Structural stiffness identification using maximum likelihood estimate method

Various structural parameter (mass, damping and stiffness) identification techniques are under active development. This paper is intended to develop a structural parameter estimation algorithm in the time-domain based on the maximum likelihood estimation (MLE), which manipulates directly on the physical parameters of the structural systems. A finite element model of the structural system is transformed into a state space matrix format. The solution of the dynamic matrix equation can be readily obtained numerically by matrix exponential method that eliminates the awesome complex eigenproblem. The maximum likelihood estimate algorithm and corresponding iteration process are derived to achieve the best matching between the model responses and measured responses. Assume that the mass and damping properties of the structure are known a priori by any means and keep unchanged, numerical example has shown that the proposed algorithm gives the ideal estimation of the stiffness parameters. The iteration process converges very fast due to some optimum properties of the maximum likelihood estimate.