Identification of viscoelastic materials and continuous-time stochastic systems

Abstract: Two system identification problems, identification of viscoelastic material properties and identification of continuous-time stochastic systems, are considered in the thesis.The viscoelastic material properties are characterised by the frequency-dependent complex modulus. In the thesis, the complex moduli for polypropylene and polymethyl methacrylate are determined by using measured strains from wave propagation experiments with axially impacted bar specimens. In a non-parametric identification technique with frequency domain data, measurements from at least three sections of the bar are needed. By increasing the number of sections and by avoiding certain sensor locations, the existing results are substantially improved. A parametric model is then fitted to the result of the non-parametric technique. Approximate expressions for the covariance matrices of the non-parametric and parametric approaches are derived. The validity of the expressions is confirmed by both numerical and real data. Two parametric model fitting techniques using time domain and frequency domain data, respectively, are also considered. Their advantages and disadvantages are discussed and a suitable model structure is found.The problem of estimating the parameters in continuous-time AR and ARXprocesses from discrete-time data is considered. A solution based on replacing the differentiation operator with a discrete-time approximation and forming a linear regression model is applied. The least squares method and the instrumental variables method must be used with some care to obtain parameter estimates of good quality. The bias for the estimated AR parameters is studied explicitly and expressions for the covariance matrices of the estimated AR and ARX parameters are derived.