Stochastic model updating: Part 1 - theory and simulated example

The usual model updating method may be considered to be deterministic since it uses measurements from a single test system to correct a nominal finite element model. There may however be variability in seemingly identical test structures and uncertainties in the finite element model. Variability in test structures may arise from many sources including geometric tolerances and the manufacturing process, and modelling uncertainties may result from the use of nominal material properties, ill-defined joint stiffnesses and rigid boundary conditions. In this paper the theory of stochastic model updating using a Monte-Carlo inverse procedure with multiple sets of experimental results is explained and then applied to the case of a simulated three degree-of-freedom system, which is used to fix ideas and also to illustrate some of the practical limitations of the method. In the companion paper, stochastic model updating is applied to a benchmark structure using a contact finite element model that includes common uncertainties in the modelling of the spot welds.