Keywords: cross-entropy, stiffness estimation, damage detection, structural health monitoring, finite element modelling.

Variations in Young's modulus due to inconsistencies in the structural material or as a result of cracking, ageing, loading or aggressive environmental conditions, may lead to significant differences in the stiffness distribution not accounted for during design. When assessing an existing structure, it is essential to quantify these discrepancies with respect to the original design, and the current loading conditions, to ensure the structure remains safe. This paper examines the use of the cross-entropy (CE) method [1] to estimate the structural parameters of a plate structure, given data from a simulated non-destructive static loading test.

The CE method presented here develops on previous work which applied cross-entropy to damage detection in one-dimensional, simply-supported beam structures, with four degrees of freedom per element [2]. The current work applies the cross-entropy method to two-dimensional plate models, with sixteen degrees of freedom per element. CE for stiffness estimation is demonstrated for a plate-type structure, but the same procedure can be extended to other structural forms. Damage is simulated by local reductions in the longitudinal Young's modulus. The method systematically searches the solution space of possible stiffness combinations, to give a plate with deflection properties close to that of the plate under investigation. If the resulting model shows irregularities in the structure, engineering judgement may be used to decide whether the structure is in need of further investigation and/or remedial work. The proposed method could be adapted to detect irregularities in other structural parameters, such as transverse stiffness, or loss in member thickness. Various parameters of the cross-entropy method are altered to investigate the sensitivity of the system to different locations and severity of damages. The effect of varying the number of measurement points on the plate is also discussed.

The cross-entropy method is shown to be able of locating and estimating damage severity in plate structures. The system is most effective with all deflection data available to it. Even as the number of data points available to the system is reduced, or the data is corrupted with noise, the algorithm still gives a reasonable indication of the damage location. A system of pre-simulation has been applied to improve the efficiency of the algorithm. This pre-simulation has been successfully carried out with fewer plate elements than the plate mesh used in the final algorithm. This ability to operate with a coarser mesh may be useful in applying the CE method to more complex systems.

1

R.Y. Rubinstein, D.P. Kroese, "The Cross-Entropy Method", Springer, New York, United States, 2004.

2

B.J. Walsh, A. González, "Assessment of the Condition of a Beam Using a Static Loading Test", Key Engineering Materials, 413-414, 269-276, 2009. doi:10.4028/www.scientific.net/KEM.413-414.269

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