Optimal sensor locations for nonparametric identification of viscoelastic materials

Abstract

The problem of optimal sensor locations in nonparametric identification of viscoelastic materials is considered. Different criteria of the covariance matrix, connected to A-and D-optimal experiment design, are considered and evaluated. The results of the paper can be used to design experiments with improved accuracy of the estimates.

Parametric identification of complex modulus

“…Another reason might be that the data model is not flexible enough to accurately describe the data. The validity of the model structure in (14) was studied in [15], and there found to be adequate for this type of experiments. In the following study, the focus will therefore be on the noise properties, since the effect of bias in the modeling of the data might be expected to be small.…”

“…The number of data points were AE = 2 18 , the sampling time Ì = 0 1 s, and the variance of the measurement noise was estimated to 2 = 4 ¡ 10 11 . Additional information on the experiments can be found in [14].…”

“…In this analysis, it is assumed that the data can be perfectly modeled by the wave propagation model in (14). As a consequence…”

“…(4). In (14), È ( ) and AE ( ) are the unknown amplitudes of waves traveling in positive and negative Ü direction, respectively. As was mentioned above, these are estimated from the free end boundary condition…”

“…The data was generated from (14), with the complex modulus given by the standard linear solid model [6,17] ( ) = 2 (…”