On the existence of a global minimum in inverse parameters identification by Self-Optimizing inverse analysis method

In this paper, a mathematical proof of the existence of a global minimum of Self-Optim (Self-Optimizing Inverse Analysis Method) cost functional is presented based upon weak-solution theory of partial differential equations. The Self-Optim provides single global minimum rather than having multiple g...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2019-02, Vol.77 (3), p.803-814
Main Authors: Yun, Gun Jin, Shang, Shen
Format: Article
Language:English
Subjects:
Anisotropic linear elasticity
Inverse problems
Non-homogeneous materials
Parameter identification
Self-Optimizing inverse analysis method
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Summary:In this paper, a mathematical proof of the existence of a global minimum of Self-Optim (Self-Optimizing Inverse Analysis Method) cost functional is presented based upon weak-solution theory of partial differential equations. The Self-Optim provides single global minimum rather than having multiple global minima corresponding to unrealistic solutions of the inverse problem. Furthermore, discrete approximation of the inverse problem and computational methods for the cost functional are proposed and the proof is numerically verified. This paper provides a rigorous mathematical foundation for applications of the Self-Optim method to various inverse problems in mechanics.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2018.10.019