An Industrial Case for Generic Uncertainty Treatment

Since many years industry regulators require an uncertainty statement to be provided with any modelling study in industrial risk assessment field. Other stakeholders at different levels follow as far as system design or risk assessment is concerned. Indeed, an overall awareness of uncertainties and a need to take it account when deciding into is spreading fast.

While many approaches, typically specific and problem driven, had been imagined and developed since late 90ies by various industries ranging from Defence to Medical, to Energy, ever widening spectrum of possible applications yielded a know-how consolidation economically sensible.

A number of academic references have been published in the 1990s originating from the risk assessment community, firstly in the United States, where major uncertainty research has been launched in the energy or military aerospace industries (Helton, Oberkampf etc.), and later on in Europe (Aven), as well as from the environmental or infrastructure impact and planning (Granger Mc Henrion, Saltelli, Cooke …). Meanwhile, some physical domains have enjoyed sectoral modelling research, such as probabilistic mechanics (e.g. Melchers) involving most recently stochastic developments.

It is only gradually that the scientific computing communities and the larger industrial computing actors have started to get seriously involved in the advanced applied mathematics and high performance computing consequences and opportunities attached to uncertainty modelling. Most historical works published in the 1990s involved some simple simulators with only rarely full-scale finite element or advanced coupled models, or physically-limited modelling efforts (such as mechanics) not recognising the genericity that did appear only later on.

Hence nowadays several major partnerships at the international level (ESREDA, MUCM, SAMSI) or the French level (IMdR) have launched ambitious works to capitalise on uncertainty treatments into generic guides that would meet virtually any industrial need. It aims at designing a common template to be followed as well as specific guidelines to methodology that might best fit the particular case typically according to the data and experts information availability, model complexity and so on.

The genuine study cases considered in these projects, all from different business areas, illustrate a startling feature : although the applications and physics involved are completely different, the implicit mathematical structure seems very similar. Moreover the methodology collections to shop in for each step are common and the choice is rather dependent on the criteria, the underlying institutional regulation or study purpose, than on the application.

Indeed the conceptual framework that fits, conceptually at least, virtually any industrial uncertainty study can be resumed by the following figure:

This scheme ought to be considered as a skeleton for a purely uncertainty part of an industrial study. So far all the three essential steps, as well as satellites B’ and C’ may be shown application free, it is rather mutually dependent.

At a conceptual level it may be one size fits all solution, meanwhile it is not assumed to be so when applied. Instead the reference guide provides the methodologies to shop from and the guidelines to chose from that handleads and educates an industrial engineer over the uncertainties aspects avoiding him becoming a specialist in this complex field. It may therefore be implemented as Software that would perform all the modelling, propagation and criteria check and would only ask some relevant questions, playing the role of Babel Fish, a translator from the industrial world to the mathematical.

When dependency structure between the steps of this application free framework is closely investigated it appears that one step directs others in many aspects – the purpose of the study (often a criterion to comply with, or a business decision making) together with some features of the available model and the study context (variables involved, deterministic or random or a bit of both). Therefore the very sensible approach to start with is to “get it from the right end” (see the box above).

This conceptual conclusion comes as an essential point for the consolidation process of building the generic uncertainty management framework.

In brief, the consolidation of uncertainty treatment practices aims at a kind of two side split for a generic industrial study. The first one would gather all the bits specific to the particular application, whereas the second one would collect the uncertainty related bits. Ideally, the uncertainty slice may prove to be a common to any application (or can be managed to become so), and might be embedded into a comprehensive Software package.

This would offer to an application specialist in charge of a whole study, the uncertainty management toolkit applicable to his field know-how.

In support to these industrial genericity efforts, some recent academic works have generalised and deepened the mathematical methodologies needed in the modelling and computing : in particular, advanced statistical computing is getting closer to uncertainty and sensitivity needs (Robert, Antoniadis, Kennedy & O’Hagan, Kleijnen, Kurowicka & Cooke etc.) : this involves for instance the field of design of experiments, meta-models, statistical learning, functional analysis of variance, advanced Bayesian algorithms, high-dimensional data analysis etc.

Project organisation

The far-reaching goals and the mixture of partners from various backgrounds and mindsets imply a careful approach to project management. Designed to lean the overall project run to its ambitious objectives it is structured into six Work Packages (WP). Moreover an innovative inner body – the “Expert College” - is designed to ensure the scientific relevance of findings / developments and permanent adjustment by the worldwide science progress.

• WP0: Coordination, Dissemination & Communication
• WP0’: Expert College
• WP1: User requirements & Specifications
• WP2: Scientific development
• WP3: Validation / Demonstration
• WP4: Industrialisation / Product durability

Each WP has a coordinator named by the Partnership, typically for its recognised proficiency in the relevant field and for his capability and willingness to combine the scientific / development mission with coordination of all involved partners. S/He organises the WP in a set of deliverables, and sets the relevant meeting schedule and dissemination events.

The key point of the project success is the close cooperation between the WPs, the planning respect and timely “lock point” identification and cancellation. The WP leader mission requires, therefore, the tight look and deep commitment to the project priorities.

Relevant tools

SALOME

SCILAB

SCOS

R-project

OpenTurns