version soumise à B2007 The 7th International B Conference LIFC, BESANCON, 17-19 January 2007 le 27.06.2006 à 19h00 le 29.06.2006 à 22h53 (version uploadé) Paper ID : 11 Corresponding author: Copyright : Walter NUNINGER & Lucie CATIAU Papier refusé. L'objectif était de faire découvrir un autre domaine d'application pour la méthode B bien que celle-ci ne soit pas appliquée en tant que telle.

Interest and prospect of B-Method for food industry Reflexion based on the optimisation of fruit drying. Walter NUNINGER1,2, Lucie CATIAU2 1

LAGIS CNRS URM 8146, 2 POLYTECH’LILLE – Dépt. Ingénierie Agroalimentaire Av. P. Langevin, F 59655, Villeneuve d’Ascq Cedex, France Tel. (+33) (0) 328.76.74.38 – Fax (+33) (0) 328.76.74.00 [email protected], [email protected]

Abstract. In this paper, we try to show how B-method can be useful in process development for food industry. Our reflexion is based on the example of the optimization of fruit drying stressing on the goal properties within the constraint and the validation of the choices. Of course many technical solutions already exist mostly developed considering technical aspects as the heat production optimization and the correct choice of the chamber temperature profile in addition to the design of the dryer itself. The significance of the Bmethod is to emphasize and improve the thoughts over the already existing system or the ones to be developed taking into account the set of objectives independently of the final technical choices. Therefore similarities with other analysis techniques like functional analysis (S.A.D.T) is obvious and it seems worthwhile to present food industry problematic in order to motivate the transfer of such method in this peculiar field. Furthermore the integration of the B-method into other design or analysis methods already used in food industry for food safety (as I.F.S norm that takes into account H.A.C.C.P method) is of great interest for the community. Of course the next step will be to adapt the data-processing aspect for proof and validity tests in a convenient form for people not accustomed to such kind of techniques. Keywords: B-method, optimization, dryer, food industry, quality, safety

1 Introduction The B-method, developed by Abrial [1][2], is based on the previous concepts of checking large routine, assigning meanings to programs, specification and validation and data refinement [3][4]. It is a conceptual method first dedicated to formal development of computer systems. It was further applied (mostly in terms of formalization of the principles of operation) for operational systems in industrial fields as car design [5] or railway control where reliability and safety are huge constraints for supervision. Although food industry is an high-risk domain due to quality commitment (organoleptic characteristics), to the need of safety production (no microbiological, chemical or physical contamination), security (equipment and human being) and environment constraints (reducing pollution and energy consumption) [6][7], it’s clear that less interest has been given to B-method as a

methodology to efficiently achieve such goals on existing systems or ones to be developed. From a technical point of view, analytical models based on identification techniques and biological scientific knowledge are used for simulation and better control ; the use of experimental design decreases the number of experiment during the development of new food products while sensorial characteristics are assessed as non instrumental variables. In food industry, the research and development is the point of meeting of various competences like automatic control, computer science and food engineering that might show some similarities with the B-method: the conceptual and formalization aspect like external and internal functional analysis (point of view of the needs or of the way the components contribute to the services) like System Analysis and Design Technic (S.A.D.T) [8], process chart, the decision tree of Critical Control Point (C.C.P) [9][10][11]. In general a functional decomposition of the process from the global to the local aspects is processed as a compromise between a low cost and a high development level. After a short presentation of the B-method, we try to bring out such interest within the brainstorming on a fruit dryer optimisation. This global goal leads to specific subsystems dealing with S.A.D.T analysis and supervision task, but in this paper we focus on the similarities and the complementary nature of the methods with respect to the properties and their corresponding tests of proof (scenarios). Finally we intend to show the expected usefulness from B-method for International Food Standard (I.F.S.) [6] as a tool to justify final technical choices of control or process equipments based on a greater expertise: it relies on the technician knowledge in terms of formalisation and on the recent validation tools. Unfortunately, we don’t have already implemented our results in terms of a B-Atelier (B-workship) et B-Toolkit [12][13].

2 Application of B-method on a fruit dryer

2.1 About B-method The B-Method is based on the notion of “abstract machine” as a way to formalize the essential functions of a system. The B-models are therefore sets of properties that the system must satisfy (relations, functions within invariants and variables or states to be more general) avoiding a too high level of description (i.e. the final technical aspect). So the “what to do ?” question should be first considered instead of the “how to do it” one. Brainstorming team should focus on the translation in B-terms of the natural comprehension of phenomenon, goal and functions. The B-Method does force the improvement of the knowledge avoiding the technical solution that might be more easily in mind using functional analysis. The B-method is based on event that might occur on the B-model as deterministic or not, but observable. Supervision and reconfiguration procedures based on diagnosis methods with robust strategies should easily be described in B-models. As introduced by Abrial et al., B-technique is based on proof at each step of decision which might lead to a validation of the final solution [1][14][2]. The proof is made with execution tests supposed to cover all expected good or bad behaviours (invariant using predicate logic, generalised substitutions for

assignments): the interesting properties are shown with model consistency checking (preserve the invariant) and refinement checking (valid refinement to other). The results to the test and the scenarios have to be described. B-atelier supports the tools [12]. Dynamic constraint should be developed too because events might last [2]. The link between the B-model and the real process is made by a dictionary (definitions) of variables and associated events that explains if something is abnormal, normal or in an accepted and controlled domain of behaviour (or even not modelled). This point is obviously of interest in a C.C.P analysis as shown further: the dictionary will precise the accepted level of some parameters. Our work concerns this step of the method. 2.2 Application to optimal dryer conception

Fig. 1. Different kinds of dryers: (a) Rotary dryer[15], (b) plate dryer, (c) fluidised spray dryer

Drying is one of the most important techniques used in food industry for conservation (organoleptic quality and safety): as a part of the fabrication process itself (stabilization and weight reduction by dehydration, even roasting) or as a secondary step (humidity control of recycled starch for moulds of gelled candy). Drying optimization can be seen according to different points of view: reduction of drying time, lower energy consumption but also improvement of the designed drying chamber to improve drying quality. Indeed many constraints should be taken into account to fix the correct humidity rate both to prevent bacteriologic contamination and achieve the different qualities: visual (limitation of lipid oxidation, of enzymatic browning and Maillard reaction), gustatory (texture, taste) and nutritional (vitamins). These considerations require a high knowledge of biology, food science and engineering in order to explain the control parameters and perturbations. Drying principle can be based either on boiling (heating the product so that water is evaporated) or driving water (within air flow and lower temperature not to alter the product). According to the type of favoured phenomenon as the convection or the conduction (to change the product temperature to dry it or even roast it), many dryer structures exist with static or dynamic product: rotary dryer with axial or radial air flow (fig. 1a), fluidised bed dryer (for pulverulent solid in dynamic or static equilibrium in a fluid), dryer with radiation (infrared or microwave), conductive drier, plate dryer (fig. 1b) and fluidized spray dryer (that avoid heating the product) (fig. 1c)

[15][16][17][18]. To avoid this gap between solutions for drying and for dryer, a first global analysis should be made without considering the technological aspect which will further satisfy the right properties to be achieved. First, drying is reducing the quantity of water in the product, characterized by the water activity (aw) depending on temperature and product structure [16][19][20][21]; it stands for a state variable. Observability might be given by weight and inside product temperature measurement that might contain sufficient information for estimation or identification. Secondly, optimization relies on the ability of making water evaporate from the fruit: the exchange between fluid (consumable fluid like air) and water in or on the fruit surface should be improved without considering the limitation of classical technical point of view. Therefore both the heat production system and the thermodynamic exchange have to be thought and modeled but further defined as properties (the gas brings the energy for evaporation thanks to the gradient of partial pressure which is further evacuated). Evidently for our problem using a laboratory dryer oven 3 sub-systems should be modeled: (1) heat quantity production (with pre-heater); (2) drying chamber (with dynamic or not of the product and fluid); (3) supervision block in charge of optimization within humidity estimation and control reconfiguration. Fig. 2 gives a summary of our point of view transcribed as B-properties. Note that at each level, the upper property has to be guaranteed which might lead to a complete transformation or change of the dryer structure or strategy of control for a more specific product. S.A.D.T Formulation (Summary)

Short analysis in terms of B-method Product with no bacteriological development. Suitable relative humidity ratio è water activity level from 0.2 to 0.5 [15] Preserve product sensory qualities (visual, gustatory, nutritional) è Tmax< 60°C [20] Heat quantity production with a gas fitted to human consumption è air flow and temperature set points Low energy cost (note that a technical solution is already chosen: exchanger). No contamination of the product. Fixed drying time guaranteed at a given temperature Give the optimal temperature gradient and duration for a two step drying è desired water activity è given first temperature and adjust the 2d drying step (T, duration) è respect of the sensorial constraint

Fig. 2. Functional analysis and short B-method transcription.

For a given dryer, what remains to decide are the temperature and air flow set points taking into account the optimization criteria (required humidity rate and limit time of

drying) and the chosen robustness degree to perturbation such as the shape of the fruit (slice, cube), its maturity that influences structure and initial humidity rate but also the relative humidity on the entering air. The B-method can be applied for each functional block and specifically for block (3): IF “the regulation is correct” THEN “(temperature, duration) set points are computed” ELSE “regulation is modified” (if not, performances will be lower). The control of production time implies: IF “humidity rate is correctly known at time t” THEN “drying is done till the required humidity is obtained”. Therefore analytical redundancy, model identification of the drying curve and error detection can be the technical solutions [22]. -insure minimisation of drying time beginning with temperature T1 based on a given structure model by Lewis [21][23] where k depends on the fruit (aw) and drying temperature T1:

x ( t ) = x e + ( x 0 − x e )e − k ( t −to) -- for this structure, models identification based on the available data with validation (depending on the identification technique) and selection (minimal reconstruction error) --- for the selected model, provide optimal choice of T2 and switching time to T2 (non linear minimisation or linear if T2 fixed). Fig. 3. Optimisation task with B-method transcription (for a 2 step drying at T1 and T2).

On Fig. 3, we give a way to solve the optimization problem in our context (where some technical parts are imposed) considering the properties to achieve without “knowing” how the control of the temperature is made, nor the cartography of chamber turbulences (controlled or natural) or the thermal exchange (position and shape of the fruit); the method is therefore more transposable. The solution is based on a two-step drying that might represent what occurs in a two-tray dryer with predrying at temperature T1 and further drying at temperature T2>T1. Motivation is that after a quick increase (usually neglected) of temperature by conduction (Fourier equation) at given T1, the free water evaporates by diffusion through the surface (Fick equation) (the more there is water, more easily it escapes from the fruit) and carried away (Darcy equation)[19][20]. But structure modifications during drying reduce this ability and a higher temperature is required to end the process (to extract the linked water); the so-called “coup de feu” (heat-stroke) [19]. The optimal T2 for a given T1, and the corresponding switching time, are given by minimisation (non linear) of the drying time for a given final humidity rate expressed thanks to an online identified model of the drying curve (to be more robust to perturbations). Note that the properties are satisfied with no assumption on the way the structure model is given, its parameters identified, the measurements made: these are technical solutions depending on additive considerations that might unfortunately lead to non-realistic

solutions (cost, sensor, time computation, too high a temperature T2 or switching time already past). In that case, this means that the B-model should be modified or adapted to these events. Our study was shortened in this paper because the goal is not the experiment itself but the interest of food industry for B-method in order to achieve higher expertise and knowledge. But another great use considering safety is developed in the following too.

3 Prospects and extension Safety commitments for Food Industry are of primordial importance and some answers to achieve “good practice” are given in the International Food Standard (I.F.S). It is a reference frame of food audit for safety common to German and French actors of the distribution [6]. For industries of international rank, three standard levels (basic, higher and recommendations) are defined through five items of observation: management of the quality system based on Hazard Analysis Critical Control Point (H.A.C.C.P) and the corresponding procedure (fig. 4); management team commitment; management of the resources; product realisation and finally the measurements, analysis and improvement. H.A.C.C.P is a systematic method applied along the food process to the analysis of microbiological, chemical and physical dangers (i.e. any event that might lead to an unsuitable product for consumption). HACCP, 7 principles

Decision tree for C.C.P

B-Method transcription

1- danger identification, occurrence evaluation and identification of preventive actions required for their control

-Microbiological, chemical, physical danger are controlled (no more C.C.P) so that the product is suitable for consumption.

2- well-defined C.C.P

-IF “danger” THEN (“always eliminated” OR “always under a suitable level”) ELSE “danger is detected”

3- determination of the target levels (suitable for consumption) 4- elaboration of supervision systems (detection) 5- definition of corrective actions (elimination, reducing occurrence probability) 6- development of control 7- creation of a documentary system

Q1.1: do preventive actions exist? Q1.2: control required for safety ? Q2: elimination or occurrence reduction (suitable level)? Q3: can unsuitable level be reached? Q4: can further step eliminate or reduce to suitable level?

-- IF “danger at suitable level” THEN {“probability of occurrence is limited” AND “level detected”} ELSE “corrective action exists”.

-- IF “danger unknown” THEN “update C.C.P data base”

Fig. 4. H.A.C.C.P principles, decision tree for C.C.P and transcription in B-method.

H.A.C.C.P introduces the notion of Critical Point Control (C.C.P) that has to be controlled by elimination or reduction of the risk (i.e. the probability of event of the danger) under an acceptable level thanks to supervision and corrective procedures. As shown previously, the complementary formalization with the B-method is clear. Bmethod can be a way of definition of the events and scenarios for the proof checking of both the expected and not expected situations. Applied at each step of the process development it will be a tool to select the correct final technical solution: the final system (based on the correct properties as B-model) will present no more C.C.P, less or correctly controlled ones. The advantage will be that the H.A.C.C.P documentation systems will almost be achieved before the realisation itself and also the periodic evaluation. Evolution of the process will be easier due to the B-models (i.e., the original properties of each part of the process should be satisfied in case of modification and the new added properties be “compatible”). The consequences of modifications of the food process that requires knowledge in several fields are then kept in mind. The decision tree of C.C.P (fig. 4) can be viewed and rewritten as model consistency checking and refinement checking as it defines the scenarios of events to be avoided or guaranteed: there is no more C.C.P otherwise it is controlled and maintained to a suitable level. So, the B-method can be extended to the analysis and the development of complex systems under a safety constraint. Independently of the technical point of view, more freedom is allowed and technical realisation is facilitated thanks to a greater expertise of the process and production equipment. As a consequence, the classical methods of diagnosis based on material or analytical redundancy, supervision and control will be thought with an already greater knowledge of the process and therefore the right option [24]. The same observation is valid for quality procedures. Indeed, hostile known events can be modelled too and their consequences which might help the definition of the material, procedure, properties thanks to the help of B-tools. Of course a more precise definition of H.A.C.C.P in B-method should be made in the future.

4 Conclusion In this paper, we summarized our functional analysis on fruit dryer optimisation based on the experiment we made with an ordinary laboratory dryer of limited performances (known as incubator or oven with recycling air). Our goal was to reduce the time of drying, surrounding the right possibilities of optimisation without being frozen because of technical solutions. This might lead to a transposable method for application of industrial size. Food engineering knowledge, Thermodynamic and analytical models, and S.A.D.T were already parts of our considerations but the Bmethod seems to improve the thoughts: indeed, it guides the definition of the properties and events (B-models), i.e. the set of stable behaviours with the break-away between them; the B-dictionary clarifies the variables (states, acceptable level, of variables,…) that explains the relation with the final system; B-proof checking allows the description of all scenarios (deterministic or no deterministic transition form normal to abnormal situation or acceptable ones ; that can be static or dynamic) and therefore adjusts the corrective action to keep the desired properties; and B-tools to

compute the formalisation (something we didn’t have opportunity to check within BAtelier or B-toolkit). It’s therefore clear that B-method should be integrated in such norm as I.F.S in this peculiar industrial field as a way to reinforce expertise on the considered food process: safety commitment and the “marche en avant” (go-ahead improvement), The B-method seems useful at any step and especially for H.A.C.C.P (risk analysis for consumable product) creating the documentary system easily through the properties to be respected by each subsystem of the real final process. This part should be developed in the future with the corresponding computing tools adapted to people not aware of such tools (generator of obligation; translator; proof checking…). Adding sensorial characteristic as properties should also be of great interest. Of course the price of development (or new analysis of existing systems) will be higher but the final cost for greater control, preventive action and process evaluation might be lower thanks to high level of good practices. The traceability should be considered too. It’s obvious that food industry is a large application domain for all kind of specific food product and many processes require more expertise as: thermal treatment (freezing, drying, roasting, sterilization ...), thermo-mechanical treatment (extruder), Cleaning In Place (C.I.P). Future is then in innovating solutions based on correct properties. As a consequence, considering I.F.S, the B-method might prove the strong implication of the management direction of the food industry. We hope to arouse some opportunity for implementation with B-Atelier. Acknowledgments. The functional analysis, food engineering and thermodynamic process of drying were first discussed with L. Catiau, Ch. Boniface and S. Nicaise during their project “Modelling procedure for fruit dryer optimisation” tutored by W. Nuninger in 2006 (students in 2nd year of engineering school Polytech’Lille – Dept. of Food Industry).

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