We apply the adjoint-weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems.

中文翻译：

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在不可压缩平面应变弹性反问题的直接求解中容纳噪声数据的方法

我们将伴随加权方程法 (AWE) 应用于不可压缩平面应变弹性的逆问题的直接解。我们表明，基于未经处理的噪声位移，剪切模量的重建可能非常差。在处理具有不连续系数的问题时，我们将这种糟糕的性能与弱形式的矫顽力损失联系起来。我们证明，通过平滑位移并将正则化项附加到 AWE 公式，可以实现重建的显着改进。通过这些改进，AWE 方法作为直接求解方法的优势可以扩展到更广泛的问题。