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...

This paper deals with model validation in structural dynamics for a family of quasiidentical structures in the context of uncertain measurements. The crucial point is for the engineer to be able to quantify the quality of the model, which is probabilistic with respect to a set of measurements from which a probability density function can be extracted. Our approach is based on the "mechanical concept" of Constitutive Relation Error Estimator (CRE), which was introduced initially in order to quantify the quality of finite element analyses, then developed in the deterministic context. Our extended CRE estimator enables us to quantify the quality of a given probabilistic model and, thus, to update and validate the model. Several examples are given, including an industrial case.

This paper deals with the structural modeling of a family of similar, actual structures taking into account uncertainties and modeling errors. Only errors of the "structural stiffness" type are considered. We develop a new theory in which what we call the Lack Of Knowledge (LOK) is defined through an internal variable, whose upper and lower bounds are stochastic, associated with each substructure. Two main questions are discussed: the impact of the basic LOKs on the predicted structural response and the reduction of the basic LOKs through the use of additional information.

The quantification of the quality of a structural dynamical model remains a major issue today, and increasingly numerous methods are being devised in order to validate a model by comparison with an experimental reference. This paper presents a theory based on the concept of Lack Of Knowledge, which consists in globalizing the various sources of errors on the substructure level using a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. These intervals defined on the different substructures are then rigorously propagated through the mechanical model in order to determine intervals with stochastic bounds including a given quantity of interest defined on the whole structure. A general strategy of reduction of the lack of knowledge is then discussed and applied to academic examples as well as industrial cases.

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