Adaptive diagnosis of faults in elastic structures by static displacement measurement: The method of selective sensitivity

Abstract

This paper develops the concept of selective sensitivity for detection of stiffness abnormalities in beams by static displacement measurement. It is demonstrated analytically for a discrete elastic model of a beam that a system of applied forces can always be chosen to produce maximum deflection sensitivity to change in selected stiffness constants, while at the same time causing zero sensitivity to changes of all other spring constants. The concept of selective sensitivity is then applied to adaptive diagnosis of the stiffness abnormality. The diagnosis algorithm is based on the idea of hierarchical halving, whereby a sequence of forces is applied in such a way as to efficiently home in on the failure location. The adaptive branching decisions of the hierarchical halving algorithm are based on a χ 2 test which accounts for uncertainty in the deflection measurements. The success rate in simulated application to a cantilever is generally high, except for small failures or for failures near the free end of the beam.