Opening the Black Box: Towards inherently interpretable energy data imputation models using building physics insight

Missing data are frequently observed by practitioners and researchers in the building energy modeling community. In this regard, advanced data-driven solutions, such as Deep Learning methods, are typically required to reflect the non-linear behavior of these anomalies. As an ongoing research question related to Deep Learning, a model's applicability to limited data settings can be explored by introducing prior knowledge in the network. This same strategy can also lead to more interpretable predictions, hence facilitating the field application of the approach. For that purpose, the aim of this paper is to propose the use of Physics-informed Denoising Autoencoders (PI-DAE) for missing data imputation in commercial buildings. In particular, the presented method enforces physics-inspired soft constraints to the loss function of a Denoising Autoencoder (DAE). In order to quantify the benefits of the physical component, an ablation study between different DAE configurations is conducted. First, three univariate DAEs are optimized separately on indoor air temperature, heating, and cooling data. Then, two multivariate DAEs are derived from the previous configurations. Eventually, a building thermal balance equation is coupled to the last multivariate configuration to obtain PI-DAE. Additionally, two commonly used benchmarks are employed to support the findings. It is shown how introducing physical knowledge in a multivariate Denoising Autoencoder can enhance the inherent model interpretability through the optimized physics-based coefficients. While no significant improvement is observed in terms of reconstruction error with the proposed PI-DAE, its enhanced robustness to varying rates of missing data and the valuable insights derived from the physics-based coefficients create opportunities for wider applications within building systems and the built environment.

Indoor Environment Data Time-Series Reconstruction Using Autoencoder Neural Networks

As the number of installed meters in buildings increases, there is a growing number of data time-series that could be used to develop data-driven models to support and optimize building operation. However, building data sets are often characterized by errors and missing values, which are considered, by the recent research, among the main limiting factors on the performance of the proposed models. Motivated by the need to address the problem of missing data in building operation, this work presents a data-driven approach to fill these gaps. In this study, three different autoencoder neural networks are trained to reconstruct missing indoor environment data time-series in a data set collected in an office building in Aachen, Germany. The models are applicable for different time-series obtained from room automation, such as indoor air temperature, relative humidity and $CO_{2}$ data streams. The results prove that the proposed methods outperform classic numerical approaches and they result in reconstructing the corresponding variables with average RMSEs of 0.42 {\deg}C, 1.30 % and 78.41 ppm, respectively.