Using inverse regression models to create gray box models for industrial facilities
Industrial facilities account for approximately one third of energy usage in the world, and effective energy assessments of these facilities require a reliable baseline energy model. Commercial and residential buildings are baselined with both simple change-point models and models that are more complex, such as Gaussian process and artificial neural networks, and these models are developed and tested with dense high-frequency data. However, industrial facilities are only baselined using change-point models, and data for the models are typically restricted to monthly utility bills and, therefore, generally sparse data. This investigation first compares the effectiveness of change-point models with that of Gaussian process models for baselining industrial facilities using only monthly utility billing information as data. Two case studies are presented to predict electricity usage and two case studies are presented to predict natural gas usage. Both change-point and Gaussian process models provided similar results, and both models meet the recommended NMBE and CV-RMSE from ASHRAE Guideline 14. Due to the simplicity and straight-forward equations of change-point models, they are better for regression analysis unless uncertainty is required. This study then investigates using three parameter cooling change-point regression models to determine the physical parameters, specifically overall heat transfer coefficient, surface area, and outdoor air mass flow rate of an industrial building through a simulation-based emulator. A simplified industrial building similar in size, energy usage, and physical parameters as a typical industrial facility was simulated in fifteen of the climate zones defined by ASHRAE using a whole building simulation program (i.e., EnergyPlus) to produce hourly data to illustrate and demonstrate the proposed approach. The change-point models showed poor results for finding the physical parameters using ambient air temperature as the independent variable. When using sol-air temperatures as the independent variable the change-point models were able to predict a lumped capacity of building envelope and outdoor air infiltration/ventilation within +/– 25 % error of actual (UA+ṀCP)/COP for most of the climate zones in the U.S.
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