Parameter identification of a linear wave equation from experimental boundary data

Christophe Roman (1, 2) , Francesco Ferrante (3) , Christophe Prieur (3)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 PECASE - Pronostic-Diagnostic Et CommAnde : Santé et Energie
3 GIPSA-INFINITY - GIPSA - Infinite Dimensional Dynamics

Parameter identification of a drill-string is studied. The system is modeled as a hyperbolic system with dynamical boundary conditions. The considered model is a wave equation with spatial dependent elasticity and viscous damping terms. The identification problem is recast as an optimization problem over an infinite dimensional space. The developped approach ensures that the estimates of the parameters lie in a given set. A gradient descent-based algorithm is proposed to generate parameters estimates based on experimental data. A thorough comparative study with more classical algorithms is presented.

Keywords: Index Terms-Parameter identification; Lagrange multiplier; inverse problems; adjoint method; wave equation; infinite dimensional systems

Domains: Automatic Control Engineering

Christophe Roman, Francesco Ferrante, Christophe Prieur. Parameter identification of a linear wave equation from experimental boundary data. IEEE Transactions on Control Systems Technology, 2021, 29 (5), pp.2166-2179. ⟨10.1109/TCST.2020.3032714⟩. ⟨hal-02985612v1⟩