Identification of model uncertainty via optimal design of experiments applied to a mechanical press

Abstract

In engineering applications almost all processes are described with the help of models. Especially forming machines heavily rely on mathematical models for control and condition monitoring. Inaccuracies during the modeling, manufacturing and assembly of these machines induce model uncertainty which impairs the controller’s performance. In this paper we propose an approach to identify model uncertainty using parameter identification, optimal design of experiments and hypothesis testing. The experimental setup is characterized by optimal sensor positions such that specific model parameters can be determined with minimal variance. This allows for the computation of confidence regions in which the real parameters or the parameter estimates from different test sets have to lie. We claim that inconsistencies in the estimated parameter values, considering their approximated confidence ellipsoids as well, cannot be explained by data uncertainty but are indicators of model uncertainty. The proposed method is demonstrated using a component of the 3D Servo Press, a multi-technology forming machine that combines spindles with eccentric servo drives.

Detection of Model Uncertainty in the Dynamic Linear-Elastic Model of Vibrations in a Truss

“…In this paper we showed that our algorithm to detect model uncertainty, which was first presented in [12], is applicable to dynamic models. We efficiently solved the OED problem with time-dependent PDE-constraints using modified BFGSupdates and adjoint methods within an SQP solver scheme.…”

“…We adopt the algorithm presented in [12] and describe the main differences when applied to a time-variant model M of a dynamic process. In general, we presuppose that a valid model should reproduce all measurements obtained with all admissible inputs at all sensor locations with the same set of parameters.…”

“…For the validation itself, we perform a classical hypothesis test from line 08 onward as documented in [12]. The threshold TOL is identical to the error of the first kind.…”

“…Due to our incomplete knowledge of the internal relations between model parameters, state variables and the time domain, the user frequently encounters model uncertainty [20]. In [12] we developed an algorithm to identify this model uncertainty using parameter estimation, optimal experimental design and classical hypothesis testing. It is the aim of this paper to extend this approach to dynamic models.…”

“…It is the aim of this paper to extend this approach to dynamic models. In the following, we adopt the framework described in [12] and extend it to meet mathematical models which are comprised of time-variant partial differential equations (PDE).…”