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Structural Engineering and Mechanics
  Volume 22, Number 4, March10 2006 , pages 401-418

An optimal regularization for structural parameter
estimation from modal response
Thanyawat Pothisiri

    Solutions to the problems of structural parameter estimation from modal response using least-squares minimization of force or displacement residuals are generally sensitive to noise in the response measurements. The sensitivity of the parameter estimates is governed by the physical characteristics of the structure and certain features of the noisy measurements. It has been shown that the regularization method can be used to reduce effects of the measurement noise on the estimation error through adding a regularization function to the parameter estimation objective function. In this paper, we adopt the regularization function as the Euclidean norm of the difference between the values of the currently estimated parameters and the a priori parameter estimates. The effect of the regularization function on the outcome of parameter estimation is determined by a regularization factor. Based on a singular value decomposition of the sensitivity matrix of the structural response, it is shown that the optimal regularization factor is obtained by using the maximum singular value of the sensitivity matrix. This selection exhibits the condition where the effect of the a priori estimates on the solutions to the parameter estimation problem is minimal. The performance of the proposed algorithm is investigated in comparison with certain algorithms selected from the literature by using a numerical example.
Key Words
    parameter estimation; measurement noise; estimation errors; regularization; singular value decomposition.
Department of Civil Engineering, Chulalongkorn University, Phayathai Road, Pathumwan, Bangkok 10330, Thailand

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