An Investigation on the Use of 1Norm Error Function for Inverse Problem based on the EEE(Equation Error Estimator) Se Hyeok Lee
ABSTRACT This paper presents a new class of 1Norm Error Function and Regularization Function for EEE(Equation Error Estimation) Method to analysis in real time. 1Norm Error Function is investigated to overcome the shifting problem (said Bias) from the exact solution for the identification of discontinuous system parameter. Bias is occurred when the measured displacements have error and 2Norm is used. Because of 2Norm character, the error in measured displacement is averaged after squared. So, the error can¡¯t be vanished and the solution is shifted from the exact solution. To overcome this problem said Bias, this paper chooses 1Norm for EEE Method. As a result, the Bias is vanished but the solution still is noisepolluted. Therefore, additionally regularization function is needed. There are two existing regularization methods to alleviate the illposedness of solution. First, 2Norm Regularization can¡¯t be applied to 1Norm Error function because there is difference of norm character. Secondly, 1Norm Regularization have same character with 1Norm Error Function and can be applied to 1Norm error function unlike 2Norm Regularization. However, the solution in this case is not exact solution all the time. Because the function space is different between 1Norm Error Function and existing 1Norm Regularization function. 1Norm Error Function exists in L1, otherwise existing 1Norm Regularization exist in L2. So this paper presents a new 1Norm Regularization in L1 like 1Norm Error Function. The validity of the proposed method is demonstrated through the identification of an inclusion in a square steal plate.
Key Word SI(System Identification), EEE(Equation Error Estimation), Bias, 1Norm Error Function, 1Norm Regularization in L1
