days of storage, showing that the ionisation method allowed a good decontamination (detection threshold: 5 CFU g -1 ). Ionization at low level (2-4 kGy) under frozen conditions to avoid lipid oxidation has already been used to obtain sterile coldsmoked salmon small blocks for bacterial interactions studies [START_REF] Brillet | Biodiversity of Listeria monocytogenes sensitivity to bacteriocin-producing Carnobacterium strains and application in sterile cold-smoked salmon[END_REF][START_REF] Joffraud | Effect of bacterial interactions on the spoilage of cold-smoked salmon[END_REF]. Figure 1 shows the growth of L. piscium and L. monocytogenes in inoculated batches. L. piscium increased from 7.0 ± 0.2 log CFU g -1 to 9.1 ± 0.1 log CFU g -1 in 7 days and remained at its maximum level during the entire storage period. L. monocytogenes was inoculated at 3.8 ± 0.1 log CFU g -1 and reached 9.2 log CFU g -1 after 14 days. For both bacteria, no lag phase was observed. These results demonstrated the adaptation of L. piscium CNCM I-4031 and L. monocytogenes RF191 to the shrimp matrix. A rapid growth of L. monocytogenes at 8°C has also been observed by Matamoros et al. (2009a) in vacuum-packed cooked shrimp and in the same products stored at 8°C under modified atmosphere containing 50% CO 2 , 30% N 2, and 20% O 2 [START_REF] Mejlholm | Shelf life and safety aspects of chilled cooked and peeled shrimps (Pandalus borealis) in modified atmosphere packaging[END_REF]. In the presence of L. piscium CNCM I-4031, L. monocytogenes count increased by approximately 1 log during the first 4 days, but then growth was totally stopped. The population was reduced by 3.4 ± 0.2 log CFU g -1 compared to the control after 10 days of storage, and this reduction lasted for 31 days (Figure 1). Considering the fact that the natural initial contamination levels of L. monocytogenes in shrimp are generally very low (< 1 CFU g -1 ; [START_REF] Paranjpye | Incidence, growth, and inactivation of Listeria monocytogenes in cooked and peeled cold-water shrimp[END_REF], the protective effect of L. piscium CNCM I-4031 demonstrated in this study could be very promising to ensure the safety of RTE shrimp toward L. monocytogenes risk. Many studies failed to correctly prevent growth of L. monocytogenes in food products by using preservatives or non-bacteriocin producing LAB. [START_REF] Richard | Evidence on inhibition of Listeria monocytogenes by divercin V41 action[END_REF] failed to prevent growth of L. monocytogenes with a non-bacteriocin mutant of C. divergens V41. [START_REF] Yamazaki | Inhibition of Listeria monocytogenes in cold-smoked salmon by Carnobacterium piscicola CS526 isolated from frozen surimi[END_REF] also failed to prevent growth of L. monocytogenes at 12°C and 20°C in cold-smoked salmon by using a non-bacteriocinogenic C. piscicola JCM 5348. [START_REF] Paranjpye | Incidence, growth, and inactivation of Listeria monocytogenes in cooked and peeled cold-water shrimp[END_REF] demonstrated that ozone and chlorine dioxide were not efficient to inhibit the growth of L. monocytogenes in cooked peeled cold-water shrimp.

In the study of [START_REF] Mejlholm | Shelf life and safety aspects of chilled cooked and peeled shrimps (Pandalus borealis) in modified atmosphere packaging[END_REF], an effect of the natural lactic flora on the growth inhibition of L. monocytogenes was observed at 2°C, but it was hugely reduced at 5°C or 8°C. Some combinations of citric, benzoic, and sorbic acids often used in industry were also not totally efficient to prevent growth of L. monocytogenes in brined shrimp [START_REF] Mejlholm | Microbial changes and growth of Listeria monocytogenes during chilled storage of brined shrimp (Pandalus borealis)[END_REF]. In our experiment, growth of L. monocytogenes stopped when L. piscium CNCM I-4031 reached its maximum population density. This phenomena is usually described as the Jameson effect [START_REF] Gimenez | Modelling and predicting the simultaneous growth of Listeria monocytogenes and spoilage micro-organisms in cold-smoked salmon[END_REF][START_REF] Ross | Predictive modeling of the growth and survival of Listeria in fishery products[END_REF]. However, the mechanisms involved in this effect are still not elucidated. In order to determine if the growth limitation of L. monocytogenes could be due to acidification, pH and organic acids production were monitored during the storage (Figure 2). The pH value remained constant (6.54-6.59) in the uninoculated batch during the whole storage time (data not shown), whereas in all inoculated batches, a pH decrease was observed suggesting that acidification can only be linked to the presence and growth of microorganisms. In samples inoculated with L. piscium CNCM I-4031, the pH value decreased rapidly from 6.58 ± 0.02 to 5.94 ± 0.13 (Figure 2) after 7 days of storage and then remained constant during storage. L. monocytogenes also reduced the pH from 6.52 ± 0.03 to 5.90 ± 0.01 but only after 17 days of storage. In the co-inoculated batch, the pH reduction was similar to the one observed in the L. piscium batch; i.e., decrease from 6.62 to 5.91 ± 0.06 after 7 days of storage. No acetic acid was produced by L. piscium and L. monocytogenes. In sterility control, the naturally occurring water phase L-lactate was constant, between 25.57-28.15 mM during the storage time. In all other batches, a L-lactic acid production was recorded. When L. piscium CNCM I-4031 was inoculated alone, the maximum concentration (52.81 ± 4.56 mM ) was observed at day 7, when the maximum cell count was reached, and coincided with the pH decrease (Figure 2). L. monocytogenes is also a L-lactic acid producer, and quite similar concentrations were noticed at the end of the growth phase (47.64 ± 0.91 mM after 17 days). In the co-inoculated batch, L-lactic acid concentration increased to 89.65 ± 1.82 mM in 7-days storage, corresponding to the sum of lactic acid produced by L. piscium and L. monocytogenes during this period. Then, a decrease to 56.16 ± 1.52 mM was observed. The lactic acid concentration in the batch inoculated with L. piscium CNCM I-4031 is similar to those obtained by Papathomopoulou and [START_REF] Fall | Inactivation of verocytotoxigenic Escherichia coli and Listeria monocytogenes co-cultured with Lactobacillus sakei in a simulated meat fermentation medium[END_REF], who demonstrated in their study that 54 mM of lactic acid at pH 4.15 had a great antimicrobial action on L. monocytogenes growth in simulated meat medium fermentated with Lactobacillus sakei. In another study, [START_REF] Juven | Growth and survival of Listeria monocytogenes in vacuum-packaged ground beef inoculated with Lactobacillus alimentarius FloraCarn L-2[END_REF] showed that 50 mM of lactic acid at pH 5.4 produced by Lactobacillus alimentarus was enough to reduce by 2 log the count of L. monocytogenes in vacuum-packed ground beef. Weak organic acids such as lactic and acetic acids are known to limit microbial growth because of their strong antimicrobial activity [START_REF] Choi | Combined effect of organic acids and supercritical carbon dioxide treatments against nonpathogenic Escherichia coli, Listeria monocytogenes, Salmonella typhimurium and E-coli O157:H7 in fresh pork[END_REF]Mejlholm and Dalgaard, 2007a). However, this antimicrobial effect is more pronounced when the pH is close to their pKa value (3.86 and 4.76 for lactic acid and diacetate, respectively), as shown in the study of [START_REF] Fall | Inactivation of verocytotoxigenic Escherichia coli and Listeria monocytogenes co-cultured with Lactobacillus sakei in a simulated meat fermentation medium[END_REF], due to toxicity of the non-dissociated fraction of weak organic acids. Comparing our results to those above, the lactic acid produced by L. piscium CNCM I-4031 at the pH value of 5.9 may have a limited effect on L. monocytogenes growth. In order to confirm this hypothesis, the SSSP V. 3.1 was used. When predicting the growth of L. monocytogenes alone, the value of the environmental parameters were: temperature (8°C), % CO 2 in headspace gas at equilibrium (45%), water phase salt (1.24), pH value (6.54), and water phase lactate (25.5 mM). When predicting growth of L. monocytogenes in the presence of lactic acid in the co-culture with L. piscium CNCM I-4031, the pH and water phase lactate used were 5.9 and 89.65 mM, respectively. The predicted and observed growth of L. monocytogenes in shrimp are shown in Figure 3. The maximum population density of L. monocytogenes RF191 observed in shrimp when inoculated alone was 9.4 log CFU g -1 , whereas the predicted density was 8.5 log CFU g -1 . The model sensibly underestimated the growth of L. monocytogenes. In the presence of 89.65 mM of lactic acid at pH (5.9), the predicted μ max and N 31 days were 0.029 h -1 and 8.5 log CFU g -1 ; whereas observed μ max and N 31 days were 0.009 h -1 and 6.1 ± 0.1 log CFU g -1 , respectively. These results showed that in shrimp meat the lactic acid produced by L. piscium CNCM I-4031 combined with the limited decrease of pH (5.9) cannot fully explain the antilisterial activity. When introducing the lactic acid bacteria count in the model, no growth of L. monocytogenes was predicted after 4 days, as observed in our study. However, the reason for the inhibition remained unknown. Matamoros et al. (2009b) have shown that the antimicrobial activity of this strain could not be linked to bacteriocin-like compounds or hydrogen peroxide. Other mechanisms like nutritional competition or synergic effects between lactic acid production and depletion for specific nutrients may be involved in this bacterial interaction. In the batch inoculated with L. piscium CNCM I-4031 alone, glucose concentration decreased from 0.36 ± 0.00% to 0.16 ± 0.01% during the first 3 days of storage and remained almost constant during the entire storage period. The same evolution was noticed in the co-inoculated batch (data not shown), whereas in the batch inoculated with L. monocytogenes alone, the glucose concentration decreased slowly from 0.43 ± 0.01% to 0.17 ± 0.01 % over 17 days of storage. The rapid consumption of glucose by the L. piscium strain could partially explain its inhibitory activity toward L. monocytogenes as it has been shown previously with a strain of Carnobacterium maltaromaticum (piscicola; [START_REF] Nilsson | Growth inhibition of Listeria monocytogenes by a non-bacteriocinogenic Carnobacterium piscicola[END_REF]. To elucidate the implication of glucose or other nutrient compounds competition in the inhibition of L. monocytogenes by L. piscium CNCM I-4031, a liquid medium simulating shrimp composition is under development.

Figure 1 .

 1 Figure 1. Growth of Lactococcus piscium CNCM I-4031 and Listeria monocytogenes RF191 in peeled and cooked shrimp packed under modified atmosphere and stored at 8°C. () L. piscium CNCM I-4031 alone; (ٗ) L. piscium CNCM I-4031 co-inoculated with L. monocytogenes RF191; (x) L. monocytogenes RF191 alone; and (▲) L. monocytogenes co-inoculated with L. piscium CNCM I-4031. Values are averages of three analyses ± standard deviation.

Figure 2 .

 2 Figure 2. L-lactic acid (dotted line) and pH (solid line) evolution in peeled and cooked shrimp packed under modified atmosphere, stored at 8°C and () inoculated with Lactococcus piscium CNCM I-4031 alone; (x) L. monocytogenes RF191 alone; and (᭹) co-inoculated with L. piscium CNCM I-4031 and L. monocytogenes RF191. Values are averages of three analyses ± standard deviation.

  Figure 3. Observed and predicted growth by the Seafod Spoilage and Safety Predictor V.3 software of Listeria monocytogenes in peeled and cooked shrimp packed under modified atmosphere and stored at 8°C. (x) observed L. monocytogenes RF191 alone; (▲) observed L. monocytogenes RF191 co-inoculated with Lactococcus piscium CNCM I-4031; (thick line) predicted L. monocytogenes alone; (thin line) predicted L. monocytogenes at pH 5.9 and with 89.65 mM of lactic acid.

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Conclusion

The inhibitory effect of L. piscium CNCM I-4031 described in this study suggests that this strain may be efficient to control L. monocytogenes growth in cooked and peeled shrimp stored in modified atmosphere at abuse temperature.


A GEOMETRIC AID DURING THE FIRST STAGES OF PRODUCT COLLABORATIVE DESIGN Denis PALLEZ, Parisa GHODOUS, Michel MARTINEZ PRISMa Laboratory -University of Lyon1 -France pallez@netcourrier.com ABSTRACT: (196 words) The technological advances carried out these last years in the field of products development led the researchers to elaborate the approaches that reduce the cost and time of product development, enhance the quality of product and help the designers to be more creative. These objectives are difficult to obtain due to a large number of phases, which should be carried out during the product development and the large number of experts of different disciplines that are involved. Currently, computer aided systems and software have concentrated on the capture and representation of geometrical shape and technical information as opposed to providing supports for product design in the earlier stages of design process. In a non-routine design, it is delicate and extremely complex to obtain the best products answering customer's specifications. The aim of this paper is to present a methodology to assist designers during the first stages of design. The objective is not to construct automatically the shape but both to automate a certain number of heavy and tiresome tasks, and assist designers during collaborative design. In best case, this assistance makes the designers' stimulation possible by presenting them solutions that they had not thought before.

ARTICLE: (3381 Words without references and figures)

The will to capitalize the know-how of firms and to reduce times of production make that one now truly approaches the CAD/CAM systems in the optics of a functional/conceptual modeling [START_REF] Minich | Vers des outils informatiques d'assistance aux phases amont de la conception -Etat de l'art[END_REF]. The development of CAD/CAM systems knew several phases; restricted themselves to geometry first, they was little by little enriched with information of higher semantic level; those information could be dedicated to specific trades that took part in the product design. By this way, features and product modeling represent an improvement of design models by adding to the geometry necessary information to the manufacture, for example.

The goal is to assist a CAD software user during the earlier stages of the product design. However the current systems are still based on geometry and in order to achieve the wished goal, it is necessary to delay computations and to introduce higher semantic level concepts [START_REF] Minich | Vers des outils informatiques d'assistance aux phases amont de la conception -Etat de l'art[END_REF]. Introducing form features carried out a first effort [START_REF] Salomons | Computer support in the design of mechanical products[END_REF]. They assemble elements of geometry of very low level (as faces or edges) to form generic entities easily handled by the engineer because they could directly be associated with functionality [START_REF] Feng | Representation of functions and features in detail design[END_REF] like sliding motion for a groove or buttress for a shouldering wall. Even if the engineer is brought to manipulate entities whose he apprehends, he is still obliged to think and to generate the product's shape to be designed. Moreover form features are essentially based on geometry as it is made by current software systems. But these ones give a too significant part to the geometrical models by encapsulating them with specific information of various activities. And it is to go against a current tendency of the research that tightens to oust geometry of its central position [START_REF] Brun | Modèle produit : les conditions de cohérence et leur évolution au cours du processus de conception[END_REF]. Research tends to reverse this inclination: it makes possible to represent the product from a more conceptual point of view in introducing functions. The latter represent the translation of the product's specifications from the first stages of the design (that are the most determining). To design a product that satisfies all its functions makes possible to obtain a product of quality, taking into account the cost, the longevity and the adaptation [START_REF] Ullman | The mechanical design process[END_REF]. Currently, only manual or assistance techniques of functions product's development exist (value analysis, Qualitative Function Deployment (Ullman 1997), FAST...). Handled information is mainly expressed in natural language (Figure 1a), which makes it not easily automatisable even if there exists models making possible to build a functional decomposition facilitating the product's simulation. FBS (Function Behaviour Structure [START_REF] Tomiyama | A CAD for functionnal Design[END_REF] [START_REF] Umeda | Supporting conceptual design based on the function-behavior-state modeler[END_REF] [START_REF] Ranta | Integration of Functionnal and Feature-based product modeling -the IMS/GNOSIS experience[END_REF] describes the product according to three levels: the first draws up functions (Figure 1b); the second specifies how to fulfill these functions by behaviors (Figure 1c) ; the last level describes behaviors like a sequence of states of the product's components (Figure 1d). Consequently, the capacity to treat functions by computer opens the way with an automation of the earlier stages of design.

However, in a more general way, one notes that methods of assistance in manufacturers products design are manual during the first phases of design because manipulated information are mainly written in natural language. As a consequence, any automation attempt will be difficult because, at this time, one knows that it is computerly and automatically hard to interpret the significance of a text. Therefore, it limits the aid proposed by the different software tools; they are more used in a verification level, as simulators for instance. So, we assume that those information can be manually translated into more easily interpretable information by a software system: the translated information are mathematical constraints on parameters of a relatively elevated semantic level (the volume of the design object, the coefficient of penetration in air and so on… Figure 1e). Those parameters are called intermediate parameters and are defined as quantifiable and measurable entities referring to the physical world and are not necessarily related to geometry. The set of constraints using intermediate parameters defines what we call the intermediate specifications (Gardan, Minich, et al. 1999a) (Gardan, Minich, et al. 1999b). It could appear abusive to suppose that the initial specifications (Figure 1a), expressed in natural language, can be translated into intermediate specifications (Figure 1e). However, in some number of cases, the thing is really possible and by this way, a starting point is obtained for the almost automatic shape synthesis. For example, in the case of a box design, aesthetics functions may be converted as the following: the ratio of length to height of the box approaches the gold number ( )

( 5 +1)/2 . The corresponding constraints would be length = ( )

( 5 +1)/2 /height. In a larger extent, the handling of a water bottle by a human being, which is a function, may be converted into constraints on the weight, the compactness and so on, which are parameters. In (Gardan, Minich, et al. 1999b), we have defined an intermediate constraint by a quadruple <IP, R, Exp, W> where IP is an intermediate parameter, R is a relation among {<, >, =, ≠} that must be considered as fuzzy relation, Exp is an arithmetic expression and W is the relative weight of the intermediate constraint in comparison with the other constraints of the intermediate specifications. For the moment, only one designer gives the weight for all the intermediate constraints.

From intermediate constraints and a library of primitive shapes (Figure 1e), we propose to size every shape of the library so that they verify the intermediate constraints (Gardan, Minich, et al. 1999a). We obtain what we called the solutions space, which contains all solutions (Figure 1f). We Figure 1: Overall architecture of the system agree that a shape is defined by what we call terminal parameters (mainly geometric and of weak semantic level: radius, length, width…). We suppose, in addition, that an expert of the design domain has provided the software system with sufficient knowledge so as to know how to translate an intermediate constraint into terminal constraints. The latter apply to terminal parameters of a parameterized shape of the library. For example, a weak penetration coefficient can result in a weak radius for the circle or a weak width and an elevated length for the rectangle whether the circle and the rectangle are parameterized shapes of the library… As the shape synthesis of primitive shapes is not very interesting from an industrial view point, we have studied different methods permitting to synthesize more complex shapes [START_REF] Gardan | Towards a specifications-to-shape translation tool[END_REF].

As we assume that terminal parameters vary in real intervals, there is a great number of shape solutions that satisfied the intermediate constraints, or even an infinite number. However, the conviviality of a shape synthesis software tool implies the presentation of a restricted number of solutions to designers. It means that it is necessary to define a method searching for the best solutions among the synthesized shape solutions; it raises two problems: to browse the set of shape solutions in intelligent manner and to compare solutions between them.

The second problem consists in defining a degree with which a solution satisfies the intermediate specifications. This degree is called Satisfaction Degree and is obtained by computing a weighted average on satisfaction degrees of intermediate constraints affected of their weight. The computation of the satisfaction degree of an intermediate constraint (cf. Figure 2) is computed from the three following information (Gardan, Minich, et al. 1999a):

-the value of the intermediate parameter for the considered solution, so-called real value,;

-the wanted value, that corresponds to the value of the mathematical expression contained in the intermediate constraint;

-a curve depending on the mathematical relation used in the intermediate constraint.

In fact, the satisfaction degree of an intermediate constraint is obtained by computing the existing gap between the real value and the wanted value on the considered curve. The computation of the intermediate specifications' satisfaction degree for a given solution is an operation called estimation.

We showed that the estimation of combined shapes (represented by a Boolean combination of primitive shapes contained in the library ≈ CSG tree) could not be deduced from the evaluation of the primitive shapes used to define combined shapes (Gardan, Minich, et al. 1999b).

Knowing how to estimate a shape solution, now we are able to browse solutions space that is modeled by variation intervals of terminal parameters for every parameterized shape of the library. As we have noticed that it seems difficult to use an exact optimization method that are mainly expressed in a mathematical way (as the Simplex method for instance), we study the possibility to apply some stochastic methods as simulated annealing method or genetic algorithms (Gardan, Minich, et al. 1999a). Then, we have proposed a method more adapted to our approach (Gardan, Minich, et al. 1999b). The latter consists first in sampling terminal parameter variation intervals. Secondly, each sample must be estimated in order to interpolate a curve in the case where the shape is defined by only one terminal parameter, a surface in the case where the shape is defined by two terminal parameters or a hyper surface in the case where the shape is defined by more than two terminal parameters. Afterwards, it is possible to determine with a mathematical method the maximum of the hyper surface. Moreover, the best solutions are obtained by sampling over again close to a certain number of maximum. Finally, shapes obtained by the application of the previous method can be presented to designers (Figure 1g). Once this step is finished, designers have to give their opinion on the selected solutions. In the case where there are not pleased with proposed shapes, and it will be often, designers have to modify intermediate specifications, modify the intermediate constraints weights, modify initial specifications of the product, add new intermediate constraints or new parameterized shape in the library, and so on… In summary, the above methodology consists in translating manually functional information in constraints on physical entities of the product to design. From this information represented by the intermediate specifications, also from a library of parameterized shapes and expert knowledge, numerous shapes solutions are synthesized. To encourage the conviviality of the software system, the most promising solutions are searched and presented to designers so as to stimulate their creativeness.

We studied the validity of our methodology in the case of a very precise domain: foundry mould design [START_REF] Gardan | A methodology for a function-to-shape translation tool in foundry[END_REF]. From an industrial viewpoint, the caster (foundry mould designer) cannot take the liberty to study and to estimate a big number of solutions in so far as the estimation of each solution is a long time consuming. Therefore, the caster uses trade rules to limit the solutions space. On the contrary, our methodology synthesizes too many solutions. So, in that study, we have modified our methodology by introducing some trade rules coming from an expert of the domain of foundry. The aim of the modifications was to reduce reasonably the solutions space by determining a priori the most promising solutions families, but by preserving an area large enough in order to preserve the property of creativity. For instance, the placement of pieces to manufacture makes the solutions space browsing difficult. So, by automatically computing the different possible arrangements of pieces in the mould in using including shape for pieces, it is possible to automatically define classes of solutions. This computation is less time consuming than testing and estimating each placement of pieces in the mould. Finally, the application of this method leads to a mould that the weight ratio is better of 40% than the one design by the caster.

Recently, we worked on the way to facilitate a collaborative function-to-form mapping. Firstly, we have studied the problem of representation of experts' multiple-view in a collaborative conceptual design environment [START_REF] Pallez | Data Architecture for Collaborative Conceptual Design[END_REF]. In that study, we have defined some coherence rules between different models. Each expert at any time can define his model and may collaborate with the other models using a STEP standard language named EXPRESS-G (cf. Figure 3). As a consequence, when one model is manipulated, corresponding effects should be made automatically in the others. Finally, in [START_REF] Pallez | Towards a Collaborative Function-to-Form Mapping[END_REF], we have improved the methodology by studying the case of a water bottle design with three different design domains: experts on materials, experts on geometry and manufacturers. The resulting methodology is a function-to-form mapping in a collaborative context and is the following:

First step : Each design domain has to define its own intermediate specifications for only one component of the product to design. The intermediate constraints are deduced from the functional decomposition of the design product regardless of the other design domains participating in the design process. As a consequence, in this step, intermediate specifications of a domain will use only physical parameters of the domain. By this way, a designer of a domain can be considered as an expert of this domain in contrary of the methodology presented previously. Second step : Next, as we are convinced that there exist relationships between constraints from one design domain to another, this step consists in establishing those constraint's relations. There is several ways to achieve this: either manually or semi-automatically by considering the rule "if two constraints from two different domains are deduced from the same function, then they are related each other". Third step : This step corresponds to the solutions space generation and it is almost the same as our previous method. For the moment, we assume that only experts of design domain who have a shapes library are in charge of proposing solutions by applying the methodology presented previously. Fourth step : Once shapes solutions are generated, experts of design domain who do not have a library must react to the proposed solutions by participating in the selection of the most promising solutions. So, in this part, experts from all design domains participate in selecting solutions. Fifth step : As it is inconceivable that a promising solution could be find after the first try of shapes solution generation and selection, designers will be obliged to collaborate in order to modify the weights of constraints and/or add other intermediate constraints and/or add other parameterized shape in their library so as to increase the satisfaction degree of promising solutions. The functionto-form mapping process starts again from the second step until a promising solution satisfies all the designers involved in the product design.

Our experience shows us that an automatic and direct mapping of the functional information to geometric information represents a very difficulty problem for the moment. Moreover, numerous authors are working on this computer-aided-design problem [START_REF] Gorti | From symbol to form: a framework for conceptual design[END_REF][START_REF] Ranta | Integration of Functionnal and Feature-based product modeling -the IMS/GNOSIS experience[END_REF], Rosenman and Gero 1996a[START_REF] Tomiyama | A CAD for functionnal Design[END_REF][START_REF] Umeda | Functional reasoning in design[END_REF][START_REF] Zhihui | On estimating the feasible solution space of design[END_REF]. To synthesize our methodology, we have previously proposed to establish a median difficulty level that is represented by the intermediate specifications. We assume that the latter is manually obtained from initial specifications mainly expressed in natural language. We concentrate on the almost automatic mapping of the previous model into one or several shapes. The intermediate specifications model is made up of a set of constraints named intermediate; each constraint is made up of physical parameter also named intermediate. These parameters are quantifiable quantities that remain to a high semantic level. Our approach is independent of design domains even though experts of design domains must define some information, necessary to a good working of the function to form mapping. However, the notion of "perimeter", for instance, remains the same whatever the design domain considered. By this way, there is knowledge capitalization and as and when designs are done, one becomes less and less necessary to consult an expert of the considered domain. Information provided by designers permit, among others, the mapping of intermediate constraints into variation intervals of terminal (geometric) parameters. A Cartesian product of intervals defines the solutions space. On one hand, we have assumed that the shapes contained in the library were primitive shapes. We can show that the addition of more elaborate shapes, or combinations of primitive's shapes, don't modify the proposed approach. However, the number of terminal parameters for those shapes increases considerably.

Our future works are numerous. First of all, in short-term, it is necessary to identify all the possible relations between constraints from different design domains in order to allow more precise communication between experts of these different domains. Then, it is important to study how to maintain the consistency of models. In that case, future works will focus on the definition and formalization of coherence rules between different models so as to improve proposed multiple-view model. Secondly, the application of our methodology in the very precise framework of foundry mould design permitted us to consider the automatic creation of shapes that would be going to enrich the library. An evolution of our methodology would consist therefore not to preserve shapes in a library but to construct these shapes automatically according to concerned design domains. The idea would be to elaborate a second intermediate model, between the intermediate specifications and the solutions space, what would permit a less abrupt passage again between functions and shapes. Moreover, according to our methodology, the estimation operation requires instantiation of a solution that is the assignment of a real value to every terminal parameter of the solution. Another improvement would consist in estimating a set of solutions rather than a unique solution: for instance, estimate the shape "circle" without knowing precisely the value of the radius. The shape "circle" is called class of solution. The possibility to estimate a class rather than a shape would permit, for example, to construct first the satisfactory classes, of which the better would be examined. Then, in the most promising classes, one would choose the most promising solutions.

In long term, future works should be related to geometric reasoning: it could be interesting for the experts to define intermediate constraints using other kind of relation. For instance, instead of using well-known mathematical relations (≤, ≥, =, ≠), experts on geometry would like to use a "look like" relation (≡) in order to introduce new experiences on shapes. Once it will be done, it will be very interesting for designers, and especially for experts who have a shape library (expert on geometry), to combine shapes contained in the library so as to be more creative. For instance, evolutionary algorithms could be used [START_REF] Taura | Application of evolutionary programming to shape design[END_REF] (Rosenman and Gero 1996b) [START_REF] Gardan | Towards a specifications-to-shape translation tool[END_REF].

Perspectives in a more general context are also numerous and often make call to other domains of research. In particular, works done in artificial intelligence could serve basis for a better semantics understanding of functional information. It would allow software system to provide a more precocious aid for the function-to-form mapping. In addition, the quality of the man-machine interface is an essential notion for appreciated software by its users. Even if improvements are brought to software which implements the function-to-form mapping, the place of designers is still very important in this mapping. So, a scrolling of the most promising solutions should be done so as to give designers the possibility to intervene when an aspect of the shape solutions suits them or displeases them. It raises important difficulties of zones designation by designers, of their interpretation from a functional point of view and how they will speak in the next step of functionto-form mapping.

If solutions follow each other in any order, the operation will be especially long and laborious for designers. To make it convivial, we foresee to present solutions so that they present a geometric continuity; by this way, their scrolling will appear like an animation. It presents the advantage to make evolve solutions in a progressive manner. To provide this geometric continuity, it is necessary to realize an algorithm that browse the solutions space and find a solution that looks like another. Another possibility is to realize a geometric morphing algorithm that converts progressively a solution into the following solution. The drawback is to generate shapes that are not solutions.

Biographical notes:

Denis PALLEZ is currently an associate professor in the department of computer sciences at the University of Lyon1, France, in the PRISMa laboratory. He obtained his PhD in computer sciences in January 2000 at the University of Metz (France). He also spent four months as an invited researcher at the institute of technology at Montreal (ETS). His research interest is in the area of CAD/CAM including conceptual and functional design, needs and functions modeling, intelligent CAD systems, shape synthesis, technical data management system.

Figure 2 :

 2 Figure 2: Satisfaction curve associated to the '=' relation for the following intermediate constraint: < IP, =, 5>

Figure 3 :

 3 Figure 3: Intermediate specifications model expressed in an EXPRESS-G format

(

  83 words) Parisa Ghodous is currently associate professor in computer science department of University of Lyon I. She is head of technical modeling team of LIGIM (Laboratory of Computer Graphics, Image and CAD/CAM Modeling). Her research expertise is in the following areas : Standards, Product data exchange and modelling, Design Process Modelling, Collaborative Modelling, Distributed Technical Data Base and Interoperability. She is in editorial boards of two journals and in the committees of many relevant international associations such as concurrent engineering, ISPE, ECPPM, Interoperability. (82 words) Michel T. Martinez is a Professor in the Engineering Department of the Institute of technology, the University of Lyon (France) and vice-head of the Advanced Manufacturing Centre (AIP) of Lyon. After a PhD degree in Computer System Technology, he conducted research on Object-oriented application development for industrial applications, CIM control system design, Assembly Process Generation and Group Technology. Since 1999, his current research interest focuses mainly on Concurrent Engineering and New factory Organisations. Actual main projects include technical data exchange and sharing, collaborative integrated development and distributed architecture for technical information technology. (92 words)


Denis Pallez

Parisa Ghodous

Christel Dartigues

Towards a Collaborative Function-to-Form Mapping

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

INTRODUCTION

The technological advances carried out these last years in the field of products development led the researchers to elaborate the approaches that reduce the cost and time of product development, enhance the quality of product and help the designers to be more creative. These objectives are difficult to obtain due to a large number of phases, which should be carried out during the product development and the large number of experts of different disciplines that are involved. Concurrent Engineering is considered as one of the key concepts that enable companies to reach these objectives (Ghodous et al. 2000a).

Concurrent engineering is a wide field of research. Researchers who are interested in concurrent engineering work on different aspects such as [START_REF] Prasad | Concurrent Engineering Fundamentals[END_REF]):

• Philosophical aspect, which deals with the boundaries of the responsibility and the authority, culture and organization management, • Methodological aspect, which deals with system thinking, approaches to system complexity, systems engineering, product realization taxonomy and system integration, • Conceptual aspect, which deals with concurrency and simultaneity, modes of concurrency and cooperation, work flow mapping and • Virtual aspect, which deals with capturing life cycle intent and information modeling.

Our work is situated on the methodological and virtual aspects. In product design, each expert works with his own applications, handles his own data, has knowledge and constraints, which are specific to his domain, and has his own point of view on the product (Ghodous et al. 2000b). This heterogeneity implies many problems, in particular information exchange and sharing with the other experts. It is thus necessary to make it possible to each expert to represent adequately its data while facilitating integration and communication of their data with the other experts. In this context, our objective is to develop a concurrent and collaborative system allowing all experts to participate on product development as soon as possible and help them to work together [START_REF] References Dartigues | Modélisation collaborative des activités de conception[END_REF]. In the next, we firstly present the function to form mapping approach as a conceptual design technique. Then, we explain why it is more realistic to consider this methodology in a collaborative context and we present enhanced version of the function to form mapping approach presented in (Gardan et al. 1999a, Gardan et al. 1999b, Pallez et al. 2001). In addition, we present the data models that are necessary to achieve a collaborative and conceptual design aided system based on this methodology. Due to reasons of normalization, these models are described using the EXPRESS-G formalism (ISO 1994). Finally, we present how the collaborative function-to-form mapping could be used in a water bottle design.

THE FUNCTION TO FORM MAPPING AS A TECHNIQUE FOR CONCEPTUAL DESIGN

The aim of any design is to develop the product Towards a Collaborative Function-to-Form Mapping

D. Pallez

University of Lyon1, PRISMa, France

P. Ghodous & C. Dartigues

University of Lyon1, LIGIM, France ABSTRACT: The technological advances carried out these last years in the field of products development led the researchers to elaborate approaches that reduce the cost and time of product development, enhance the quality of product and help the designers to be more creative. Currently, computer aided systems have concentrated on the capture and representation of geometrical shape and technical information as opposed to provide supports for product design in the earlier stages of design process. The aim of this paper is to present a methodology to aid designers during the first stages of design. The standard models using the STEP standard are proposed in order to ensure co-operative and collaborative works during the first stages of design. Then, we apply our methodology in the case of a bottle design by considering multiple designers' viewpoints.

as earlier as possible. In a non-routine design, it is delicate and extremely complex to obtain the best products answering customer's specifications. Indeed, a great number of different experts of different disciplines participate in product design. The difficulty lies in the fact that those persons have to collaborate. Shape is today the main representation of a product, even though the current trend is to remove geometry from its central position in order to add high-level information [START_REF] Gorti | From Symbol to Form: A Framework for Conceptual Design[END_REF][START_REF] Szykman | Design Repositories: Engineering Design's new Knowledge Base[END_REF][START_REF] Szykman | The role of knowledge in next-generation product development systems[END_REF]. Therefore, the function to form mapping appears to be one of the most important activities of the design process and up till now happened manually. This activity is very important both for choices that are made and for the amount of work that it represents.

That is why we have the desire to assist designers in the first stages of product design. The objective is not to construct automatically the shape but both to automate a certain number of heavy and tiresome tasks, and assist designers during the first stages of design. In best case, this assistance makes the designers' stimulation possible by presenting them solutions that they had not thought before.

We suppose that the first information we have at our disposal are included in the customer's specifications, which are expressed in natural language (Figure 1a). Due to the functional decomposition (Figure 1b) eventually using functions of making, maintaining, prevention, control [START_REF] Keuneke | Device Representation. The significance of functional knowledge[END_REF]) and allowing [START_REF] Mcdowell | Conceptual design for polymer composite assemblies[END_REF], behaviors of the product could be identified (Figure 1c) in order to respect the philosophy of FBS [START_REF] Ranta | Integration of Functional and Feature-based product modelling --the IMS/GNOSIS experience[END_REF][START_REF] Tomiyama | A CAD for functional Design[END_REF], Umeda et al. 1996). Next, with the help of the same philosophy, the structure of the product can be obtained. This previous model can be identified as a set of product's components linked by assembly relation (Figure 1d). Actions achieved by designers in the traditional FBS methodology (represented by Figure 1a to Figure 1d) are currently manual. Assisting designers during those phases is difficult due to the fact that manipulated information are mainly expressed in natural language. That is why we attempt to formalize some design information in order to partially automate the shape mapping (Figure 1e to Figure 1g).

In some cases, we have noticed that a function can also be decomposed into a set of constraints on physical parameters, called intermediate specifications (Figure 1e). Only such design cases will be considered in next sections. Decomposition that consists in translating functions into constraints on physical parameters can correspond to the "function → structure" reasoning techniques identified in [START_REF] Hsu | Current research in the conceptual design of mechanical products[END_REF]. Physical parameters are defined as quantifiable and measurable entities referring to the physical world. For instance, in the case of a box design, aesthetics functions may be converted as the following: the ratio of length to height of the box approaches the gold number ( )

( 5 +1)/2 . The corresponding constraints would be length = ( )

( 5 +1)/2 /height. In a larger extent, the handling of a water bottle by a human being, which is a function, may be converted into constraints on the weight, the compactness and so on, which are parameters. Physical parameters used in the intermediate specifications are called intermediate parameters (Gardan et al. 1999a, Gardan et al. 1999b) Figure 1. Overall architecture of the system solution shapes to designers that achieved those intermediate constraints. As those constraints are deduced from functions, solution shapes satisfy functions.

In order to reduce the complexity, the function-toform mapping is first applied on non-assembly components. The product's shape may be obtained by using the function-to-form mapping for each component of the product structure's and by assembling shapes of each component. Some assembly problems will still remain and it will be necessary to define a new kind of intermediate constraints that permit to take into account assembly problems. This axis of research is not treated in this paper. As a consequence, we assume afterwards that a component is a rigid, finite and homogenous solid that contains no other components.

So, our methodology consists in (Gardan et al. 1999a) proposing a set of solutions, called solutions space (Figure 1f). Each shape of the solutions space is deduced and constructed from:

• intermediate constraints;

• a library of parameterized shapes;

• algorithms that translate intermediate constraints into constraints on parameters which depend directly on the parameterized shape chosen in the library. Those constraints are called terminal constraints in order to distinguish them from intermediate constraints. Parameters that define a parameterized shape and used in terminal constraints are called terminal parameters. For instance, the radius of a sphere, the width, the length and the height of a box are terminal parameters. One intermediate constraint can generate several terminal constraints. As a consequence, we have to compute the intersection between the all generated terminal constraints into intervals of variation for each terminal parameter (Gardan et al. 1999a). For instance, if an intermediate constraint generates a terminal constraint such as "length greater than 5" and another intermediate constraint generates another terminal constraint such as "length less than 10", the system needs to compute those terminal constraints in order to obtain values that are possible for each terminal parameters. Then, previous algorithms must be seen as knowledge of the design domain because they represent expert's rules.

Once one knows algorithms that translate intermediate specifications into constraints on terminal parameters, a parameterized shape can be chosen in the library and the computation of variation intervals generates solution shapes. Next to this, one can consider that several shapes could be proposed to the user in so far as the design problem is underconstraint. So, we must detect the shapes, which best satisfy the intermediate constraints (Figure 1g). To do that, we have defined a Satisfaction Degree SD ic (s) of an intermediate constraint ic for a given shape s as a real number in the [0,1] interval (Gardan et al. 1999a). This number expresses the quality with which s satisfies the intermediate constraint ic. If SD ic (s) is near zero, the constraint is badly satisfied, if it is near one, the constraint is well satisfied.

One has to consider the function-to-form mapping as a means of generating solutions shapes for one component that may give ideas to the designer. We applied this methodology within the framework of a filling system for foundry mould design [START_REF] Gardan | A methodology for a function-to-shape translation tool in foundry[END_REF]. We validated the methodology by taking the specificity of the foundry (trade features) into account. We showed that this approach was applicable in this case and that we obtained quickly results better than those based on an expert's knowledge.

In fact, the method presented in this section ( § 2) was firstly thought for only one designer. Nonetheless, in real products design, it will be difficult for one designer to apply this methodology due to the large number of constraints to manage.

A more suitable methodology would be to distinguish between intermediate constraints from a design domain and intermediate constraints from another design domain. As a consequence, we treat in the next section the way to apply our function-toform mapping in a collaborative context with the aim of reducing productivity time but also with the aim of managing a lot of expert's points of view.

METHODOLOGY APPLIED IN A COLLABORATIVE CONTEXT

As it seems to be unrealistic to design the product shape only by one designer due to a large number of design domain that take part in product design, we propose to put the previous methodology in a collaborative context.

First of all, the different stages that consist in translating product's specifications (Figure 1a) into intermediate specifications (Figure 1e) and corresponding to the FBS methodology are unchanged except the fact that there is at least one expert per design domain. Consequently, we can group the intermediate constraints based on the same design domain together. This is the starting point of our collaborative methodology.

We have already discussed about collaborative function to form mapping in [START_REF] Pallez | Data Architecture for Collaborative Conceptual Design[END_REF] where the methodology consisted in generating a solutions space for each design domain and then merging solutions spaces into one using a suitable technique that has to be defined (Figure 2). The proposed steps were to find the most promising solutions of the merged shapes solutions space and to show them to designers. As it is utopian to consider that the solution could be found in one time, the possibility to change or to expand the functional decomposition is given to designers. As a consequence, information (behaviors, structure and so on…) deduced from functions also may have changed. Consequently, designers have to modify information deduced from functions and to apply all the steps again and again until to find a shape solution that satisfies all the design domains.

The methodology represented by the diagram of the Figure 2 is possible only if an expert of a design domain is capable of generating shapes solutions from intermediate constraints. That is to say, the expert is capable of defining its own primitive shape library. However, one can find some design domains where experts cannot generate any solutions as regards geometry. Nevertheless, those design domains might be linked with the shape of the design product even if the experts are not able to generate shapes solutions. That is why we have to extend our collaborative methodology in a more general context; i.e. the methodology has to be applicable in a lot of design domains, even in design domains in which experts do not have shapes library.

By this way, we present in next paragraphs an improvement of our collaborative methodology presented in [START_REF] Pallez | Data Architecture for Collaborative Conceptual Design[END_REF]). The following methodology has to be used when expert of a design domain do not have a shape library.

With previous regards, the collaborative function to form mapping should be the following: 1 First of all, each design domain has to define its own intermediate specifications (IS) for only one component of the product to design. The intermediate constraints are deduced from the functional decomposition of the design product regardless of the other design domains participating in the design process. As a consequence, in this step, intermediate specifications of a domain will use only physical parameters of the domain. By this way, a designer of a domain can be considered as an expert of this domain in contrary of the methodology presented in § 2 in which only one designer have to manage with physical parameters coming from different design domains. 2 Next, as we are convinced that there exist relationships between constraints from one design domain to another, this step consists in establishing those constraint's relations. There is several ways to achieve this. The first one is the traditional and well-known manner: experts of all design domains involved in the design process have to find manually links between all the intermediate constraints. sign domains. 5 As it is inconceivable that a promising solution could be find after the first try of shapes solution generation and selection, we consider that intermediate specifications have to be more refined in order to propose most promising solutions to designers. As a consequence, designers have to modify their intermediate specifications in collaboration with designers from other design domains in so far as some constraints are related to other constraints from other design domains. So, in this step, designers may modify the weights of constraints and/or add other intermediate constraints and/or add other parameterized shape in their library. The function-to-form mapping process starts again from the second step until a promising solution satisfies all the designers involved in the product design. The methodology presented above must be seen as a progressive and iterative method in which designers are assisted by a computer application that proposes solution shapes. As experts have to exchange data in order to ensure the collaborative function-to-form mapping, we discuss in the next section standard models that capture concepts related to this methodology.

PROPOSED MODEL FOR REPRESENTATION OF EXPERT VIEWPOINT

The analysis of current works on product modeling shows that current single fixed representations are inadequate to model the various concepts present in multidisciplinary product development situation. Consequently, the dynamic representation of multiple views of a product based on functional contexts seems to be necessary.

Depending on the view taken, certain properties and descriptions of the object become relevant. A comprehensive model of a product must be able to built depending on the particular need.

Consider the example of the mechanical part. The mechanical design model of this product is different of electrical engineer's model or thermal model. Any model should allow a dynamic evolution and must be capable of accommodating multiple concepts unambiguously and consistently so that the elements could not be duplicated. Any inconsistencies between the various models have to be discovered and corrected. This process may go through several iterations. The result is a set of models, one per consulting discipline, where, although each set represents the product using a different point of view, the comprehensive representation is consistent. There is no attempt to integrate the various sets into one set.

The basic description of a product differs from one viewer to another. Each view may represent a product with different elements and different com-position hierarchies. No one model contains a full comprehensive description of the product but each model should be consistent regarding to the object being described. Different descriptions of the same elements and different subsets of these descriptions in different models exist.

Some models used for product description are shown in Figure 3. We detail the model of intermediate specifications detailed in §2.

Viewpoint model represents the information about a product from a particular view and the relationships between the different viewpoints. Several functions are related to each viewpoint.

Purpose explains why an object does what it does and it is related to the human socio-cultural environment concept. The purpose model represents the purpose and the relationship between the purposes.

Function is what an object does. Functional model represents function and the different relationships between the functions.

Behavior is how the object does what is does. Behavior model represents the behavior, the relationships between the behaviors and the relationships with functions.

Structure is what the object is. We use the STEP standard to represent the concepts related to product data (the structure of product and its relations with other models such as shape, materials, tolerances, etc). The definition of a product in the STEP product data model is any physical object, which is produced by either natural or manufacturing processes. Any part or assembly that contributes to a product is also considered to be a product. A car is a product while its wheels and engine assemblies are considered as other products. Furthermore, each of these products can be further decomposed into smaller components or products.

The details of these models are described in (Ghodous et al. 2000b).

In this paper, due to the function form mapping technique, we have introduced the intermediate specifications model. We present the detail of this model in the following.

We represent the intermediate specifications concepts by EXPRESS-G formalism (Figure 4). EXPRESS-G is a graphical language developed by ISO 10303 STEP (ISO 1994). The EXPRESS-G basic notations used in figures include entities (rectangles); super-type/subtype relationships (thick solid lines); required attributes (normal lines); relationship for optional attributes (dashed lines). Additionally, the direction of an attribute is symbolized by an open circle, where the circle represents the "many" side of a "one to many" relationship.

In Figure 4, the intermediate specifications are a set of different intermediate constraints. The intermediate constraints are elaborated from functions that characterize the product. As functions relate to a given view point (mechanical view point, electrical view point, thermal view point and so on), the intermediate constraints also relate to this same viewpoint. On the other hand, each intermediate constraint is defined on a component, i.e.: is related to the structure of the product (entities Product-Definition and Product-Definition-Relationship).

The intermediate constraints are expressed in the following way: first of all, an intermediate constraint described by an expression. This expression contains an intermediate parameter (which can be the volume, the weight or any engineering parameter), a relation (<, >, =, ≠, etc.) and a mathematical expression, which can possibly include other intermediate parameters. With each intermediate constraint are associated two weights: a local weight and a total weight. These weights are used to give a list of priority of the constraints that must be carried out for the expert on a precise field (local weight) and for all of the experts (total weight).

Lastly, due to the fact that each expert handles his own whole of constraints, there are relations between them (IC-Relationship). These relations are of two types. We define the Same_as relation, which expresses the fact that two experts handle the same constraint. Their expression and their total weight will be then identical, but their local weight might be different. We also define the NCU relation (Next Constraint Usage), which means that an intermedi-ate constraint can be compose of one or more other constraints.

CASE STUDY: A WATER BOTTLE EXAMPLE

In this section, we present the way to use our methodology and our models in a real case, which is the design of a water bottle.

First of all, we have to define information obtained manually during the first stages of design, that is the elaboration of functions, behaviors, structure of components and intermediate specifications (Figure 1a-e). The considered functions are: to hold one liter and a half of drinking water (1), not to be heavy (2), to be handled by a human-being (3), to be stable (4), to be compressible (5), to be packaged (6), to stand a force of 50 Newton (7), to be impervious to natural daylight [START_REF] References Dartigues | Modélisation collaborative des activités de conception[END_REF], to be fine-looking (9), to be emptied (10), to be filled [START_REF] Hsu | Current research in the conceptual design of mechanical products[END_REF]. All those functions have to be refined in order to obtain a functional decomposition; however, the eleven functions are enough to understand our methodology in the next. Secondly, the design process recommends extracting behaviors from functions. As we did not express how to model behaviors, we will leave this step out in so far as it permits to deduce components of the design product which are in our case the body and the cap of the bottle. In this section, we only consider the shape design of the bottle's body in so far as we assume that we design the shape of the product component by component without regarding assembly problems (see § 2). The next step concerns precisely the elaboration of intermediate specifications. As in all product design, we have to take into consideration several viewpoints. In the case of a water bottle design, we consider three design domains: an expert on materials who may be a chemist, an expert on geometry and a manufacturer. It is obvious that it is not an exhaustive list of design domains. Figure 5 The second step of our methodology is the comparison of the intermediate constraints to themselves in order to identify relationships that could exist: for instance, there is a link between constraint 4 of the expert on geometry and constraints 1 and 2 of the manufacturer (Figure 5). In one hand, a 'Same_Relation_As' relation can be used between constraints 4 and constraints 1 because the same mathematical (≤) is used on the same intermediate parameter in the two constraints; on the other hand, a 'Same_Parameter_As' relation can be used between constraints 4 and 2. In addition, a 'Mathematical' relation could be used to link constraints 4 of the expert on geometry and constraints 2 of the materials' expert.

The third step of proposed methodology consists in using parameterized shapes library and experts knowledge to generate shapes that satisfy the inter-mediate constraints. At first, only the expert on geometry can generate a shape solution in so far as he is the only one who owns a shape library (Figure 6a). In our example, we consider that he could generate three kinds of solutions (Figure 6b): a hollow sphere, a hollow cylinder and a hollow box.

The next step allows the expert on materials and the manufacturer rejecting solutions represented by a sphere or a box because they are not stable and finelooking enough.

Then, the last step allows the expert on geometry to modify his intermediate specifications by adding the constraints "Nb_Contact_Point_Plane ≥ 3; 5; 10; F4", which means the number of contacts between a point of the shape and a plane is greater than 3 to ensure the stability of the bottle (function 4) (Figure 6c). Moreover, all the experts are agree with the fact that the solutions are not handled enough. So the expert on geometry is proposed to add new parameters to the primitive shape of the library. Next to this, the step 3 of the methodology is applied. The possible resulting solutions of previous modifications are represented in (Figure 6d). It is understandable that the sphere could have been rejected because it is not really stable (function 4) and it is possible that the hollow box has been rejected because its dissatisfaction with too many intermediate constraints. By modifying and adding a certain number of constraints and by applying our methodology (Figure 6e), we may assume that the collaboration of all the experts during the design process will converge on good solutions that may be improved by experts' experiences in order to find the solution (Figure 6f).

E XPERT ON G EOMETRY

M ANUFACTURER E XPERT ON M ATERIALS F1: to hold one liter and a half of drinking water, F2: not to be heavy, F3: to be handled by a human-being, F4: to be stable, F5: to be compressible, F6: to be packaged, F7: to stand a force of 50 Newton, F8: to be impervious to natural daylight, F9: to be fine-looking, F10: to be emptied, F11: to be filled The analysis of current works on product modeling shows that current single fixed representations are inadequate to model the various concepts present in multidisciplinary product development situation. Consequently, the dynamic representation of multiple views of a product based on functional contexts seems to be necessary. In this paper, we have studied the problem of representation of experts' multipleview in a collaborative conceptual design environment. We have considered the function to form mapping approach as a conceptual design method and we have presented the way to apply this methodology in a collaborative context by considering a real example: a water bottle design with three different design domains.

Our future works are numerous. First of all, in short-term, it is necessary to identify all the possible relations between to constraints in order to allow more precise communication between experts of different design domains. Then, it is important to study how to maintain the consistency of models. We have defined some coherence rules between different models. Each expert at any time can define his model and may collaborate with the other models. As a consequence, when one model is corresponding effects will be made automatically in the other. In that case, future works will focus on the definition and formalization of these rules to improve proposed multiple-view model.

In long term, future works are related to geometric reasoning: it could be interesting for the experts to define intermediate constraints using other kind of relation. For instance, instead of using well-known mathematical relations (≤, ≥, =, ≠), the expert on geometry would like to use a "look like" relation (≡) in order to introduce new experiences on shapes. Once it will be done, it will be very interesting for designers, and especially for experts who have a shape library (expert on geometry), to combine shapes contained in the library so as to be more creative.

Figure 2 .

 2 Figure2. Collaborative methodology proposed in[START_REF] Pallez | Data Architecture for Collaborative Conceptual Design[END_REF]

Figure 3 .

 3 Figure 3. Some necessary models and their relationship

Figure 4 .

 4 Figure 4. Intermediate specifications model expressed in an EXPRESS-G format

Figure 5 .

 5 Figure 5. Intermediate specifications and considered functions for a water bottle

Figure 6 .

 6 Figure6. How the bottle shape is obtain using the methodology?

ACKNOWLEDGMENTS

We thank Christian Minich and Estelle Perrin from the CMCAO team of the university of Reims (France) who took part in the elaboration of the case study.