Unsupervised Fault Detection for Building Air Handling Unit Systems Using Deep Variational Mixture of Principal Component Analyzers

Incomplete data is the most common but tricky problem for data-driven energy and building solutions. Due to sensor errors or communication failures, raw building data with missing data points are rarely satisfactory for fault detection and diagnosis (FDD) applications. In this paper, a new framework named a deep variational mixture of principal component analyzers (DV-MPPCA) is proposed to address the building FDD problem with incomplete data. DV-MPPCA is the combination of a variational autoencoder (VAE) model for data compression and a mixture of principal component analyzers (MPPCA) for density estimation. To construct an integrated framework comprising both VAE and MPPCA, we introduce a novel methodology that represents the algebraic model of MPPCA within the architecture of a neural network. This innovative architecture undergoes optimization through the minimization of a designated loss function. Subsequently, the refined and optimized framework is harnessed as an unsupervised fault detection model for a real-world air handling unit (AHU) system designed by the ASHRAE research project 1312 (RP-1312). Furthermore, by incorporating the modified evidence lower bound (ELBO) loss function within the VAE, the resulting DV-MPPCA framework exhibits exceptional performance when confronted with incomplete AHU datasets, even with high missing rates. Empirical findings substantiate the supremacy of DV-MPPCA over other contemporary classic and deep models. Impressively, even with a missing rate as modest as 10%, DV-MPPCA consistently delivers outstanding performance, achieving F1-scores of 98.10%, 93.50%, and 81.57% for the Summer, Winter, and Spring datasets, respectively. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the fact that raw building data with missing data points are not qualitative enough for direct use in fault detection and diagnosis (FDD) applications. To resolve this problem, existing studies manipulated imputation algorithms in the preprocessing step to prepare the data for constructing FDD models and impute missing points in test instances during the online monitoring process. However, this step makes an overall FDD framework cumbersome. Therefore, instead of utilizing a data imputation method as a separately operating model, we adopt VAE in our framework to exclude the contribution of missing points during the offline modeling and online monitoring processes. This modification of VAE helps our framework be immune to incomplete data. For reproducibility and future improvement by other researchers, the complete source code of this study is provided in the following repository: https://github.com/viettra-xai/DV-MPPCA.

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