By Dermot P B McGovern; et al
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As an example of a discriminant let us consider a truss. 1:37) representing the undamaged bars. 37) is adjusted to the damaged state. The adjustment factors aKi can serve as discriminants in this case, where localization is identical with designating a fault in a particular bar. 3 Symptoms of Non-linear Systems Various types of non-linearities are shown in Fig. 13. Nonlinear behaviour can result from modifications of a linearly behaving system. The symptoms discussed in the previous section can also be applied for non-linear systems.
The linear model for a plate with a crack leads to modified boundary conditions for the open crack, and these are handled by introducing additional nodes in the FE model, which means enlarging the orders of the related matrices, and therefore introducing additional DOF (modes). 1 and Fig. 7 . 1. 1. Natural frequencies [Hz] of the plate shown in Fig. 4 N 65 o a) a Fig. 7. Eigenmodes of a plate with a hole and a crack. •. Sn+l,n Sn,n+1 Sn+l,n+1 U(n+l)n U(n+l)n+1 o 34 b c Fig. 7. (continued) 2.
We shall return to these equations for fault detection and localization in Sect. 6. Subsystem modelling. Subsystem modelling is useful for various purposes: to reduce the orders of the models to be analyzed, to control the degree of coarseness of the model parametrization, to investigate submodel (component) sensitivity to parameter modifications, and to localize faults in the corresponding submodels. 37) i=1 where the vector aK contains the real dimensionless design parameters aKi. 38) 28 2. Review of Tools and Concepts of Diagnosis with respect to variations of the real factors aKi.