Summary statistics for quasi-stationary air velocity time series based on asynchronous velocity components

¹ Department of the Built Environment, Building Physics, Eindhoven University of Technology (TU/e), Eindhoven, NL
² Department of Civil Engineering, Building Physics and Sustainable Design, KU Leuven, Ghent, BE
³ Department of the Built Environment, Building Performance, Eindhoven University of Technology (TU/e), Eindhoven, NL

Abstract

In indoor environments, variables that are commonly measured, such as air velocity, are not always normally distributed. This may present complications if one is interested in reporting summary statistics, such as the mean and standard deviation, since non-normally distributed variables cannot be treated the same way as normally distributed variables. This study focuses on a methodology that allows one to estimate the mean air velocity magnitude and the uncertainty of the mean for non-uniform experimental data sets. The original data used to showcase the method consists of three velocity time series representing Cartesian velocity components. The three time series are obtained at quasi-steady state via asynchronous measurements in a classroom facility. The methodology is showcased using one data point, corresponding to one measurement location in the center of the room. The goal is to obtain the estimate of the mean velocity magnitude at that location. The velocity components are bootstrapped using moving block bootstrapping, and various combinations of the mean velocity components are further sampled to obtain an estimate of the mean velocity magnitude. Although researchers are not advised to use asynchronous velocity measurements, it is possible that such practices are unavoidable, for example, due to lack of equipment. This study presents a methodology that allows one to obtain an estimate of the mean velocity magnitude in situations where the data is non-normally distributed and summary statistics, such as the standard deviation, are not usable.