A robust gray-box modeling methodology for variable-speed direct-expansion systems with limited training data

Abstract

• A robust training method against limited training data is proposed for DX units. • The methodology identifies the most influential parameters to estimate. • More estimation parameters result in degraded parameter accuracy. • Model prediction accuracy is highly dependent on training data size. Compared to physics-based models, the gray-box modeling approach has clear advantages including reduced engineering efforts in the model development phase, higher computational efficiency, improved accuracy and reduced uncertainties. In this paper, we present a gray-box steady-state modeling methodology for variable-speed direct-expansion systems that is robust against limited training data. The methodology incorporates a dual-stage training scheme, where component models are identified separately, and then integrated through continuity constraints to establish a system model trained on a higher hierarch. To further improve model reliability and robustness, the training methodology incorporates two commissioning techniques, i.e., significance ranking and de-correlation, to down-select the estimation parameters according to the quality of the training data. To demonstrate the efficacy, the proposed modeling methodology was applied to a 3-ton variable-speed heat pump. Qualities of the identified models were evaluated in terms of parameter accuracy and model prediction accuracy against variable training data sizes. Robustness of the methodology was demonstrated in achieving reasonable model accuracies with limited training data.