Statistical data analysis method for multizonal airflow measurement using multiple kinds of perfluorocarbon tracer gas

Conventional multiple types of perfluorocarbon tracers use the number of gases equal to the number of zones (n). The possible nxn+n airflows are solved from the mass balance of the gas and the airflow balance. However, some airflows may not occur because of the actual interzonal geometry, and the introduction of unnecessary, unknown parameters can impair the accuracy of the estimations. Also, various error factors often yield an irrational negative airflow rate. Conventional methods have insufficient procedure for the evaluation of error. This study describes a way to use the least-squares technique to improve the precision of estimates and to evaluate reliability. From the equations' residual the error variance and covariance matrix Λ _q of the estimated airflow rate error is deduced and also the coefficient of determinant using the residual square sum and total variation is introduced. Further the error matrix _mΛ _q caused by the measurement error of the gas concentration and gas emission rate is deduced. The discrepancy ratio of the model premise is defined by dividing the former diagonal elements by the latter ones. Moreover the index of irrationality of the estimated negative airflow rate is defined based on the difference of the three estimation methods results.