Parameter Identification of a Linear Wave Equation From Experimental Boundary Data

Abstract

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.

A Filtering-Based Stochastic Gradient Estimation Method for Multivariate Pseudo-Linear Systems Using the Partial Coupling Concept

“…As is well known, the estimate θi−1 (k) of the (i − 1)th subsystem at time k is closer to the true value θ than the estimate θi (k − 1) of the ith subsystem at time k − 1. Accordingly, in Algorithm ( 36)- (39), substitute θi−1 (k) for θi (k − 1) on the right-hand side of Equation ( 36), and substitute θm (k − 1) for θ1 (k − 1) in Equation ( 36) when i = 1. To conclude, the filtering-based multivariate partially coupled generalized extended stochastic gradient (F-M-PC-GESG) algorithm is as follows.…”

“…Zhang and Ding proposed an optimal adaptive filtering algorithm for filter design by combining the data filtering approach with the gradient method [38]. Roman et al derived a gradient descent method for identifying parameters of a linear wave equation from experimental boundary data [39]. Chen et al identified parameters of time-delay rational state-space systems and presented two improved gradient descent algorithms by utilizing an intelligent search method and a momentum method, which had faster convergence speeds and higher computational efficiencies [40].…”

PI output feedback for the wave PDE with second order dynamical boundary conditions

“…An identification procedure has been proposed in [14] for the system (1) without source terms on experimental data. This means the considered problem can be associated with a experimental setup.…”