استفاده از تجزیه و تحلیل حساسیت در شبیه سازی انرژی ساختمان : ترکیبی از روش اثرات ابتدایی اول و مرتبه دوم

Sensitivity analysis plays an important role in the understanding of complex models. It helps to identify the influence of input parameters in relation to the outputs. It can also be a tool to understand the behavior of the model and can then facilitate 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 an apartment building, a sensitivity analysis is performed using the method of elementary effects (also known as the Morris method), including an analysis of the interactions between the input parameters (second-order analysis). The usefulness of higher-order analysis is highlighted to support the results of the first-order analysis better. Several aspects are tackled to implement the multi-order sensitivity analysis efficiently: interval size of the variables, the management of non-linearity and the usefulness of various outputs.

Energy consumption related to the building sector is recognized as a major part of the total energy consumption worldwide (37% of the final energy consumption in the EU in 2004) [1] and consequently a significant source of greenhouse gas emissions [2]. The growth in population, building services and comfort levels guarantees that this tendency will continue in the forthcoming years. Many tools have been developed to model the energy consumption in buildings (EnergyPlus, TRNSYS, ESP-r), particularly for end uses such as space heating and cooling, ventilation and lighting. In most cases, such models take into account coupling between phenomena (e.g. interactions between occupancy, micro-climate, envelope, HVAC, etc.) through coupling of different specialized sub-models and by using a large number of diverse input variables. Sensitivity analysis can help in understanding the relative influence of input parameters on the output [3]. In the field of building energy models, combining sensitivity analysis and simulations tools can be useful as it helps to rank the input parameters (or family of parameters) and then to select the most appropriate to be considered, depending on the objective of the modeling. For example, this is particularly interesting when the modeling objective is related to the building design (e.g. sketch stage of the design, modeling retrofitting scenarios according to the only available input data) or when it is to define archetypes. Another application is in the development stage of the tools, and more precisely the definition of possible simplification of models or in the validation of assumptions in the selection of input parameters that must be considered. In these cases, and depending on the objectives of the tool developed, some sub-models and their corresponding input data may become secondary. A solution consists of using a detailed model in the upstream stage, combined with a sensitivity analysis in order to rank the set of parameters and identify the coupling between them. Then, the selection of the most important variable helps to define the structure of the simplified model. In this study, we propose combining the implementation of ESP-r [4] with two sensitivity analysis techniques: the Morris method [5] and an extension of this methodology for the analysis of interactions between the parameters [6]. In Section 2, sensitivity analysis methods are quickly reviewed. Then, the elementary effects method and its second-order variant are described, together with the apartment building test case (Section 3). Finally, results are presented and discussed for the two methods used (Section 4).

In this work, first- and second-order sensitivity analyzes have been combined. The Morris method and its extension have been applied to a building thermal simulation case study, using ESP-r to calculate the output. Among the results of this approach, the first order-analysis has demonstrated that, even if a precise ranking between the input parameters is not relevant, they can be split into different families in order to discuss their importance. This first order analysis helps to identify possible non-linearity or interactions of higher orders. The usefulness of considering various forms for the output function (kWh/year, kWh/year m3, ln(kWh/year m3)) has been explored, in particular to reduce the number of variables affected by these non-linearities or interactions. For instance, specific values per m3 (or per m2) reduce the correlation to the size-related parameters. Moreover, considering the logarithm of the output helps to identify the origin of some of the non-linearity. It is worth noting that investigating various model outputs does not require additional simulation runs: the same set of simulation trajectories is used and only complementary post-processing is needed. This remark can be extended to any transformed output calculated from model output and input variables. For those parameters still remaining in the area of high standard deviation, it has been demonstrated how the implementation of the second-order sensitivity analysis can be helpful to sort variables and to specify their interaction in pairs. It has also been shown how the usefulness of the upper-order analysis is amplified when combined with the different forms for the output. A new way of presenting results from the Morris method has been proposed to classify parameters (or couples of parameters in the case of second-order analysis) according to their sensitivity: linear-, monotonic-, almost monotonic or highly non-linear/interaction-of-higher-order). The value of sensitivity analysis using the elementary effects method has been clearly established. In any case, for a given building being simulated with a specific modeling tool, no general sensitivity can be derived: the results depend on the input parameters, with fixed values or varying values (and for the latter, their variation range). Thus, sensitivity analysis must be performed for each particular situation, in relation to modeling goals, with a careful choice of variation intervals. Its conclusions are valid only for this particular situation. The choice of variation interval for each input parameter must be related to either a constrained range for decision variables or an uncertainty domain for exogenous variables.