  Ultra-low temperature (ULT) freezers store perishable bio-contents and have
high energy consumption, which highlight a demand for reliable methods for
intelligent surveillance and smart energy management. This study introduces a
novel grey-box modelling approach based on stochastic differential equations to
describe the heat dynamics of the ULT freezing chambers. The proposed modelling
approach only requires temperature data measured by the embedded sensors and
uses data from the regular operation periods for model identification. The
model encompasses three states: chamber temperature, envelope temperature, and
local evaporator temperature. Special attention is given to the local
evaporator temperature state, which is modelled as a time-variant system, to
characterize the time delay and dynamic variations in cooling intensity. Two
ULT freezers with different operational patterns are modelled. The unknown
model parameters are estimated using the maximum likelihood method. The results
demonstrate that the models can accurately predict the chamber temperature
measured by the control probe (RMSE < 0.19 {\deg}C) and are promising to be
applied for forecasting future states. In addition, the model for local
evaporator temperature can effectively adapt to different operational patterns
and provide insight into the local cooling supply status. The proposed approach
greatly promotes the practical feasibility of grey-box modelling of the heat
dynamics for ULT freezers and can serve several potential digital applications.
A major limitation of the modelling approach is the low identifiability, which
can potentially be addressed by inferring model parameters based on relative
parameter changes.
