Keywords: model validation, model updating, modal correlation, spacecraft dynamic analysis, structural uncertainties, modelling errors, Monte Carlo simulation.

The main aim of the finite element model updating in structural dynamics is to generate improved numerical models which may be applied in order to obtain predictions for alternative loading arrangements and modified structural configurations. This goal can be reached by localising and subsequently correcting the real error sources in the model. The problem of error localisation and model updating has been attacked by a number of researchers who have employed a variety of approaches. The introduction of robust optimisation codes has led to the use of a concept which attempts to directly minimise an objective function which estimates the differences between computed and measured results, for example modal data [1,2]. In practice when the distance between the model and the experimental results is sufficiently "close", the model is said to be valid.

Usually the mathematical model update process is based on deterministic approaches, i.e. is based on the attempt to match, as closely as possible, the results of a deterministic numerical analysis, with that of a single physical test, without taking into account the natural dispersion or scatter inherent to all physical structures. This approach can lead to unreliable results or be misleading and incorrect conclusions on the quality of the model may be concluded. This results in limited confidence in the model which can only be partially compensated by the use of uncertainty or safety factors. It would be therefore highly desirable, if not necessary, to consider the scatter as an integral part of the model and to establish correlation and validation techniques that take this scatter into account. In this way, deterministic "point-to-point" comparison is replaced by a much more robust "cloud-to-cloud" comparison where each cloud contains a full stochastic description of the model including scatter among its observed variables. In principle the stochastic approach could enable discrimination between irreducible uncertainties and reducible uncertainties (i.e. modelling errors) and it could also allow the assessment of the robustness of the correlation.

Although numerous stochastic techniques and tools exist today, it is necessary to adapt their use to the particular needs of spacecraft model validation. For example spacecraft testing is usually performed at a system level using a single specimen thus limiting the availability of experimentally measured uncertainty. Also, the need to use existing deterministic validation criteria such as the modal assurance criterion (MAC) must be taken into account to maintain compatibility with current practice. This was the aim of the recently completed EDIS project [3] carried out under the technical management of the European Space Agency and performed by a consortium of european industries.

The paper reviews the traditional approach to model updating of spacecraft structural dynamic models by means of deterministic design sensitivity and optimisation techniques. Then it presents the objectives, the logic and some results of the EDIS project along with a closer look at some applications performed at ESTEC, the European Space Research and Technology Centre.

The stochastic approach is more complex and much more computationally expensive than deterministic methods and the characterization of structural uncertainties necessary to implement the approach can be difficult and time-consuming. On the other hand the stochastic model validation provides a larger and important amount of additional information on the correlation and updating process and permits the assessment of the robustness of the validation. In fact the approach takes into account the uncertainties associated with the input variables of the finite element model as well as the scatter in test data. Moreover, through MCS input and output relationships may be examined over the entire design space instead of being limited to a localized gradient, therefore the updating process is, potentially, much more powerful in terms of correlation and error localization performances.

1

Blakely, K., Bush, R. "Using MSC/NASTRAN to Match Dynamic Test Data", Proceedings of the International Conference on Structural Dynamics Modelling, Milton Keynes, UK, pp. 411-420, July 1993.

2

Calvi A., Morris A.J. "Updating of large-scale structural dynamic models by a semi-automatic two-level optimisation procedure", Proc. of the European Conference on Spacecraft Structures, Materials and Mechanical Testing, Noordwijk, The Netherlands, December 2000.

3

Calvi A., Canay M.A., Pavón M.T. "Validation of Spacecraft Structural Dynamic Models based on a Stochastic Methodology", in Topping B.H.V. and Mota Soares C.A. (Editors), Proc. of the 7th International Conference on Computational Structures Technology, Civil-Comp Press, Stirling, UK, paper 110, 2004. doi:10.4203/ccp.79.110

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