59442 - Probabilistic Approach for Optimizing Uncertainties of Input Variables to Reach a Desired Confidence Level 

The development of jet engines is typically accompanied by measurement campaigns to mitigate technical risks at an early design stage and to validate the specified performance. Often different configurations are compared in order to determine the superior one. But due to uncertainties in boundary conditions, geometry and sensors, the derived performance values are subject to uncertainty as well. When the output uncertainties are estimated using safety factors, which account for a worst-case scenario, this leads to a conservative estimation. Assuming that the desired difference in performance metrics is small compared to the associated uncertainty, it can consequently be hard to conclude on the superiority of the configurations.
In this paper, a probabilistic approach is used to optimize the uncertainties of the output values of interest. For this, the measurement process is executed virtually taking the low-speed research compressor of TU Dresden as a test case. In the first step, a sampling for the uncertainties associated to boundary conditions and geometry is created. Then, Computational Fluid Dynamics (CFD) calculations for these samples are executed. Afterwards, the virtual measurements are performed. Therefor the real value of the measurement quantity of interest is extracted from the CFD calculation and then merged with a measurement uncertainty. Finally, these virtual measurements are evaluated in the same way as it is done for the measurements to derive the output values.
Evaluating the sample allows to obtain the associated uncertainties and hence the confidence levels of a measurement campaign which are to be optimized. Firstly the system behavior is approximated with an inner meta model. This can be used to create an outer meta model describing the relationship between the uncertainties of the input variables and the uncertainties of the output variables. By evaluating the outer meta model it is possible to identify important input variables effecting the uncertainty of the output variables. Finally, the outer meta model is used to optimize the uncertainties of input variables in order to obtain a target uncertainty of output variables.