Sobol Indices for Dimension Adaptivity in Sparse Grids

2016 ◽  
pp. 371-395
Author(s):  
Richard P. Dwight ◽  
Stijn G. L. Desmedt ◽  
Pejman Shoeibi Omrani
Keyword(s):  
Sparse Grids ◽  
Sobol Indices

Computation of the Sobol' Indices using Importance Sampling

2014 ◽  
Author(s):  
Pierre Beaurepaire ◽  
Matteo Broggi ◽  
Edoardo Patelli
Keyword(s):  
Importance Sampling ◽  
Sobol Indices

scholarly journals A Model for the Thermal Behaviour of an Offshore Cable Installed in a J-Tube

Proceedings ◽  
2020 ◽  
Vol 58 (1) ◽  
pp. 31
Author(s):  
Jeremy Arancio ◽  
Ahmed Ould El Moctar ◽  
Minh Nguyen Tuan ◽  
Faradj Tayat ◽  
Jean-Philippe Roques
Keyword(s):  
Sensitivity Analysis ◽  
Numerical Model ◽  
Thermal Behaviour ◽  
Energy Production ◽  
Power Transmission ◽  
Temperature Fields ◽  
Sobol Indices ◽  
Lumped Element ◽  
Thermal Phenomena ◽  
The Impact

In the race for energy production, supplier companies are concerned by the thermal rating of offshore cables installed in a J-tube, not covered by IEC 60287 standards, and are now looking for solutions to optimize this type of system. This paper presents a numerical model capable of calculating temperature fields of a power transmission cable installed in a J-tube, based on the lumped element method. This model is validated against the existing literature. A sensitivity analysis performed using Sobol indices is then presented in order to understand the impact of the different parameters involved in the heating of the cable. This analysis provides an understanding of the thermal phenomena in the J-tube and paves the way for potential technical and economic solutions to increase the ampacity of offshore cables installed in a J-tube.

B-splines on sparse grids for surrogates in uncertainty quantification

2021 ◽  
Vol 209 ◽  
pp. 107430
Author(s):  
Michael F. Rehme ◽  
Fabian Franzelin ◽  
Dirk Pflüger
Keyword(s):  
Uncertainty Quantification ◽  
Sparse Grids ◽  
B Splines

scholarly journals Variance-based global sensitivity analysis and beyond in life cycle assessment: an application to geothermal heating networks

2021 ◽  
Author(s):  
Marc Jaxa-Rozen ◽  
Astu Sam Pratiwi ◽  
Evelina Trutnevyte
Keyword(s):  
Sensitivity Analysis ◽  
Life Cycle Assessment ◽  
Environmental Impacts ◽  
Spectral Clustering ◽  
Global Sensitivity Analysis ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Geothermal Heating ◽  
Trade Offs ◽  
Heating Networks

Abstract Purpose Global sensitivity analysis increasingly replaces manual sensitivity analysis in life cycle assessment (LCA). Variance-based global sensitivity analysis identifies influential uncertain model input parameters by estimating so-called Sobol indices that represent each parameter’s contribution to the variance in model output. However, this technique can potentially be unreliable when analyzing non-normal model outputs, and it does not inform analysts about specific values of the model input or output that may be decision-relevant. We demonstrate three emerging methods that build on variance-based global sensitivity analysis and that can provide new insights on uncertainty in typical LCA applications that present non-normal output distributions, trade-offs between environmental impacts, and interactions between model inputs. Methods To identify influential model inputs, trade-offs, and decision-relevant interactions, we implement techniques for distribution-based global sensitivity analysis (PAWN technique), spectral clustering, and scenario discovery (patient rule induction method: PRIM). We choose these techniques because they are applicable with generic Monte Carlo sampling and common LCA software. We compare these techniques with variance-based Sobol indices, using a previously published LCA case study of geothermal heating networks. We assess eight environmental impacts under uncertainty for three design alternatives, spanning different geothermal production temperatures and heating network configurations. Results In the application case on geothermal heating networks, PAWN distribution-based sensitivity indices generally identify influential model parameters consistently with Sobol indices. However, some discrepancies highlight the potentially misleading interpretation of Sobol indices on the non-normal distributions obtained in our analysis, where variance may not meaningfully describe uncertainty. Spectral clustering highlights groups of model results that present different trade-offs between environmental impacts. Compared to second-order Sobol interaction indices, PRIM then provides more precise information regarding the combinations of input values associated with these different groups of calculated impacts. PAWN indices, spectral clustering, and PRIM have a computational advantage because they yield stable results at relatively small sample sizes (n = 12,000), unlike Sobol indices (n = 100,000 for second-order indices). Conclusions We recommend adding these new techniques to global sensitivity analysis in LCA as they give more precise as well as additional insights on uncertainty regardless of the distribution of the model outputs. PAWN distribution-based global sensitivity analysis provides a computationally efficient assessment of input sensitivities as compared to variance-based global sensitivity analysis. The combination of clustering and scenario discovery enables analysts to precisely identify combinations of input parameters or uncertainties associated with different outcomes of environmental impacts.

scholarly journals Calculations of Sobol indices for the Gaussian process metamodel

2009 ◽  
Vol 94 (3) ◽  
pp. 742-751 ◽  
Author(s):  
Amandine Marrel ◽  
Bertrand Iooss ◽  
Béatrice Laurent ◽  
Olivier Roustant
Keyword(s):  
Gaussian Process ◽  
Sobol Indices

Polynomial Representation of the Gaussian Process

2018 ◽  
Author(s):  
Jesper Kristensen ◽  
Isaac Asher ◽  
Liping Wang
Keyword(s):  
Gaussian Process ◽  
Basis Functions ◽  
Training Data ◽  
Computational Time ◽  
High Dimensional ◽  
High Dimensional Model Representation ◽  
Analysis Tool ◽  
Sobol Indices ◽  
Robust Fitting ◽  
Uncertainty Estimates

Gaussian Process (GP) regression is a well-established probabilistic meta-modeling and data analysis tool. The posterior distribution of the GP parameters can be estimated using, e.g., Markov Chain Monte Carlo (MCMC). The ability to make predictions is a key aspect of using such surrogate models. To make a GP prediction, the MCMC chain as well as the training data are required. For some applications, GP predictions can require too much computational time and/or memory, especially for many training data points. This motivates the present work to represent the GP in an equivalent polynomial (or other global functional) form called a portable GP. The portable GP inherits many benefits of the GP including feature ranking via Sobol indices, robust fitting to non-linear and high-dimensional data, accurate uncertainty estimates, etc. The framework expands the GP in a high-dimensional model representation (HDMR). After fitting each HDMR basis function with a polynomial, they are all added together to form the portable GP. A ranking of which basis functions to use in the fitting process is automatically provided via Sobol indices. The uncertainty from the fitting process can be propagated to the final GP polynomial estimate. In applications where speed and accuracy are paramount, spline fits to the basis functions give very good results. Finally, portable BHM provides an alternative set of assumptions with regards to extrapolation behavior which may be more appropriate than the assumptions inherent in GPs.

scholarly journals Sensitivity analysis of a coupled hydrodynamic-vegetation model using the effectively subsampled quadratures method (ESQM v5.2)

2017 ◽  
Vol 10 (12) ◽  
pp. 4511-4523 ◽  
Author(s):  
Tarandeep S. Kalra ◽  
Alfredo Aretxabaleta ◽  
Pranay Seshadri ◽  
Neil K. Ganju ◽  
Alexis Beudin
Keyword(s):  
Sensitivity Analysis ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Aquatic Vegetation ◽  
Three Dimensional ◽  
Sensitivity Analyses ◽  
Stem Density ◽  
Sobol Indices ◽  
Plant Stem ◽  
Wave Induced

Abstract. Coastal hydrodynamics can be greatly affected by the presence of submerged aquatic vegetation. The effect of vegetation has been incorporated into the Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system. The vegetation implementation includes the plant-induced three-dimensional drag, in-canopy wave-induced streaming, and the production of turbulent kinetic energy by the presence of vegetation. In this study, we evaluate the sensitivity of the flow and wave dynamics to vegetation parameters using Sobol' indices and a least squares polynomial approach referred to as the Effective Quadratures method. This method reduces the number of simulations needed for evaluating Sobol' indices and provides a robust, practical, and efficient approach for the parameter sensitivity analysis. The evaluation of Sobol' indices shows that kinetic energy, turbulent kinetic energy, and water level changes are affected by plant stem density, height, and, to a lesser degree, diameter. Wave dissipation is mostly dependent on the variation in plant stem density. Performing sensitivity analyses for the vegetation module in COAWST provides guidance to optimize efforts and reduce exploration of parameter space for future observational and modeling work.

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