非线性和线性流变数据的同时拟合：防止错误的确定性
On simultaneous fitting of nonlinear and linear rheology data: Preventing a false sense of certainty
摘要：
不确定性通过计算传播，下至分子尺度以推断微观结构特征，上至宏观尺度以预测流动模拟。在这里，我们研究不确定性量化的顺序（两步）与同时（一次全部）拟合方法与线性和弱非线性流变数据。使用一个例子的组合数据集上的小振幅振荡剪切（SAOS）和中等振幅振荡剪切（MAOS）的线性缠结聚合物熔体（顺式-1，4-聚异戊二烯），我们证明了与多模式Giesekus模型的拟合参数的不确定性是如何显着低估的顺序拟合，因为忽略了模型参数的相关性。这些结果是令人惊讶的，因为弱非线性数据与线性数据只有一个渐进的步骤，但它对线性模型参数的校准有显着的影响。同样，非线性参数估计值和不确定性受到同时拟合中考虑线性数据的影响。为了比较非线性参数（Giesekus模型的迁移率参数{α_i}）的多模谱，我们基于与高频MAOS极限相关的谱的矩导出新的平均测量。光谱平均值也对顺序拟合与同时拟合敏感。我们的研究结果揭示了使用同时拟合诚实的不确定性量化的重要性，即使是弱非线性数据。
英文摘要：
Uncertainty propagates through calculations, down to molecular scales to infer microstructural features, and up to macroscopic scales with predictive flow simulations. Here we study uncertainty quantification for sequential (two-step) versus simultaneous (all at once) fitting methods with linear and weakly-nonlinear rheological data. Using an example of a combined dataset on small-amplitude oscillatory shear (SAOS) and medium-amplitude oscillatory shear (MAOS) for a linear entangled polymer melt (cis-1,4-polyisoprene), we demonstrate with a multi-mode Giesekus model how the fit parameter uncertainties are significantly under-estimated with the sequential fit because of the neglect of model parameter correlations. These results are surprising because weakly-nonlinear data is only an asymptotic step away from the linear data, yet it has significant impact on calibrating the linear model parameters. Similarly, the nonlinear parameter estimates and uncertainties are impacted by considering the linear data in a simultaneous fit. To compare multi-mode spectra of nonlinear parameters (mobility parameters {α_i} from the Giesekus model), we derive new average measures based on moments of the spectra related to the high-frequency MAOS limit. The spectral averages are also sensitive to sequential versus simultaneous fitting. Our results reveal the importance of using simultaneous fitting for honest uncertainty quantification, even with weakly-nonlinear data.
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