Global sensitivity analysis of computer models with functional inputs

Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This paper aims to illustrate different variance-based sensitivity analysis techniques, based on the so-called Sobol indices, when some input variables are functional, such as stochastic processes or random spatial fields. In this work, we focus on large cpu time computer codes which need a preliminary meta-modeling step before performing the sensitivity analysis. We propose the use of the joint modeling approach, i.e., modeling simultaneously the mean and the dispersion of the code outputs using two interlinked Generalized Linear Models (GLM) or Generalized Additive Models (GAM). The ``mean'' model allows to estimate the sensitivity indices of each scalar input variables, while the ``dispersion'' model allows to derive the total sensitivity index of the functional input variables. The proposed approach is compared to some classical SA methodologies on an analytical function. Lastly, the proposed methodology is applied to a concrete industrial computer code that simulates the nuclear fuel irradiation

Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels

The global sensitivity analysis method, used to quantify the influence of uncertain input variables on the response variability of a numerical model, is applicable to deterministic computer code (for which the same set of input variables gives always the same output value). This paper proposes a global sensitivity analysis methodology for stochastic computer code (having a variability induced by some uncontrollable variables). The framework of the joint modeling of the mean and dispersion of heteroscedastic data is used. To deal with the complexity of computer experiment outputs, non parametric joint models (based on Generalized Additive Models and Gaussian processes) are discussed. The relevance of these new models is analyzed in terms of the obtained variance-based sensitivity indices with two case studies. Results show that the joint modeling approach leads accurate sensitivity index estimations even when clear heteroscedasticity is present

A model-based methodology for managing technological risk

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Role of Low Carbon Energy Technologies in Near Term Energy Policy

In the first part of this thesis, we use a multi-model framework to examine a set of possible future energy scenarios resulting from R&D portfolios of Solar, Nuclear, Carbon Capture and Storage (CCS), Bio-Fuels, Bio-Electricity and Batteries for electric transportation. We show that CCS significantly complements Bio-Electricity, while most of the other energy technology pairs are substitutes. From the probabilistic analysis of future energy scenarios we observe that portfolios with CCS tend to stochastically dominate those without CCS; portfolios with only renewables tend to be stochastically dominated by others; and that there are clear decreasing marginal returns to scale. We also find that, with higher damage risk, there is more incentive for technical advancement in CCS and less incentive for development of Solar energy technology. In the second part of this thesis, we examine the optimal R&D portfolio changes at the different R&D budget levels and how risk in climate damages affects the optimal R&D portfolio. We find that the optimal portfolio is generally not robust to risk, and the optimal investments in the energy technologies vary with risk in climate damages; however R&D investments in certain energy technologies, such as Nuclear, are robust under the different risk cases. We note that while CCS plays a significant role in the optimal portfolio when there is no risk in climate damages, it plays an even more significant role in the higher climate damage risk cases. We also find that R&D investment in the Biofuels energy technology increases significantly with increase in climate damage risk, while Solar, Batteries for Electric Transportation and Bio-Electricity technologies go out of favor with increases in climate damage risk. We also propose a methodology for obtaining solutions to subset portfolio problems, based on the characteristics of the individual technologies. We prove that the subset portfolio problem is optimal if the individual technology does not interact with any of the other technologies, we confirm this in our empirical portfolio problem. In the third part of this thesis, we conduct an illustrative global sensitivity analysis on a large scale integrated assessment model with a view to determining the primary drivers of uncertainty in the model and examining the effect of structural uncertainty on the model. We compare our results to a previous paper which conducted a one factor at a time sensitivity analysis and find that both sensitivity methods provide the same result which is different from findings from the previous paper. We find that model interactions are present even in our very limited illustrative analysis. We also conduct most of the steps needed for a full global sensitivity analysis of the model and highlight the challenges in conducting this analysis on the GCAM model. We show that there exist a need for global sensitivity analysis for accurate determination of the principal drivers of uncertainty in integrated models

Global sensitivity analysis for models with spatially dependent outputs

International audienceThe global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu time-expensive computer code with an inexpensive mathematical function, which predicts the computer code output. The common metamodel-based sensitivity analysis methods are well-suited for computer codes with scalar outputs. However, in the environmental domain, as in many areas of application, the numerical model outputs are often spatial maps, which may also vary with time. In this paper, we introduce an innovative method to obtain a spatial map of Sobol' indices with a minimal number of numerical model computations. It is based upon the functional decomposition of the spatial output onto a wavelet basis and the metamodeling of the wavelet coefficients by the Gaussian process. An analytical example is presented to clarify the various steps of our methodology. This technique is then applied to a real hydrogeological case: for each model input variable, a spatial map of Sobol' indices is thus obtained

Developing Efficient Strategies For Global Sensitivity Analysis Of Complex Environmental Systems Models

Complex Environmental Systems Models (CESMs) have been developed and applied as vital tools to tackle the ecological, water, food, and energy crises that humanity faces, and have been used widely to support decision-making about management of the quality and quantity of Earth’s resources. CESMs are often controlled by many interacting and uncertain parameters, and typically integrate data from multiple sources at different spatio-temporal scales, which make them highly complex. Global Sensitivity Analysis (GSA) techniques have proven to be promising for deepening our understanding of the model complexity and interactions between various parameters and providing helpful recommendations for further model development and data acquisition. Aside from the complexity issue, the computationally expensive nature of the CESMs precludes effective application of the existing GSA techniques in quantifying the global influence of each parameter on variability of the CESMs’ outputs. This is because a comprehensive sensitivity analysis often requires performing a very large number of model runs. Therefore, there is a need to break down this barrier by the development of more efficient strategies for sensitivity analysis. The research undertaken in this dissertation is mainly focused on alleviating the computational burden associated with GSA of the computationally expensive CESMs through developing efficiency-increasing strategies for robust sensitivity analysis. This is accomplished by: (1) proposing an efficient sequential sampling strategy for robust sampling-based analysis of CESMs; (2) developing an automated parameter grouping strategy of high-dimensional CESMs, (3) introducing a new robustness measure for convergence assessment of the GSA methods; and (4) investigating time-saving strategies for handling simulation failures/crashes during the sensitivity analysis of computationally expensive CESMs. This dissertation provides a set of innovative numerical techniques that can be used in conjunction with any GSA algorithm and be integrated in model building and systems analysis procedures in any field where models are used. A range of analytical test functions and environmental models with varying complexity and dimensionality are utilized across this research to test the performance of the proposed methods. These methods, which are embedded in the VARS–TOOL software package, can also provide information useful for diagnostic testing, parameter identifiability analysis, model simplification, model calibration, and experimental design. They can be further applied to address a range of decision making-related problems such as characterizing the main causes of risk in the context of probabilistic risk assessment and exploring the CESMs’ sensitivity to a wide range of plausible future changes (e.g., hydrometeorological conditions) in the context of scenario analysis

Is VARS more intuitive and efficient than Sobol' indices?

The Variogram Analysis of Response Surfaces (VARS) has been proposed by Razavi and Gupta as a new comprehensive framework in sensitivity analysis. According to these authors, VARS provides a more intuitive notion of sensitivity and it is much more computationally efficient than Sobol' indices. Here we review these arguments and critically compare the performance of VARS-TO, for total-order index, against the total-order Jansen estimator. We argue that, unlike classic variance-based methods, VARS lacks a clear definition of what an "important" factor is, and show that the alleged computational superiority of VARS does not withstand scrutiny. We conclude that while VARS enriches the spectrum of existing methods for sensitivity analysis, especially for a diagnostic use of mathematical models, it complements rather than substitutes classic estimators used in variance-based sensitivity analysis.Comment: Currently under review in Environmental Modelling & Softwar