ABSTRACT
ABSTRACT: The more and more common task of bridge monitoring demands a mathematically based method for the symbiosis of all the measured data in view of the structural system.
The aim of the newly developed method was the combination of all measured data in one physical (mechanical) system which is based on the structural system of the bridge. Of great importance was the easy understanding of the method, and this was the prior reason for starting from the Finite Element Method. The different steps of solving the problem are:
– mechanical modelling (e.g. beam bending theory for simplicity) – discretization (finite elements) – mathematical modelling by applying Hermitian Polynomials (of third order) as shape functions – the Gaussian least squares method as related variational principle which allow to add the
constraints from the structural system as side equations with Lagrangian Multipliers – of basic importance is the separation of the sum of least squares of the different physical (mechan-
ical) quantities because they have no common metric. Only after the regression formulation for the different quantities, the coupling with respect to the mechanical system can be performed.
