## Sensitivity analysis in building design: Recommendation of sensitivity analysis methods for the building design process

Student thesis: Master thesis (including HD thesis)

- Christina Thyssen Kjær
- Rasmus Kjærsgaard Sunesen

4. term, Indoor Environmental and Energy Engineering, Master (Master Programme)

This project is motivated by the increasing complexity of the building process, with a greater focus on holistic building, where sustainability is involved. This can make it difficult to make the right choices for the decision makers in the building design process, as the choice can have an impact on both indoor climate, energy consumption, economy and architecture. Normally, changes are made to the building's design by changing one parameter at a time, which has been found to be disadvantageous. This is partly since it is a slow process and that it depends on the order in which the parameters are changed, which is why it can be difficult to find the most optimal solution.

A more advantageous way to find the optimal solutions is by using the Monte Carlo method. For the Monte Carlo method, the parameters are varied independently, enabling multiple solutions to be investigated at the same time. Using the Monte Carlo method, it is also possible to use sensitivity analysis methods, which can give an overview of which parameters that have most influence on the output, which could, for example, be the building's energy consumption. The sensitivity analysis methods have different characteristics such as accuracy and computational resources as well as their complexity. This means that it is not arbitrary which sensitivity analysis method is chosen to use. Therefore, in this project, eight sensitivity analysis methods are investigated to determine which ones are most advantageous to use in the building design process. The study is based on eight test functions and two BSim models, from which the sensitivity analysis methods are evaluated based on their accuracy and convergence rate with respect to both Factor Fixing and Factor Prioritization.

Factor Fixing and Factor Prioritization are two settings that can be used with the Monte Carlo method in the design process. Factor Fixing is used to distinguish parameters with negligible influence on the output from the remaining parameters, thereby focusing on the significant parameters. This considers that the parameters can influence each other, which is why the total-order sensitivity index is used. Factor Prioritization is performed after Factor Fixing, where the parameters are prioritized so that it is known which parameters that have the greatest influence on the output. Among other things, this can be used when the decision makers meet to discuss the building's design.

In order to investigate the accuracy, the sensitivity analysis method Sobol is used as a basis of comparison, since it is considered very accurate in other literature. The accuracy is divided into two parts; one for Factor Fixing and one for Factor Prioritization. For Factor Fixing, the maximum difference is found between Sobol's total-order sensitivity values and the values of the remaining sensitivity analysis methods, from which the sensitivity analysis methods are assigned a category according to the difference. The same is done for Factor Prioritization, however, with Sobol's first-order sensitivity values. In addition, Factor Prioritisation examines how the sensitivity analysis methods rank the parameters in relation to Sobol's first-order ranking.

To determine the convergence rate of the sensitivity analysis methods, it is examined how many simulations is used before the difference between simulation j and N's standardized values is less than 1%. This method is used for both Factor Fixing and Factor Prioritization, where Factor Prioritization also examines convergence in relation to ranking.

Based on the established method, the sensitivity analysis methods TOM, Morris, Extended Morris and Sobol are found most useful for Factor Fixing, as they all can find the total-order sensitivity index. In addition, it has been found that TOM and Sobol have better accuracy than Morris and Extended Morris, to which TOM uses fewer simulations than Sobol and is easier to use as it can use the commonly used sampling methods.

For Factor Prioritization, it has been found that SRC, Pearson, Spearman, PAWN and Sobol all find the first-order sensitivity index. For PAWN, it has been found that it uses many simulations to converge and that its sampling method leaves large areas of the design space unexplored, making it less useful for Factor Prioritization. The SRC shows surprisingly good results as it manages to maintain good precision even at low R² values. Pearson and Spearman also have shown good results, though not to the same degree as SRC, which is why they are not as useful. Since SRC gives good results, uses few simulations and is self-validating, it is obvious to use as the first trial for Factor Prioritization. If it appears that the R² value is low, Sobol can be used as an alternative, however, it requires more simulations to converge.

A more advantageous way to find the optimal solutions is by using the Monte Carlo method. For the Monte Carlo method, the parameters are varied independently, enabling multiple solutions to be investigated at the same time. Using the Monte Carlo method, it is also possible to use sensitivity analysis methods, which can give an overview of which parameters that have most influence on the output, which could, for example, be the building's energy consumption. The sensitivity analysis methods have different characteristics such as accuracy and computational resources as well as their complexity. This means that it is not arbitrary which sensitivity analysis method is chosen to use. Therefore, in this project, eight sensitivity analysis methods are investigated to determine which ones are most advantageous to use in the building design process. The study is based on eight test functions and two BSim models, from which the sensitivity analysis methods are evaluated based on their accuracy and convergence rate with respect to both Factor Fixing and Factor Prioritization.

Factor Fixing and Factor Prioritization are two settings that can be used with the Monte Carlo method in the design process. Factor Fixing is used to distinguish parameters with negligible influence on the output from the remaining parameters, thereby focusing on the significant parameters. This considers that the parameters can influence each other, which is why the total-order sensitivity index is used. Factor Prioritization is performed after Factor Fixing, where the parameters are prioritized so that it is known which parameters that have the greatest influence on the output. Among other things, this can be used when the decision makers meet to discuss the building's design.

In order to investigate the accuracy, the sensitivity analysis method Sobol is used as a basis of comparison, since it is considered very accurate in other literature. The accuracy is divided into two parts; one for Factor Fixing and one for Factor Prioritization. For Factor Fixing, the maximum difference is found between Sobol's total-order sensitivity values and the values of the remaining sensitivity analysis methods, from which the sensitivity analysis methods are assigned a category according to the difference. The same is done for Factor Prioritization, however, with Sobol's first-order sensitivity values. In addition, Factor Prioritisation examines how the sensitivity analysis methods rank the parameters in relation to Sobol's first-order ranking.

To determine the convergence rate of the sensitivity analysis methods, it is examined how many simulations is used before the difference between simulation j and N's standardized values is less than 1%. This method is used for both Factor Fixing and Factor Prioritization, where Factor Prioritization also examines convergence in relation to ranking.

Based on the established method, the sensitivity analysis methods TOM, Morris, Extended Morris and Sobol are found most useful for Factor Fixing, as they all can find the total-order sensitivity index. In addition, it has been found that TOM and Sobol have better accuracy than Morris and Extended Morris, to which TOM uses fewer simulations than Sobol and is easier to use as it can use the commonly used sampling methods.

For Factor Prioritization, it has been found that SRC, Pearson, Spearman, PAWN and Sobol all find the first-order sensitivity index. For PAWN, it has been found that it uses many simulations to converge and that its sampling method leaves large areas of the design space unexplored, making it less useful for Factor Prioritization. The SRC shows surprisingly good results as it manages to maintain good precision even at low R² values. Pearson and Spearman also have shown good results, though not to the same degree as SRC, which is why they are not as useful. Since SRC gives good results, uses few simulations and is self-validating, it is obvious to use as the first trial for Factor Prioritization. If it appears that the R² value is low, Sobol can be used as an alternative, however, it requires more simulations to converge.

Language | English |
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Publication date | 10 Jun 2020 |

Number of pages | 137 |