The potential reduction in energy consumption for space heating in buildings realised by the use of predictive control systems directly depends on the prediction accuracy of the building thermal behaviour model. Hence, model calibration methods that allow improved prediction accuracy for specific buildings have received significant scientific interest. An extension of this work is the potential use of calibrated models to estimate the thermal properties of an existing building, using measurements collected from the actual building, rather than relying on building specifications.

Simplified thermal network models, often expressed as grey-box Resistor-Capacitor circuit analogue models, have been successfully applied in the prediction setting. However, the use of such models as soft sensors for the thermal properties of a building requires an assumption of physical interpretation of the estimated parameters. The parameters of these models are estimated under the effects of both epistemic and aleatoric uncertainty, in the model structure and the calibration data. This uncertainty is propagated to the estimated parameters. Depending on the model structure and the dynamic information content in the data, the parameters may not be identifiable, thus resulting in ambiguous point estimates.

In this paper, the Profile Likelihood method, typical of a frequentist interpretation of parameter estimation, is used to diagnose parameter identifiability by projecting the likelihood function onto each parameter. If a Bayesian framework is used, treating the parameters as random variables with a probability distribution in the parameter space, projections of the posterior distribution can be studied by using the Profile Posterior method. The latter results in projections that are similar to the marginal distributions obtained by the popular Markov Chain Monte Carlo method. The different approaches are applied and compared for five experimental cases based on observed data. Ambiguity of the estimated parameters is resolved by the application of a prior distribution derived from a priori knowledge, or by appropriate modification of the model structure. The posterior predictive distribution of the model output predictions is shown to be mostly unaffected by the parameter non-identifiability.

通过使用预测控制系统实现的建筑物空间供暖能耗的潜在降低直接取决于建筑物热行为模型的预测精度。因此，能够提高特定建筑物的预测精度的模型校准方法已经引起了广泛的科学兴趣。这项工作的扩展是可以使用校准模型来估计现有建筑物的热特性，该模型使用从实际建筑物中收集的测量数据来评估，而不是依赖于建筑物规范。

简化的热网络模型（通常表示为灰盒电阻电容电路模拟模型）已成功应用于预测设置中。但是，将此类模型用作建筑物热属性的软传感器时，需要对估算参数进行物理解释。这些模型的参数下两者的效果估计认知和肆意的不确定性，在模型结构和校准数据。该不确定性传播到估计的参数。根据模型结构和数据中的动态信息内容，参数可能无法识别，从而导致歧义点估计。

在本文中，通常采用参数估计的解释的轮廓似然法，通过将似然函数投影到每个参数上来诊断参数可识别性。如果使用贝叶斯框架，将参数视为在参数空间中具有概率分布的随机变量，则可以通过使用轮廓后验方法研究后验分布的投影。后者导致的投影类似于通过流行的马尔可夫链蒙特卡洛方法获得的边际分布。根据观察到的五个实验案例，采用了不同的方法并进行了比较数据。通过应用从先验知识中得出的先验分布，或通过对模型结构进行适当的修改，可以解决估计参数的不确定性。模型输出预测的后验预测分布显示大部分不受参数不可识别性的影响。