Plouraboué Franck, Thiam E Ibrahima, Delmotte Blaise, Climent Eric
Institut de Mécanique des Fluides de Toulouse (IMFT) , Université de Toulouse , CNRS , INPT , UPS , Allée du Pr. Camille Soula , 31400 Toulouse , France.
Proc Math Phys Eng Sci. 2017 Jan;473(2197):20160517. doi: 10.1098/rspa.2016.0517.
In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.
在本文中，我们探讨了被动或主动微游动体本构参数的可识别性。我们首先提出了一个使用珠子模型描述来刻画纤维或微游动体的通用框架。通过运用运动学约束公式来描述纤维、鞭毛或纤毛，我们从计算接触力中找到了弹性本构参数与广义速度之间的显式线性关系。这种线性公式进而使人们能够明确地处理可识别性条件并求解参数识别问题。我们表明，主动驱动力和被动参数均可独立识别，但不能同时识别。我们还使用贝叶斯方法为存在高斯噪声的类似朗之万驱动力情况下的广义弹性参数提供了无偏估计量。这些理论结果在各种配置中得到了说明，展示了所提出的直接参数识别方法的有效性。所提出估计量的收敛性通过数值方法成功进行了检验。
