Fig 1.
The office cell model used as the case study.
Table 1.
Properties of the office cell building model in various climates.
Table 2.
The office cell building energy model parameter values.
Table 3.
Surrogate models used in the study.
Fig 2.
Average time needed to train various ML models using 5-fold cross validation for all four simulated values (H, C, L and E) for one combination of climate, obstacle type, orientation and heating and cooling set points of the building model, depending on the sample size.
The ML models N1, N2 and N3 are ANNs with one, two and three hidden layers of neurons, respectively, while X1, X2 and X3 are XGBoost models with learning rates set at 0.3, 0.1 and 0.03, respectively.
Fig 3.
Distribution of CV(RMSE) values for the cases of 2 inputs and 8 inputs over different ML models and different loads.
The ML models N1, N2 and N3 are ANNs with one, two and three hidden layers of neurons, respectively, while X1, X2 and X3 are XGBoost models with learning rates set at 0.3, 0.1 and 0.03, respectively.
Fig 4.
Distribution of CV(RMSE) values for the cases of LHS, MIPT and MIPTf sampling methods over different ML models and different loads.
The ML models N1, N2 and N3 are ANNs with one, two and three hidden layers of neurons, respectively, while X1, X2 and X3 are XGBoost models with learning rates set at 0.3, 0.1 and 0.03, respectively.CV(RMSE) values were computed for the ANN models with two inputs and the XGBoost models with eight inputs, as suggested in Subsection 3.1.
Fig 5.
Distribution of CV(RMSE) values for different ML models and different loads.
The ML models N1, N2 and N3 are ANNs with one, two and three hidden layers of neurons, respectively, while X1, X2 and X3 are XGBoost models with learning rates set at 0.3, 0.1 and 0.03, respectively. The axes for CV(RMSE) values were set individually due to differences in their ranges for different loads. Outliers, which are especially present for models N2 and N3, are not shown. Following suggestions in Subsections 3.1 and 3.2, the coefficients of variation were computed for the sample points selected by the MIPTf sampling method, the ANN models with two inputs and the XGBoost models with eight inputs.
Fig 6.
Distribution of CV(RMSE) values for the best performing XGBoost models X2 with learning rate 0.1, eight inputs and MIPTf sampling for different loads in different climates.
Insets shows the distributions of CV values of the simulated loads for the office cell model in these climates.
Fig 7.
Distribution of CV(RMSE) values for the best performing X2 models with learning rate 0.1, eight inputs and MIPTf sampling, trained over the samples with varying sizes containing 12, 25, 50 and 100 points, respectively.
Fig 8.
Relative errors of cooling load predictions for the four X2 models with learning rate 0.1, eight inputs and MIPTf sampling, trained over the samples of sizes 12, 25, 50 and 100, respectively, for the particular case of New York climate with southern orientation, no obstacles, hsp = 21°C and csp = 24°C.
Black diamond shapes depict the sample (d, h) points whose simulated loads were used for training the models. The samples were built iteratively, so that the sample of size 12 represents the first 12 points of the largest sample of size 100, etc.
Fig 9.
Diagrams of the predictions of heating loads (left column) and cooling loads (right column) of the XGBoost model ensembles X12, X25, X50 and X100, together with the actual simulated loads shown in the last row, for the office cell model in the New York climate with southern orientation, no obstacles, hsp = 21°C and csp = 24°C.
Fig 10.
Diagrams of the predictions of lighting loads (left column) and equivalent primary energy needs (right column) of the XGBoost model ensembles X12, X25, X50 and X100, together with the actual simulated loads shown in the last row, for the office cell model in the New York climate with southern orientation, no obstacles, hsp = 21°C and csp = 24°C.