Bayesian inference for thermal response test parameter estimation and uncertainty assessment
Bayesian inference for thermal response test parameter estimation and uncertainty assessment
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DOI：
10.1016/j.apenergy.2017.10.034
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发表时间：
2018-01-01
期刊：
影响因子：
11.2
通讯作者：
Ooka, Ryozo
中科院分区：
文献类型：
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作者：
Choi, Wonjun;Kikumoto, Hideki;Ooka, Ryozo
土壤有效导热系数和井眼热阻是地源热泵设计所需的重要参数。现场热响应测试（TRT）被认为是可靠的，以获得这些参数，但解释TRT数据的确定性方法可能会导致显着的不确定性估计。鉴于这两个参数对地源热泵应用的影响，量化不确定性是必要的。为此，在这项研究中，我们开发了一种基于贝叶斯推理的随机方法来估计这两个参数和相关的不确定性。数值生成的噪声TRT数据和参考沙箱TRT数据被用来验证所提出的方法。利用获得的后验概率密度函数提取参数的点估计及其可信区间。将该方法应用于现场TRT数据，验证了该方法的有效性，并分析了测试时间与估算精度之间的关系。ASHRAE建议的最小TRT时间为36 h，有效导热系数的不确定性约为+/- 21%。然而，估计的不确定性随着TRT时间的增加呈指数下降，在TRT时间54 h后为+/- 8.3%，低于一般可接受的不确定性范围+/-10%。根据所获得的结果，建议最小TRT时间为50 h，预计在大多数情况下，72 h将产生足够准确的估计值。
The effective ground thermal conductivity and borehole thermal resistance constitute information needed to design a ground-source heat pump (GSHP). In situ thermal response tests (TRTs) are considered reliable to obtain these parameters, but interpreting TRT data by a deterministic approach may result in significant uncertainties in the estimates. In light of the impact of the two parameters on GSHP applications, the quantification of uncertainties is necessary. For this purpose, in this study, we develop a stochastic method based on Bayesian inference to estimate the two parameters and associated uncertainties. Numerically generated noisy TRT data and reference sandbox TRT data were used to verify the proposed method. The posterior probability density functions obtained were used to extract the point estimates of the parameters and their credible intervals. Following its verification, the proposed method was applied to in situ TRT data, and the relationship between test time and estimation accuracy was examined. The minimum TRT time of 36 h recommended by ASHRAE produced an uncertainty of similar to +/- 21% for effective thermal conductivity. However, the uncertainty of estimation decreased exponentially with increasing TRT time, and was +/- 8.3% after a TRT time of 54 h, lower than the generally acceptable range of uncertainty of +/- 10%. Based on the obtained results, a minimum TRT time of 50 h is suggested and that of 72 h is expected to produce sufficiently accurate estimates for most cases.