项目名称: 基于分数阶微积分理论的粘弹性本构模型参数反演及应用
项目编号: No.11472161
项目类型: 面上项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 蒋晓芸
作者单位: 山东大学
项目金额: 85万元
中文摘要: 分数阶粘弹性本构模型具有明确的应用背景,其模型的建立及正问题求解是近年来国际上学术界的一个热点问题,已有许多成熟的结果,然而,对于分数阶粘弹性本构模型参数反演问题的研究才处于起步阶段,本项目的研究是借助分数阶微积分、流变学等理论发展分数阶粘弹性本构模型正逆问题的数值模拟技术。拟发展基于分数阶导数离散格式的修正的Levenberg-Marquardt最小二乘反演算法并研究分数阶粘弹性液体由于平板振荡引起的流动的参数反演问题;发展利用贝叶斯方法进行分数阶粘弹性模型参数估计的多宗量反演方法,并验证计算结果的合理性;结合相应实验数据,通过反演方法来确定粘弹性本构模型中未知的分数阶导数阶数和其它本构参数,实现对分数阶粘弹性模型的本构参数的识别并讨论不同参数对于粘弹性流体复杂流动特性的影响,从而建立起一套新的求解分数阶粘弹性本构模型反问题的方法体系。
中文关键词: 粘弹性流体;分数阶微积分;参数反演;数值模拟;分数阶本构模型
英文摘要: The fractional viscoelastic constitutive modes have tremendous applications in science and technology. Modelling and solving for direct problem of the fractional viscoelastic constitutive mode have received great attention recently. However, identification of parameters on fractional viscoelastic constitutive model is still in early stages. This research plan devotes to developing numerical simulation technologies for direct and inverse problems of complex viscoelastic constitutive modes based on the fractional calculus theory and theory of rheology. It is planned to develop the inversion algorithm of Levenberg-Marquardt least-squares using discrete format of fractional derivative and to study the parametric inversion problem of generalized viscoelastic liquid flow caused by oscillatory plate.Based on Bayesian theory, a multi-variables inverse method to estimate the parameters of fractional viscoelastic model will be designed. The validity of constitutive parameters of fractional viscoelastic model will be achieved and the influence of different parameters on the viscoelastic fluid flow characteristics will be discussed in order to establish a new methodology for solving inverse problems of fractional viscoelastic model.
英文关键词: viscoelatic fluid;fractionalcalculus;parametric inversion;numerical simulation;fractional constitutive model