A COMPARISON OF THE TIME-DOMAIN AND LAPLACE-DOMAIN LEAST SQUARES PARAMETER ESTIMATION FOR MODELING PROPERTIES OF VISCOELASTIC MATERIALS

Based on a parameterized Volterra integral function, a parameterized model was previously stated for describing certain time-dependent mechanical properties of viscoelastic materials. Model parameters are material-specific and need to be optimally estimated for each material. To this end, two parameter estimation methodologies are compared. The first parameter estimation problem is formulated as a least squares problem (LSP) based on fitting the time domain parameterized model to time domain experimental data. This approach encounters computational difficulties due to the analytical complexity of the underlying model. To address these difficulties, prior works formulated the alternate parameter estimation problem by applying the Laplace transform to the Volterra integral model and fitting this to regressed experimental data that is similarly transformed. Thus, a Laplace domain least squares problem (LDLSP) is stated. The effectiveness of solving the LDLSP for computing optimal parameter estimates has been shown empirically in prior works. This work develops a mathematical foundation by which to compare the use of the LSP and the LDLSP. Each minimization problem is viewed as the minimization of distance between two functions from the same underlying space C[a,b] of functions f: [a, b] ‚ R. The notion of distance on the underlying space is different for each problem, and these two definitions of distance are induced from two corresponding norms. The two norms are shown to be non-equivalent, and the implications of this are discussed in terms of using one minimization problem as an approximation to the other. An example is provided to show how the mathematical insight also motivates an improved application of the LDLSP.

• Dandurand Brian
• Irina Viktorova
• Sof'ya Alekseeva

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