Page 50 - IJAMD-2-1

International Journal of AI for
Materials and Design
ML-based MPC for multizone BAC

Q cool,lb ≤ Q ≤ Q cool,ub (III) For this study, four ML algorithms – SVM, RF, NARX,
cool
−0.5 ≤ PMV ≤ 0.5 (IV) and LSTM – were selected for evaluation. Following
the testbed setup, historical operational data from the
where Q, W, N, and ϵ refer to the cooling power, building was collected over 2 months. This dataset was
weighting factor, number of control intervals within one then preprocessed and divided into training, validation,
prediction horizon, and slack variable, respectively. The and testing subsets. Each ML model underwent training,
subscripts cool, t, k, ref, lb, and ub refer to cooling, current prediction, and evaluation processes. The model
time, index of the time step, preferred PMV (i.e., PMV = 0), demonstrating the best prediction accuracy was selected
lower bound, and upper bound, respectively. The slack for the construction of the MPC system in this study. Below,
variable (ϵ) is used for constraint relaxation. In addition, we elaborate on dataset creation, model evaluation criteria,
the coefficient of performance (COP) of the cooling system model selection (including hyperparameter tuning), and
is assumed to be constant at 3.7 as per the specification the results of the training process.
of the ACMV system. The three terms on the right-hand
side of Equation II correspond to the cost functions related 4.1. Data collection and model evaluation
to cooling energy consumption, thermal discomfort, 4.1.1. Dataset creation
and constraint violation. The variables associated with
the multizone MPC are summarized in Table 2. A more The dataset used for model training was derived from
detailed explanation of Equations I-IV is provided in the historical data collected from the baseline measurement
Appendix. phase from August to October 2021 as part of the project’s test
plan. Given Singapore’s consistently low month-to-month
4. ML model development for MPC climatic variations throughout the year, this three-month
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baseline dataset, inclusive of outdoor conditions, can be
ML model training plays a pivotal role in developing considered representative of the entire year. However, it is
predictive models for MPC. This section outlines the important to acknowledge that the model should ideally
approach used to select, train, and evaluate neural be trained on a dataset capturing a full range of weather
network models for predicting PMV. This study frames conditions and building operational characteristics. In
the prediction of PMV as a regression task, given the regions experiencing significant seasonal climate variations,
continuous nature of this comfort index. An overview of a more extensive dataset covering a longer period would be
the model training process and its integration into the necessary. Furthermore, certain model parameters – such
MPC framework is presented in Figure 3. as the lag length for the NARX model or the input depth for
the LSTM model, defining the context window for learning
Table 2. Summary of variables used in multizone MPC
temporal patterns – may need adjustment to accommodate
Variable type Variable type Variables Description these variations. Such adaptation could introduce challenges
in MPC in ML models related to computational costs, overfitting, and vanishing
Manipulated Inputs Q cool Cooling power gradients, which require careful consideration. Future
variable supplied by FCU research will focus on validating the model’s performance
Measured Temperature Outdoor ambient across diverse climatic zones and exploring strategies to
disturbances temperature enhance its generalizability.
Solar heat Measured from solar In the current study, the input variables include cooling
gain irradiance power, outdoor temperature, solar irradiance, occupancy,
Adjacent PMV of mean radiant temperature, and the current indoor PMV,
PMV adjacent/connected whereas the output is future indoor PMV prediction.
zones
Occupancy Occupancy A summary of the collected data is provided in Table 2.
measured from CO 2 4.1.2. Handling historical data
concentration in
return air The dataset comprises 15,606 time steps, recorded at 6-min
Mean radiant Mean radiant intervals. Data preprocessing included dimensionality
temperature temperature reduction and Z-score normalization to minimize scale
State variable PMV Current indoor effects and improve computational efficiency. The data
PMV were partitioned into training (70%), validation (15%), and
Output variable Output PMV Indoor PMV testing (15%) subsets to facilitate model development and
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Abbreviations: FCU: Fan coil unit; ML: Machine learning; MPC: Model evaluation. The Z-score standardization formula used is
predictive control; PMV: Predicted mean vote. shown in Equation V:

Volume 2 Issue 1 (2025) 44 doi: 10.36922/ijamd.8161