Optimal parameter estimation in a landslide motion model using the adjoint method

This work proposes an optimal approach for parameter estimation in a landslide motion, based on the so-called adjoint method. The system is described by an extended sliding-consolidation model composed of an ordinary differential equation and 1D parabolic partial differential equation that represents landslide motion and pore pressure evolution respectively. The key feature of this model is pore pressure feedback, which regulates landslide motion and leads to coupling between both differential equations. Parameters to be estimated include the friction and dilatancy angle of the material. The objective functional for the optimal estimation is composed of: i) a cost function defined as the least square error between measurements and related simulated values, and ii) a product of Lagrange variables and system dynamics. A variational approach is applied to get the gradients of the cost functional with respect to parameters to be estimated and adjoint model. The cost functional is optimized, employing the steepest descent method to estimate parameters. Finally, the presented optimal estimation method is validated on a simulated test case.