On a Theory of the Quantification of the Lack of Knowledge (LOK) in Structural Computation

Still today, some of the phenomena which occur in structural dynamics cannot be described, even using a properly updated model: some uncertainties remain. This paper presents the basic concepts of a new theory which uses the concept of Lack of Knowledge (LOK) to model the uncertainty using two bounds of the energy in each substructure. The inverse problem, which consists in determining the Lack of Knowledge for each substructure from test results on the whole structure, has been studied on a simple example. NOMENCLATURE Ω A real structure from a family of similar ones E A substructure of Ω KE Stiffness matrix of E {φi,ωi} Eigenmode/eigenfrequency (rd/s) pair φki Value at the kth DOF of φi eE Strain energy of E (mE ,m − E ) Basic Lack of Knowledge for E (mE ,m − E ) Bounds of the basic Lack of Knowledge for E F ( mE ,m − E ) Cost function for the identification process ω2 low iexp 99%-lower bound of the experimental ω 2 i ω iexp 99%-upper bound of the experimental ω 2 i ω2 low i ( mE ,m − E ) 99%-lower bound of the LOK-modelled ωi ω i ( mE ,m − E ) 99%-upper bound of the LOK-modelled ωi φlow kiexp 99%-lower bound of the experimental φki φ kiexp 99%-upper bound of the experimental φki φlow ki ( mE ,m − E ) 99%-lower bound of the LOK-modelled φki φ ki ( mE ,m − E ) 99%-upper bound of the LOK-modelled φki The overlined quantities are related to the theoretical, deterministic model.