MADUSE - Modelling Product Variability and Data Uncertainty in Structural Dynamics Engineering
Project Description
 Overall objectives This project addresses methods for numerical simulation of dynamic behaviour of structures. Current industrial procedures for structural product analysis employ deterministic finite element models. But it is generally acknowledged that deterministic models are often oversimplified. Non-deterministic modelling procedures take into account aspects of uncertainty and variability. Scientific research in numerical methods in engineering has brought forward a number of very capable methods to model the effect of variability or uncertainties on technical characteristics of products. The objective of the present project is to research and develop methods to explicitly take design parameter uncertainty and actual product variability into account in the design process itself. The research will integrate various disciplines, including mechanical engineering, numerical modelling, mathematical methods, optimisation etc. Providing mechanical engineers with a more solid background in advanced mathematical methods and stochastic techniques and on the other hand confronting mathematicians with the application field of mechanical engineering is expected to generate a significant synergy and technology transfer effect. The developed approach must have the following capabilities: - The types and number of uncertain parameters should be unlimited:
- material and structural properties
- uncertainties on loads and boundary conditions
An order of magnitude of uncertainty intervals on parameters up to ą10% is envisaged, while the constraints for treating larger uncertainties will be researched. In the project, models with increasing numbers of uncertain parameters will be treated, up to at least 100 in the industrial scale applications. - output requirements : the establishment of worst case situations by predicting response levels that can neverbe exceeded by any parameter combination that is within the specified input ranges
- performance of methods : the size of the deterministic FE model should in principle be unlimited. In the project, model sizes of increasing complexity will be studied up to industrial vehicle body models of at least 500.000 degrees of freedom. The calculation time should not exceed 100 times the time needed for 1 conventional deterministic FE analysis run, regardless of the number of uncertain parameters.
This will involve realising the following technical objectives: - The general requirements on the developed methods are:
- To quantify the typical uncertainties on the design parameters as well as the typical scatter on the structural responses, and this for selected structure types
- To investigate how the uncertainties on the input parameters of components models (e.g. material characteristics, . . . ) and built-up models need to be characterised in terms of ranges, distributions and models.
- To develop and validate methods that allow the variability of the response to be estimated for given uncertainties on the parameters of component models and built-up models and this in a reasonable time (e.g. less than x times nominal calculation). Several approaches will be investigated within the project:
- perturbation methods (for low levels of uncertainty) using sensitivity formulations and functions
- stochastic methods (Monte-Carlo and advanced Monte Carlo simulation methods)
- fuzzy finite element methods (interval arithmetic)
- Design of Experiment (DOE) based methods integrated with formal Optimisation Strategies
- to make a critical assessment and comparison between the probabilistic (stochastic) and the possibilistic (Fuzzy-FE) approaches, evaluating complementarities, application focus and range etc.
- To study how the knowledge on the propagation of uncertainties can be used in the process of optimising the structural dynamics behaviour of a product. This involves:
- the development of methods which allow optimisation for a trade-o. between performance and variability, through design for allowable worst cases
- the development of an approach for the Robust Design of structures, minimizing sensitivity of product performance on uncertain parameters
- to validate the developed methods on industrial cases and hence demonstrate the actual industrial applicability of the concepts and techniques (improve the state-of-the-use).
- The developed approach should support the use of (or at least compatibility with) standard Finite element solvers such as NASTRAN, ANSYS or ABAQUS.
The following objectives related to training and dissemination will be realised: - development of European Training Course on uncertainty and variability, and organisation of this course on regular intervals in order to reach a significant researcher and user base throughout Europe
- in-depth training of a significant number of early stage researchers on the various approaches of uncertainty and variability through participation in the technology and methodology research program
- preparation of a set of tutorials on the problem of uncertainty and variability and on the various methods
- preparation of a set of documented benchmarks (with freely accessible models and data, as well as analysis results) supporting the tutorials and lowering the threshold for getting involved with the problem and the methods. It is only by seeing very clearly the impact of uncertain parameters on the outcome of simulations that engineers will start getting concerned about the usefulness of their "nominal model" simulations.
- preparation of a set of documented industrial case examples, showing the practical impact in the industrial design practice (making clear this is not just an academic exercise)
- development and maintenance of a project web-site which will not only reflect the project work, but which also will serve as a reference site for the problem of uncertainty in modelling, including the tutorials and benchmarks, training material, case histories, literature reviews and links to all relevant actors in the field
- preparation and presentation of journal and conference papers on the research outcome
- the co-ordinator organises the biennial ISMA conference on Noise & Vibration Engineering. This conference attracts participants from industry and academia and it addresses scientific and technical progress in the field of structural dynamics and technical acoustics. In the course of the project, the conference will be organised in September 2004, September 2006 and September 2008. Specific sessions will be organised on the topic of the project.
- organisation of at least 2 public domain workshops dedicated to the topic of uncertainty and variability in structural modelling, and organise dedicated sessions at general structural analysis conferences
- development of teaching modules for including a consistent education on the topic of uncertainty and variability in the curriculum of Mechanical Engineers, making the awareness on the problem and the potential solutions to address this "baseline" engineering knowledge.
Finally, it is a project objective that all early stage researchers involved in the research training program also get a thorough training in the general aspects of research and research management by participation to the continuous education programs at their host institutes. Some specific training modules will be developed hereto. Overall approach and methodology In order to develop a generic procedure to predict bounds on structural response in conditions with parameter uncertainties, 4 di.erent routes corresponding to 4 modelling concepts are explored, aiming to develop an integrated approach for structural optimisation of industrial products: Monte Carlo simulation A user-defined number of samples is generated. For each one a deterministic (FE) analysis is run and a frequency response function is calculated. Statistical analysis is required to interpret the response and to relate it to structural design. The research focuses on reducing the computational effort by extending variance reduction techniques (VRT).
Fuzzy Finite Element approach Fuzzy numbers represent uncertain model parameters or boundary conditions. In the model simulation, the conventional arithmetic is replaced by a generalised arithmetic for fuzzy numbers. Finally, bounds on structural response are predicted.
Component Mode Synthesis CMS is used in deterministic analysis. It may be extremely useful for performing variability investigations because it reduces model size drastically. Intelligent application of CMS, especially with large, assembled, structures, improves computational e.ciency considerably, when several analysis runs have to be done. Uncertainty is now included by assuming that the substructure natural frequencies are random variables.
Design Of Experiments DOE with Response Surface Model (RSM) methodology is a general approach to facilitate design procedures that involve many parameters, each of which needs an optimum setting. The DOE provides a minimal set of experiments that yield enough points to estimate an RSM of certain order, allowing to provide insight in functional relations between input variables and the true responses. It is a technique, which can be used in conjunction to almost any "what if" design problem (also Monte Carlo analysis) and it is mainly used in technical applications.
Optimisation techniques will be developed for effective structural design optimisation, taking into account parameter uncertainties.
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