The MADUSE project involved 23 engineers from 14 countries who worked over three years to develop advanced methodologies for dealing with uncertainty in structural dynamics engineering. They characterized uncertainty as either variability, which causes scatter over different realizations, or epistemic uncertainty from a lack of knowledge. Probabilistic models using probability density functions were used to treat variability, while possibilistic models using intervals or fuzzy numbers handled epistemic uncertainty. The project applied these methods to predict the effects of uncertainty on the dynamic response of a vehicle's windshield and chassis sub-frame. It proved the feasibility of numerical procedures for both aleatory and epistemic uncertainty in large finite element models with many uncertain parameters without excessive computational cost.

1. MADUSE Report Summary
Project reference: 505164
Funded under: FP6-MOBILITY
Country: Belgium
Contact
VANDEPITTE, Dirk
Final Activity Report Summary - MADUSE (Modelling Product Variability and Data
Uncertainty in Structural Dynamics Engineering)
Few things are certain in real life. Nevertheless, one thing is absolutely certain: it is illusive to expect that engineers know the
precise answer to technical problems, even with the most advanced knowledge that is available today. A technical product or
process is described by a multitude of parameters of all kinds. These parameters may take values that vary over time or over
all the individual realisations of a nominally identical case. Even with precise quality, control scatter is inevitable. And still, for
some parameters, it may even be difficult to get a reliable estimate. Modern society however expects advanced technical
products with high quality which are cheap and available after a development cycle that gets increasingly shorter. In order for
the product development cycle to be effective, the engineer has to take into account all parameter uncertainties and scatters
that may possibly occur, preferably during in an early design stage.
In the Marie Curie network MADUSE, 23 engineers from 14 countries worked for more than three years at six universities and
three companies to develop advanced methodologies that dealt with non-determinism.
First of all, the nature of uncertainty was characterised as either variability, also called aleatory uncertainty, in which scatter
occurred over different realisations, or epistemic uncertainty, in which insufficient knowledge was available to determine the
precise value of a parameter. Likewise, there were two categories of methods, with each one applying to one category. A
variability case was treated with a probabilistic model, using probability density functions. An epistemic uncertainty case on
the other hand was handled with a possibilistic model, using interval or fuzzy numbers.
Both model categories required a quite different approach. Input data was different, and so were numerical formalisms to
capture the type of non-determinism and calculation procedures that predicted how the uncertainty propagated through the
analysis. Ultimately, the interpretation of the final result was also very different. Probabilistic methods allowed for a statistical
interpretation, whereas possibilistic methods only gave bounds on the output quantities.
The network focussed on the application of dynamic response calculation, a technical field of continuously increasing
importance. Although several industrial sectors were within the scope of the project, the automotive sector was the main
project driver. The network did not only develop theoretical methods, but also paid close attention to real industrial practice
from its very beginning. The principal cases of study were the windshield of one passenger car and the chassis sub-frame of
another car. The first test case was a layered structure with uncertain and temperature-dependent material properties and the
second was a welded structure with relatively complicated geometry. The sources of uncertainty were very different in both
cases, and so were the conditions in which they materialised. The network partners used advanced experimental methods and
cutting-edge numerical simulation tools based on finite element models to predict the effects of non-determinism as they
appeared in real-life operation of the vehicle. The project proved the feasibility of numerical procedures for both aleatory and
epistemic uncertainty, even for large finite element models with many uncertain parameters, without excessive computational
cost. It was anticipated that industry would use the ever increasing power of processors to take into account the effects of
uncertainty in product development procedures.
The methods that were developed were not only useful for structural dynamics and reliability but also for other structural and
fluid mechanics’ applications and, at a following stage, for bio-systems. The network took the initiative to set up a web site that
demonstrated the highlights and recent developments in non-deterministic approaches, namely www.ndaportal.com.
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Last updated on 2011-11-23
Retrieved on 2015-03-04
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