Page 52 - IJAMD-2-1

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

Table 3. Hyperparameters optimization methods for the PMV prediction models
Model name Hyperparameters tuned
SVM 1. Box constraint (C): Balances model complexity and training error. Higher values lead to better fit but risk overfitting.
2. Kernel scale (σ): Determines the shape of the RBF kernel, controlling the decision boundary’s flexibility.
3. Epsilon (ε): Specifies the tolerance level for prediction errors, influencing model robustness.
Bayesian optimization identified the optimal hyperparameters, with the kernel scale showing the most significant impact on accuracy.
RF 1. Number of trees: Determines the number of decision trees in the ensemble. More trees generally increase accuracy but also
computational cost.
2. Minimum leaf size: Regulates the minimum number of samples in a leaf node to control model complexity and prevent overfitting.
3. Number of predictors for splitting: Adjusted to optimize feature selection at each decision split.
Bayesian optimization was used for hyperparameter tuning, revealing that increasing the number of trees enhanced prediction
accuracy, while smaller leaf sizes improved granularity but increased training time.
NARX neural The NARX model structure involved determining the number of neurons in the hidden layer and lag lengths for inputs and outputs.
network Bayesian optimization was applied to identify the optimal combination of hyperparameters.
LSTM LSTM model training involved tuning the number of LSTM units and dropout rates to prevent overfitting and learning rates.
Bayesian optimization and trial-and-error methods were used to achieve optimal model configurations.
Abbreviations: LSTM: Long short-term memory; NARX: Non-linear autoregressive network with exogenous inputs; PMV: Predicted mean vote;
RBF: Radial basis function; RF: Random forest; SVM: Support vector machine.

Table 4. Summary of ML model training

ML model MAE Maximum Computing cost (s)
(Test prediction Training Prediction Total
dataset) error
SVM 0.1041 0.4810 235 1 a 236
RF 0.1040 0.4200 18 a 450 468
NARX 0.0623 a 0.3140 a 96 2 98 a
LSTM 0.0843 0.4830 840 26 866
a
Note: Best results.
Abbreviations: LSTM: Long short-term memory; MAE: Mean absolute
error; ML: Machine learning; NARX: Non-linear autoregressive
network with exogenous inputs; RF: Random forest; SVM: Support
vector machine.
applicability in scenarios characterized by strong temporal
dependencies. 20
The NARX model exhibited the best accuracy and
generalization among all models, along with the lowest Figure 4. Feature sensitivity analysis of predictors
Abbreviation: PMV: Predicted mean vote.
computational cost. Potential improvements in NARX’s
accuracy could be achieved by increasing the number of
hidden layers, but this would increase computational time. with limited computational resources, NARX is preferable.
Conversely, for complex systems where accuracy is
The LSTM model significantly outperformed the non- paramount, LSTM is more appropriate. Given that NARX
ANN models in PMV prediction, displaying substantially achieved the lowest test and prediction errors, along with
better prediction accuracy. However, it did not show an the lowest combined training and prediction cost, it was
advantage in generalization, as indicated by its maximum selected for integration into the MPC framework in this
prediction error. The LSTM model required the highest study.
training times due to the computational complexity of
LSTM cells. Thus, its superior prediction accuracy came at 5. Results and discussion
a higher computational cost. In this section, the performance of the MPC system is
In summary, ANN models outperformed non-ANN compared against the baseline BMS mode of operation.
models in terms of accuracy. Among the ANN models, Data collected over a 7-day period for both the BMS and
the choice between NARX and LSTM depends on specific MPC systems indicated that the statistical variations of
application requirements. For real-time implementation outdoor temperature and solar radiation were similar.

Volume 2 Issue 1 (2025) 46 doi: 10.36922/ijamd.8161