State and parameter estimation in 1-D hyperbolic PDEs based on an adjoint method

详细信息    查看全文

• 作者：Van Tri Nguyen^a ; ^{van-tri.nguyen@gipsa-lab.grenoble-inp.fr" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Didier Georges^a ; ^{didier.georges@gipsa-lab.grenoble-inp.fr" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Gildas Besanç ; on^a ; ^b ; ^{gildas.besancon@gipsa-lab.grenoble-inp.fr" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：State estimation ; Parameter estimation ; Hyperbolic system ; Adjoint method ; Inverse problem ; Saint-Venant model ; Lighthill&ndash ; Whitham&ndash ; Richards model
• 刊名：Automatica
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：67
• 期：Complete
• 页码：185-191
• 全文大小：576 K

文摘

An optimal estimation method for state and distributed parameters in 1-D hyperbolic system based on adjoint method is proposed in this paper. A general form of the partial differential equations governing the dynamics of system is first introduced. In this equation, the initial condition or state variable as well as some empirical parameters are supposed to be unknown and need to be estimated. The Lagrangian multiplier method is used to connect the dynamics of the system and the cost function defined as the least square error between the simulation values and the measurements. The adjoint state method is applied to the objective functional in order to get the adjoint system and the gradients with respect to parameters and initial state. The objective functional is minimized by Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. Due to the non-linearity of both direct and adjoint system, the nonlinear explicit Lax–Wendroff scheme is used to solve them numerically. The presented optimal estimation approach is validated by two illustrative examples, the first one about state and parameter estimation in a traffic flow, and the second one in an overland flow system.