Keywords: model validation, stochastic correlation, model updating, dynamic analysis, Monte Carlo simulation, spacecraft model.

The correlation and mathematical model update process of spacecraft structural dynamic models usually relies on a deterministic approach, which can lead to unreliable or misleading results and induce wrong conclusions on the quality of the model [1]. Recently, the European Space Agency (ESA) proposed a study, EDIS (Enhancements of Dynamic Identification for Spacecraft) on stochastic correlation and validation of structural dynamic models. The study is performed by a consortium of European industries, EADS CASA Espacio, Astrium/Toulouse and Intespace with partners Top Modal and MSC/Software. The study is in progress under the technical management of the European Space Agency.

The overall goal of the project is to demonstrate the feasibility and interest of a stochastic approach to the validation of spacecraft structural dynamic models. This is accomplished by extending and adapting current deterministic model validation techniques by taking into consideration the presence of scatter or dispersion in both simulation and experimentation.

This paper describes the logic, the basic principles and some preliminary results of a novel approach for the validation of structural dynamic models. The major advantage is that scatter, which is neglected in the traditional deterministic approach, is now part of the correlation and updating process. The approach provides an important amount of additional information on the correlation and validation process and allows assessing the robustness of the validation.

The correlation is performed between meta-models, the computational one generated via Monte Carlo simulation, and the experimental one, generated via stochastic modal identification (a meta-model is a collection of samples or observations obtained for a number of input and output variables). The updating process is, potentially, much more powerful in terms of correlation and error localization performances, since is not restricted to the short-sighted and linearized world based on traditional sensitivity approaches but uses Monte Carlo design improvement techniques. On the other hand the proposed approach is more complex and much more computationally expensive than deterministic methods and the characterization of structural uncertainties necessary to implement the approach is sometimes difficult and time-consuming.

A dedicated software tool has been developed. The EDIS software [2] runs in conjunction with the ST-ORMRstochastic simulation and model improvement software code [3] as well as the MSC/NASTRANRfinite element code. The EDIS software is written entirely using MATLABRand can therefore run on any MATLAB-supported platform. STORM is the software code used to perform all stochastic simulation, model improvement and statistical post processing. The current version of STORM (V 2.2.2) is used in the EDIS project with no particular modifications or enhancements. Concerning NASTRAN, real mode solver sequence 103 is used. The objective function value (representing the distance between the current shot and the target during the Stochastic Design Improvement (SDI) process in ST-ORM) is calculated using a weighted combination of distances between natural frequencies, mode shapes, effective transmissibilities and effective masses.

To illustrate the stochastic correlation and validation process, the academic model elaborated within the project is considered. The academic model is a simple bending beam represented by a series of 8 identical rigid beam elements with uniformly distributed mass connected by hinges with rotational stiffnesses.

The results provided by the simple academic case are rather promising but do not allow drawing any definitive conclusion on the worthiness of the stochastic approach. The application of the approach to a real-life spacecraft finite element model is in progress within the EDIS project.

1

Calvi A., Garcia de Paredes S., Roy N., Lefevre Y.M., "On the Development of a Stochastic Approach for the Validation of Spacecraft Structural Dynamic Models", Proc. European Conference on Spacecraft Structures, Materials and Mechanical Testing, Toulouse, France, 2002.

2

EDIS. "A Stochastic Software Tool for Modal Identification and Model Validation". User's Manual, ESA Contract 16022/02/NL/CK, February 2004.

3

ST-ORM. "A Meta-computing system for Stochastic Optimisation and Robustness Management". User's Manual, September 2002.

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