# Spatial Flow-Field Approximation Using Few Thermodynamic Measurements Part II: Uncertainty Assessments

## TL;DR

This paper develops a frequentist uncertainty propagation framework for thermodynamic measurements, introducing new metrics to better assess spatial sampling and measurement imprecision uncertainties in turbomachinery.

## Contribution

It presents a novel, data-centric framework with two new uncertainty metrics for more accurate spatial sampling and measurement uncertainty assessment.

## Key findings

- Measurement uncertainties have a larger impact than probe placement errors.
- Traditional metrics underestimate sampling uncertainty in non-uniform patterns.
- The proposed metrics are easy to compute and broadly applicable.

## Abstract

In this second part of our two-part paper, we provide a detailed, frequentist framework for propagating uncertainties within our multivariate linear least squares model. This permits us to quantify the impact of uncertainties in thermodynamic measurements---arising from calibrations and the data acquisition system---and the correlations therein, along with uncertainties in probe positions. We show how the former has a much larger effect (relatively) than uncertainties in probe placement. We use this non-deterministic framework to demonstrate why the well-worn metric for assessing spatial sampling uncertainty falls short of providing an accurate characterization of the effect of a few spatial measurements. In other words, it does not accurately describe the uncertainty associated with sampling a non-uniform pattern with a few circumferentially scattered rakes. To this end, we argue that our data-centric framework can offer a more rigorous characterization of this uncertainty. Our paper proposes two new uncertainty metrics: one for characterizing spatial sampling uncertainty and another for capturing the impact of measurement imprecision in individual probes. These metrics are rigorously derived in our paper and their ease in computation permits them to be widely adopted by the turbomachinery community for carrying out uncertainty assessments.