Uncertainty Analysis for Calm Water Tow Tank Measurements

Abstract

Uncertainty quantification is critical in the analysis and interpretation of experimental data. Tow-tank testing of high-speed planing craft is subject to various sources of uncertainty, both systematic and random, which impact the overall uncertainty in the estimate. This paper presents an approach for quantifying and combining the different sources of uncertainty in these types of experiments. A linear mixed-effect model is proposed to account for variability both between experimental runs and within experimental runs in the random uncertainty. Expressions for the combined uncertainty, and associated degrees of freedom, are developed. The paper offers a step-by-step guide for using the proposed method to construct confidence intervals, and shows a detailed example for a single testing condition. The results demonstrate that the proposed method provides larger estimates of random uncertainty when the within-run variability is of a magnitude similar to the between-run variability. This translates to larger combined uncertainties—and wider confidence intervals—when the random uncertainty is a major contributor to the combined uncertainty. The paper includes estimates and associated expanded, combined uncertainties for speed, sinkage, and trim based on experimental data from high-speed model testing conducted at the U.S. Naval Academy in August 2013 and May 2014. 1. Introduction Uncertainty analysis is a critical component to any experimental investigation. When data are collected or measurements are made, it is for the purpose of assisting with decision-making, such as risk assessments in design or validating simulation results. Uncertainty analysis is a way to estimate the likely magnitude of difference between a test result and the "true" value, an unknown quantity. Moffat (1982) states that quantification of "[uncertainty is the prediction of the uncertainty interval which should be associated with an experimental result, based on observations of the scatter in the raw data used in calculating the result." There are significant challenges in identifying and quantifying the uncertainties associated with the measurements, and development of a formal procedure for uncertainty analysis has been progressing for over 60 years (Kline & McClintock 1953; Abernathy et al. 1985; Moffat 1982; Moffat 1985; ISO 1995; Coleman & Steele 2009; AIAA 1995; ASME 2013; ITTC 2008). However, tow tank testing and, in particular, testing of high-speed craft, create unique challenges that are often not covered sufficiently in the existing guidelines.