A gray-box model for real-time transient temperature predictions in data centers

In response to the need to improve the energy efficiency of data centers (DCs), system designers now incorporate solutions such as continuous performance monitoring, automated diagnostics, and optimal control. While these solutions must ideally be able to predict transient conditions, in particular real time DC temperatures, existing forecasting methods are inadequate because they (1) make restrictive assumptions about system configurations, (2) are extremely time-consuming for real time applications, (3) are accurate only over limited time horizons, (4) fail to accurately model the effects of operating conditions, such as cooling unit operation conditions and server workloads, or (5) ignore important facets of the flow physics and heat transfer that can lead to large prediction errors in extrapolative predictions. To address these deficiencies, we develop a gray-box model that combines machine learning with the thermofluid transport equations relevant for a row-based cooled DC to predict transient temperatures in server CPUs and cold air inlet to the servers. An artificial neural network (ANN) embedded in the gray-box model predicts pressures, which provide inputs for the thermofluid transport equations that predict the spatio-temporal temperature distributions. The model is validated with experimental measurements for different (1) server workload distributions, (2) cooling unit set-point temperatures and (3) the airflow of the cooling units. This gray-box model exhibits superior performance compared to a conventional zonal temperature prediction model and an advanced black-box model that is based on a nonlinear autoregressive exogenous model. An application of the gray-box model involves a case study to detect cooling unit fan failure in a row-based DC cooling system.