Wojciech Gryglas, ZA, MEiL, PW, Application of POD method to optimal design of experiment

Ability to automate and optimize instrumentation strategy is crucial to improving the cost, accuracy, and robustness of complex flow experiment setup. For this purpose, it is proposed to use optimization methodology that is based on covariance minimization by utilizing the A­-criterion. To be able to construct A-­criterion the Fisher Information Matrix is required, which can be obtained from a model built using the Proper Orthogonal Decomposition (POD) method as a surrogate model. POD based approach ensures the stability of the optimization process and allows to formulate generic methodology which is problem independent. Furthermore, thanks to the availability of the surrogate model, it allows reconstructing solution in the whole measurement domain basing only on the data gathered from the optimized sensor locations. The POD model construction requires performing a set of numerical simulations of the phenomenon that is being measured for the range of all permissible parameters. The number of CFD calculations can be large nevertheless, they can be performed in parallel with minimal human interaction. The amount of gained information from simulations allows predicting locations where the measurement uncertainty will be minimized. The proposed optimization methodology was verified in two stages. Firstly, validation was performed basing on a virtual experiment data. The data was prepared by introducing random error to the simulation results obtained using a fine grid mesh. Verification was carried out for the flow around NACA 0012 profile and for the turbine cascade. The second verification stage was based on real experimental data. The data came from the transonic wind tunnel measurement. It consisted of 69 pressure measurements around turbine blade. The aim of the test was to select an optimal subset of the 69 pressure measurements that would provide maximum information. Then, using only selected data, the whole pressure profile was reconstructed and compared with all 69 measurements. Both validation cases confirmed the efficiency of the proposed methodology.

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