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Research Group Numerical Mathematics (Partial Differential Equations)
Research Group Numerical Mathematics (Partial Differential Equations)

Model Predictive Parameter and State Estimation and Optimal Sensor Placement

General Information

sfbtr96

Keywords

  • parameter and state estimation in thermo-mechanical models
  • model predictive methods
  • optimal sensor placement

Project Description

In Phase II we developed an efficient, self-calibrating identification method to estimate the temperature state of a machine tool as well as the resulting TCP displacement, using as few temperature sensors as possible. This model-driven approach requires uncertain and, in general, time-dependent parameters such as heat exchange coefficients between machine bed and the environment to be permanently adjusted. To this end, we developed and implemented a data assimilation method to simultaneously estimate parameters and temperature states. In order to meet the requirement of using only a small number of temperature sensors while, at the same time, improving the estimation precision, we developed optimal experimental design methods. Robust optimization methods were used to obtain good reconstruction results independently of the operating point. The methods were verified using measurements obtained from the machine bed integrator. In order to reduce the computational effort, we compared several model order reduction techniques in the context of sensor placement.

It is the goal of the project in phase III to master spatially as well as temporally strongly varying parameters and heat sources. These occur, e.g., from the usage of lubricating coolants and due to the deployment of shavings during processing. To achieve this goal, we will need to develop tailored estimators to quantify the uncertainties and, on the other hand, devise modern mathematical methods such as space/time tensor methods in order to guarantee the real time capabilities of the digital machine image. Moreover, we will take into account displacement and strain measurements in the TCP estimation in addition to temperature measurements, which constitutes a significant extension to the data assimilation and optimal sensor placement methods.

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