Determination of an optimal regularization factor in system identification with Tikhonov regularization for linear elastic continua. (Q2761973)

The paper illustrates that the system identification algorithm with a regularization leads to a solution of generalized average between a priori estimates and a posteriori solution. The a priori estimates represent known baseline properties of system parameters, and the a posteriori solution denotes the solution obtained by using the given measured data. A new idea of the geometric mean scheme (GMS) is proposed to select optimal regularization factors in nonlinear inverse problems for linear elastic continua. In the GMS, the optimal regularization factor is defined as the geometric mean between the maximum and minimum singular values for balancing maximum and minimum effects of the a priori estimates and the a posteriori solution in a generalized average sense. Two examples are presented to demonstrate the effectiveness of the GMS.