Measurement of Spatially Distributed Quantities
Accurate measurement of the average value of a spatially distributed quantity is notoriously difficult especially if the spatial distribution changes with operating conditions, for example: the average temperature of a fluid in a stratified storage tank (Arahal et al., 2008; Kreuzinger et al., 2008; Belessiotis et al., 2010); the average value of the air temperature in a large office (Jassar et al., 2009, 2011; Liao and Dexter, 2010); or the average value of the flow rate of a fluid flowing through a pipe or duct which has a large cross-sectional area (Tan and Dexter, 2005; Wichman and Braun, 2009; Yu et al., 2011). The main problem with modern electronic sensors is not usually measurement noise, drift or poor calibration that can be eliminated during commissioning, but sensor bias (an offset between the average value of the measurement and the true value of the measured variable).
For example, accurate measurement of the temperature and velocity of the air flowing down a large duct is extremely difficult when there are significant variations in the temperature and velocity over the cross-section of the duct (Carling and Isakson, 1999). Currently available sensors for measuring air temperature and airflow rates in ducts are either inaccurate or expensive. Even commercial multi-point averaging sensors can produce large errors if they are used in certain locations (e.g. immediately downstream of a mixing box; Robinson, 1999). Efficient ...