Finite Element Model Updating Using Cross-Entrophy

This paper presents the potential of the cross-entropy method to surmise the properties
of a simply supported beam using as input the response of the structure to a moving
load. The beam model is discretised into a number of elementary beams with assumed
initial statistical distributions of stiffness. Then, an optimisation procedure based on
cross-entropy is employed to minimise differences between simulated measurements
and the results of the theoretical finite element beam model. The procedure consists of
generating a large sample of stiffness distributions for each elementary beam, and
selecting those fitting the measured response best. Then, the parameters of the
statistical distribution of stiffness assumed for each elementary beam (mean and
standard deviation) are updated using the stiffness values of those combinations of
elementary beams giving a best solution. It is an iterative procedure where the mean
value of each distribution tends towards the true stiffness in successive iterations. The
level of accuracy is limited by the quantity and quality of the available measurements.
Therefore, the standard deviation of the final stiffness for each beam element (once
further iterations do not lead to a reduction of the error) provides an estimation of the
reliability of the prediction. Here, the method is demonstrated for the characterisation
of the stiffness distribution of a beam from the simulated response to a moving load.
First, deflections are calculated using a finite element beam model with assumed
initial stiffness properties. There will be a record of simulated responses per
measurement point that cross-entropy will try to imitate by adjusting and improving
estimations of stiffness in successive iterations. The results show cross-entropy can be
used as a valuable tool to estimate structural parameters and it has huge scope for
applications in model calibration, bridge weigh-in-motion and monitoring.