Model validation in the presence of uncertain experimental data

Abstract

If you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.Abstract In this paper, we discuss the application of the constitutive relation error (CRE) to model updating and validation in the context of uncertain measurements. First, a parallel is drawn between the CRE method and a general theory for inverse problems proposed by Tarantola. Then, an extension of the classical CRE method considering uncertain measurements is proposed. It is shown that the proposed mechanics-based approach for model validation is very effective in filtering noise in the experimental data. The method is applied to an industrial structure, the SYLDA5, which is a satellite support for Ariane5. The results demonstrate the robustness of the method in actual industrial situations. IntroductionIn the age of virtual prototyping, a major requirement for the designer is to be able to rely on the numerical models built for the prediction of the mechanical behavior of structures. This crucial point is addressed by the field of model validation, whose most critical objective is to develop error measures capable of quantifying the quality of the numerical (approximate) model with respect to the (reference) measurements, i.e. to build a meaningful measure of the distance between the model and the measurements. The meaning of the measure of the distance between the approximate model and the reference model is of paramount importance for decision-making: what can be considered to be an acceptable value of this distance which makes the model valid?Model updating has been widely studied for many years, as shown by the state-of-the-art review in Mottershead and Friswell (1993). Many of the methods proposed did not attempt to provide a meaningful error measure which could be used for validation. The first model updating methods which appeared fall in the "direct method" category in which corrections of the mass and stiffness matrices of the model are sought without considering the physical meaning of the modifications. Within this category, a first set of methods is based on the search for minimum norm corrections (Baruch, 1982;Berman and Nagy, 1983). A second set of methods is closely related to control theory (Kaouk and Zimmerman, 1994;Zimmerman and Kaouk, 1992). The main drawback of...

Validation of structural dynamics models containing uncertainties

“…A complete parallel with Tarantola's theory [34] was identified recently in [38]. This option requires a choice of norm of the "statistical" type for the unreliable experimental information, a direction which, until now, has been followed only in [37].…”

“…In [37], a statistical interpretation of the norm to be applied to the measurements in direct relation to the covariance matrix was advocated as being the only possible choice if the data are scarce for a first true attempt to extend the constitutive relation error to the stochastic case. In [38], this statement was shown to be excessive and equally effective choices were presented. In this paper, we go further than these previous works, considering that the model is probabilistic, too.…”

“…It is deliberately "mechanics-oriented" and derives from works on verification and validation we did for the deterministic case based on the concept of constitutive relation error. The extension of the constitutive relation error to the stochastic case presents no serious difficulty in the particular case where the model is deterministic and the experimental data contain noise [4,38]. Through a number of examples, it was shown that the approach, which is purely mechanical, is perfectly consistent.…”

“…if the results obtained from the model match the experimental data. The extension to the modified constitutive relation error discussed here satisfies this fundamental requirement: it is based on [38]. It is still completely "mechanicsoriented" regarding the norms used.…”

Lack of knowledge in structural model validation

“…Most advanced approaches rely on the updating of deterministic dynamic parameters (stiffness, mass, damping) based on free or forced vibration tests [1,2]. Probabilistic models are investigated in [3][4][5]. The final result is an updated structural model which, evidently, cannot reproduce the behavior of the family of actual structures under consideration perfectly.…”