Homotopy based stochastic finite element model updating with correlated static measurement data

Abstract

This paper focuses on studying the impaction of the correlation between the measurement data on structural model updating. A new homotopy based stochastic finite element model updating frame is constructed to cope with the correlated static measurement data. To judge whether considering the correlation of the measurement data, the sensitivity analysis of structural responses about structural parameters is implemented firstly. Then the discrete Karhunen–Loeve expansion is utilized to transform the correlated measurement data into a linear combination of multiple independent random variables. Furthermore, a novel stochastic model updating equation about the correlated static measurement data is set up, and is solved by the homotopy stochastic finite element method. It is significant to check the consistence of the correlation coefficients of the responses of the updated model with those of the measured data when the correlation actually exists. In this case, the proposed approach can effectively update the structural model.