2 Building Technology Group, Massachusetts Institute of Technology
4 RESULTS AND DISCUSSION
4.1 Existing Building Energy Consumption
To better understand the results from multi-objective optimization, Figure 3 breaks down the energy consumption by end use for each apartment building. In all three apartments, interior equipment loads dominate, constituting as much as 76% of total energy consumption.
None of the retrofit options considered in this study address the interior equipment loads, which limits performance improvements. The apartments differ in the relative contribution of heating, cooling, and lighting energy consumption. The second largest contributor to the total load, is heating energy in the Pedro Sousa apartment but cooling energy in the João Barata and Carlos Camelo apartments. Overall, interior lighting represents the smallest contributor to total energy consumption.
Figure 3. Breakdown of energy consumption by end use for existing apartments.
4.2 Multi-Objective Optimization
Figure 4 shows the resulting Pareto optimal designs as well as a stratified sample within the design space for each apartment. The Pareto optimal designs for each apartment are the result of approximately 7,000 evaluations of the surrogate model as part of the genetic algorithm. Using a detailed energy simulation that takes 10-30 seconds per iteration, each plot would take 1-3 days to produce. Each iteration with a Kriging surrogate model takes 0.0006 seconds, so each plot took less than 4 minutes to produce.
Carlos Camelo João Barata Pedro Sousa
0% 25% 50% 75% 100%
Percent of Total Energy Use
Heating Cooling Interior Lighting Interior Equipment
The results show that some retrofits within the design space result in increased total energy use relative to the existing building. However, all the Pareto optimal designs use less energy than the existing building. The normalized total energy use and retrofit cost vary by apartment.
Figure 4. Multi-objective performance for a stratified sample and Pareto optimal designs for each SusCity apartment.
4.3 Model Error
Figure 5. a) Surrogate model predictions (b) percent difference as a function of simulated energy use.
Figure 5a shows the surrogate model predictions for total energy use relative to a detailed simulation in EnergyPlus for a stratified sample in the design space and the Pareto optimal designs. The ideal case is when the surrogate model prediction exactly matches the simulated value and is represented by a solid line with a slope of 1. Dashed lines representing ±1% of the ideal case are included for reference. Figure 5b shows the percent error as a function of the simulated total energy use to give a sense of how error varies through the design space. Surrogate model error in Pareto optimal designs tends to be higher for extremely low and high values of total energy represented in that set of designs. Error within the design space can also be higher at extreme values for energy use – such as the for energy use larger than 500 MJ/m2 in the Joao Barata apartment. Generally, the percent error within the design space oscillates around 0%. Interestingly, for the similar
values of total energy use, the Pareto optimal design will generally have a larger percent difference relative to the design space.
Figure 6. Global model error for a stratified sample and Pareto optimal designs for each SusCity apartment.
Figure 6 shows the CV of the RMSE for a stratified sample within the design space and Pareto optimal designs for each SusCity apartment. For all three apartments the CV is higher in the Pareto optimal set than the general design space. This is consistent with the results found in Figure 5, that surrogate model error is higher in the set of Pareto optimal designs.
The results show that the distribution of values for each design variable varies among the three apartments. Several variables have a bimodal distributions, meaning that the optimal designs are highly concentrated at their minimum or maximum such. These extremes are likely driving the higher surrogate model error for Pareto optimal designs observed in Figures 5 and 6.
Figure 7. Distribution of design variable values for the Pareto optimal set for each SusCity apartment.
Figure 7 shows the distribution of design variables in the Pareto optimal set as a violin plot. This type of plot is similar to a box plot in that it shows the range of values, but the shape and width is reflective of the probability density of the data at different values. The y-axis scale
4.2%
Carlos Camelo Joao Barata Pedro Sousa
Apartment Pedro Sousa Joao Barata Carlos Camelo
23
Pedro Sousa Joao Barata Carlos Camelo
0.00 0.05 0.10 (W/m2-K)(m)(m)(ACH)(-/-)
reflects the minimum and maximum value of each design variable from Table 2.
This suggests that current practice of stratified sampling for training surrogate models is inadequate for applications to optimization, because we are not interested in a uniform error throughout the design space. In the case of optimization, we are seeking out extreme design values to minimize performance objectives, which increases the error of the surrogate model. The challenge is we do not know the relationship between design variable values and the performance objectives a priori. An approach for future research could be to use optimization outputs to retrain the surrogate model in a narrower region within the design space. This approach to adaptively update the surrogate model has precedent in optimization literature [18].
5 CONCLUSIONS
In this research we combined surrogate modeling with multi-objective optimization to identify energy and cost-effective retrofits for three residential apartments in Lisbon, Portugal. To validate this approach, we reviewed the surrogate model error as a function of the simulated value for total energy and found a higher magnitude of percent error for extremely high or low values. Reviewing the global surrogate model error showed that designs in the Pareto optimal set had higher values of CV, meaning these predictions have greater variance. Further work should explore alternative approaches to sampling and training the surrogate model to reduce error for the Pareto optimal designs, which is the value of interest for multi-objective optimization.
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