Thierry Alex Mara

Random balance designs for the estimation of first order global sensitivity indices

We present two methods for the estimation of main effects in global sensitivity analysis. The methods adopt Satterthwaites application of random balance designs in regression problems, and extend it to sensitivity analysis of model output for non-linear, non-additive models. Finite as well as infinite ranges for model input factors are allowed. The methods are easier to implement than any other method available for global sensitivity analysis, and reduce significantly the computational cost of the analysis. We test their performance on different test cases, including an international benchmark on safety assessment for nuclear waste disposal originally carried out by OECD/NEA.

Variance-based sensitivity indices for models with dependent inputs

Computational models are intensively used in engineering for risk analysis or prediction of future outcomes. Uncertainty and sensitivity analyses are of great help in these purposes. Although several methods exist to perform variance-based sensitivity analysis of model output with independent inputs only a few are proposed in the literature in the case of dependent inputs. This is explained by the fact that the theoretical framework for the independent case is set and a univocal set of variance-based sensitivity indices is defined. In the present work, we propose a set of variance-based sensitivity indices to perform sensitivity analysis of models with dependent inputs. These measures allow us to distinguish between the mutual dependent contribution and the independent contribution of an input to the model response variance. Their definition relies on a specific orthogonalisation of the inputs and ANOVA-representations of the model output. In the applications, we show the interest of the new sensitivity indices for model simplification setting.

A node pruning algorithm based on a Fourier amplitude sensitivity test method

In this paper, we propose a new pruning algorithm to obtain the optimal number of hidden units of a single layer of a fully connected neural network (NN). The technique relies on a global sensitivity analysis of model output. The relevance of the hidden nodes is determined by analysing the Fourier decomposition of the variance of the model output. Each hidden unit is assigned a ratio (the fraction of variance which the unit accounts for) that gives their ranking. This quantitative information therefore leads to a suggestion of the most favorable units to eliminate. Experimental results suggest that the method can be seen as an effective tool available to the user in controlling the complexity in NNs.

Use of Global Sensitivity Analysis and Polynomial Chaos Expansion for Interpretation of Non-reactive Transport Experiments in Laboratory-Scale Porous Media

In this work, we show how the use of global sensitivity analysis (GSA) in conjunction with the polynomial chaos expansion (PCE) methodology can provide relevant information for the interpretation of transport experiments in laboratory-scale heterogeneous porous media. We perform GSA by calculating the Sobol indices, which provide a variance-based importance measure of the effects of uncertain parameters on the output of a chosen interpretive transport model. The choice of PCE has the following two benefits: (1) it provides the global sensitivity indices in a straightforward manner, and (2) PCE can serve as a surrogate model for the calibration of parameters. The coefficients of the PCE are computed by probabilistic collocation. The methodology is applied to two nonreactive transport experiments available in the literature, while considering both transient and pseudo steady state transport regimes. This method allows a rigorous investigation of the relative effects and importance of different uncertain quantities, which include boundary conditions as well as porous medium hydraulic and dispersive parameters. The parameters that are most relevant to depicting the systems behavior can then be evaluated. In addition, one can assess the space-time distribution of measurement points, which is the most influential factor for the identifiability of parameters. Our work indicates that these methods can be valuable tools in the proper design of model-based transport experiments.

Extension of the RBD-FAST method to the computation of global sensitivity indices

This paper deals with the sensitivity analysis method named Fourier amplitude sensitivity test (FAST). This method is known to be very robust for the computation of global sensitivity indices but their computational cost remains prohibitive for complex and large dimensional models. Recent developments in the implementation of FAST by use of the random balance designs (RBD) technique have allowed significant reduction of the computational cost. The method is now called RBD-FAST. The drawback of this improvement is that only individual first-order sensitivity indices can be computed. In this article, an extension of RBD is derived for the estimation of any global sensitivity indices of individual factor or group of factors. Several tests are proposed to compare the performances of classical FAST and RBD-FAST.

On the thermal behaviour of roof-mounted radiant barriers under tropical and humid climatic conditions: modelling and empirical validation

This paper deals with the empirical validation of a building thermal model, which includes a roof-mounted radiant barrier. We first present the thermal model, developed with a building simulation code prototype, the objective being to increase understanding of the thermal phenomena that govern the behaviour of the whole building. We then describe the experimental test cell, with emphasis on the details of the roof. A sensitivity analysis technique is applied to the model which shows that convective heat transfer is of great importance for the dry-air temperature of the roof air layer. The origin of the disagreement between measurements and model predictions is then identified as being due to one of the convective heat transfer coefficients. Once this is modified the agreement is found to be acceptable.

Building ventilation: A pressure airflow model computer generation and elements of validation

The calculation of airflows is of great importance for detailed building thermal simulation computer codes, these airflows most frequently constituting an important thermal coupling between the building and the outside on one hand, and the different thermal zones on the other. The driving effects of air movement, which are the wind and the thermal buoyancy, are briefly outlined and we look closely at their coupling in the case of buildings, by exploring the difficulties associated with large openings. Some numerical problems tied to the resolving of the non-linear system established are also covered. Part of a detailled simulation software (CODYRUN), the numerical implementation of this airflow model is explained, insisting on data organization and processing allowing the calculation of the airflows. Comparisons are then made between the model results and in one hand analytical expressions and in another and experimental measurements in case of a collective dwelling.

Sky temperature modelisation and applications in building simulation

The sky temperature is an important parameter for simulation codes in building studies. A preliminary campaign of validation of a simulation software CODYRUN has demonstrated the misinterpretation of the radiative exchanges of long waves between the building and its environment. A bibliographical research has then led to the use models using dry air temperature to estimate sky temperature. However, these models has not been completely satisfactory as far as night clear sky are concerned. In this case, sky temperature remains overestimated. A research of a non linear model has been undertaken, leading to the use of neural networks with satisfactory results. Sky temperature is then calculated and reinjected into the simulation code. Comparison between simulated temperature and measures has turned to be acceptable.

Empirical validation of the thermal model of a passive solar cell test

Abstract The paper deals with an empirical validation of a building thermal model. We put the emphasis on sensitivity analysis and on research of inputs/residual correlation to improve our model. In this paper, we apply a sensitivity analysis technique in the frequency domain to point out the more important parameters of the model. Then, we compare measured and predicted data of indoor dry-air temperature. When the model is not accurate enough, recourse to time–frequency analysis is of great help to identify the inputs responsible for the major part of error. In our approach, two samples of experimental data are required. The first one is used to calibrate our model, the second one to really validate the optimized model.

Reactive Transport Parameter Estimation and Global Sensitivity Analysis Using Sparse Polynomial Chaos Expansion

We present in this paper a new strategy based on the use of polynomial chaos expansion (PCE) for both global sensitivity analysis and parameter optimization. To limit the number of evaluations of the direct model, we develop a simple and efficient procedure to construct a sparse PCE where only coefficients that have a significant contribution to the variance of the model are retained. Parameter estimation is performed using an adaptive procedure where the intervals of variation of the parameters are progressively reduced using information from sensitivity analysis calculated using the sparse PCE. The strategy is shown to be effective for the parameter estimation of two reactive transport problems: a synthetic reactive transport problem involving the Freundlich sorption isotherm and a field experiment of Valocchi et al. (Water Resources Research 17:1517–1527, 1981) involving nonlinear ion exchange reactions.