A New Approach to the Dynamic Parameter Estimation of a Viscoelastic System

Abstract

This work involves the study of newtonian transitory flow regimes in a rigid tube that has been extended to include an elastic enclosure. Three different techniques have been applied and compared. The first approach is the classical one, in which the calculations, which are based on the Laplace transform, enable direct integration of the Navier-Stokes equations and make it possible to determine longitudinal velocity and fluid flow. The solution, however, involves real or complex parameters that are solutions to a nonlinear equation involving Bessel functions. Where the flow regime in the tube is oscillating, we find a natural frequency of oscillation there, and a flow damping ratio. A comparison will be made with the other two methods partly on the basis of these two parameters. The second is an approach based on time series analysis of flow in the tube, and consists in applying auto-regressive moving-average (ARMA) models to the fluid flow in order to identify the natural frequency and the damping coefficient of the flow. The flow series analyzed by this method come from two sources: 1. The flow series obtained from the theoretical solution using the first method; these flow series were artificially contaminated with random noise to simulate real situations. 2. The flow series obtained experimentally by direct measurement and integration of the velocity profile in the tube. Finally, with the third technique, the experimental method, we have succeeded in validating the first two approaches. The approach based on the analysis of the time series through the use of ARMA models appears to perform best and is the simplest to use.