**Determination of an Optimal Regularization Factor**

**
in System Identification with Tikhonov Regularization for Linear Elastic Continua**

**H.W. Park, S. Shin, and H.S. Lee**

**ABSTRACT**

This paper presents a geometric mean scheme (GMS) to determine an optimal regularization factor for Tikhonov regularization technique in the system identification problems of linear elastic continua. The characteristics of nonlinear inverse problems and the role of the regu-larization are investigated by the singular value decomposition of a sensitivity matrix of re-sponses. It is shown that the regularization results in a solution of a generalized average between the a priori estimates and the a posteriori solution. Based on this observation, the optimal regularization factor is defined as the geometric mean between the maximum singular value and the minimum singular value of the sensitivity matrix of responses. The validity of the GMS is demonstrated through two numerical examples with measurement errors and modeling errors.

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