Dmitry Kucharavy
email: dmitry.kucharavy@insa-strasbourg.fr

Roland De
email: roland.deguio@insa-strasbourg.fr

PROBLEMS OF FORECAST 1

Keywords: Technology Forecast, Laws of Technical systems evolution, Analysis of Contradictions

The ability to foresee future technology is a key task of Innovative Design. The paper focuses on the obstacles to reliable prediction of technological evolution for the purpose of Innovative Design. First, a brief analysis of problems for existing forecasting methods is presented. The causes for the complexity of technology prediction are discussed in the context of reduction of the forecast errors. Second, using a contradiction analysis, a set of problems related to technology forecast is proposed. Third, the paper examines how some knowledge from the Theory of Inventive Problem Solving (TRIZ) can be applied in response to forecasting problems. Fourth, conclusions are drawn about the perspectives for reliable technology forecasting.

Introduction

Let us start with an idea that "…Any system which depends on human reliability is unreliable 2 …" Why is reliable technology forecast so urgent today? The Problem might be formulated in the following way: If technology forecasting practice remains at the present level, it is necessary to significantly improve the efficiency of design to make it possible to develop adequate technologies in a short period in response to new demands (like Green House Gases -GHG Effect reduction or covering exploded nuclear reactor); If technology forecasting is more efficient, it is possible to develop an adequate technology for coping with the new requirements without being in a hurry (if GHG Effect could have been predicted 50 years before it appeared). Thus, in order to survive in a highly technological environment, an efficient engineering design and production are not enough. The absence of efficient and reliable forecast limits decision makers and the pace of changes.

What if we look at technology forecast from the problem-solving viewpoint? Let us assume that a problem situation can be defined as a difference between the actual state and the target situation (objectives). In other words, Problem = Target situation -Actual state (or Target situation = Actual state + Changes, where Changes include Typical solutions and Problems). Where do objectives come from? They come from the vision of future. When a certain technical problem is discussed, the vision of future appears as a result of a technology forecast. Even if the formal forecasting was not performed the intuitive one was done.

What is a problem origin in such reasoning? The target situation seems unreachable. However, what if the vision about future is wrong? The Problem could be defined in the wrong way. It is a common place today that a solution fails more often because a wrong problem has been chosen rather than because a wrong path to the right problem was followed. "…We suffer more from the good solutions for wrong problems, but not from weak solutions for right problems…" [Russell L. Ackoff -an American scientist in operations research and systems theory; iconoclastic management authority, advocates a ''systemic'' approach to innovation] Why do we need a reliable technology forecast? From the technological viewpoint, it is required for setting priorities for research and development; and definition of the right problems instead of approaching whole of believable. From the social standpoint it is essential for assessing and managing threats of emergent technologies and new scientific discoveries in advance as well as an for adaption of social institutions, such as educational system, for coming changes. From the business environment context it is substantial for efficient management of intellectual property and for extension of technological competitiveness of products, processes, and services.

This paper seeks to discuss a set of problems related to a reliable technology forecast.

Specific terms definition

Let us define the specific terms that used in this paper: Event is a physical effect (changes), that occurs in a particular place of space, at a particular point in time. An Event can be defined by several features, such as physical content of changes, location in space and time (What? Where (How large)? When (How long)?). In order to unify the applied descriptions, the ENV (Element-Name of Feature-Value of Feature) model is used to describe Events. For details about the ENV model, see Khomenko [START_REF] Khomenko | Materials for seminars: OTSM-TRIZ: Main technologies of problem solving[END_REF]. According to the ENV model physical contents, place and time are considered and described as features.

Time is an artificial concept (method) to put in order the observed events and to measure relative duration of processes. Discussion of the epistemology of time is beyond the scope of the given paper.

Present is a set of events that occurs in a particular place of space. Future is a set of events that may be affected by some events in Present. One of the crucial questions of any forecast can be formulated as follows: "How to recognise which events in present will influence the future and which ones will not affect it?" Another critical question is: "How to foresee uncertainties that will affect future as well?"

Past is a set of events that may influence the events in Present.

Technology forecast

The difference between forecasting methods and forecast results (model description) is presented in Table 1. Researchers in the field of future technologies differentiate between technology forecasting, technology foresight, technology intelligence, technology road mapping, and technology assessment [START_REF] Porter | Technology futures analysis: Toward integration of the field and new methods[END_REF]. The given paper mainly deals with the technology forecasting. For instance, a forecast usually answers the question "What will happen?" while a plan describes "What should happen". There are dozens of different definitions of technology forecast in literature [some of them can be found in 2, 3, 4, 5]. In the context of the present research we use the following definition: "Technology forecast is a comprehensible description of emergence, performance, features, or impacts of a technology in a particular place of a particular point of time in the future".

Often, scenarios building methods lead to a hierarchical set of descriptions about future events. The number of possible events described increases exponentially with the number of levels. From the practical viewpoint, time limitations do admit to analyse multiple alternative. That is why we intensify the initial situation and propose not to admit to have any "IF" in a forecast description. Consequently, scenarios methods are not considered to belong forecast methods.

I F A B C D IF IF IF A B C D E F G H Figure 1.2.

Multiplication of scenarios

In order to be precise with a technology forecast the system approach is inevitable [START_REF] Schnaars | Megamistakes: forecasting and the myth of rapid technological change[END_REF][START_REF] Altshuller | About forecasting of technical systems development[END_REF]. Using a Multi-screen analysis different levels of details can be recognized for any technology forecast:

1. sub-micro (technology, product, process) 2. micro (company, group of companies) 3. industry (competitors by the same product, competitors by the same function) 4. macro (financial, economic community, country) 5. super-macro (environment, demographic, etc.) Such a list can be expanded in both sides. What complicates a technology forecast is interconnections between all these levels. It is evident that an efficient forecasting process has to provide a means for a simultaneous work on several levels.

We propose to define the efficiency of technology forecast as a ratio between a reliable forecast and aggregated expenses necessary to perform forecasting, where a reliable forecast is characterized by accuracy of forecast and transparency of the forecasting process while aggregated expenses include resources spent on development and communication of forecast results. This working model of technology forecast efficiency is introduced in order to make it possible to measure the difference between "good" and "not so good" forecasts while comparing two forecasts about the same question.

Review of forecasting practice

Existing forecasting methods

Existing forecasting methods can be classified in various ways. In Principles of Forecasting, edited by J.S. Armstrong [START_REF]PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioner[END_REF] all forecasting methods are classified into ten categories. The methodological tree starts from the division of all methods into two categories: Judgmental and Statistical. The proposed classification helps to choose an appropriate method or combine several methods for particular objectives and conditions.

In scope of research about Technology Future Analysis [START_REF] Porter | Technology futures analysis: Toward integration of the field and new methods[END_REF], fifty-two methods (including TRIZ) are classified into qualitative (soft) and quantitative (hard) as well as grouped according to nine "families": Creativity, Descriptive and Matrices, Statistical, Expert opinion, Monitoring and Intelligence, Modeling and Simulation, Scenarios, Trend analysis, and Valuing/Decision/Economic. Each method can be considered as Normative (beginning the process with a perceived future need) or Exploratory (beginning the process with extrapolation of current technological capabilities). Such classification is supposed to serve the choosing and combination methods in accordance with particular situation conditions. The idea of Directed Evolution [START_REF] Zlotin | Directed Evolution. Philosophy, Theory and Practice[END_REF], which is well-known in the TRIZ society, belongs to Normative forecasting.

In his classical book [START_REF] Makridakis | FORECASTING: methods and applications[END_REF] Markidakis and co-authors subdivide fifteen groups of forecasting methods into five categories: traditional time series methods, advanced forecasting methods, approaches to long-term forecasting, major statistical combination methods, and judgmental forecasting.

Some practitioners [START_REF] Vanston | Better forecast, better plans, better results[END_REF] categorize forecasting methods according to different ways people view the future. Five groups are distinguished: Extrapolators, Pattern Analysts, Goal Analysts, Counter Punchers, and Intuitors for twenty-four different analyses. This classification helps to customize set of methods to initial vision of forecast users about technology future and forecasting.

(Technology forecasting using TRIZ and concepts based on works of G.Altshuller are discussed below in section 3.1.)

The review of the existing methods for forecasting shows that single method is never used for practical technology forecast. The necessity for a combination of methods become apparent when formulating generic conflicting requirements for any method of analysis: the Method should be short and simple, in order to be easy-to-learn, easy-to-apply, easy-tointegrate into super-systems (e.g. planning and decision making processed for forecasting); BUT the Method should be redundant and complex, in order to be reliable, to have one universal method instead of multiple, in order to decrease the probability of application mistakes; and to secure achievement of the initial goals.

From the TRIZ viewpoint, one of the typical solutions for a conflict "complex vs. easy" is performing segmentation and then building a new system from the segmented parts in accordance with the requirements of a specific situation. Thus, it seems obvious that at present combinations of several methods are preferred to a single one.

It is not evident however, how a combination of methods influences the technology forecast errors. Normally, methods are combined in order to reinforce the weakness of one method by the strength of another. However, when several methods are combined, new forecast errors can appear as a result of the synergy effects. At present, the question of measurability of forecast errors arising as a result of an integration of several methods remains unanswered.

In order to review the existing technology forecast methods in a holistic and systemic way we propose to classify all forecasting methods from the point of view of a problem solving approach by indicating which problem or a set of problems a given method addresses and aims to resolve.

In order to illustrate our point better, let us consider a method of Role-playing [4, p.p.15-30] that is used to forecast decisions. Using the same data, depending on a given role ("cost analyst" or "feasibility analyst"), a forecaster can obtain different forecast results. Moreover, Role-playing works on simulation of interactions between roles A and B, when several participants try to simulate decision making in order to forecast a decision.

Which problems are solved by this method? It is necessary to note, that there are many problems that remain unsolved and eventually influence the accuracy of such a forecast. Nevertheless, the evident advantage of Role-playing is that it applies a mechanism decreasing subjective biases of forecasters: Forecaster should have personal inclinations, because he has subjective opinions; BUT Forecaster should not have personal inclinations, because they decrease the accuracy of a forecast.

Another interesting point is that Role-playing works with interactions, rather than with subjects. In accordance with a systemic approach (a Multi-screen scheme of thinking, or the so-called System operator) a forecast will be more efficient when interactions rather than just separate objects are taken into consideration. It is quite obvious that in order to forecast a future of some transportation technology, it is inevitable to analyze interactions of such technology with present and future social, environmental, and economic contexts. Role playing offers no formal mechanisms for performing systemic thinking; nevertheless, its primary focus is on interactions: forecaster has to analyze interactions between objects, in order to improve the accuracy of a technology forecast; BUT forecaster has to analyze separated objects, because interactions appear when objects start to act and react.

Thus, Role-playing offers a concept solution to the two problems in a network of problems dealing with a technology forecast. Further on, we will describe this network and categorize the existing forecast methods according to the problems from the network.

Technology forecast errors

In order to be confident about a technology forecast, one crucial question should be answered with certainty, "How can one distinguish between valid and invalid forecasts?" Or, in other words, "How to measure errors and accuracy of forecasting results?" When reformulating the above question in the form of conflicting requirements, we arrive at the following contradiction: the Difference (between valid and invalid forecasts) should be measurable, in order to evaluate the technology forecast with minimum bias; BUT the Difference cannot be measurable, because forecasted events will happen in future.

One of well-known definitions [START_REF]PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioner[END_REF] proposes to identify a forecast error as the difference between the forecasted value (F) and the actual value (A). The accuracy of forecast is used as an optimist's term for forecast errors. Regarding the definition of forecast given above (section 2.1, 2.2), the value of technology forecast is presented through event, time, and place characteristics. Thus, an invalid forecast may be a result of a mistake in terms of event (what happened?), time (when?), and place (where?). In a general sense, in order to judge a technology forecast it is necessary to be able to measure both a forecasted value and a real value. The difficulty arises only because these two values are separated in time.

What typical solutions exist for improving accuracy of technology forecasting? In case of a short term forecast, when qualitative methods are used, recalculation can be performed several times and the resulting model can be tuned in an interactive mode to better fit the reality. The interactive techniques for tuning forecast equations are well known in data mining area.

In case of a long-term technology forecast, it is interesting to consider the experience of the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) [START_REF] Kameoka | A challenge of integrating technology foresight and assessment in industrial strategy development and policymaking[END_REF]. Starting from the early 1970s, MEXT has been conducting a regular Delphi survey every 5 years. Surveys have involved more than thousand experts (last two survey involved more than three thousand) and aimed at forecasting long-term trends in various fields of technology with forecast time horizon of thirty years. Thus, the technology forecast is updated regularly (every 5years) to decrease errors. It is necessary to note that the applied methods are regularly modified as well in order to reduce errors of technology forecast.

Both examples we consider use a similar solution concept: to forecast, to wait for the forecast time to come, and to compare the forecasted value (F) with the actual value (A).

The second example shows us a much more expensive way for improving forecast methods with the purpose of evaluation of the validity of a technology forecast. Such an expensive way is not acceptable for most of the technology forecast demands. Thus, the question about the difference between valid and invalid forecasts needs to be answered mostly for medium and long-term technology forecasts.

There are many qualitative ways for performing forecast evaluation. For instance, it was proposed [START_REF] Schnaars | Five Modern Lessons from a 55-Year-Old Technological Forecast[END_REF] to use a set of characteristics such as: market impact, market timing, predicted use, and social impact. The market impact can be evaluated as strong, moderate, weak, or virtually none; the market timing can be on target or optimistic; while predicted use can be characterised as mostly right, mixed, right, mostly wrong, wrong; etc.

Such quantitative evaluations appear easy-to-use, however they lead to the same problem: forecasted events should happen in order to perform a definite evaluation of a forecast.

Problems of technology forecasts

In order to build a network of problems, the initial set of problems should be collected. For the purpose of the present research, it was decided to group the problems according to four stages of a technology forecast life cycle: Design stage; Developing stage; Application of a forecast stage and Retirement-and-Update forecast models stage.

In order to focus on the most difficult technology forecast problems the literature review and practical case study were performed. According to literature [for example 2, 10] and the practice of forecasting a technological future of a new product, most mistakes are made in medium and long-term forecasting dealing with pioneering and new-to-the-world technologies.

Let us try to define what is meant under "a new product"? Crawford's list [START_REF] Crawford | New product management[END_REF] distinguishes six types of new products:

cost improvement (reduced cost versions of a product for the existing market);

-product improvement (new versions of existing products, targeted at the existing market); -line extension (innovations added to the existing product lines and targeted at the actual market); -market extension (taking existing products to new markets); -new category entry (new-to-the-company product and new-to-the-company market, but not new to the general market); -new-to-the-world (radically different products). For practical use of a technology forecast it is proposed to distinguish four types of new product/technologies:

-new version of a product (e.g. a new bicycle without a chain, with a new lighting system, with a new break system; high capacity small batteries; low price small batteries); -new market penetration (e.g. German bikes to the Russian market; high capacity batteries for toys); -new family of products (e.g. mountain bikes; fast rechargeable batteries; noisecancelling headphones); -new-to-the-world (e.g. a new personal transport instead of bicycle; a small stationary commercial fuel cell). Another issue to define is the difference between short-term and long-term forecast. It is proposed to use the life cycle of a product/technology as a unit for measuring the difference between short-term, medium-term and long-term forecasts from the market viewpoint. For instance, if the life cycle of computer mouse is determined as 24 months, a short-term technology forecast for computer mouse has time horizon below 36 months, while a longterm forecast will exceed 48 months.

However, when the life cycle is reduced as a result of changes in the nearest super-system, the definition of a short-term forecast for a certain product could be changed as well. For instance, cathode ray tube (CRT) displays have the life cycle of about 8 to 10 years. However, increasing prices for office and living space in combination with electricity price rise lead to replacement of CRT displays and TV sets by slim and energy efficient products faster than an old fashion CRT really stops functioning.

Short-term and long-term forecasts have different duration in time for production and for service companies. For instance, industrial companies have longer time horizons for new product forecasts (on the average 34 months) than consumer firms (18 months) [START_REF] Kahn | An exploratory Investigation of new product forecasting practices[END_REF].

The problems presented below are pertinent to medium and long-term forecasts of a new family of products and new-to-the-world technologies. The literature review reports that for the first two groups of new products when a short-term forecast is formal quantitative methods in combination with a proper management of forecasting projects gives an adequate accuracy of forecasting.

Due to the format of the given paper, it appears impossible to focus on all the stages of a product life cycle. Therefore further on we will focus on two stages only, namely those of Forecast Design and Forecast Model Development.

Design of forecast stage can be subdivided into three major steps: problem formulation, information gathering, and selection on an appropriate method(s).

It is difficult to overestimate the importance of forecasting problem definition. The answer usually depends on the question. The way the problem is defined determines the whole forecasting process. For example, a question such as "When technology 'A' will reach the commercial level?" already assumes that the technology will succeed. A new product forecast is usually connected with many limitations, such as a shortage of data, a limited time for an analysis, general uncertainty surrounding a new product, no marketplace for a new product etc.

Many questions appear at the step of problem formulation: How to find the right problem? How to purge one's mind from existing theories and predilections? How to structure a forecasting problem? What are the evaluation criteria for measuring the accuracy of an answer to the formulated problem? Normally there are conflicting requirements hiding behind each question.

One of the primary contradictions at this step can be defined as follows: Problem has to be formulated precisely to be able to use the forecast results for decision making; BUT Problem has to be formulated approximately, in order to avoid predilection and the influence of dominant concepts.

At the step of information collection frequently occurring complaints are "not enough data" or "no data yet". A list of generic questions for this step may looks as followings:

-What data are to be collected? o How to prove the validity of the collected data? o How to be sure about the reliability of the data? -Why do we need to collect data? -How to use existing (subjective) data most effectively? -How to incorporate the existing ideas into the picture after the data collection? -How to interpret the collected data? One should be aware that the problem of signal-noise often hides behind the so-called lack of data. If we assume that all data are available, the time necessary for data processing will increase dramatically. Thus, we face the following problem: How to recognize events in present and past that will influence the forecasted future? In other words, how to collect "signal-data" and avoid spending time and resources on "noise-data"?

At the step of an appropriate method selection the following questions may appear:

-How to know about most efficient methods for a particular situation? -How to select right method(s) out of a set of methods? -How to evaluate the selected methods or how to be sure about the chosen techniques? -How to apply the selected methods in the most effective way? One of the contradictions that appears at this stage relates to specific competences: in order to make the right choice of a method(s) it is necessary to be a specialist in all known forecasting methodologies, BUT it is necessary to be a specialist in a particular domain of knowledge, in order to be able to perform forecasting and to valuate the obtained results.

The stage of Forecast Model development can be presented through three basic steps: method(s) implementation including evolvement of the forecast models, evaluation of the applied methods, and evaluation of the forecast models.

Most of forecast problems are concentrated at the step of methods implementation. Some problems are generic and appear when facing such questions: How to assess uncertainties? How to keep forecasting methods simple? How to perform a realistic representation and link obtained results with contexts (super-systems)? How to reach an agreement in a working team that consists of specialists with various competences and different visions? Which reasoning, causal or naive3 will be appropriate for a particular forecast?

Another group of problems is linked with the nature of selected methods. For qualitative methods most critical queries to satisfy are the following: How to measure (to be objective) with qualitative criteria and expectations of different experts? How to frame questions to experts in order to avoid misunderstandings and biases? How to combine diverse quantitative criteria and forecasts? How to scale in time quantitative proposals of forecasting? It is necessary to note that judgmental methods are usually limited by what people perceive as feasible that depends in fact on their shared beliefs and their restricted imagination.

For quantitative approaches many problems are generated by the following questions: How to match models with underlying phenomena? How many parameters will be enough to provide a useful result for a certain time horizon? How to present new quality results (unknown novelty) using quantitative output of models? Limitations of quantitative approaches come indirect way through boundaries of applied models and are similar to limitations of statistical methods.

Combination of quantitative methods with qualitative ones, as well as performing qualitative forecasting with a support of quantitative approaches helps to improve the accuracy of forecasting [START_REF] Makridakis | FORECASTING: methods and applications[END_REF][START_REF]PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioner[END_REF][START_REF] Kameoka | A challenge of integrating technology foresight and assessment in industrial strategy development and policymaking[END_REF]. At the same time, it generates another complex bunch of problems and consumes a lot of resources. One of practical ways to improve the reliability of a forecast and to avoid large errors is a combination of forecast results obtained by various methods (combination at the level of results). However, such a combination requires extra time and decrease prediction probability of uncertainties. A valuable forecast presents an event that seemed improbable at the time of a forecast, but was proven by reality. The step of evaluation of applied methods plays an important role, especially for a technology forecast. If the applied method(s) is not transparent or it uses some hidden assumptions, the results of forecast have minimal value even if they can be proven by reality in the future. Thus, simple methods are often chosen, even if they provide less accurate results. In order to be evaluated, it is necessary to disclose a method completely, but in order to understand method fully, it is necessary to spend a lot of time and effort. Applied method(s) should be tailored to the forecast problem, but they have to be tested before in practice. In order to realize a complex of problems related to method(s) evaluation see Table 1. Features of forecasting (process) and forecast (results) above.

In order to structure the collected problems, it is necessary to disclose contradictions that lie behind of the questions described above. Figure 2.3.1 presents a fragment of the associated contradictions.

Field experiments

TRIZ and forecast

One of the authors of this paper has dealt with TRIZ and OTSM-TRIZ (General Theory of Advanced Thinking) for more than fifteen years. It seems evident that first forecast practice was based on the ideas of G.S. Altshuller [START_REF] Altshuller | About forecasting of technical systems development[END_REF][START_REF] Altshuller | Cybernetics[END_REF] and other researches from the TRIZ society [START_REF] Altshuller | SEARCH FOR NEW IDEAS: from insight to technology (theory and practise of inventive problem solving[END_REF][START_REF] Zlotin | Laws of Evolution and Forecasting for Technical Systems[END_REF][START_REF] Salamatov | System of The Laws of Technical Systems Evolution, in Chance to Adventure[END_REF]. Some of those ideas appeared in the English language publications as translations or rediscoveries after 1991 and they continue to be under development in the international TRIZ society.

It is evident that a new innovative solution is normally developed as a result of problem solving. Such a solution requires time and effort to be implemented in practice. As a result, solving an inventive problem causes technology evolution. As soon TRIZ and its posterior generations are based on the objective laws of technology evolution, these laws can be purposefully applied to foresee the technological future. (Discussion of the laws of evolution discovered in the context of TRIZ research remains beyond the scope of this paper.) Most of the observed publications about TRIZ technology forecasting speculate about the S-curve of system evolution, ideality, multiple technology trends (patterns) and laws of technical systems evolution. On a closer examination, the law of increasing ideality of technical systems is nothing more than a sequent of analysis of several S-curves for several generations of a system (to measure time, to move load -transportation; to deliver information, etc.). The inherent meaning of the S-curve becomes evident when the reason for such a shape of system evolution is clarified. Limitations of resources drive system evolution. As soon as resources expire, a given system has to be replaced by a new generation of system. This next generation will spend fewer resources of space, energy and substance for satisfying the needs.

When applying the S-curve for technology forecast, one comes across a number of questions. Let us consider some of them: How to define the main index of an analyzed system in a computable way? How to scale the S-curve in time? How to accurately define the position of the analyzed system on the S-curve? It is interesting to notice that some of these questions considered in the context of the research dealing with genetic algorithm development [START_REF] Goldberg | The design of innovation: lessons from and for competent genetic algorithms[END_REF].

One of the authors of this paper successfully applied the S-curve analysis in combination with resources and contradiction analysis for forecasting the future of a technical system at the end of 1999. As was proven later that the results of the forecast with a time horizon of three years corresponded to reality with quarter accuracy and forecast was right for three countries out of five forecasted. This experience gave an over optimistic viewpoint for the applied approach. Several express forecasts performed in the period from 2000 to 2003 just reinforced this optimistic viewpoint.

New product technology forecast

An improved approach was tested in 2004 for forecasting the future of Stationary Fuel Cell technology in framework of a project with European Institute for Energy Research (EIfER, Karlsruhe, Germany). The results of first phase of the project were recognized as unsatisfied. Among other reasons, an analysis of causes for failure showed drawbacks of the applied forecasting methodology. It was concluded that the methodology which was successfully applied for technologies in the second or third phases cannot be applied to a technology in the first phase of evolution (before point α on the S-curve). In addition, it was required to improve the transparency of the forecasting methodology.

The project dealing with Forecasting of Stationary Fuel Cell technology was redesigned and restarted. Using the results of the first phase of the project, the initial forecast problem was reformulated and divided into three questions:

1. What will be the Evolution of the market penetration for Stationary Fuel Cell (SFC)? 2. What will be the evolution of the SFC in comparing to competitive technologies? 3. What is the best path towards the ideal system of SFC? It was assumed that all questions would be answered for a fixed market (countries and regions) (Where?); for three power ranges (What?); for a time horizon: up to 2050 (with a nonlinear scale of time). (When?)

At the next step, a set of critical features was formulated in accordance with the rules of ENV modeling [START_REF] Khomenko | Materials for seminars: OTSM-TRIZ: Main technologies of problem solving[END_REF]. In order to estimate a gap between the required values of formulated features and the actual ones, an analysis of best samples was performed. The results of the analysis were presented in the shape of radar diagrams (see Fig. 3.2.1) for alternative technologies vs. required values of critical features.

In order to estimate limitations of resources a network of contradictions [START_REF] Cavallucci | Towards inventive design through management of contradictions[END_REF] (Map of Problems) was developed in accordance with required values of critical parameters. An analysis of the network (see Fig 3 .2.2) in accordance with resources limitation support timing of technology forecast and answering for some of the formulated questions. On the other hand, such a map of problems supports the monitoring of new technologies impacts to the market capacity of small SFC. Every new patent of the project result can be associated with a problem from the map and the impact of such novelty can be examined in a systemic way. Results of the second phase of the project were reported in June 2005 with a positive feedback. It was decided to continue the project in order to build comprehensive answers to the formulated questions.

Preliminary results

The results of the present study should be considered preliminary. These results offer the following:

1. Despite many existing methods, medium and long-term technology forecast of a new family of products and new-to-the-world technologies is not accurate enough to validate expenses for forecasting. The accuracy (mostly timing and social impact) of obtained technology forecasts is usually far from required. 2. Most currently applied methods aimed to satisfy the needs of a long-term technology forecast are modifications of Delphi surveys and scenarios building. Often they are applied in combination. 3. Knowledge extracted from the Theory of inventive problem solving (TRIZ) and its posterior generations can contribute to the accuracy of technology forecasting, but it should be done carefully taking into account the peculiarity of a forecast problem. 4. Complex forecasting methods do not necessarily provide more accurate forecast results than simple methods. Simple methods are less subjected to data inaccuracy than complex ones, while implementation expenses for simple methods are lower. As a result, the efficiency of simple forecast methods is higher. 5. The choice of a forecast method(s) mostly depends on data availability. A formal method(s) is reproducible, however it does not work well with qualitative parameters. 6. The efficiency of an existing forecasting method depends upon a forecasting horizon.

Increasing the time horizon of a forecast dramatically decrease the efficiency of methods.

7. The efficiency of forecasting depends not only on applied method(s) but also the management of the whole forecast process. Effective method(s) can lead to poor results if project management is careless.

Concluding remarks

This paper aimed to demonstrate a set of problems that need to be solved on the way to a reliable technology forecasting. The collected set of problems should be structured in the shape of a map of problems and this map should be validated through further research.

It is also necessary to improve the transparency of a forecasting technique(s) in order to improve the applicability of proposed ideas and approaches.

The efficiency of next generation forecasting methods should suffer less from increased time horizons. It is necessary to propose a mode for description of uncertainties in a comprehensible way in order to communicate them and to be prepared for real threats rather than only for probable or believable ones.

Figure 2 . 3 . 1 .

 231 Figure 2.3.1. Prototypes of contradictions surrounding the accuracy of a forecast

Figure 3 . 2 . 2 .

 322 Figure 3.2.1. S-curve of Technical System evolution

Figure 3 . 2 . 1 .

 321 Figure 3.2.1. Example of results for critical features analysis for Proton Exchange Membrane Fuel Cell (PEMFC)

Figure 3 . 2 . 2 .

 322 Figure 3.2.2. A fragment of the contradiction network for a small SFC (PEMFC)

Table 1 Features of forecasting (process) and forecast (results) Forecasting (process) forecast (result)

 1

	Cost effective in practice	Accuracy.
	o profitability (computer,	Improved decisions (as a result of
	human resources, etc.);	application).
	o timeless in providing	Ease of interpretation (in order to
	forecast.	understand results and origins).
	Flexibility in application	Ease to update.
	Easy in using available data	Intelligibility.
	Transparency	Readability.
	Operability	Confidence.
	o easy-to-implement;	Validity.
	o easy-to-use;	Describing a technology at some time in
	o sensitivity for input data;	the future
	o easy-to-develop or	o Emergence;
	universality (e.g. using	o Performance;
	extensions without	o Features;
	changing the main	o Impacts;
	procedure);	Consists of:
	o stable in time.	o emerging technology
	Reliability	characteristics,
	Ability to identify:	o development pathways;
	o future technology	o potential impacts on social and
	developments, and	business environments.
	o their interactions with	Explains interactions between:
	society	o events.
		o trends, and
		o actions.

Does not include personal bias (bias free).

Article was prepared for ETRIA TRIZ Future

(Graz, November 16-18, Austria) conference. Last update: November 28, 2005 2 Merphy's laws (Gilb's Laws of Unreliability)

Naïve model -a model that assumes things will behave as they have in the past.[START_REF]PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioner[END_REF]

Acknowledgements

We wish to acknowledge the European Institute for Energy Research (EIfER), Karlsruhe for support of the research on Technology forecasting. We also would like to thank our colleagues from LICIA team of the Laboratory of Engineering Design (LGéCo, INSA Strasbourg) for their questions and discussions that helped to clarify many points presented in this paper. Alexander Sokol provided a lot of corrections and advices about language and readability of this version of paper.

All of these reflections are supported by the research experience gained in the project with the European Institute for Energy Research (


Jean-Yves Gauthier
email: jean-yves.gauthier@ens2m.fr

Arnaud Hubert

Joël Abadie

Nicolas Chaillet

Christian Lexcellent

Modeling and control of micro-mechatronic devices: application of variational and energetic methods for micro-actuator design

This paper is focused on a modeling procedure wellsuited for the design of micro-mechatronic systems and especially for micro-actuators. The purpose of this publication is to show that the variational and energetical methods is not only wellsuited to model classical micro-mechatronic devices but that they are also well-suited to include complex dynamical behaviour such as non-linearity and hysteretical behaviour. This procedure is applied to the design of a new actuator using one of the relatively new smart materials, the Magnetic Shape Memory Alloys (MSMAs). It should be stressed that the presented approach can be extented to a great range of other smart materials and that the description can be easily extented up to the control level.

I. INTRODUCTION

Micro-mechatronic devices are systems including mechatronic elements at the mini-and microscopic scale. Presently, most of these devices concern actuators and sensors applications. Indeed, at this scale, the use of multi-components systems to develop a mechatronic function is not convenient because of integration difficulties. Therefore a great part of these applications use smart materials because they can achieve a sensing and actuation function in an integrated and distributed way. This paper is focused on a modeling procedure well-suited to micro-actuators design. In a first step, some headlines will be given concerning variational and energetic methods for the modeling and design procedures. These procedures will be applied for the design of a new actuator using one of the relatively new smart materials, the Magnetic Shape Memory Alloys (MSMAs). Even if, this method is applied to MSMAs materials, it should be stressed that this approach can be extented to a great range of other smart materials.

II. VARIATIONAL AND ENERGETIC METHODS FOR THE MICRO-ACTUATOR DESIGN

For the modeling of any micro-mechatronic systems, the design has to take into account different physical fields. For the example of an MSMA actuator, a thermo-magnetomechanical model is required. During the first design step of classical actuators (not requiring a mechatronic approach), each physical field is usually studied independently and the coupling effects are taken into account in a second step using numerical computations such as the Finite Elements Analysis (FEA). Nevertheless, for mechatronic systems and especially when the size of the device is reduced, the coupling effects become predominant as it is the case for the use of smart materials. The coupling effects must then be taken into account from the first step of the design procedure. At this stage, the FEA are not usually relevant because of the computing time and the necessity to already have the geometry of the devices at one's disposal. Indeed, it is necessary to use a synthesis tool for the design procedure instead of an analysis tool to make the first design choices. This tool must also be multi-physical and in this purpose, the only relevant method is to adopt an energetic point of view because energy is the only common point between different fields of physics.

For the mechatronic field, such a relevant tool is the Bond Graph method. It is a muti-physical, graphical and energetical tool well-suited for the design procedure. The last edition of the reference book on the subject [START_REF] Karnopp | System Dynamics: Modeling and Simulation of Mechatronic Systems[END_REF] emphasises this point by adding the subtitle Modeling and Simulation of Mechatronic Systems to the title of the book. As the Bond-graph method is a relevant and efficient tool for mechatronic devices design and modeling, it is nevertheless limited for micro-mechatronic devices because it is difficult to model distributed parameters systems described by Partial Differential Equations with this tool. In such a case, variational methods are much more relevant. These variational methods in an energetical context include the Lagrangian and Hamiltonian formalisms ( [START_REF] Crandall | Dynamics of Mechanical and Electromechanical Systems[END_REF], [START_REF] Hammond | Energy Methods in Electromagnetism[END_REF], [START_REF] Goldstein | Classical Mechanics[END_REF], [START_REF] Lanczos | The Variational Principe of Mechanics[END_REF]). These methods can model discret parameters systems (lumped parameters physics) as well as distributed parameters systems (continuum physics) in a similar way. These methods are also the bases of approximate methods such as the Finite Elements Analysis Technique. Some recent textbooks on mechatronic modeling emphasises this point in beeing completely based on the Lagrangian modeling for mechatronic devices as well as for micro-mechatronic devices using piezoelectric materials ([6], [START_REF] Nogarede | Électrodynamique Appliquée[END_REF]).

A. Conservative systems

The lagrangian formalism is a modeling technique based on some energy functions used with the Hamilton principle [4] [5]. This principle postulates that the variation of an action S between two times on a real path is always equal to zero. This action is the lagrangian L(q, q, t) integrated between the two times t 1 et t 2 :

S = t2 t1 L dt ⇒ δS = 0 on a real path (1)
For the particular case of non-relativist systems, the lagrangian function is the difference between a kinetic co-energy T * ( q) and a potential energy V(q) [START_REF] Crandall | Dynamics of Mechanical and Electromechanical Systems[END_REF]. For conservative systems (i.e. closed and non-dissipative), L does not depend explicitely on the time t:

L(q, q) = T * ( q) -V(q) (2)
A variational calculus on the Hamilton principle leads to the set of n Lagrange equations:

∂L ∂q i - d dt ∂L ∂ qi = 0 i ∈ [1, n] (3)
where ∂L ∂qi are the generalized forces and p i = ∂L ∂ qi are the generalized momentums.

The Hamilton formalism is an extension of the lagrangian formalism which uses a Legendre transformation to substitute the time rate functions q in the lagrangian L(q, q) for the generalized momentum p = ∂L ∂ q in a new energy function called the hamiltonian function H(q, p):

H(q, p) = p • q -L(q, q) (4)
In such a case, the hamiltonian function corresponds to the total energy expressed with coordinates q and momentums p instead of coordinates q and velocities q:

H(q, p) = T (p) + V(q) (5)
Then the n second order Lagrange equations are transformed into a set of 2n first order Hamilton equations:

       qi = ∂H ∂p i ṗi = - ∂H ∂q i i ∈ [1, n] (6)
With this formalism, x = q p T can be chosen as the state of the system and ( 6) becomes the state-space model of the system:

d dt q p = f q (q, p) f p (q, p) (7)

B. Dissipative and controlled systems

The previous variational procedures are defined for conservative systems, nevertheless this formalism can be extended to the non-conservative case (open and dissipative) and also to systems that include kinematic constraints.

An open system means that it exchanges some energy with an outer system. This is the case when we try to control the system with an external force f ext depending explicitely on the time t. In this case, we also speak about non-autonomous systems. A dissipative system means that some part of the inner energy is non-available during any motion of the system. A system with kinematic constraints mean that there is some geometric or topologic constraints on the admissible motion of this system. These kinematic constraints can be taken into account in the dynamical equations using a Lagrange multiplier technique.

To take into account all these phenomena, we make use of an extented lagrangian function L :

• the external generalized forces f ext (q, t) are taking into account in the variation of L by adding their virtual works δW ext = f ext (q, t) • δq ; • dissipations by static and viscous frictions are taking into account by adding their dissipated energies variations δQ s (q) and δQ v ( q). The dissipation by viscous friction

Q v ( q) is calculated with a Rayleigh dissipation function R( q) like Q v ( q) = t2 t1 R( q) dt ;
• the holonomic kinematic constraints c(q) = 0 are taking into account with a Lagrange multipliers technique by adding the term -λ • δc(q) to the variation δL . Finally, we have:

δL = δL + f ext • δq + δQ s + δQ v -λ • δc (8)
The Hamilton principle using δL gives the following Lagrange equations:

∂L ∂q i - d dt ∂L ∂ qi - ∂R ∂ qi + ∂Q s ∂q i + f ext,i -λ i • ∂c i ∂q i = 0 (9)
The extented lagrangian function for a controlled dissipative system with kinematic constraints can also be transformed into an extented hamiltonian function. This leads to the following Hamilton equations:

       qi = ∂H ∂p i ṗi = - ∂H ∂q i - ∂R ∂ qi + ∂Q s ∂q i + f ext,i -λ i • ∂c i ∂q i (10)
C. Thermodynamics of irreversible processes as a way to define dissipative potential for nonlinear systems

The previous Lagrange and Hamilton formalisms are wellsuited to conservative systems and can also be extented to take into account the dissipative and exchanges phenomona. The connexion with thermodynamics is therefore direct because, except for the choice of the relevant coordinates, the hamiltonian function H(q, p) corresponds to the total energy E T (q, q), the energetical function used in thermodynamics. The point of view of thermodynamics of irreversible processes is a phenomenological point of view directed toward the storage, the available and the dissipated energies.

The first law of the thermodynamic states that the total energy -or the hamiltonian -is always conserved in a close system and its variation gives rise to an energy exchange in an open system [START_REF] Callen | Thermodynamics and an introduction to thermostatistics[END_REF]. The exchange appears through an heat exchange Q e and a work exchange W e corresponding in particular to mechanical, electromechanical, thermal, chemical,..., exchange processes. The energy exchange depends on the path and then, work and heat exchanges are not state variables:

dE T = dQ e + dW e (11)
In thermodynamics, the total energy is not the only relevant energetical functional and some other thermodynamic state functions as the internal energy U, the Helmholtz Free energy F, the Gibbs free energy G can be used instead. They are defined using a Legendre transformation applied to the total energy as it was the case between the lagrangian and the hamiltonian functions.

In thermodynamical systems, we must notice a strong distinction between the work and heat exchange because when the first one is reversible, the second one is always irreversible. It implies that some energy is unavaible in the stored energy. The lost energy contributes to the increase of the total entropy ( dS i ≥ 0 with S i the irreversible entropy). This is stated as the second law of the thermodynamic and leads to the Clausius-Duhem inequality of irreversible behaviour. With T the temperature of the system and dD the increment of dissipation, we have:

T • dS i = dD ≥ 0 (12)
The purpose of thermodynamics of irreversible processes with internal variables [START_REF] Maugin | The thermomechanics of nonlinear irreversible behaviors, an introduction[END_REF] is to select relevant internal variables, for example z i describing an internal working of the system and added as a complementary variable in the expression of any thermodynamic potential P. For such an internal variable z j , we also define π j the dual thermodynamic force as π j = ∂P ∂zj . These additional variables permit to explain and to compute the Clausius-Duhem inequality and then to determine the dissipation resulting from the irreversibility of the processus:

dD = T • dS i = j π j • z j (13)
That permits to define a dissipation potential or a Rayleigh function for the lagrangian or hamiltonian formalism applied to a dissipative system.

III. APPLICATION OF AN MSMA BASED ACTUATOR A. Characteristic of MSMAs and general description of the system

MSMAs are relatively new smart materials combining the properties of classical Shape Memory Alloys and the properties of magnetostrictive materials [START_REF] Gauthier | Conversion d'énergie magnéto-thermo-mécanique dans les alliages mémoire de forme magnétiques[END_REF]. The thermo-magnetomechanical behavior of such a material is quite difficult to model because of a strong nonlinear and hysteretical behavior [START_REF] Gauthier | Modeling rearrangement process of martensite platelets in a magnetic shape memory alloy Ni 2 MnGa single crystal under magnetic field and (or) stress action[END_REF] (c.f. FIG. 1 for an example of stress versus strain according to the magnetic field level).

For such a thermo-magneto-mechanical behavior, it is impossible to use quadratic Rayleigh function to describe the dissipation potential of the material and it makes sense to use the thermodynamics of irreversible processes with internal variables coupled with the lagrangian/hamiltonian formalism to propose a dynamical model of the system.

A scheme and a photograph of the MSMA device used as an exemple of the modeling procedure is presented on the FIG. 2. A magnetic circuit including a coil and a ferromagnetic core permits to create a magnetic field inside an air-gap where an MSMA sample is inserted. This sample is attached at one extremity to the fixed support and at the other extremity to a mobile load. The weight of the load permits to pre-stress the MSMA sample to obtain a motion in both directions. Gravitational and inertial effects of the load have to be taken into account. The coil is supplied by an home-made switching power amplifier (200 V -2 A). The displacement of the load is measured with a laser sensor (Keyence LK-152) and the control is performed using a DSP board (dSpace). A PC is used for the displacement signal acquisition and to control the complete system.

B. Modeling of the device

The modeling procedure is based on the computation of the Hamiltonian function for the full device. All the energetical terms of this function are expressed for each sub-system of the device:

• the non-linear electromagnetical behaviour of the electrical (coil) and magnetical circuits (based on a lumped parameters circuit), • the thermo-magneto-mechanical behaviour of the MSM material (based on the thermodynamics of irreversible processes), • the mechanical behaviour of the load driven by the actuator (based on classical Lagrangian mechanics). The different energetical terms of the full device are described on the FIG. 3. More details about each energetical expression may be found in [START_REF] Gauthier | Nonlinear hamiltonian modelling of magnetic shape memory alloy based actuators[END_REF].

1) Magnetic circuit: To model the core and the magnetic circuit, an electrical network including resistances and inductances was used. This lumped-parameters model permits to take into account the magnetic leakage in the surrounding air and the ferromagnetic saturation of the core without any timeconsuming numerical computation such as the finite elements method. The different inductances in this electrical network are respectively associated with the magnetic flux accross the Fe-Si core, the leakage magnetic flux in the surrounding air, the magnetic flux accross the airgap, and lastly the magnetic flux accross the MSMA. It must be stressed that the inductances of the core and MSMA are not constant parameters but they take into account the nonlinear magnetic behaviours of these two materials. For the coil's quantities, a global form is used: the electric charge q c is the generalized coordinate q 1 , the current I is the generalized velocity q1 , the magnetic flux φ is the generalized momentum p 1 . For the other magnetic quantities, a local form is used: the magnetic excitation field D i corresponds to the generalized coordinate, the curvilinear integral H i •l i along the path l i corresponds to the generalized velocity, the flux B i • S i accross the surface S i is the generalized momentum. l F e , l l , l a and l are respectively the ferromagnetic core, leakage, airgap and MSMA mean flux path lengths. The dissipation due to eddy-currents are neglected because the laminated Fe-Si magnetic core limits them drastically. Joule effect losses in the coil are taken into account with a classical quadratic dissipation potential (Rayleigh function R 1 ).

The magnetic energy W mag in this circuit depends on the magnetic fields B i (generalized momentum p i ) in the volume V and we have:

H = W mag = V Bi o H i (b)db • dV ( 14
)
The magnetic energy stored in the Fe-Si core takes into account the nonlinear saturated magnetic behaviour of the Fe-Si material with an arctan shape function. The generalized external force applied to this sub-system is the voltage applied to the coil f ext = u(t). Ampère's law (Kirchhoff's Current Law) gives some algebraic relations between coordinates resulting in the definition of two kinematic constraints c 1 (q) = 0 and c 2 (q) = 0 (c.f. [START_REF] Gauthier | Nonlinear hamiltonian modelling of magnetic shape memory alloy based actuators[END_REF]).

2) MSMA: Two types of generalized coordinates are considered in the MSMA modelling. The first ones, the temperature T , the strain ε and the magnetic field H are classical thermodynamic variables. They are associated with three thermodynamic forces, the entropy s, the mechanical stress σ and the magnetization of the MSMA M . The coordinate T is not used afterwards because of the isothermic working of the actuator and the constant value of thermic part of the Helmholtz free energy F therm . The second type of generalized coordinates appears only in the frame of the thermodynamics of irreversible processes with internal variables. As explained previously, an internal variable is a generalized coordinate characterizing an internal working of the material not directly linked to any external forces. This variable permits to take into account the memory effect of the material. For the MSMA, the volume fraction z is such an internal variable (c.f. [START_REF] Gauthier | Modeling rearrangement process of martensite platelets in a magnetic shape memory alloy Ni 2 MnGa single crystal under magnetic field and (or) stress action[END_REF]).

The Hamiltonian function of the MSMA sample corresponds to its total energy. Because of the size and weight of the MSMA sample compared to the size and weight of the load, the influence of the potential and the kinetic energies of MSMA is quite low in the complete device energy and therefore these two terms can be neglected. The hamiltonian function of the MSMA sample of volume V M SM A can be expressed as:

H M SM A = V M SM A • (F mech + F mag ) + p 2 z 2m z + p 2 ε 2m ε (15)
with F mech and F mag , the mechanical and magnetical Helmholtz free energies, m z and m ε inertial parameters corresponding respectively to the z and ε variables. The internal variable z was introduced to model the dissipative hysteretical behaviour of the material. In order to satisfy the second thermodynamic law, z is used to define the Clausius-Duhem inequality:

dD = π f * (z, ż) • dz ≥ 0 (16)
with π f * (z, ż) the thermodynamic force associated with z.

The expression of π f * (z, ż) will not be detailled in this paper and can be found in [START_REF] Gauthier | Nonlinear hamiltonian modelling of magnetic shape memory alloy based actuators[END_REF] but this expression can be used to express the dissipation power P hyst .

3) Load: The driven load energy includes a kinetic energy (T load = 1 2m p 2

x with m the mass of the load) and a gravity potential energy (V load = mgx with g the gravity constant). The viscous friction of the load in the surrrounding air is modelled using a quadratic dissipation potential (Rayleigh function R 2 = f 2 ẋ2 with f the viscous friction coefficient). Moreover the load attached to the MSMA sample gives an algebraic relation between the strain ε and the displacement x and gives an other kinematic constraint c 3 (q). By adding all the previous sub-system energies, the Hamiltonian function H of the full system can be written and this expression permits to obtain 16 Hamilton equations. Among these 16 equations, 8 are associated with the time rate of coordinates and 8 with the time rate of momentums. The 8 equations associated with the time rate of coordinates gives 8 definitions of variables:

• the first Hamilton equation is the definition of the inductance creating the magnetic flux φ, • the four following Hamilton equations are the definition of the magnetic fields H i , • the three following Hamilton equations are the definition of the relations between the momentum p i and the velocities qi for q i ∈ {z, ε, x}. The 8 equations associated with the time rate of momentums give 8 relations that can be rewritten to obtain 4 physical equations, one constitutive equation for the MSMA and finally the value of the three Lagrange multipliers:

• the dynamic electrical equation (Voltage Kirchoff's Law),

• two equations for the conservation of magnetic fluxes in the magnetic circuit, • the dynamic equation of the load (Newton's law),

• the quasi-static behaviour of the MSM material (the constitutive equation), • the values of the three Lagrange multipliers

C. Discussion on the quasi-static and dynamic behaviour and on the energy distribution

To verify the prediction of the model, a sufficiently slow voltage ramp was applied as an input to verify the quasi-static model behaviour. The Fig. 4 presents the voltage, current and displacement of the actuator versus time for the experimental and the simulation values. The maximum reachable displacement is about 550 micrometres after a current ramp satured at 1 A. Then, a voltage step is applied to extract the dynamical behaviour of this system. The Fig. 5 It is interesting to mention that the dynamical effect combined with the nonlinear MSMA behaviour permits to obtain a larger reachable strain in the dynamic mode than in the quasistatic mode. This is due to the decrease of the compressive stress applied to the MSMA sample when the acceleration of the load appears in dynamic mode. The simulation results appear reasonably accurate compared with the experimental measurements. The computation of different energetical terms of this MSMA simple actuator were computed.

The external energy W ext supplied to the device is an electrical ones. As the energy exchange is dW ext = u(t) • dq c , the energy supply rate corresponding to the the electrical power is therefore Ẇext = u(t) • I(t). The heat exchange was not measured on the experimental bench but the dissipation by Joule effect can be computed as Q joule = t 0 R 1 ( q1 ) dt. The computations show that the main part of the supply energy is dissipated as heat losses into the coil. This confirms that MSMA as well as classical Shape Memory Alloys are not attractive materials from the efficiency point of view.

The rest of the available energy is divided into the coil and core magnetic energies (recoverable energies) and into an energy transfer to the MSMA and to the load. A part of the MSMA energy is lost in the hysteretical loop of the material behavior Q hyst = t 0 P hyst dt when the other is converted through the electromechanical energy conversion process. The result of this energy conversion is then distributed as a viscous friction process Q viscous = t 0 R 2 ( ẋ) dt, a potential energy V load (x) and a kinetic energy T load (p x ). We observe that the practical available mechanical energies (kinetic T load and potential V load ) are quite small compared to the input energy. In the quasi-static mode, the MSMA elastic energy corresponding to the mechanical Helmholtz free energy F mech minus its interaction part F int (due to the compatibility between martensite variant, c.f. [START_REF] Gauthier | Nonlinear hamiltonian modelling of magnetic shape memory alloy based actuators[END_REF]), the kinetic energy T load , and viscous losses Q viscous are constant.

The differences between dynamic mode and quasi-static mode can also be discussed. In the dynamic working mode, an energy transfer between the MSMA elastic energy and the kinetic energy T load exists. Actually, this elastic energy increases when some energy is supplied to the system, then decreases to a lower value than beginning because of kinetic energy T load . At this time, V load can increase to a higher value than in quasi-static mode. The dissipation is more important for Q hyst and Q viscous in the dynamic case than in the quasistatic but Q joule is lower in the dynamic case because the time range is smaller than in quasi-static mode.

It should be stressed that for this actuator, less than 8 to 11 mJ are recovered by the load for 5 to 20 Joules supplied to the actuator. These results clearly show a poor actuator efficiency. Because the main energetic losses are due to the Joule effect, an efficient actuator is an actuator which can hold a displacement value without keeping a current into the coil. This problem can be partially solved by using a Push-Pull actuator design working by voltage pulses: two MSMA samples and two magnetic circuits are used in an antagonistic way in order to obtain a multi-stable actuator. This kind of actuator was also designed and studied by the authors in [START_REF] Gauthier | Multistable actuator based on magnetic shape memory alloys[END_REF], [START_REF]Magnetic shape memory alloy and actuator design[END_REF].

IV. CONCLUSION

The purpose of this paper was to present on a simple MSMA actuator example that the variational and energetical methods is not only well-suited to model classical micro-mechatronic devices such as these described on references [START_REF] Preumont | Mechatronics : Dynamics of Electromechanical and Piezoelectric Systems[END_REF] [START_REF] Nogarede | Électrodynamique Appliquée[END_REF] but that they are also well-suited to include complex dynamical behaviour such as non-linearity and hysteretical behaviour. On this paper, the choice was made to applied these modeling techniques to a simple MSMA based actuator, nevertheless it could also be conveniently applied to any other micromechatronic systems using other non-linear and hysteretical smart materials. In a next paper, it will also be shown that this variational and energetic modeling procedure can be easily extented up to the control level because some important tools based on energetical concepts exist in the control field to explore the stability and to design efficient control laws (Lyapunov function, dissipativity, passivity, energy shaping, port-hamiltonian modeling as reported in [START_REF] Ortega | Passivitybased Control of Euler-Lagrange Systems[END_REF], [START_REF] Van Der Schaft | L 2 -Gain and Passivity Techniques in Nonlinear Control[END_REF] and [START_REF] Astolfi | Lagrangian and Hamiltonian Methods for Nonlinear Control[END_REF]).

Fig. 1 .

 1 Fig.1. Mechanical stress versus strain with and without a magnetic field for a cyclic charging (simulation: solid line, experimental results: cross points)

Fig. 2 .Fig. 3 .

 23 Fig. 2. Description of the simple MSMA actuator: (a) scheme of the device, (b) photograph of the device.

Fig. 5 .

 5 Fig. 5. Dynamic behaviour of the system: voltage, current and displacement versus time (simulation: dotted line, experimental results: solid line).

  reports also the voltage, current and displacement versus time (this graph uses a smaller

		1										100
		0.8										80
	Current (A)	0.4 0.6			Current							40 60	Voltage (V)
		0.2									Voltage	20
		0										0
		0 0		0.2 0.2		0.4 0.4		0.6 0.6		0.8 0.8		1 1
							Time(s)
		800
	Displacement (µ m)	200 400 600
		0
		0		0.2		0.4		0.6		0.8		1
							time(s)
	Fig. 4. Quasi-static behaviour of the system: voltage, current and displace-
	ment versus time (simulation: dotted line, experimental results: solid line).
	time range). The maximum reachable displacement is now
	about 750 micrometres for a 1 A current step.
		1										100
		0.8		Current								80
	Current (A)	0.4 0.6							Voltage			40 60	Voltage (V)
		0.2										20
		0										0
		0 0	0.01 0.01	0.02 0.02	0.03 0.03	0.04 0.04	0.05 0.05	0.06 0.06	0.07 0.07	0.08 0.08	0.09 0.09	0.1 0.1
							Time(s)
		800
	Displacement (µ m)	200 400 600
		0
		0	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09	0.1
							time(s)