### Abstract

Conventional multi-zonal ventilation measurement methods by multiple types of perfluorocarbon tracers use a number of different gases equal to the number of zones (n). The possible n×n+n airflows are estimated from the mass balance of the gases and the airflow balance. However, some airflows may not occur because of inter-zonal geometry, and the introduction of unnecessary, unknown parameters can impair the accuracy of the estimation. Also, various error factors often yield an irrational negative airflow rate. Conventional methods are insufficient for the evaluation of error. This study describes a way of using the least-squares technique to improve the precision of estimation and to evaluate reliability. From the equations' residual, the error variance-covariance matrix Λ_{q} of the estimated airflow rate error is deduced. In addition, the coefficient of determinant using the residual sum of squares and total variation is introduced. Furthermore, the error matrix _{m}Λ_{q} from the measurement errors in the gas concentration and gas emission rate is deduced. The discrepancy ratio of the model premises is defined by dividing the diagonal elements of the former by those of the latter. Moreover, the index of irrationality of the estimated negative airflow rate is defined, based on the different results of the three estimation methods. Some numerical experiments are also carried out to verify the flow rate estimation and the reliability evaluation theory.

Original language | English |
---|---|

Pages (from-to) | 546-557 |

Number of pages | 12 |

Journal | Building and Environment |

Volume | 44 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 Mar |

### Fingerprint

### Keywords

- Error analysis
- Least squares
- Multi-zonal airflow measurement
- Perfluorocarbon tracer gas

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Environmental Engineering
- Geography, Planning and Development
- Building and Construction

### Cite this

*Building and Environment*,

*44*(3), 546-557. https://doi.org/10.1016/j.buildenv.2008.04.014

**Statistical data analysis method for multi-zonal airflow measurement using multiple kinds of perfluorocarbon tracer gas.** / Okuyama, Hiroyasu; Onishi, Yoshinori; Tanabe, Shinichi; Kashihara, Seiichi.

Research output: Contribution to journal › Article

*Building and Environment*, vol. 44, no. 3, pp. 546-557. https://doi.org/10.1016/j.buildenv.2008.04.014

}

TY - JOUR

T1 - Statistical data analysis method for multi-zonal airflow measurement using multiple kinds of perfluorocarbon tracer gas

AU - Okuyama, Hiroyasu

AU - Onishi, Yoshinori

AU - Tanabe, Shinichi

AU - Kashihara, Seiichi

PY - 2009/3

Y1 - 2009/3

N2 - Conventional multi-zonal ventilation measurement methods by multiple types of perfluorocarbon tracers use a number of different gases equal to the number of zones (n). The possible n×n+n airflows are estimated from the mass balance of the gases and the airflow balance. However, some airflows may not occur because of inter-zonal geometry, and the introduction of unnecessary, unknown parameters can impair the accuracy of the estimation. Also, various error factors often yield an irrational negative airflow rate. Conventional methods are insufficient for the evaluation of error. This study describes a way of using the least-squares technique to improve the precision of estimation and to evaluate reliability. From the equations' residual, the error variance-covariance matrix Λq of the estimated airflow rate error is deduced. In addition, the coefficient of determinant using the residual sum of squares and total variation is introduced. Furthermore, the error matrix mΛq from the measurement errors in the gas concentration and gas emission rate is deduced. The discrepancy ratio of the model premises is defined by dividing the diagonal elements of the former by those of the latter. Moreover, the index of irrationality of the estimated negative airflow rate is defined, based on the different results of the three estimation methods. Some numerical experiments are also carried out to verify the flow rate estimation and the reliability evaluation theory.

AB - Conventional multi-zonal ventilation measurement methods by multiple types of perfluorocarbon tracers use a number of different gases equal to the number of zones (n). The possible n×n+n airflows are estimated from the mass balance of the gases and the airflow balance. However, some airflows may not occur because of inter-zonal geometry, and the introduction of unnecessary, unknown parameters can impair the accuracy of the estimation. Also, various error factors often yield an irrational negative airflow rate. Conventional methods are insufficient for the evaluation of error. This study describes a way of using the least-squares technique to improve the precision of estimation and to evaluate reliability. From the equations' residual, the error variance-covariance matrix Λq of the estimated airflow rate error is deduced. In addition, the coefficient of determinant using the residual sum of squares and total variation is introduced. Furthermore, the error matrix mΛq from the measurement errors in the gas concentration and gas emission rate is deduced. The discrepancy ratio of the model premises is defined by dividing the diagonal elements of the former by those of the latter. Moreover, the index of irrationality of the estimated negative airflow rate is defined, based on the different results of the three estimation methods. Some numerical experiments are also carried out to verify the flow rate estimation and the reliability evaluation theory.

KW - Error analysis

KW - Least squares

KW - Multi-zonal airflow measurement

KW - Perfluorocarbon tracer gas

UR - http://www.scopus.com/inward/record.url?scp=56349124626&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56349124626&partnerID=8YFLogxK

U2 - 10.1016/j.buildenv.2008.04.014

DO - 10.1016/j.buildenv.2008.04.014

M3 - Article

VL - 44

SP - 546

EP - 557

JO - Building and Environment

JF - Building and Environment

SN - 0360-1323

IS - 3

ER -