On a strategy for the reduction of the lack of knowledge (LOK) in model validation

Abstract

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.

Validation of structural dynamics models containing uncertainties

“…This approach, which is an extension of works done in the deterministic framework, follows the guiding principle that part of the model is used as the reference. After updating, there remains a residual error which characterizes a certain lack of knowledge of the model whose evaluation is the focus of a new theory which is under development [42].…”

Computational Structural Mechanics

“…Obviously, such a model does not yield a "perfect" prediction of the response. There are numerous sources of uncertainties and modeling errors, which we describe using the concept of Lack Of Knowledge [2,3,18,19] . The structure being studied is defined as an assembly of substructures E in which the connections can be viewed as special substructures.…”

Uncertainties in structural dynamics: overview and comparative analysis of methods

“…Let Ω be a family of real and quasi-identical structures, each being modeled as an assembly of several substructures E. To each substructure E two positive scalar random variables m − E (θ) and m + E (θ) are associated, called basic LOKs and defined in [20,49] as follows:…”