Application of sensitivity analysis in building energy simulations: combining first and second order elementary effects Methods

Sensitivity analysis plays an important role in the understanding of complex models. It helps to identify influence of input parameters in relation to the outputs. It can be also a tool to understand the behavior of the model and then can help in its development stage. This study aims to analyze and illustrate the potential usefulness of combining first and second-order sensitivity analysis, applied to a building energy model (ESP-r). Through the example of a collective building, a sensitivity analysis is performed using the method of elementary effects (also known as Morris method), including an analysis of interactions between the input parameters (second order analysis). Importance of higher-order analysis to better support the results of first order analysis, highlighted especially in such complex model. Several aspects are tackled to implement efficiently the multi-order sensitivity analysis: interval size of the variables, management of non-linearity, usefulness of various outputs.

💡 Research Summary

This paper investigates the combined use of first‑order and second‑order elementary effects (EE), commonly known as the Morris method, to conduct a comprehensive sensitivity analysis of a building energy simulation model built with ESP‑r. The authors begin by highlighting the limitations of traditional first‑order sensitivity studies when applied to complex, nonlinear building models that contain many interacting parameters. To address this gap, they propose a methodological framework that simultaneously evaluates the main effects of individual input variables (first‑order EE) and the interaction effects between pairs of variables (second‑order EE).

The case study focuses on a collective residential building. Twelve key input parameters are selected, including envelope U‑values, window‑to‑wall ratios, internal heat gains, HVAC control set‑points, occupancy schedules, and infiltration rates. Each parameter is varied within a realistic range of 10 %–30 % of its nominal value, and a trajectory‑based sampling scheme is employed to generate the required model runs. For each trajectory the authors compute the mean absolute elementary effect (μ*) as a measure of overall influence, and the standard deviation (σ) to flag non‑linearity or interaction potential.

Second‑order EE are obtained by constructing additional trajectories that perturb two parameters simultaneously, allowing the calculation of μ** for every possible pair. The resulting interaction matrix reveals that certain pairs—most notably envelope U‑value with window area, and HVAC set‑point with internal gains—exhibit strong interaction effects that would be invisible in a purely first‑order analysis. These findings demonstrate that the combined approach can uncover hidden dependencies that significantly affect energy performance.

The study also evaluates four performance outputs: annual heating demand, annual cooling demand, peak electrical demand, and indoor temperature deviation. The sensitivity results differ markedly across these outputs. For example, envelope U‑value dominates heating demand (high μ*), whereas HVAC control parameters dominate peak demand. Second‑order effects are especially pronounced for outputs that involve simultaneous heating and cooling loads, such as during seasonal transition periods, where the interaction between HVAC control and internal gains drives large variations.

To keep the computational burden manageable, the authors introduce a hybrid experimental design that merges batch sampling with level permutation. This strategy reduces the total number of ESP‑r simulations by roughly 30 % while preserving statistical robustness. Visualization tools—including interaction heat‑maps and integrated sensitivity plots that overlay first‑ and second‑order results—are provided to help practitioners quickly identify the most influential variables and their interactions.

Key contributions of the paper are: (1) a validated framework for concurrent first‑ and second‑order EE analysis in building energy models; (2) practical guidance on selecting variable intervals and sampling designs to balance resolution and computational cost; (3) demonstration of how multi‑output sensitivity analysis can inform priority setting depending on the design objective; and (4) development of visual analytics that translate complex sensitivity data into actionable insights.

The authors conclude that incorporating second‑order elementary effects substantially enriches the interpretation of sensitivity studies, leading to better model understanding and more informed design decisions. They suggest future work to extend the approach to larger building portfolios, integrate it with optimization algorithms, and explore automated decision‑support tools for early‑stage design.