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

机译:自优化逆分析方法在逆参数辨识中存在全局最小值

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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. (C) 2018 Elsevier Ltd. All rights reserved.
机译:本文基于偏微分方程的弱解理论,给出了自最优(自优化逆分析方法)成本函数全局最小值存在的数学证明。 Self-Optim提供单个全局最小值,而不是对应于反问题的不现实解决方案而具有多个全局最小值。此外,提出了反问题的离散逼近和成本函数的计算方法,并对数值证明进行了验证。本文为将自优化方法应用于力学中的各种反问题提供了严格的数学基础。 (C)2018 Elsevier Ltd.保留所有权利。

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