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Analyse de sensibilité pour des modèles stochastiques à entrées dépendantes : application en énergétique du bâtiment

Abstract : Buildings represent one of the main levers of action to optimize energy efficiency and reducing emissions of CO2. To understand how perform energy consumption of a building, different studies have been conducted on the thermal performance both the point of view of design and model calibration as the climate change impact. Energy performance can be optimized according to these studies by evaluating the degree of uncertainty due to each of the variables or parameters that may influence performance. This stage is called sensitivity analysis.Most building studies in the literature are placed in a static framework that does not represent the evolution of the system. The variables whose sensitivity to be studied are either considered at a given time or the input-output models are not dynamic. It became necessary to develop methods that take into account both the dependence of the inputs and the temporal dimension which itself always involves dependence. Among the different methods of sensitivity analysis, we have focused on the global method, based on the calculation of Sobol sensitivity indices. Sobol index of a parameter (or group of parameters) is a statistical indicator of easy interpretation. It allows to measure the importance of this parameter (or group of parameters) on the variability of a scalar quantity of interest, depending on the model output. Sensitivity indices allow to rank input parameters according to their influence on the output.Sobol indices can be calculated in different ways. We focused on the Pick and Freeze method based on sampling. This is based on a fundamental assumption and in practice often unverified : inputs independence. This led us statistically to develop new techniques to take into account the dynamic characteristic of inputs and dependents both in time and in every moment. Our work focuses on methods that can bring back to the case of independent inputs. Our concern was modelled in a flexible way inputs, easily transferable to other concrete situations and allowing relatively easy simulations. The input-output relationships are not important as the only constraint, of course not trivial, possible simulation.In order to reproduce the temporal relationship between the variables, we chose to consider an index dependent, in the non-stationary case (especially if there are seasonal phenomena), on the time of calculation and quantify the variability of output not not only to the variability of the input at time, but also to the same variability from previous times. This vision allows to introduce the concept of usable memory for the calculation of the sensitivity.The second method that we have developed is an estimation method of Sobol indices for static dependent inputs a priori. It may nevertheless be implemented for dynamic inputs with short memory but the calculations are then very heavy when the number of inputs are large or own important memories. This method allows to separate dependent variables of any law in independent variables uniformly distributed.Easy to implement these estimation methods developed are not based on assumptions of independence of inputs. It then allows a wide range of applications.This method applied to an existing building can help improve energy management and can be useful in the design from the implementation scenarios. We could show different situations by analysing the variable order according to the sensitivities from measurements on a test building. Two criteria were studied. A criterion of comfort: the study of indoor temperature and performance criteria: the heating energy.
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Mathilde Grandjacques. Analyse de sensibilité pour des modèles stochastiques à entrées dépendantes : application en énergétique du bâtiment. Energie électrique. Université Grenoble Alpes, 2015. Français. ⟨NNT : 2015GREAT109⟩. ⟨tel-01266397⟩

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