*This work presents a framework for predicting unknown input distributions for turbomachinery applications starting from scarce experimental measurements. The problem is relevant to turbomachinery where important parameters such as the turbine inlet temperature are obtained using indirect measurements.*

*The framework needs two main aspects: an equivalence in a probabilistic sense and an efficient (sparse) Non-Intrusive Polynomial Chaos formulation able to deal with scarce data. Firstly, the upscaling equivalence is defined by a Probability Density Function (PDF) matching approach. By representing the inputs of a computational model of a turbine with a generalised Polynomial Chaos Expansion (gPCE), the stochastic upscaling problem can be recast as an optimisation problem. Coefficients of the gPCE are found such that when the uncertainties are propagated through the model an output PDF is generated which is probabilistically equivalent to the experimental outputs.  Probabilistic equivalence was defind using the Kolmogorov-Smirnov distance as a metric of statistical distance between distributions. Secondly, in order to define a data driven framework able to deal with scarce data a Sparse Approximation for Moment Based Polynomial Chaos was used. Not only can this data-driven framework deal with scarcity but it is also more computationally efficiient than Monte Carlo methods as it requires fewer evaluations of the model per iteration of the optimisation algorithm. *

*The results show a good agreement between measured data and what was predicted by the proposed framework.*


Uncertainty Quantification and Missing Data for Turbomachinery With Probabilistic Equivalence and Arbitrary Polynomial Chaos, Applied to Scroll Compressors

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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