This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled sys...This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.展开更多
An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approx...An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.展开更多
基金supported by the Natural Science Foundation of Chongqing Municipal Education Commission(KJ1706167)and the Program for the introduction of High-Level Talents(1756006,1752003).
文摘This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.
文摘An advanced Gauss pseudospectral method(AGPM) was proposed to estimate the parameters of the continuous-time(CT)Hammerstein model.The nonlinear part of the Hammerstein system is approximated with pseudospectral approximation method.The linear part was written as a controllable canonical form to circumvent the high order time-derivative of the input and output(I/O) signals,which could multiply the measurement noise in the identification procession.Furthermore,an output error minimization was constructed for the CT Hammerstein model identification,which was then transcribed into a nonlinear programming(NLP) problem by AGPM.AGPM could converge to the true values of the CT Hammerstein model with few interpolated Legendre-Gauss(LG) nodes.Lastly,two illustrative examples were proposed to verify the accuracy and efficiency of the method.
