An Investigation on the Use of 1-Norm

    Error Function for Inverse Problem

    based on the EEE(Equation Error Estimator)

    Se Hyeok Lee

 

ABSTRACT

This paper presents a new class of 1-Norm Error Function and Regularization Function for EEE(Equation Error Estimation) Method to analysis in real time. 1-Norm 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 2-Norm is used. Because of 2-Norm character, the error in measured displacement is averaged after squared. So, the error caní»t be vanished and the solution is shifted from the exact solution. To overcome this problem said Bias, this paper chooses 1-Norm for EEE Method. As a result, the Bias is vanished but the solution still is noise-polluted. Therefore, additionally regularization function is needed. There are two existing regularization methods to alleviate the ill-posedness of solution. First, 2-Norm Regularization caní»t be applied to 1-Norm Error function because there is differ-ence of norm character. Secondly, 1-Norm Regularization have same character with 1-Norm Error Function and can be applied to 1-Norm error function unlike 2-Norm Regularization. However, the solution in this case is not exact solution all the time. Because the function space is different between 1-Norm Error Function and exist-ing 1-Norm Regularization function. 1-Norm Error Function exists in L1, other-wise existing 1-Norm Regularization exist in L2. So this paper presents a new 1-Norm Regularization in L1 like 1-Norm Error Function. The validity of the pro-posed method is demonstrated through the identification of an inclusion in a square steal plate.

 

Key Word

SI(System Identification), EEE(Equation Error Estimation), Bias, 1-Norm Error Function, 1-Norm Regularization in L1

 

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