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Toy model: Sobol index estimation in function of time. Left one used 500 points and right one 25000 points.
Source publication
This paper address sensibility theory for dynamic models, linking correlated
inputs to observed outputs. Usual estimation methods of Sobol indices are based
on the fact that the input variables are independent. We present in this paper
a method to overpass this constraint for Gaussian processes of high dimension
in a time related framework. A gener...
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Citations
... This calculation needs the independence of the inputs, but has no constraints on their distribution. Here, the indices are estimated using sampling such as Quasi Monte Carlo (Grandjacques, 2014). The estimators of expectation and variances require a high number of samples. ...
Purpose
The thermal modelling of an electrical machine is difficult because the thermal behavior depends on its geometry, the used materials and its manufacturing process. In the paper, such a thermal model is used during the sizing process by optimization of a hybrid electric vehicle (HEV). This paper aims to deal with the sensitivities of thermal parameters on temperatures inside the electrical machine to allow the assessment of the influence of thermal parameters that are hard to assess.
Design/methodology/approach
A sensitivity analysis by Sobol indices is used to assess the sensitivities of the thermal parameters on electrical machine temperatures. As the optimization process needs fast computations, a lumped parameter thermal network (LPTN) is proposed for the thermal modelling of the machine, because of its fastness. This is also useful for the Sobol method that needs too many calls to this thermal model. This model is also used in a global model of a hybrid vehicle.
Findings
The difficulty is the thermal modelling of the machine on the validity domain of the sizing problem. The Sobol indices allow to find where a modelling effort has to be carried out.
Research limitations/implications
The Sobol indices have a significant value according to the number of calls of the model and their type (first-order, total, etc.). Therefore, the quality of the thermal sensitivity analysis is a compromise between computation times and modelling accuracy.
Practical implications
Thermal modelling of an electrical machine in a sizing process by optimization.
Originality/value
The use of Sobol indices for the sensitivity analysis of the thermal parameters of an electrical machine.
... In order to contribute to the uncertainty management in modelling, we have proposed some approaches for improving the reliability of building energy and thermal models. Grandjacques et al. [23] developed sensitivity analysis methods for dependent and dynamic inputs based on the method of Pick and Freeze for the estimation of Sobol's indexes. These methods were applied for an existing platform building in France to take into account both the dynamic aspect of the inputs (room temperatures, heating system, presence of occupancy, inertia of heat exchange) and the one of the output. ...
Building thermal modelling plays an important role in managing the thermal comfort and the energy consumption of buildings. A major challenge for modellers is how to deal with uncertainty problems in order to have a robust model with an acceptable computational time for the improvement of predictive control. This paper presents a methodology which allows obtaining the good model of a controllable thermal zone able to adapt regularly to the measurements by a robust identification procedure. Its input data are achieved by the modelling simplification of adjacent zones under uncontrollable uncertainties. This method is applied for a multi-zone positive energy building in south of France to validate our approach.
KeywordsEnergy in buildingsRobust identificationPredictive controlThermal envelope modelling
