Discovering a one-dimensional active subspace to quantify multidisciplinary uncertainty in satellite system design

Hu, Xiaoqian; Parks, Geoffrey T.; Chen, Xiaoqian; Seshadri, Pranay

doi:10.1016/j.asr.2015.11.001

Cited by 25 publications

(13 citation statements)

References 10 publications

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“…Along the active variables, the observation changes more, on average, than along any other direction in the parameter space. The method has mainly been applied to engineering-related models (e.g., Constantine et al, 2015a, b;Constantine and Doostan, 2017;Hu et al, 2016Hu et al, , 2017Glaws et al, 2017;Grey and Constantine, 2018;Li et al, 2019); however, recently it has also successfully been applied to coupled surface-subsurface-flow simulations. Jefferson et al (2015) used the coupled subsurfaceland-surface model ParFlow-CLM to study the sensitivity of energy fluxes to vegetation and land-surface parameters.…”

Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces

Erdal

Cirpka

2019

Hydrol. Earth Syst. Sci.

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Abstract. Integrated hydrological modeling of domains with complex subsurface features requires many highly uncertain parameters. Performing a global uncertainty analysis using an ensemble of model runs can help bring clarity as to which of these parameters really influence system behavior and for which high parameter uncertainty does not result in similarly high uncertainty of model predictions. However, already creating a sufficiently large ensemble of model simulation for the global sensitivity analysis can be challenging, as many combinations of model parameters can lead to unrealistic model behavior. In this work we use the method of active subspaces to perform a global sensitivity analysis. While building up the ensemble, we use the already-existing ensemble members to construct low-order meta-models based on the first two active-subspace dimensions. The meta-models are used to pre-determine whether a random parameter combination in the stochastic sampling is likely to result in unrealistic behavior so that such a parameter combination is excluded without running the computationally expensive full model. An important reason for choosing the active-subspace method is that both the activity score of the global sensitivity analysis and the meta-models can easily be understood and visualized. We test the approach on a subsurface-flow model including uncertain hydraulic parameters, uncertain boundary conditions and uncertain geological structure. We show that sufficiently detailed active subspaces exist for most observations of interest. The pre-selection by the meta-model significantly reduces the number of full-model runs that must be rejected due to unrealistic behavior. An essential but difficult part in active-subspace sampling using complex models is approximating the gradient of the simulated observation with respect to all parameters. We show that this can effectively and meaningfully be done with second-order polynomials.

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Section: Introductionmentioning

confidence: 99%

Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces

Erdal

Cirpka

2019

Hydrol. Earth Syst. Sci.

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“…In this case, we resort to modeling the gradients using function evaluations; for example, finite difference approximations of partial derivatives are the slope of a plane that interpolates two nearby function evaluations. The approach outlined in Algorithm 2, based on a least-squares-fit linear approximation of f (x), has been unreasonably and surprisingly effective for uncovering one-dimensional active subspaces in a range of applications from integrated hydrological modeling [36] to multiphysics scramjet modeling [1] to satellite system modeling [37]. Algorithm 2 Linear model-based approach for estimating a one-dimensional active subspace; see [20, Algorithm 1.3].…”

Section: Inriamentioning

confidence: 99%

Forward and backward uncertainty quantification with active subspaces: Application to hypersonic flows around a cylinder

Cortesi

Constantine

Magin

et al. 2020

Journal of Computational Physics

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We perform a Bayesian calibration of the freestream velocity and density starting from measurements of the pressure and heat flux at the stagnation point of a hypersonic highenthalpy flow around a cylinder. The objective is to explore the possibility of using stagnation heat flux measurements, together with pressure measurements, to rebuild freestream conditions since such measurements are available for recent space missions but not exploited for freestream characterization. First, we formulate an algorithm of mesh adaptation, enabling accurate numerical solutions in an automatic way for a given set of inputs. Secondly, active subspaces are used to find a low-dimensional dependence structures in the input-to-output map of the forward numerical solver. Then, surrogate models on the active variables are used to accelerate the forward uncertainty propagation by Monte Carlo sampling and the Markov Chain Monte Carlo sampling of the posterior distribution for Bayesian inversion. A preliminary sensitivity analysis with sparse Polynomial Dimensional Decomposition is performed on the chemical model of the air mixture, to determine the most influential uncertain chemical parameters in the forward problem. Then, the forward and backward methodologies are applied to the simulation of a hypersonic flow around a cylinder, in conditions for which experimental data are available, revealing new insights towards the potential exploitation of heat flux data for freestream rebuilding.

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“…An increasingly popular global-sensitivity approach is the method of active subspaces (e.g., Constantine et al, 2014;Constantine and Diaz, 2017). While been designed for engineering applications (e.g., Constantine et al, 2015a, b;Hu et al, 2016;Glaws et al, 2017;Constantine and Doostan, 2017;Hu et al, 2017;Grey and Constantine, 2018;Li et al, 2019), it has recently been used with good performance in hydrology (e.g., Gilbert et al, 2016;Jefferson et al, 2015Jefferson et al, , 2017Teixeira Parente et al, 2019), including a recent study of ours (Erdal and Cirpka, 2019).…”

Section: Introductionmentioning

confidence: 99%

Technical Note: Improved sampling of behavioral subsurface flow model parameters using active subspaces

Erdal

Cirpka

2020

Hydrol. Earth Syst. Sci.

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Abstract. In global sensitivity analysis and ensemble-based model calibration, it is essential to create a large enough sample of model simulations with different parameters that all yield plausible model results. This can be difficult if a priori plausible parameter combinations frequently yield non-behavioral model results. In a previous study (Erdal and Cirpka, 2019), we developed and tested a parameter-sampling scheme based on active-subspace decomposition. While in principle this scheme worked well, it still implied testing a substantial fraction of parameter combinations that ultimately had to be discarded because of implausible model results. This technical note presents an improved sampling scheme and illustrates its simplicity and efficiency by a small test case. The new sampling scheme can be tuned to either outperform the original implementation by improving the sampling efficiency while maintaining the accuracy of the result or by improving the accuracy of the result while maintaining the sampling efficiency.

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Discovering a one-dimensional active subspace to quantify multidisciplinary uncertainty in satellite system design

Cited by 25 publications

References 10 publications

Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces

Global sensitivity analysis and adaptive stochastic sampling of a subsurface-flow model using active subspaces

Forward and backward uncertainty quantification with active subspaces: Application to hypersonic flows around a cylinder

Technical Note: Improved sampling of behavioral subsurface flow model parameters using active subspaces

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