Data-Driven Spatio-Temporal Modelling and Optimal Sensor Placement for a Digital Twin Set-Up

Abstract

A computationally efficient predictive digital twin (DT) of a small-scale greenhouse needs an accurate and faster modelling of key variables such as the temperature field and flow field within the greenhouse. This involves: (a) optimally placing sensors in the experimental set-up and (b) developing fast predictive models. In this work, for a greenhouse set-up, the former requirement fulfilled first by identifying the optimal sensor locations for temperature measurements using the QR column pivoting on a tailored basis. Here, the tailored basis is the low-dimensional representation of hi-fidelity computational fluid dynamics (CFD) flow data, and these tailored basis are obtained using proper orthogonal decomposition (POD). To validate the method, the full temperature field inside the greenhouse is then reconstructed for an unseen parameter (inflow condition) using the temperature values from a few synthetic sensor locations in the CFD model. To reconstruct the flow-fields using a faster predictive model than the hi-fidelity CFD model, a long-short term memory (LSTM) method based on a reduced-order model (ROM) is used. The LSTM learns the temporal dynamics of coefficients associated with the POD-generated velocity basis modes. The LSTM-POD ROM model is used to predict the temporal evolution of velocity fields for our DT case, and the predictions are qualitatively similar to those obtained from hi-fidelity numerical models. Thus, the two data-driven tools have shown potential in enabling the forecasting and monitoring of key variables in a digital twin of a greenhouse. In future work, there is scope for improvements in the reconstruction accuracy by involving deep-learning-based corrective source term approaches.

Keywords

• dimensionality reduction
• forecasting
• LSTM
• POD
• QR pivoting
• digital twin