Uncertainty analysis of a virtual water flow measurement in building energy consumption monitoring

The virtual flow meter introduced in this article is developed by calculating water flow rates through two measurable inputs (differential pressure measurements and pump speed measurements) and a calibrated pump curve. However, due to the fact that the flow measurements are achieved by indirect calculations based on multiple input variable measurements, the possibility of error is significantly increased compared with direct flow measurements. This article first introduces the mechanism of virtual flow measurements, analyzes typical errors that can result in incorrect flow readings, and compares the sensitivity index of each input variable and its error impacts on the output variable. Finally, experimental results are presented to validate the uncertainty analysis. As a result, the pump speed is found to be the most influential variable in determining the accuracy of the virtual flow meter. The experiment shows that, compared with the measurement results of an ultrasonic flow meter, a 1% error at full scale (i.e., twice the pump design flow rate) can be achieved with 95% confidence. The analysis in this article demonstrates a theoretical method to quantify the propagated uncertainties of the virtual flow meter through its input variable uncertainties.