### Abstract

For the design of ground-source heat pumps (GSHPs), two design parameters, namely the ground thermal conductivity and borehole thermal resistance are estimated by interpreting thermal response test (TRT) data using a physical model. In most cases, the parameters are fitted to the measured data assuming that the chosen model can fully reproduce the actual physical response. However, two significant sources of error make the estimation uncertain: random error from experiments and structural bias error that describes the discrepancy between the model and actual physical phenomena. Generally, these two error sources are not evaluated separately. As a result, the suitability of selected models to correctly infer parameters from TRTs are not well understood. In this study, the Bayesian calibration framework proposed by Kennedy and O'Hagan is employed to estimate the GSHP design parameters and quantify the random and structural errors in the inference. The calibration framework enables us to examine structural errors in the commonly used infinite line source model arising due to the conditions in which the TRT takes place. Two in situ TRT datasets were used: TRT1, influenced by contextual disturbances from the outdoor environment, and TRT2, influenced by a strong groundwater flow caused by heavy rainfall. We show that the Bayesian calibration framework is able to quantify the structural errors in the TRT interpretation and therefore can yield more accurate estimates of design parameters with full quantification of uncertainties.

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

Pages (from-to) | 1473-1485 |

Number of pages | 13 |

Journal | Applied Energy |

Volume | 228 |

DOIs | |

Publication status | Published - 2018 Oct 15 |

### Fingerprint

### Keywords

- Bayesian calibration
- Ground-source heat pump (GSHP)
- Groundwater flow
- Parameter estimation
- Structural biased error
- Thermal response test (TRT)
- Uncertainty assessment

### ASJC Scopus subject areas

- Building and Construction
- Energy(all)
- Mechanical Engineering
- Management, Monitoring, Policy and Law

### Cite this

*Applied Energy*,

*228*, 1473-1485. https://doi.org/10.1016/j.apenergy.2018.06.147

**Bayesian inference of structural error in inverse models of thermal response tests.** / Choi, Wonjun; Menberg, Kathrin; Kikumoto, Hideki; Heo, Yeonsook; Choudhary, Ruchi; Ooka, Ryozo.

Research output: Contribution to journal › Article

*Applied Energy*, vol. 228, pp. 1473-1485. https://doi.org/10.1016/j.apenergy.2018.06.147

}

TY - JOUR

T1 - Bayesian inference of structural error in inverse models of thermal response tests

AU - Choi, Wonjun

AU - Menberg, Kathrin

AU - Kikumoto, Hideki

AU - Heo, Yeonsook

AU - Choudhary, Ruchi

AU - Ooka, Ryozo

PY - 2018/10/15

Y1 - 2018/10/15

N2 - For the design of ground-source heat pumps (GSHPs), two design parameters, namely the ground thermal conductivity and borehole thermal resistance are estimated by interpreting thermal response test (TRT) data using a physical model. In most cases, the parameters are fitted to the measured data assuming that the chosen model can fully reproduce the actual physical response. However, two significant sources of error make the estimation uncertain: random error from experiments and structural bias error that describes the discrepancy between the model and actual physical phenomena. Generally, these two error sources are not evaluated separately. As a result, the suitability of selected models to correctly infer parameters from TRTs are not well understood. In this study, the Bayesian calibration framework proposed by Kennedy and O'Hagan is employed to estimate the GSHP design parameters and quantify the random and structural errors in the inference. The calibration framework enables us to examine structural errors in the commonly used infinite line source model arising due to the conditions in which the TRT takes place. Two in situ TRT datasets were used: TRT1, influenced by contextual disturbances from the outdoor environment, and TRT2, influenced by a strong groundwater flow caused by heavy rainfall. We show that the Bayesian calibration framework is able to quantify the structural errors in the TRT interpretation and therefore can yield more accurate estimates of design parameters with full quantification of uncertainties.

AB - For the design of ground-source heat pumps (GSHPs), two design parameters, namely the ground thermal conductivity and borehole thermal resistance are estimated by interpreting thermal response test (TRT) data using a physical model. In most cases, the parameters are fitted to the measured data assuming that the chosen model can fully reproduce the actual physical response. However, two significant sources of error make the estimation uncertain: random error from experiments and structural bias error that describes the discrepancy between the model and actual physical phenomena. Generally, these two error sources are not evaluated separately. As a result, the suitability of selected models to correctly infer parameters from TRTs are not well understood. In this study, the Bayesian calibration framework proposed by Kennedy and O'Hagan is employed to estimate the GSHP design parameters and quantify the random and structural errors in the inference. The calibration framework enables us to examine structural errors in the commonly used infinite line source model arising due to the conditions in which the TRT takes place. Two in situ TRT datasets were used: TRT1, influenced by contextual disturbances from the outdoor environment, and TRT2, influenced by a strong groundwater flow caused by heavy rainfall. We show that the Bayesian calibration framework is able to quantify the structural errors in the TRT interpretation and therefore can yield more accurate estimates of design parameters with full quantification of uncertainties.

KW - Bayesian calibration

KW - Ground-source heat pump (GSHP)

KW - Groundwater flow

KW - Parameter estimation

KW - Structural biased error

KW - Thermal response test (TRT)

KW - Uncertainty assessment

UR - http://www.scopus.com/inward/record.url?scp=85050088118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050088118&partnerID=8YFLogxK

U2 - 10.1016/j.apenergy.2018.06.147

DO - 10.1016/j.apenergy.2018.06.147

M3 - Article

AN - SCOPUS:85050088118

VL - 228

SP - 1473

EP - 1485

JO - Applied Energy

JF - Applied Energy

SN - 0306-2619

ER -