Influence of the error description on model-based design of experiments. (15th August 2019) - Reichert, I.; Olney, P.; Lahmer, T.
Highlights: The type of measurement error has an influence on the optimal experimental design. Influence of the noise level is existing, but smaller than the one of the errortype. Fisher Information Matrix only accounts for random errors. Mean-squared error approach considers random and systematic errors. Different sensor setups are found to be optimal for different DoE methods. Abstract: Measurement noise and errors are inherent to all experimental measurements, thus it is necessary to consider them while optimally designing any experiment. The scope of this paper is to determine the influence of various error descriptions in the measurement data considering different approaches for the model-based design of experiments. The considered types of error are: random and systematic. The random error is assumed to be normally distributed wita finite variance. The systematic error is represented in two ways: either as a relative factor to the "exact" data or as a drift related to measurement time. Combinations of these types of error form the used error descriptions. Basically, two methods of finding the optimal experimental design are used: one is based on the Fisher Information Matrix (FIM) and the other one is using mean-squared reconstruction errors (MSE). Based on an application example which is a cantilever beam, a slender civil structure, consisting of two different materials, implemented by the Young's modulus, the optimal designs for three sensor locations are calculated for 28 different error combinations which differ in error type and noise level. The results for the best sensor setups are displayed and discussed depending on the method used for the design of the experiment and the error description. The evaluation of the two approaches shows that the FIM does not take systematic errors into account and also it is not depending on the random noise level, whereas the MSE approach is considering systematic errors, but to its disadvantage, it is computationally much more costly.