Model updating using multivalued Frequency Response Curves (FRCs) is an important approach to construct a strongly nonlinear model. Residues between the predicted and measured FRCs are usually computed for updating, while the updating precision may be impacted by the measurement noise at local DOFs. In this paper, based on multivalued Global Shape Curve Criterion (GSCC) and Global Amplitude Curve Criterion (GACC), a novel nonlinear model updating method is proposed, to utilize global correlations to update complex nonlinear models. Through arclength-based separation, multivalued GSCCs/GACCs are quantified between multivalued FRCs obtained from prediction and measurement. Afterwards, a correlation-map is established to exclude false global correlation characteristics within multivalued correlations. Analytical sensitivities of the retained true global correlations to nonlinear parameters are derived and finally model updating is conducted. A simulation study is performed on a numerical nonlinear model. Updating successfully handles complex multivalued FRCs with up to 8 bifurcations. The proposed updating further indirectly identifies a strong magnet nonlinearity of a real beam test rig, through multivalued responses measured at Mode 3. The updated results show the validity and superiority of the proposed method.

中文翻译：

---

使用多值全局相关分析对强非线性动态系统进行模型更新

使用多值频率响应曲线（FRC）进行模型更新是构建强非线性模型的重要方法。通常计算预测和测量的 FRC 之间的残差进行更新，而更新精度可能会受到局部自由度测量噪声的影响。本文基于多值全局形状曲线准则（GSCC）和全局振幅曲线准则（GACC），提出了一种新颖的非线性模型更新方法，利用全局相关性来更新复杂的非线性模型。通过基于弧长的分离，在从预测和测量获得的多值 FRC 之间对多值 GSCC/GACC 进行量化。然后，建立相关图以排除多值相关内的错误全局相关特征。导出保留的真实全局相关性对非线性参数的分析灵敏度，并最终进行模型更新。对数值非线性模型进行了模拟研究。更新成功处理了具有多达 8 个分叉的复杂多值 FRC。所提出的更新通过在模式 3 下测量的多值响应进一步间接识别真实梁试验台的强磁体非线性。更新的结果表明了所提出方法的有效性和优越性。