This paper presents a methodology for the inverse identification of linearly viscoelastic material parameters in the context of steady-state dynamics using interior data. The inverse problem of viscoelasticity imaging is solved by minimizing a modified error in constitutive equation (MECE) functional, subject to the conservation of linear momentum. The treatment is applicable to configurations where boundary conditions may be partially or completely underspecified. The MECE functional measures the discrepancy in the constitutive equations that connect kinematically admissible strains and dynamically admissible stresses, and also incorporates the measurement data in a quadratic penalty term. Regularization of the problem is achieved through a penalty parameter in combination with the discrepancy principle due to Morozov. Numerical results demonstrate the robust performance of the method in situations where the available measurement data is incomplete and corrupted by noise of varying levels.

中文翻译：

---

基于内部数据的频域粘弹性成像本构方程方法的修正误差

本文提出了一种在稳态动力学背景下使用内部数据逆识别线性粘弹性材料参数的方法。粘弹性成像的逆问题通过最小化本构方程 (MECE) 函数中的修正误差来解决，受线性动量守恒的约束。该处理适用于可能部分或完全未指定边界条件的配置。MECE 函数测量连接运动学容许应变和动态容许应力的本构方程中的差异，并将测量数据合并到二次惩罚项中。问题的正则化是通过惩罚参数结合 Morozov 的差异原则来实现的。