Sylvain Lenfle

Christoph Loch

Has Megaproject Management Lost Its Way? Lessons from History

Why do megaprojects frequently encounter performance problems, crisis and even failure, and how can this be averted? From the Eurotunnel linking Britain and France to expansion of the Panama Canal, huge projects often run off course or encounter nagging roadblocks. In this article, we illustrate three core management shortcomings that have significantly contributed to performance problems in megaprojects: the management of uncertainty, of stakeholders, and of contractors. We then draw on history -the Manhattan Project to develop the atomic bomb during World War II, and Cold War-era space and defense projects like Polaris and Apollo -to show that knowledge of how to overcome these issues has long existed, and could be used effectively in some megaprojects today. For example, Manhattan Project manager General Groves realized that big unforeseeable uncertainties in designing atomic weapons required discrete project management skills including flexibility, but these techniques have since been pushed aside in a managerial push for control that became the phased-planning or "stage-gate" process philosophy. And while some 1940s and 1950s successes may not be repeated today with the same managerial methods, because stakeholder complexity was lower at a time when huge projects served "national priorities," we argue that some mid-20th Century managerial techniques such as maintaining a common direction would help improve modern megaprojects.

The performance track record of megaprojects is dismal, even though the basic ingredients of successful large project management are not new. Put simply, the trick is to combine uncertainty in dealing with the difficulties of long time horizons and nonstandard technologies with stakeholder complexity as expressed through the involvement of multiple powerful interested parties. (Flyvbjerg and Cowi 2004). This challenge was conquered in the successful creation of the atomic bomb in the 1940s; but 70 years on, some of the lessons of the Manhattan Project are not being heeded, and modern megaprojects are the poorer because of it.

Take the nuclear reactor industry, a poster child for delays and budget overruns. The current generation II EPR reactors were announced as the future in 2003, and construction began on the first project in Finland in 2005 with plans to launch operation in 2009. But this project will (as of the status in August 2015) not start operating before 2018 and has already incurred a cost escalation from €3.3B to €8.5B (World Nuclear Association 2015). Another project using the EPR technology in Flamanville in France is now expected to take more than double the original time frame and cost €9B rather than the initial estimate of €3.3B. (Le Monde, April 21, 2015). The Hinkley Point C project in the UK is too early in its construction to show large overruns, but to reflect high risks there are hefty price guarantees built into its building contract. (Taylor 2016, Chapter 12).

Nuclear power is not alone: Studies show that 90% of major projects are over budget, with overruns of above 50% being common (Flyvbjerg 2011). A country-specific study in Germany found that among 170 megaprojects, the average budget overrun was 73% [START_REF] Kostka | Grossprojekte in Deutschland-zwischen Ambition und Realität[END_REF]. One study calls big cost overruns the "iron law of megaprojects." [START_REF] Flybjerg | What You Should Know About Megaprojects and Why: An Overview[END_REF] So this chapter illustrates that it is possible to identify a few core management shortcomings that have significantly contributed to such systemic-like failures. We then show that knowledge of how to address these shortcomings existed and was partly applied as early as during the Second World War. Third, we will use this review of past knowledge in order to sketch some recommendations for managerial measures that might help improve performance of megaproject management today.

Three Common Causes of Megaproject Failures

When we describe the spectacular failures of large projects over the last decades, three overarching themes arise.

Underestimation of, or Refusal to Acknowledge, Uncertainty.

Megaprojects are often started on the assumption that with enough planning, the design and project plan can be firmly designed at the beginning. But over long time frames, with non-standard technology and multiple interested parties, it is impossible to plan for everything -and parties then slip into a damaging fight for control that results in multiple redesigns and additional costs.

A case in point is the Circored project, a pioneering iron ore reduction facility to produce pure iron briquettes undertaken in Trinidad [START_REF] Loch | The Circored Project A, B and C. INSEAD Case Study[END_REF]. The project started in 1995 with a target start of production in 1999, owned and run by the iron ore company Cleveland Cliffs using a new technology that Lurgi AG had developed and tested in a small prototype. An intensive risk analysis suggested that all problems could be anticipated and managed, but many unforeseen problems occurred in the scale-up, delaying the project by two years. Though the project ultimately succeeded technically, the delay made the facility vulnerable to the commodity price meltdown of 2002 and thus unprofitable. Ultimately, Cleveland Cliffs wrote the plant off and sold it at a steep discount to Mittal.

A key reason for the failure is that while Lurgi understood its technology's immaturity and technical risks, the plant owner rejected a longer testing phase on grounds that risks could be contained through proper planning and analysis. So ensuing problems had to be dealt with reactively, costing more in time and money than if properly addressed to begin with.

Stakeholder Neglect or Mismanagement.

Megaprojects normally require coalitions of active partners in addition to the support or at least passive tolerance of external stakeholders who don't participate directly. Peril inevitably results when stakeholders are ignored, or when a false agreement is finessed, causing conflicts to fester hidden behind wooly political statements.

A famous example is the Eurotunnel project, which dug a 50-km twin-tunnel under the English Channel between 1987 and 1994, through which passenger and freight trains now pass between Calais and Dover. The initial project had a seven-year duration and a (1987) budget of £4.8B, but ran over by 29% in schedule (after the original opening target of June 1993, freight operations started in May 1994 but full operations were not achieved until December 1994), and ran over budget by 65% for a total cost of £8B. Also, some initial specifications were not achieved, with trains running through the tunnel at 80km/h compared to the original target of 160km/h -thus extending travel time and reducing tunnel capacity. But most importantly, the operator, Eurotunnel plc, came out of the project so debt burdened that it could not turn a profit, and shareholders lost their investment twice [START_REF] Garg | Eurotunnel: Eyes Wide Shut[END_REF], until finally the banks forgave a significant percentage of the debt in 2013.

The Eurotunnel troubles were not rooted in uncertainty: although some new tunneling machinery was used, related problems were quickly handled, and initial projections of revenues and operating profits turned out to be fairly close.

Instead, the root cause for Eurotunnel's woes was in the fraught relationships among the stakeholders: the construction consortium and the later operator Eurotunnel were in constant conflict and embroiled in lawsuits; the banks managed to transfer all risks, including inflation, to Eurotunnel, which resulted in a three-month work holdup and an inflated debt burden.

Stakeholder conflicts are a major source of project problems and are especially dangerous for megaprojects, which by their very nature involve many parties with the power to exert influence. Whenever a party is ignored, or when an agreement forces one party into agreement or superficially glosses over differences in views or interests, then these agreements likely break apart when changes disrupt the equilibrium -at which point the parties then no longer collaborate but work against one another (Loch et al. 2015).

Inflexible Contractor Management (Prominently, Awarding Work to the

Lowest Bidder).

Many parties have to collaborate in order to accomplish megaprojects owing to their sheer size and variety of expertise required. The well-known practice of "bid low and sue later" is caused by project owners awarding contracts on the basis of the lowest bid price, forcing contractors to bid aggressively and then work inflexibly -asking for more compensation with every change in the project.

This was observed already 30 years ago [START_REF] Mcdonald | Construction Contracts: Shifting Risk or Generating a Claim?[END_REF], and is still alive and well -and criticized by a German government commission that examined practices in large public works projects [START_REF] Kammholz | Bericht rügt Deutschlands Vresagen als Bauherr[END_REF]. A globally visible specific example is in the $5.25B megaproject for the expansion of the Panama Canal, which invited bids in 2009 and was scheduled to open in 2014. A Spanish-led consortium of construction firms won the $3.2B bid for the locks of the 50-mile waterway, underbidding a US-led rival consortium by $1B. But in 2014 the consortium demanded a $1.6B compensation from the Panama Canal Authority (PCA), the project owner, citing "breaches of contract" (for example, claiming they were misled about geological ground conditions). The dispute has already delayed the project to mid 2015. However, concerns were voiced right at the outset that the bid was too low, and that a cost increase would be required at some point [START_REF] Kriel | Insight: Lowball bid comes back to haunt Panama Canal expansion[END_REF]. Although the PCA defends the original bid as reasonable, experts openly discuss the aggressive underbidding strategy used [START_REF] Economist | Your money on your locks[END_REF].

Interactions Among the Themes

These three root causes of problems are even more difficult to address because they strongly interact. For example, stakeholders in the Eurotunnel project had differing interests such as the short-term view of the constructor versus the long-term operator's view. In an atmosphere of mutual distrust, even moderate uncertainties are difficult to address, leading to disputes (such as over cost overruns) and even further distrust. As a result, collaboration becomes even harder.

Yet although these challenges are difficult to address, there are potential solutions that have been ignored. Relevant knowledge has been available for seven decades, but much of this knowledge has been disregarded and not used effectively in the project community -as we describe next.

What Project Management Already Knew in the 1940s

The irony is that, historically, there were projects where these three problems were in fact overcome. This is particularly true of World War II and large postwar US military and space projects which, interestingly, are the roots of contemporary project management. Indeed, the Manhattan, Atlas, Polaris and Apollo projects, to name the most famous ones, were managed very successfully, and on schedule. It is therefore interesting to draw lessons from these cases. At the conceptual level, these projects did two crucial things right.

First, on the organizational level, they created almost from scratch a dedicated organization to overcome the traditional bureaucratic fights that plagued major R&D projects. The development of Intercontinental Ballistic Missiles (ICBM) within the US Air Force and the Navy is typical of this strategy. Consider briefly the Polaris case [START_REF] Sapolsky | Inventing Systems Integration[END_REF]. The problem was to coordinate and integrate the functionally defined branches or bureaus and the dozens of firms involved. Moreover, as a new technology, ballistic missiles did not fit easily into the existing weapons acquisition structures: it was neither a bomber, nor a bomb, nor a guided missile. To overcome this problem, the Navy created the Special Project Office (SPO), a new body that had complete autonomy and power to manage the Polaris project. It was supervised by a brilliant and powerful project manager, Admiral William F. Raborn, who infused a sense of dedication and urgency into the entire team. He said: "Our religion was to build Polaris." (Spinardi, 1994, p. 35) The creation of this structure constitutes unquestionably one of the key success factors of the Polaris project [START_REF] Sapolsky | The Polaris System Development[END_REF]). And we find a similar logic, a dedicated organization led by a brilliant project manager, in all the aforementioned projects (the Manhattan Engineer District and L. Groves, the Western Development Division of the USAF and B. Schriever, The Office of Manned Space Flight and S. Phillips). Therefore, the success of these projects rested on "doing what it took" with almost unlimited project management power, supported by almost complete autonomy to take the right actions in the interest of achieving the goals.

Second, concerning the management of uncertainty, these PMs developed brilliant insights. They understood, right from the outset, that one does not know what one does not know. This cannot be more clearly stated than by General Groves when he stated that, given the huge unforeseeable uncertainties of the design of the atomic bomb, they were "proceeding in the dark" (Groves 1962, p. 40) and, therefore "had to abandon completely all normal orderly procedures" (ibid, p. 72).

What is fascinating is that they drew the right managerial conclusions: they combined experimentation (e.g., in the form of pilots), parallel pursuit of alternatives, and dedicated (possibly costly) actions to gather information as part of the core project activities. The Manhattan Project forcefully demonstrates the relevance of this approach: acknowledging that it was impossible to define, at the outset, the right design of an atomic bomb, Groves and the steering committee decided to simultaneously explore different technical solutions both for the production of fissionable materials and for the design of the bomb. This explains why the two bombs dropped on Japan had completely different designs and also how they succeeded in such a short time to overcome the tremendous scientific and engineering challenges. [START_REF] Lenfle | The Strategy of Parallel Approaches in Projects with Unforeseeable Uncertainty: The Manhattan Case in Retrospect[END_REF] This strategy was directly transferred to the ICBM Atlas project (and others) through discussions between Groves, Oppenheimer and B. Schriever, chief of the Western Development Division of the USAF [START_REF] Hughes | Rescuing Prometheus[END_REF].

It is sobering for project management how these lessons have been lost in the course of the institutionalization of the discipline. Indeed, the principles of uncertainty management were theoretically well understood in the 1950s, especially the need for experimentation and adjustment, and the advantage of starting multiple parallel trials on subprojects in order to assure one successful outcome [START_REF] Alchian | A proper role of systems analysis[END_REF][START_REF] Arrow | Economic aspects of military research and development[END_REF][START_REF] Klein | Application of Operations Research to Development Decisions[END_REF]. However, these principles had completely disappeared from PM textbooks and have only recently been rediscovered (from the view of multiple disciplines, e.g., [START_REF] Leonard-Barton | Wellsprings of Knowledge[END_REF][START_REF] Loch | Managing the Unknown: a New Approach to Managing Projects Under High Uncertainty[END_REF]. [START_REF] Lenfle | Lost Roots: How Project Management Came to Emphasize Control over Flexibility and Novelty[END_REF] show how flexible approaches to uncertainty were abandoned in favor of a more control-oriented view of PM as the accomplishment of a clearly defined goal through a phased / stage-gate logic.

This process unfolded in three dimensions [START_REF] Lenfle | Lost Roots: How Project Management Came to Emphasize Control over Flexibility and Novelty[END_REF]):

1. On the political side, the deployment of ballistic missiles completely changed the context. The fear of a "missile gap" disappeared and the sense of utmost urgency of the military megaprojects faded away. This led to an important reorganization within the DoD in the form of the Defense Reorganization Act of 1958, which greatly increased the power of the Secretary of Defense over the armed services. It gave him the authority to "transfer, reassign, abolish or consolidate" service functions, and control over the budget. This paved the way for the "McNamara revolution." Coming from the Ford Motor Company, Robert McNamara, named Secretary of Defense in 1961, started a complete reorganization of the planning process in the DoD. His objective was to consolidate planning and budgeting, which hitherto had been two separate processes. He pursued his objective with the implementation of the famous Program Planning and Budgeting System (PPBS). This process was antipodean with the logic of the early missile projects and prompted a complete reversal in project management. Indeed, it emphasized the complete definition of the system before its development in order to limit uncertainty and institutionalize a phased approach. This de facto eliminated parallel trials and concurrency. Therefore, the phasedplanning approach (now called Stage-Gate) became the project management model of the DoD and the newly formed NASA. This was enforced by the diffusion of managerial tools like PERT. In particular, a NASA/DoD PERT/Cost Guide was issued in 1962 and became part of the bidding process of both administrations, transforming these tools into de facto standards for project management. This limited the scope of project management for the ensuing decades. From now on, strategy was centralized at the DoD and Project Management's role was to execute given missions.

2. This shift had a theoretical counterpart. Indeed, the McNamara revolution was theoretically grounded in RAND thinking and its faith in rational decision making. 1This view was clearly expressed by Charles Hitch, an eminent RAND member who later became comptroller of the Department of Defense under McNamara. In 1960, he published The Economics of Defense in the Nuclear Age, which introduced a broad audience to a view of defense as an economic problem of resource allocation to achieve a desired objective. This view had major consequences for project management: the focus gradually changed from the "performance at all costs" attitude of the first missiles projects to one of optimizing the cost/performance ratio. This new logic is clearly visible in the early literature on project management. For example, Systems Analysis and Project Management (1968) by Cleland and King became a classic. The book is typical of the phased logic. It consists of two parts that corresponded to the two key project phases. The first advocated the power of systems analysis to analyze complex strategic issues and define project missions. The second part dealt with project execution and emphasized the need to create a specific project organization to integrate stakeholder contributions, along with project planning and control using formal methods. The result of all of these events was that by the early 1970s, the phased approach had become "natural."

3. The last stage of this standardization process was the creation, in 1969, of a professional organization: the US Project Management Institute. Indeed, the years following the success of Polaris saw a plethora of publications and an intense promotion of the PERT/CPM method by numerous consulting firms (Vaszonyi 1970).

The planning method was viewed as synonymous with success in the management of large projects. The idea of a professional association arose in this context within the tight-knit community of PERT and CPM users (R. Archibald, E. Benett, J. Snyder, N. Engman, J. Gordon Davis and S. Gallagher). Since all its founders were project control experts, it was natural for the PMI to focus on control tools, such as PERT/ CPM. Therefore, for the next two decades, "modern project management" became equated with PERT/CPM after Polaris and the MacNamara revolution (Snyder 1987).

This, as the reader will recognize, provides the basic principles of the dominant model of project management today, the stage-gate process. The problem is that this rational view of project management oversimplifies the processes at stake, particularly for innovative projects and for megaprojects with their inbuilt unforeseeability (because of long time frames and stakeholder complexity). Moreover, this leads, as argued by Lenfle and Loch, to misinterpretations of the success factors of these projects. For example, Apollo is remembered in the project literature for the setting up of a complex project management system organized around a phased approach [START_REF] Seamans | Project Apollo. The Though Decisions[END_REF][START_REF] Johnson | The Secret of Apollo. Systems Management in American and European Space Programs[END_REF]. While this unquestionably contributed to getting back on track during the project crisis of 1962-63, this narrow view neglects the upstream exploratory work and the fact that the phased approach was implemented quite late in the project. However, the fact is that this control-oriented approach of project management remains dominant today.

The Limitations of the Breakthrough Project Management Styles of the 1950s

Based on the previous discussion, we might ask the question whether the issue is to "get some of the capability of the 1940s and 1950s back." But this, we think, would be too simple. Indeed, these projects unfolded in a very specific context and, therefore, were not exposed to the full spectrum of complications that face the megaprojects of today.

One has to remember that, for all these projects, the context was the highest level of national urgency either because of World War II (Manhattan) or the Cold War with the USSR (Atlas, Polaris and Apollo). This had two major consequences.

First, the project goals reflected the military nature of the missions and were, in a sense, "simple" (although technically impressive): build a nuclear bomb, build a missile that can hit a small target from a long distance, start the missile from a submarine, or go to the moon2 . These do not reflect the goal complexity of projects that, today, inevitably have a societal component.

Second, the Cold War and the competition with the Soviets led to the suppression of any debate around the projects. It is useful here to remember John F. Kennedy's address to the Congress that formally launched the Moon project:

"If we are to win the battle that is going on around the world between freedom and tyranny, if we are to win the battle for men's minds, the dramatic achievements in space which occurred in recent weeks should have made clear to us all, as did the Sputnik in 1957, the impact of this adventure on the minds of men everywhere who are attempting to make a determination of which road they should take. (…) We go into space because whatever mankind must undertake, free men must fully share. (…) I believe this Nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to earth. No single space project in this period will be more impressive to mankind, or more important for the long-range exploration of space; and none will be so difficult or expensive to accomplish." John F. Kennedy, Special Message to the Congress on Urgent National Needs, May 25, 1961.

Indeed, if the stakes were "the battle between freedom and tyranny," there could be no debates around the project3 . In other words, if we rely on contemporary concepts, stakeholder disagreements were absent or small. There were no parties that stopped support, or protesters that blocked further work, because they no longer agreed with changed outcomes, or external groups that demanded transparency and accountability.

This was also true for supplier management. These project teams had huge power over their suppliers -again, these were military projects where suppliers were paid well but had to unquestioningly carry out orders. In fact, the entire organization was designed to avoid politics. As demonstrated by [START_REF] Hughes | Rescuing Prometheus[END_REF] for Atlas and [START_REF] Sapolsky | The Polaris System Development[END_REF] for Polaris, the main goal of the creation of the WDD and the SPO was explicitly to avoid the bureaucratic fights and politicking that, traditionally, plagued large R&D projects. They were, in a sense, "closed" projects [START_REF] Edwards | The Closed World. Computers and the Politics of Discourse in Cold War America[END_REF][START_REF] Hughes | Rescuing Prometheus[END_REF]. Politics was reduced to the army and the government. There could be debates, but no protest outside likely to stop the project (Beard 1976). It was possible for Admiral Raborn to "build a fence to keep the rest of the Navy off of us" (Sapolsky, p. 124) and to "engineer the politics of the program so as to provide resources without interference" (Spinardi,. Therefore, the question of stakeholder management was literally out of the scope.

This very specific context disappeared with the end of the Cold War and the emergence of a networked world -it is no longer the case in megaprojects today. Now the challenge is to manage megaprojects in an "open" context in which no project team can hope to keep the outside world behind a fence. In this perspective, T. [START_REF] Hughes | Rescuing Prometheus[END_REF] brilliantly demonstrates that the "system engineering" methods developed for military projects failed when confronted with civil megaprojects like the famous Boston Central Artery Tunnel. Here, the challenge was to deal with the messy complexity of multiple stakeholders, each with different objectives and constraints. F. Salvucci, the Boston CA/T key figure, had to patiently negotiate his way through the maze of the Boston area, discussing with engineers, community groups, the City, the State of Massachussets, etc., around to-be-defined criteria, such as the design of a bridge. Therefore, as argued by [START_REF] Loch | The Circored Project A, B and C. INSEAD Case Study[END_REF], "The traditional view of the 'project client' as the single focal interlocutor of the project vanishes, giving place to a complex fuzzy system of diversified actors that has to be 'managed' in novel sophisticated governance and communication processes" (p. 201-202). The problem is all the more important because, they argue, there is an ever-growing demand of accountability for public and private megaprojects. General Groves never had to deal with this situation.

In other words, we can't simply go back to the heyday of 1950s project managementwhat worked brilliantly then would be insufficient today. And yet, it is still worthwhile to repeat the lessons on uncertainty management from the 1950s, as some of the recent failed megaprojects simply violated what is known about uncertainty management. Moreover, knowledge on all three key drivers of megaproject failure has slowly accumulated over the last 50 years, not only on uncertainty management but also on stakeholder and contractor management. We will review the ley lessons of this knowledge history in the last section.

Lessons and Recommendations

Managing Uncertainty

Building on the work from the 1940s described earlier, project management theory has, since the stage-gate process became dominant, been able to articulate that many projects are characterized by variation (many small influences causing a possible range of duration and costs on a particular activity), which can be addressed by buffers, and foreseeable uncertainty or risk (identifiable and understood influences that the project team cannot be sure will occur, so different outcomes are possible), which can be addressed by planned and "programmed" risk management that "triggers" contingent actions depending on which risks occur [START_REF] De Meyer | Managing project uncertainty: from variation to chaos[END_REF]. However, megaprojects suffer also from unforeseen uncertainty, which can't be identified during project planning. The team either is unaware of the event's possibility or cannot create the contingencies. Unforeseeable uncertainty may be caused by large "unthinkable" events, or by many influences (including stakeholder actions) that interact through complexity. Unforeseeable uncertainty requires more flexible and "emergent" approaches than smaller uncertainty levels do (and than the stage-gate process has allowed for).

Still, the presence of unforeseeable uncertainty can be diagnosed. For example, discovery-driven planning [START_REF] Mcgrath | The Entrepreneurial Mindset: Strategies for Continuously Creating Opportunity in the Age of Uncertainty[END_REF]MacMillan 1995, 2000) proposes to explicitly acknowledge that unknown unknowns exist and to uncover them with analyses such as assumptions checklists. Similarly, [START_REF] Loch | Diagnosing Unforeseeable Uncertainty in a New Venture[END_REF] illustrated with the example of a start-up venture project how the presence of unknown influences can be diagnosed by systematically probing for knowledge gaps in the project, building intuition about areas where unknown events may be looming. Two fundamental approaches exist for this level of unforeseeable uncertainty: trial-and-error learning and selectionism [START_REF] Leonard-Barton | Wellsprings of Knowledge[END_REF], Pich et al. 2002[START_REF] Loch | Managing the Unknown: a New Approach to Managing Projects Under High Uncertainty[END_REF].

Under trial-and-error learning, the team starts moving towards one outcome (the best it can identify), but is prepared to repeatedly and fundamentally change both the outcome and the course of action as new information becomes available. Exploratory experiments, aimed at gaining information without necessarily contributing "progress", are an important part of this approach; failure of such experiments is a source of learning rather than a mistake. It is therefore important to track the learning and reduction in knowledge gaps rather than tracking only the progress towards a target.

Well-known examples are pharmaceutical development projects, in which promising indications often emerge during large scale trials via unexpected (positive) side effects.

Alternatively, the team might choose to "hedge" and opt for selectionism, or pursuing multiple approaches in parallel, observing what works and what doesn't (without necessarily having a full explanation why) and choosing the best approach ex post facto. Examples of this approach abound, including Microsoft's pursuit of several operating systems during the 1980s (Beinhocker 1999), or "product churning" by the Japanese consumer electronics companies in the early 1990s (Stalk and Webber 1993).

In a large-scale empirical study of 65 new venture projects, [START_REF] Sommer | Managing Complexity and Unforeseeable Uncertainty in Startup Companies: an Empirical Study[END_REF] showed that the best combination of learning and selectionism, as measured by their effect on project success, depends on the level of unforeseeable uncertainty in the project and the complexity of the project (Figure 1). When both uncertainty and complexity are low (lower left quadrant), planning and standard risk management are up to the task and the most efficient. When unforeseeable uncertainty looms large, be flexible and apply trial and error. When complexity is high, use parallel trials and narrow the field down to the best as soon as possible. The hardest situation is in the upper right quadrant, which is where megaprojects usually find themselves and where unforeseeable uncertainty and project complexity combine. It turned out that the highest success level was associated with parallel trials if they could be kept alive until uncertainty had been reduced to the point that all important risks were known. Otherwise, trial and error performed better. Of course, in any large project, trial and error and selectionism can be combined and applied differently across sub-projects. The largest challenge lies in the managerial structures and control-mindedness in large corporations, partially prompted by the stage-gate process revolution of the 1960s that we have discussed earlier. It makes it very difficult for managers in large organizations to take on risks. For example, one study on "breakthrough innovation" in large companies shows that they use a stage-gate-like approach to selecting and executing large innovations, which pushes managers to conservativism and early termination of risky projects (He 2015). Similarly, [START_REF] Sehti | Stage-Gate Controls, Learning Failure, and Adverse Effects on Novel New Products[END_REF] demonstrated that the Stage-Gate Process leads to project inflexibility, which, for innovative projects, is synonymous with failure. Even more fundamentally, the stage-gate process has shaped an "aesthetic" of eliminating uncertainty and experimentation through rigid upfront planning and control. For example, a study of relationships between startups and investors found that investors reacted with "punishment" (i.e., by enforcing business reviews) to evidence of parallel trials and (to a lesser degree) trial and error iterations [START_REF] Loch | Managing Risk and Responding to Uncertainty: How Entrepreneurs and VCs Can Improve Their Effectiveness[END_REF]. Managers are, in principle, fully capable of intelligently responding to unforeseeable uncertainty, as R&D management and many experienced project management organizations amply demonstrate. However, much education is needed in order to equip management in many (particularly public) organizations, investors, and critically the public, of the flexibility required to deal with uncertainty.

Stakeholder Management and Project Governance

No universally agreed "national agenda" exists any longer, based on which the brilliant projects in the 1950s could successfully proceed, because megaprojects touch on too many interests and agendas to still be able to be pushed by any central will.

Consultation and involvement of powerful interested parties has become a must. On the other hand, political compromises do not make good bases for decisions, and muddled goals and inconsistent decisions based on fluctuating agreements destroy projects. How can these two imperatives be reconciled? This is a question of project governance.

Project teams execute, but the scope and strategic positioning of a project is set at the level of project governance, typically at the level of the "steering committee" (SC). Loch et al. (2015) examined effective and non-effective SC practices in 17 complex and uncertain projects (innovation as well as organizational change), and found that the SC is the place where representation of interests (including consultation) needs to be combined with the production of a shared project vision and the translation of this vision into operational plans -in order to effectively identify conflicts and solutions as the environment of the project changes.

Several specific principles arise from the study:

-Stakeholder representation: the SC needs to represent the most important and powerful parties that have an interest in the megaproject (such as government, suppliers, or customers). At the same time, the size of the SC must not grow too large (by allowing "anyone with interest to participate") because large groups become too difficult to manage and keep together. -Goal agreement: The SC has the critical responsibility to articulate a project vision that is at least acceptable to all parties, and then translate it into operational goals and targets that expose key conflicts. "Motherhood and apple pie" goals regularly get thrown out during later operational phases when conflicts inevitably do occur. Only if the conflicts are negotiated at the outset (in a way that maintains a shared project vision) can the goals evolve and change in negotiated ways that allow maintaining a shared vision.

-Staying informed and renegotiating during crises. The SC must invest enough time and effort to understand the key issues of the project (insisting on translation of technical language and issues into the strategic policy or business language that is needed to maintain the strategic positioning of the project). The SC must also invest the time and effort to stay informed, so when changes and crises occur (both inevitable over the time horizon of megaprojects), project modifications can be renegotiated in ways so the parties maintain their agreement/support. If a party feels excluded or taken advantage of, projects fail, but if the SC can successfully manage one crisis together, it becomes stronger in managing the next.

-Keeping the project team aligned. The SC must maintain a position of control, which means in this context understanding the key issues rather than maintaining and enforcing ("come what may") an initial project plan. Trust needs to be built with the project team that bad news and changes are treated reasonably, demanding solutions and accountability, but not looking for scapegoats to punish -otherwise, information about the true status of the project will not be forthcoming. This is necessary because changes will happen in a megaproject, and the SC needs to set up itself as well as its project team to be able to address these changes in ways that do not lead to the typical symptoms of megaproject disasters -such as mission creep, late mission changes because of political maneuvering, accumulated unaddressed problems, or the falling out with an important stakeholder.

Several key challenges exist that make these principles difficult to achieve: Interest conflicts and differences in thinking styles among stakeholders make the achievement of true alignment a long affair (leading to longer planning times) and consume significant managerial effort during a project. The temptations are ever present to not invest enough effort, or to exploit political circumstances of unbalanced power to one's own advantage. This is also where the widely observed temptation of "low-balling early [on costs] and then present a fait-accompli to the stakeholders" (Flybjerg 2007) comes in. While this is certainly true in some cases, it is not inevitable. Evidence in Loch et al. (2015) suggests that if the SC represents stakeholders and seeks the dialogue with them, and if it is sufficiently involved with the project team to be able to follow and evaluate progress, success overestimation can be avoided. Of course, this leaves out situations where a skeptical public (or political establishment) is simply not willing to accept a project under a realistic scenario, and the only way to get the project approved is "lying" about it. But whoever engages in misrepresentations in order to get the project started ("they will learn and change their minds later") is running severe risks both for their own careers, as the project later runs into difficulties pre-programmed by the unrealistic initial estimates, and for the public, whose faith in project execution capabilities becomes undermined. Yes, it may be true that (for example) the Eurotunnel was a significant macro-economic success in hindsight, connecting London and Paris in ways that were previously unthinkable. But on the way there, many shareholders lost their money and careers of good people involved were damaged, and so initial overpromising is perilous and not advisable even if one might be able to construct a long-term justification for it.

Contractor Management

Contracts are core vehicles of governing partners and the sub-contractors of pieces of work in projects, and they form a complex web of relationships in megaprojects. But contracts can handle only limited complexity (a contract can quickly run into thousands of pages, which means they become ineffective), and they are inflexible where flexibility is required to deal with the inevitable changes in megaprojects. "A contract is a dangerous instrument and should always be approached with trepidation and caution. … Theoretically, the aim of a written contract is to achieve certainty of obligation of each party, the avoidance of ambiguities, and such definiteness of understanding as to preclude ultimate controversy. In practice, construction contracts are generally formed not to definitely fix obligations, but to avoid obligations" (MacDonald and Evans 1998, 1-2). Specifically, contracts cause the temptation to explore gaps in the understanding of the counterparty to create obligations that one can then exploit -a fallacious expectation because the other side usually finds a way to sooner or later stall in their turn or to retaliate. [START_REF] Von Branconi | Contracting for Major Projects: Eight Business Levers for Top Management[END_REF] The well-known temptation to "bid low and sue later" falls in this context, but it often leads to protracted business and legal battles, victimizing the project.

Much evidence has been accumulated that contracts need to be designed with flexibility, and they need to be complemented with relationships. A good example is the celebrated Heathrow Terminal 5 project, which applied an integrated approach that incorporated careful strategic governance (accomplishing system integration), within diligent process management that included supplier selection by track record (rather than the lowest bid price) and flexible contracts that rewarded problem solving (Davies et al. 2009b). The project owner BAA "changed the rules of the game" by creating a new type of agreement based on two fundamental principles: the client bears the risk and works collaboratively with contractors in integrated project teams. BAA had to take responsibility for risks and uncertainties, whilst creating an environment within which suppliers could find solutions. Suppliers were repaid all the costs on a cost-transparent "open book" basis and incentivized to improve their performance and innovate by bonuses for exceeding previously agreed "target costs" and completion dates. If the performance of a project exceeds target costs, the profits are shared among team members. This contractual approach was underpinned by routines to expose and manage risks rather than transfer or bury them, and offered incentives for innovation and problem solving (Davies et al. 2009a, 24-25).

The Heathrow T5 project addressed one fundamental problem with contracts---they cannot specify all desired outcomes beforehand in the complex and uncertain environment of a megaproject, and fixing any outcomes (no matter with how many "contingencies) opens up incentive conflicts when contractors either cannot deliver or can deliver in unforeseen ways. The cost-reimbursement contracts with "innovation bonuses" offered a way out of this dilemma. But it is possible to go even further in turning contracts from fixed outcome descriptions into vehicles for collaborative problem solving. One example for this is the OSA Alliance between Orange (France Telecom's mobile telephone arm) with its partners in managing roaming, the complicated agreements that allow regional telecom operators to provide service for a customer from other regions and get reimbursed by the telecom operator who has a contract with the customer and charges this customer for the roaming [START_REF] Van Der Heyden | Orange Group's Open Seamless Alliance (OSA)[END_REF]. The "contract" that partner operators in the alliance signed up for did not specify any specific collaboration procedures or outcomes, but was nothing but a specification of a collaborative problem solving procedure: how would the group make decisions in setting up a technical system, or a customer agreement, or a revenue sharing when it arose. Decisions were indeed made by voting, with safeguards that neither the large operators (with a revenue majority) nor the many small operators (with most votes) could force through agreements. Each specific agreement itself (what would normally be seen as a contract) became a mere technical description. This structure of agreements allowed the partners to keep collaborating flexibly and robustly in an environment of changing technologies and regulatory regimes (the regulatory bodies tightened rules on roaming which had become very profitable). However, when we discuss such collaboration structures with project and program managers, they usually are very uncomfortable because it feels to them like a "loss of control." This is another example of the control "aesthetics" that the dominance of the stage-gate process has created in project management.

And yet, there are again large challenges in adopting these new methods that would allow addressing the systematic problems that have plagued megaprojects. The temptation to use "market forces" to depress prices to contractors, using unbalanced power to get one's way (if only for a short period), is ever present. As a case in point, the Heathrow T5 owner BAA was acquired in 2006 and, "in a complete reversal of strategy (and to the surprise of many in the UK construction industry) decided to revert back to the traditional role of client as procurer rather than project manager, relying on "riskshifting contracts", detailed up-front specifications and inflexible routines" [START_REF] Davies | Dynamic capabilities for a complex project: The case of London Heathrow Terminal 5[END_REF].

Similarly, the authors have discussed the OSA "framework contract" approach with managers from many companies and have witnessed directly how deeply threatening managers find such an approach -it feels to them like they are giving away control over their own fate. Yet another cultural and "aesthetic" influence that has been connected to the stage-gate process, which adds a specific definition of "professional standards" to the earlier mentioned short-term temptations in making it very difficult to make the new methods in megaproject management enter the mainstream.

Conclusion

System engineering and technical complexity are well understood, but uncertainty and stakeholder complexity are still the big challenges for megaprojects. Avenues have been identified to address these challenges that require behavioral changes: these include resisting the temptation to press one's own advantage with contractors; accepting some loss of predictability and control; patience in bringing the multiple sides to the table that are always present in megaprojects, and the discipline to maintain a common direction that allows progress-directed decision making rather than merely conflict-avoiding compromises. Many of these techniques will require companies to learn new and potentially daunting behavior; but in fact many of these managerial mechanisms are tried and true techniques that worked wonders for megaprojects a few generations ago and could help point the way to a brighter future for huge projects in the future.

Figure 1 :

 1 Figure 1: When to choose trial-and-error-learning or selectionism (from Sommer et al. 2009)

McNamara's thinking was rooted in and had a major impact on "cold war rationality," i.e. the belief that one could find the optimal solution beforehand. Here, the reader may refer to[START_REF] Erickson | How Reason Almost Lost its Mind. The Strange Career of Cold War Rationality[END_REF].

Apollo is an ambiguous case since it is a civil project largely managed by the military after 1963.

On the Manhattan Project, there was no debate simply because it was a "black", completely secret, project. Even Harry Truman, Roosevelt's vice-president, ignored the existence of the project until he became president in April 1945.


Carla Scotti

Bernadette Julier

Improving alfalfa forage quality

Legume Perspectives

Issue 4 • July 2014

RESEARCH

Improving alfalfa forage quality by Carla SCOTTI 1 * and Bernadette JULIER 2

Abstract: Morphological and physiological traits contributing to the nutritive value of alfalfa forage are examined at harvesting and during a productive cycle. Leaf-to-stem ratio and the dynamics of development of stem internodes appear the main factors driving the nutritive value at the plant level. Withinpopulation variation for these traits, in addition to between-population variation, can be exploited to improve digestibility and protein content. Key words: alfalfa, crude protein, fiber fractions, leaf-to-stem ratio

The nutritive value of alfalfa forage is mainly a result of the forage chemical composition and in particular of the content of crude protein and fiber fractions (neutral detergent fiber, NDF, acid detergent fiber, ADF, and acid detergent lignin, ADL) estimating the proportion and composition of cell walls. ADF and ADL contents show strong negative correlation with ruminal digestibility of forage.

An alfalfa stem at harvest time includes a series of internodes separated by nodes carrying a leaf, and a branch (vegetative nodes) and/or a flower or pod (reproductive nodes). Proteins are mainly located in the the green and healthy leaves. Leaf protein content shows a limited variation (25% -30% of biomass) that is determined by leaf position along the stem, with the highest contents in the upper young leaves exposed to light. Similarly, fiber content of the leaves is rather stable (20% -25% NDF, 15% -18% ADF). Stems, on the contrary, show a high variation for fiber content that is related to the developmental stage of the internodes (not yet elongating, elongating or mature). In the basal internodes, the mature stage implies a higher content in secondary lignified vascular tissues (mainly xylem) than in elongating internodes. ADF content of stem portions can vary from 55% in the basal internodes to 40% in the apical ones. In parallel, _________________________________________________________________________________________________________ [START_REF] Guines | Among-and within-cultivar variability for histological traits of lucerne (Medicago sativa L.) stem[END_REF] Consiglio per la Ricerca e la Sperimentazione in Agricoltura, Centro di Ricerca per le Produzioni Foraggere e Lattiero-Casearie, Lodi, Italy (carla.scotti@entecra.it) [START_REF] Guo | Improvement of in-rumen digestibility of alfalfa forage by genetic manipulation of lignin 0-methyltransferases[END_REF] INRA, UR4, Unité de Recherche Pluridisciplinaire Prairies et Plantes Fourragères, Lusignan, France protein content varies from 9% -11% to 16% -20% from the basis to the top of the stem. The dynamics of shoot elongation during a regrowth affects the forage quality through changes in the proportion of leaves and the developmental stage of the internodes (3). At the beginning of regrowth just after harvest, the biomass of leaves is prevailing as internodes have not yet entered the elongation phase. When the stems reach about 30 cm height, the proportion of leaves has decreased but most internodes are still in the elongation stage. Around the phenological stage of 50% green bud stem, when the stems can reach 80 cm to 100 cm height, stem biomass becomes prevalent as a result of internode elongation, and most internodes are in a mature stage with high lignification; leaf biomass remains stable, as newly formed leaves are counterbalanced by the senescence and loss of older leaves triggered by the decline of incidence radiation (4). As a consequence, protein and fiber contents of alfalfa forage are mainly driven by the leaf-tostem biomass ratio and secondly by the developmental stage of internodes. (Fig. 1).

The main strategies adopted to improve alfalfa protein content and digestibility rely on these morpho-physiological traits. One strategy is improving alfalfa tolerance to an early cutting schedule (e.g. cutting at 5% blooming), which implies plant selection for early restoration of nitrogen root reserves in order to fuel the shoot regrowth and ensure sufficient crop persistence (4). A second strategy is to act on the stem morphology by increasing the node number, decreasing the average internode length and making it more uniform along the stem. That resulted in higher leaf-to-stem ratio (0.80 vs. 0.76 in experimental synthetics selected for short and long internodes, respectively) and a final increase of CP production per plant (5). Since the development stage is negatively correlated with plant CP concentration and positively related with fiber fractions content, one further strategy is the uncouplement of growing and development processes by selection for high DM production and delayed triggering to reproductive phase (high vegetative-to-reproductive node ratio).

Within-population variation for plant and stem morphology, multifoliolate trait and rate of secondary wall deposition (1) can account for a major fraction of the genetic variation in digestibility among alfalfa plants with comparable biomass production. Highthroughput screening of forage nutritive value by means of near infrared reflectance spectroscopy (NIRS) is currently used to exploit such variation. One last strategy for the genetic improvement of alfalfa stem quality relies on genetic transformation applied to a crucial point of the lignin metabolic pathway (2). Interestingly, alfalfa higher stem digestibility could positively impact not only on ruminant nutrition but also on bio-conversion processing for ethanol production. ■

Figure 1 .

 1 Figure 1. Relationship between forage digestibility or ADF content and leaf proportion in the biomass (from Lemaire and Allirand, Fourrages, 1993)


Charly Talatizi

Marie-Hélène Aumeunier
email: marie-helene.aumeunier@cea.fr

Fabrice Rigollet

Mickael Le Bohec

Christophe Le Niliot

Albrecht Herrmann

Solving the Infrared Reflections Contribution by Inversion of Synthetic Diagnostics: first results on WEST

Keywords: infrared thermography, emissivity, reflections, Ray Tracing Monte Carlo, Radiosity method, inverse problem

Infrared (IR) diagnostics are used to measure plasma-facing components (PFC) surface temperature in fusion devices. However, the interpretation of such images is complex in all-reflective environments because of unknown emissivity and multiple reflections issues. In order to assess these challenges an iterative inversion method based on a fast photonic model, the radiosity method, has been developed. This method is applied to two different direct models based on different geometries, Sec-Tore and RADIOS, in order to estimate temperatures from experimental-like data simulated with a Monte Carlo ray-tracing code with diffuse reflective surfaces or specularly reflective surfaces. RADIOS allows retrieving temperature on colder targets (lower than 200°C) with errors of 33% and the peak temperatures with errors of 6%.

Introduction

In fusion devices, infrared (IR) cameras are key diagnostics to monitor Plasma-Facing Components (PFC) submitted to high heat flux (10MW/m² in steady-state, up to 20MW/m²). Measuring accurately PFC surface temperature is also mandatory to ensure machine protection and optimize plasma operation. For example, the WEST device is equipped with 12 IR cameras looking at the First Wall (FW), the heating antennas and the divertor, the most critical component receiving heat flux up to 20 MW/m² [START_REF] Courtois | Design and status of the new WEST IR thermography system[END_REF]. Nevertheless, the use of all-metallic materials (mainly stainless steel, tungsten and beryllium) with low and variable emissivity (ε ~ 0.1-0.3 in the IR bandwidth considered [3µm, 5µm]) makes the surface temperature measurement difficult [START_REF] Courtois | Design and status of the new WEST IR thermography system[END_REF]. Indeed, the radiance collected by the IR camera includes both the thermal radiation emitted by the target and a parasitic radiation coming from the surroundings of the target. Furthermore, target emissivity changes with the surface temperature. This causes major errors on the surface temperature measurement that we need to address in order to achieve high power and safe plasma operation. IR synthetic diagnostic has been used to quantify accurately, for each camera, the impact on the surface temperature measurement of inaccurate emissivity, the reflections and camera resolution [2]- [START_REF] Talatizi | Thermique et sciences de l'information, Tome1[END_REF]. The use of this synthetic diagnostic has proven that this can lead to major errors on surface temperature measurement up to 100% for colder targets (temperature lower than 150°C) and 50% for hot targets (maximum temperature around 1300°C). This paper presents the results of an inverse method aiming to retrieve the true surface temperature of the PFC by solving low emissivity and additional parasitic flux coming from the reflections. This method relies on the comparison and the least squares minimization between the experimental IR image and a synthetic IR image (obtained through a direct model or forward model). Two reduced photonic models have been developed, tested and compared on WEST tokamak-like numerical prototype.

Generating IR images

In a first step, the inverse method proposed in this paper has been developed and tested from IR simulated images generated with a synthetic diagnostic. This synthetic diagnostic is based on a Monte Carlo ray-tracing (MCRT) code of ANSYS-SPEOS company [5] able to propagate rays in 3D geometry taking into account complex thermoradiative properties of materials and inhomogeneous 3D temperature fields as inputs. Geometrical camera parameters (focal length, detector size) are used to reproduce the 2D IR image and the collected radiance by each pixel. The MCRT code is currently the most sophisticated and reliable code to deal with complex geometrical and physics models and so generate realistic infrared images. Nevertheless, it is not so far adapted to deal with the forward relation between data and model parameters for the nonlinear inverse problem we want to address here; especially due to the required computing time (10 hour with 4 cores to generate a synthetic image with 2-3% precision). This leads to develop reduced direct models able to compute quickly the IR images under some assumptions and approximations described in section 3. In this paper the MCRT is used for generating experimental-like synthetic data as replacement of the experimental data in order to test the developed inverse method and its range of validity.

Figure 1 describes the thermal scene used as benchmark to test the proposed method aiming to retrieve the surface temperature by filtering reflections. In this first step, a simplified geometry of the vessel is considered without including specific components such as the heating antennas, the bumpers and so on. In the same way, a uniform temperature (fixed at 90°C) is considered for the first wall, the upper divertor and the baffle. The emissivity value is also assumed uniform and fixed for each component. Even though these considerations do not accurately reflect the reality, this first step is mandatory to demonstrate the method validity and performance. A temperature profile is applied on the lower divertor that roughly reproduces the heat loads in a tokamak with two strike points and a toroidal modulation of a 20° period to reproduce the ripple effect. The considered materials are Tungsten for the lower divertor, the baffle and the upper divertor with an emissivity of 0.1 and Stainless Steel for the first wall with an emissivity of 0.3 fitting roughly with the literature [START_REF] Touloukian | Thermophysical properties of high temperature solid materials[END_REF]. The camera model reproduces the view of WEST standard divertor view [START_REF] Courtois | Design and status of the new WEST IR thermography system[END_REF] with a spectral IR range of ∆λ=4.3 µm -4.4 µm. The precision of simulated IR map will depend on the number of rays launched in the MCRT code. The simulated experimental images are characterized by a statistic noise around 2% of the collected radiance for colder targets. The inverse method relies on iterative loop as described in Figure 2 which consists in retrieving the model's parameters (here temperature) by minimizing the difference between experimental and simulated data. The simulated data comes from a direct photonic model. In this paper, two direct models are tested and compared: a simplified model so-called Sec-tore (section 3.2.2) and a reduced model so-called RADIOS (section 3.3.3). In [START_REF] Talatizi | [END_REF], the inversion method is tested in an inverse crime situation meaning that the synthetic data used to replace the experimental data come from the same forward model used for inversion, with an additive Gaussian white noise.

In this paper, the experimental-like data are simulated with an independent and more sophisticated code described in section 2. We are interested in retrieving the surface temperature by solving the reflections but assuming that emissivity is known. Solving the emissivity is also mandatory in a fully reflective environment and is possible with such a method and a first feasibility study is proven in [START_REF] Talatizi | Thermique et sciences de l'information, Tome1[END_REF]. This assumes known and quite uniform temperatures on the components which can be achieved during specific operations (such as baking and machine conditioning).

Forward Model

A forward model includes the modeling of tokamak geometry, the thermal scene (3d temperature field), the optical and thermal-radiative properties of materials and the camera. The 3D geometry and the camera model are fixed whereas the 3D distribution of temperature and the optical properties of materials can change. The two developed forward models are based on the same radiosity method (section 3.2.1) to compute the collected flux by camera pixel.

Radiosity Method

The radiosity method is a common method for computing the inter-reflections of light assuming all diffuse reflecting surfaces or Lambertian reflection, meaning that the part of reflected flux is the same in all the directions of observation [START_REF] Siegel | Thermal Radiation heat transfer[END_REF]- [START_REF] Sillion | Radiosity and Global Illumination[END_REF]. Considering a scene composed of N individual surfaces (patches), the method consists in computing the radiosity J vector [N] that contains the total radiation leaving each patch of the scene in all directions per unit area. This energy includes both the emitted energy and the reflected one coming from all the other patches in the enclosure as described in equation (1).

1 ( ( ) ) ( ) π - = - 0 J I R ε F ε L T (1)
With, I is the identity matrix [N×N], R(ε) the diagonal reflectivity matrix [N×N] where each reflectivity is given by ρj=1-εj (j=1 to N), F = (FAj→Ak) the view factors matrix

[N×N] and πεL 0 (T) the emissive power vector [N] which is then called the "source term". L 0 (T) is the black-body radiance at temperature T given by Planck function integrated in the spectral range of the IR camera. The view factor in the above equation is defined as the fraction (between 0 and 1) of flux leaving the surface Aj and reaching the surface Ak:

cos cos 1 → = ∫ ∫ j k j k j k A A jk k j A A j jk F dA dA A r θ θ υ π (2)
With υjk is the obstruction factor between patches j and k¸ θj the angle between the normal of the surface j and the closest distance between the surfaces j and k and θk the angle same angle for surface k, Aj is the area of the surface j [START_REF] Siegel | Thermal Radiation heat transfer[END_REF]. For a given geometry, the view factors matrix is computed only once (12 hours with parallel computing). When all the radiosities Jj of the N patches are computed, the 3D to 2D projection is achieved with an OpenGL routine to provide the observable quantity, that is the 2D IR image (made of 640 x 256 pixels) for the given view of the simulated IR camera.

Sec-Tore

Sec-Tore is a simplified model based on a 20° toroidal sector of a numerical prototype of the WEST tokamak closed by two black-body surfaces at the environment temperature. This geometry has been designed in order to prevent any obstruction between two patches of the 3D scene to compute simple view factors (through an integral contour [START_REF] Francisco | Calculation of view factors for complex geometries using Stokes' theorem[END_REF]). Sec-Tore is made of N=11.787 patches that lead to a computation of over 69 million view factors.

Figure 3 shows the geometry of Sec-Tore and the corresponding modeled image (67.122 pixels) used in the inversion method. The emissivities of the environment and the lower divertor are assumed known (see Figure 1) as well as the temperature of the environment and the black body surfaces. The 8.796 patches of the lower divertor are regrouped in 1.560 bigger patches. The parameters to be estimated are the 1.560 temperatures of the lower divertor.

RADIOS

RADIOS is a reduced model based on a hierarchical adaptive method [START_REF] Bohec | Congrès Français de Thermique[END_REF] allowing to compute only the most important view factors of the scene at the last level of resolution. This criterion of importance is related to the Region of Interest (RoI) of the 3D scene on which are located the parameters to be estimated. The idea is that some initially coarse patches in the whole tokamak are refined (and the corresponding shape factor are computed) only if their contribution to the radiosity of the ROI patches is important (at a given precision level). Such a method allows considering the whole torus (contrary to the Sec-Tore considering only 20° of the tokamak) as well as the obstructions between patches enabling to add more components to the model such as the baffle. Typically, the geometry used in the MCRT code is made of meshes constituted of 2 million elementary surfaces. Without the classical method used in Sec-Tore, 2.10 12 view factors should be computed, whereas 7.8 million view factors are computed with the hierarchical adaptive method.

Figure 4 shows the mapping of a temperature field on the last level of resolution of the meshes with the ROI identified. The RoI is composed of 1.391 patches, which corresponds to the number of parameters to be estimated in the 3D scene.

Figure 4 -Illustration of the last level of resolution for a numerical prototype of WEST with the corresponding mapping of temperature

The reduced method RADIOS uses also Gebhart factors as an additional criterion of refinement of the meshes as presented in [START_REF] Bohec | Congrès Français de Thermique[END_REF]. As Figure 5 shows, Gebhart factors are a "generalized" version of the view factors taking into account the radiative properties of the patches [START_REF] Michael | Radiative Heat Transfer[END_REF]- [START_REF] Leduc | [END_REF]. The Gebhart factors between Sj and Sk, also called absorption factors, represent the fraction of the energy initially emitted by Sj that is absorbed finally by Sk, taking into account all the possible reflecting paths in the scene. To complete the direct model package the same projection based on OpenGL used for Sec-Tore is applied to RADIOS to produce the final synthetic IR image of the scene.

Parameters Estimation Problem

The parameters estimation is based on Ordinary Least Squares (OLS) method [START_REF] Rémy | Thermal Measurements and Inverse Techniques, Chapter 9 Nonlinear Estimation Problems[END_REF]. The minimization will occur on a RoI of IR images of m pixels. This RoI can be a profile, an area of image, a list of some particular pixels, etc.

The OLS minimization uses a Gauss-Newton algorithm to update the parameters at each iteration. That is based on the inversion of the S T S information matrix [p×p] with p the numbers of parameters to be estimated:

( ) ( ) ( ) ( ) ( ) ( ) 1 1 ˆˆ-+ = + - k k k T T OLS OLS mes OLS mo x x S S S y y x (3)
where ˆOLS

x is the vector of the p parameters to be estimated (temperature here), ymes the vecor of m data, ymo the vector of the m outputs of the direct model and k the iteration number. The specificity of this method is that it estimates 3D parameters (temperatures of the patches of the divertor) from a 2D observable which are the pixels of the IR camera. The number of parameters p is not necessarily equal to the number of measurements m as it depends on the resolution of the camera. Additionally, certain patches that share the same properties (in reality or by assumption) can be regrouped in macro patches covered by several pixels, hence different pixels bear the same information regarding one parameter of the model. Each column j of the sensitivity (or Jacobian) matrix S [m×p] contains the sensitivity coefficient of the model to the parameter xj (j=1 to p) computed along pixels of interest si (i=1 to m) given by equation (4) [START_REF] Aster | Parameter Estimation and Inverse Problems[END_REF]- [START_REF] Rémy | Thermal Measurements and Inverse Techniques, Chapter 9 Nonlinear Estimation Problems[END_REF]:

( , ) ( ) , 1 , 1 k mo i j i j x for k j y s S s j to p i to m x ≠ ∂ = = = ∂ x (4)
Nevertheless, as proven in [START_REF] Talatizi | [END_REF], the temperature estimation becomes a linear problem by considering the radiance parameters L 0 (T) (related to the temperature T via the Planck function) in equation (3). Then, the radiance parameters can be directly computed with equation (5):

( ) ( )

1 0 ˆ- = - T T OLS 0 r r r mes c c

L S S S y S L

(5)

with, L 0 the black body radiance of target from which the temperature will be deduced, Sr the sensitivity matrix for the estimated parameters, (Sr T Sr) -1 Sr T the inversion operator, ScL 0 c the reduced sensitivities of the forward model with respect to the known parameters (that is L 0 (Tenv) where Tenv is the temperature of all components in the tokamak except the lower divertor). The vector yshift= ymes-ScL 0 c is called the shifted data. As a result, the solution is quickly computed without any iterations since the problem is linear (four seconds with 16 G0 RAM and 3.5 GHz CPU).

The solution takes also into account the standard deviation σi of noise measurement. The noise measurement is considered additive with zero mean and a Gaussian distribution. The standard deviation of the noise is assessed as a constant fraction (typically 2% as indicated in section 2 such as the values obtained from the MCRT simulations) of the radiance collected by each pixel. The noise covariance matrixΨ is given by (6)(7):

2 2 2 1 2   =    m diag σ σ σ Ψ (6)
The solution of the Maximum Likelihood (ML) estimation [START_REF] Aster | Parameter Estimation and Inverse Problems[END_REF] is given by equation ( 7):

0 1 1 1 ˆ( ) ( ) - - - = - T T ML 0 r r r mes c c

L S Ψ S S Ψ y S L (7)

The covariance matrix of ML estimator is given by:

0 1 1 ĉov( ) ( ) - - = = T ML r r C L S Ψ S (8)
The 95% confidence intervals associated to the i th estimated parameters (j=1 to p) are computed from the diagonal components of this covariance matrix:

0 1/ 2 , ˆ1.96 ( ) ± ⋅ ML j jj L C .
Table 1 summarizes the main figures for the temperature estimation for Sec-Tore and RADIOS models. The temperature estimation is carried out on a sector of 20° (67.122 pixels for Sec-tore, 49.527 pixels for RADIOS).

The estimation with Sec-Tore aims to retrieve the temperature of 1.560 "macro-patches" located on the lower divertor whereas the estimation with RADIOS aims to estimate 1.391 parameters of the patches of 3D ROI of the hierarchical method. RADIOS allows identifying less parameters because some parameters on the outer side of the lower divertor are not monitored by the camera due to the baffle obstruction. The temperature of these patches is assumed equal to the last patches monitored next to the baffle's edge.

Results

Diffuse Case

The first temperature estimation is performed considering a diffuse surface. The synthetic data are generated from the MCRT code, considering purely diffuse reflective materials (or Lambertian reflectance for which the apparent temperature is the same for any observer's angle of view). Two simulated images are generated: one without the baffle for the estimation conducted with Sec-Tore and one with a baffle for the estimation with RADIOS. The emissivities of the components are fixed to their value of the literature (0.1 for the lower divertor, the upper divertor and the baffle, 0.3 for the first wall as stated in section 2 and further to [START_REF] Touloukian | Thermophysical properties of high temperature solid materials[END_REF]). The temperature of the environment (all surfaces but lower divertor) is assumed known and fixed to its value of 90°C. Comparison with the optimal radiance profile obtained with the temperature estimated by the inverse method Sec Tore (blue). (b): 3D temperature profile estimated with Sec-Tore (blue) with the associated levels of confidence and with RADIOS (green) in the case of synthetic measurements with diffuse reflective surfaces. Profiles correspond to the green lines drawn on the 3D view of Figure 7, the origin being on the inner side.

Sec-Tore enables to estimate the peak temperatures with an error lower than 1% for the maximum temperatures (around 800°C). However, the temperature of the colder part is estimated with an error higher than 166%. This is due to the black-body vertical closing surfaces at Tenv (see Figure 3) that appear to be a wrong boundary condition to model radiation exchange between the lower divertor and the complete tore (Sec-Tore is limited to a toroidal section of 20°). As expected, RADIOS (modeling the complete 360° tore with hierarchical radiative method) enables to estimate the lower targets temperature with a much lower mean error of 32%. Nevertheless, RADIOS estimation of the peak temperatures is not as good as the Sec-Tore estimation: it is mainly due to the high sensitivity of RADIOS to the noise measurements (synthetized by the MCRT code here). To a slightly lesser extent, these errors can be due to approximations in the forward modeling (approximations of camera viewing and geometry) compared to the real world (here synthetic diagnostic). One should pay peculiar attention when real experimental data will be processed.

Figure 7 shows the mapping of the estimated temperatures for RADIOS and Sec-Tore on the 3D surface compared to the true temperature used as input of the MCRT code. The black patches on RADIOS side are parameters that could not be estimated because the model is too sensitive to the noise contained in the simulated data. 110 parameters over 1.391 parameters are not estimated.

Specular case

The second temperature estimation considers high specular reflectance surface. The synthetic data are generated considering a Bidirectional Reflectance Distribution Function (BRDF) which is a combination of 2% Lambertian reflectance and 98% of specular reflection with a Gaussian distribution of 8° width around the specular direction. Figure 8 compares the simulated images with the MCRT code in case of diffuse and specular surfaces and considering the presence of the baffle. emission. The radiance profiles are quite similar except for the extreme pixels (number 160 and more) impacted by the presence of baffle. There is less signal near the baffle as well as more statistic noise. Concerning the noise, the specular simulations show that the statistic noise represents around 25% of the signal on the colder targets compared to the diffuse relative noise of 2%. Figure 9 also shows the convergence of the radiance optimal parameters profile (left) and the corresponding results of the estimated 3D temperatures (right).

Figure 9 -(a): Synthetic noisy measurements (radiance profiles) built with the MCRT code in the case of specular reflective surfaces without baffle (red) and with baffle (green). Comparison with the optimal radiance profile obtained with the temperature estimated by the inverse method Sec-Tore (blue). (b): 3D temperature profile estimated with Sec-Tore (blue) with the associated levels of confidence and with RADIOS (green) in the case of synthetic measurements with specular reflective surfaces. Profiles correspond to the green lines drawn on the 3D view of Figure 7, the origin being on the inner side. .

On one hand, Sec-Tore enables to retrieve all parameters to be estimated. The radiance profiles on Figure 9(a) show the halo of reflection on the inner side in the form of the bump on the left of the profiles (pixels 0 to 70). The convergence of the model regarding the radiances is still good however, the temperature estimation is not so good especially for the halo of reflection. Indeed, the bump on the radiance profile is interpreted by the model as an increased emission of the component in this area and not as a specular pattern of reflection. As a result, the estimated temperature is higher in the matching area (up to 300°C instead of 90°C). The estimated temperature on the colder targets (less prone to reflections) is around 200°C, which represents an error of 120% compared to the previous errors of around 166%. Last, the increase of relative statistic noise on the measurement degrades the confidence levels associated to the temperature estimations (error bars larger than in diffuse case about 2% of the value for Sec-Tore and 4% for RADIOS in diffuse case versus 12% for Sec-Tore and 10-50% for RADIOS in specular case).

On the other hand, RADIOS enables to retrieve only 891 parameters out of the 1.391 estimated parameters (around 60% estimated parameters). This is due to an increase of statistic noise in the simulated experimental-like data when considering specular reflective surfaces. Nevertheless, the estimation of the peak is as good as the estimation considering diffuse reflective surfaces with errors from 1% to 8%. It is worth noting that retrieved parameters out of the peak are the ones located in the area prone to reflections where the halo of reflection is considered by the algorithm as a much hotter zone than it really is.

Figure 10 shows the relative errors on the estimated surface temperature ((estimated-true)/true in %) with Sec-Tore and RADIOS for diffuse reflective surfaces as well as specular reflective surfaces. The true temperature profile used as input of the MCRT code is also plotted to locate the position of the peaks. Profiles corresponds to the green lines drawn on the 3D view of Figure 7, the origin being on the inner side.

RADIOS allows estimating less parameters than Sec-Tore because of the presence of the baffle and because some parameters cannot be estimated due to the statistic noise of the simulated data.

Figure 10 shows the mean error of the temperature estimation. As expected the temperature peak at 800°C, which is less affected by parasitic reflections, is retrieved with a good accuracy (better than 1% both for diffuse and specular surfaces). The advantage of the RADIOS model (considering the whole torus) is quite proven for colder targets (temperature around 90°C) in the diffuse case since it allows reducing the surface temperature error to 33% from 166% with the Sec-Tore model. The specular case is more complicated to analyze. Indeed, the additional parasitic light coming from specular reflection is not uniform along the target due to angular dependence of reflectivity. As a result, a kind of bump is observed along the luminance profile (Figure 10b). As the model used for the inversion assumes Lambertian reflections, the bump is interpreted as an increase of emittance and so the algorithm finds a solution with a higher temperature than expected. This leads to larger temperature errors using both models Sec-Tore and RADIOS up to more than 200%.This illustrates and quantify the limits of the radiosity method considering diffuse reflecting surfaces to retrieve temperatures of specular reflecting surfaces. The next step should be to enhance the direct model taking into account the specular behavior of the reflectance model based on previous studies as described in [START_REF] Immel | A Radiosity Method for Non-Diffuse Environments[END_REF].

Table 2 summarizes the results of the temperature estimation with both Sec-Tore and RADIOS for diffuse reflective surfaces and specularly reflective surfaces. RADIOS gives results of temperature estimation with a mean error of 32% on the colder targets and 1 to 8% error for the peak temperature. As mentioned in section 4.1 this degradation of the peak temperature estimation is due to approximations in the modeling of RADIOS and noise statistic.

Conclusion

This paper presents the results of an inverse method aiming to retrieve the true surface temperature from IR measurements solving low emissivity and the additional parasitic flux coming from the reflections. In the inverse method presented here, the temperature estimation is carried out with two different forward radiative models, both using radiosity calculations but based on two different geometries: Sec-Tore and RADIOS. On one hand, Sec-Tore only considers a toroidal 20° sector of a tokamak closed by two black-body surfaces with very simple components and no obstructions between elementary patches. On the other hand, RADIOS considers a whole torus and can deal with obstructions between patches and then can include more realistic components such as the baffle into the model. To test the method, the IR measurements are replaced by synthetic experimental-like data simulated with a MCRT code considering diffuse or highly specular reflective surfaces.

In the case of diffuse reflective surfaces, Sec-Tore gives good results for the peak temperature estimation with error of 1%. However, due to the boundary condition of black body surfaces closing the 20° sector, the error on colder targets temperature estimation reaches 166%. RADIOS gives better results for the colder targets temperature estimation with a mean of error of 32% but the peak temperature estimation is degraded by approximations in the modeling, with respect to the MCRT code that generated the synthetic data (geometry sometimes simplified to limit the number of total (a) (b) patches). The temperature estimations with RADIOS is also currently limited by the sensitivity of the inversion process to the noise existing on the synthetic measurements. This leads to the impossibility to estimate some parameters. These issues should be reduced by improving the conditioning of the model by using regularization methods (such as Tikhonov regularization [START_REF] Tikhonov | Solutions of Ill-Posed Problems[END_REF]), optimization under constraints or with a priori values of some parameters.

In the case of specular reflective surfaces, the temperature estimation with Sec-Tore and RADIOS still gives good results for the peak temperature, but the temperature estimation of colder targets, prone to reflections, is more chaotic with great errors. This result was expected as the radiosity method assumes diffuse surfaces and cannot interpret specular patterns of reflection. The next challenge will be to take into account specular surfaces in RADIOS.

Nevertheless, the developed inverse method has proved very promising for retrieving the true temperature by filtering reflections. Furthermore, as the temperature estimation problem is linear and relies only on a matrix product based on the pre-computed and stored Jacobian (eq. ( 7)), this inverse method could be compatible with real-time application.

Figure 1 -Figure 2 -

 12 Figure 1 -Geometry used as input of the MCRT simulation (left) and the resulting simulated IR image (right) 3. Inverse method 3.1 Approach description

Figure 3 -

 3 Figure 3 -Illustration of the 3D model of Sec-Tore with a thermal field applied to the mesh (right) and the resulting modeled image after the OpenGL projection (right)

Figure 5 -

 5 Figure 5 -Usual view factors compared to Gebhart factors taking into account all radiative paths (direct and indirect)

Figure 6 (

 6 Figure 6(a) shows the radiance profiles along the divertor simulated with MCRT considering or not baffle emission: the difference is not significant which allows comparing the results of Sec Tore and RADIOS without bias. This figure also shows the good convergence of the modeled radiance with the Sec-Tore model towards the simulated ones with the MCRT code. Figure6(b)shows the estimated temperature profiles with both Sec-Tore and RADIOS compared to the true surface temperature used as input of the MCRT simulation.

Figure 6 -

 6 Figure 6 -(a): Synthetic noisy measurements (radiance profiles) built with the MCRT code in the case of diffuse reflective surfaces without baffle (red) and with baffle (green). Comparison with the optimal radiance profile obtained with the temperature estimated by the inverse method Sec Tore (blue). (b): 3D temperature profile estimated with Sec-Tore (blue) with the associated levels of confidence and with RADIOS (green) in the case of synthetic measurements with diffuse reflective surfaces. Profiles correspond to the green lines drawn on the 3D view of Figure 7, the origin being on the inner side.

Figure 7 -

 7 Figure 7 -3D mapping of the estimated temperatures with RADIOS (left) and with Sec-Tore (right) compared to the true temperature used as input of the MCRT code (middle)

Figure 8 -Figure 8

 88 Figure 8 -Synthetics measured radiance maps provided by the MCRT code in the case of fully diffuse reflective surfaces (left) and mainly specular reflective surfaces (right) with logarithmic color bars Figure 8 shows that the specular reflective materials cause two patterns (halos) of reflections on both side of the strike points: on the inner side of the lower divertor and close to the baffle. These patterns are due to reflections of the environment (vessel wall) at 90°C. The estimation assumptions are the same as for the diffuse case (environment temperature and emissivities known).Figure 9(a) shows the simulated radiance profile with the MCRT code considering or not the baffle obstruction and

Figure 9 (

 9 Figure8shows that the specular reflective materials cause two patterns (halos) of reflections on both side of the strike points: on the inner side of the lower divertor and close to the baffle. These patterns are due to reflections of the environment (vessel wall) at 90°C. The estimation assumptions are the same as for the diffuse case (environment temperature and emissivities known). Figure9(a) shows the simulated radiance profile with the MCRT code considering or not the baffle obstruction and

Figure 10 -

 10 Figure 10 -(a): Relative errors on the estimated temperatures with Sec-Tore for diffuse reflective surfaces (blue) and RADIOS (green) superimposed with the true temperature profile (black). (b): Relative errors on the estimated temperatures with Sec-Tore for specular reflective surfaces (blue) and RADIOS (green) superimposed with the true temperature profile (black).Profiles corresponds to the green lines drawn on the 3D view of Figure7, the origin being on the inner side.

Table 1 .

 1 Main figures for the temperature estimation for Sec-

	Tore and RADIOS models
	Model	Torus part	View factors	m Pixels used	p Parameters estimated
	Sec-Tore	20°	69M	67.122	1.560
	RADIOS	360°	7.8M	49.527	1.391

Table 2 .

 2 Comparison of the results estimation with Sec-Tore and RADIOS.

	Reflection model	Temperature location	Sec-Tore	RADIOS
	Diffuse	Hot Peak Cold targets	1% 166%	6% 33%
		Hot Peak	< 1%	/
	Specular	Cold targets	106%-223%	/

Acknowledgements

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the EURATOM research and training programme 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.