Benchmarking Active Subspace methods of generalised sensitivity analysis against variance-based Sobol' and Morris methods with established test functions

2022 ◽  
pp. 105310
Author(s):  
Xifu Sun ◽  
Barry Croke ◽  
Anthony Jakeman ◽  
Stephen Roberts
Keyword(s):  
Sensitivity Analysis ◽  
Test Functions ◽  
Subspace Methods ◽  
Active Subspace ◽  
Generalised Sensitivity Analysis

Modelling of Nitrification at the Mogden Treatment Works

1989 ◽  
Vol 21 (4-5) ◽  
pp. 305-314
Author(s):  
J. P. Lumbers ◽  
S. C. Cook ◽  
G. A. Thomas
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo Simulation ◽  
River Basin Management ◽  
Independent Data ◽  
Activated Sludge Process ◽  
Basin Management ◽  
Alternative Control ◽  
Control Actions ◽  
Parameter Values ◽  
Generalised Sensitivity Analysis

An application of a dynamic model of the activated sludge process is described within the context of real-time river basin management. The model has been calibrated and validated on independent data and then applied to investigate losses of nitrification at the Mogden Works. Monte Carlo simulation and generalised sensitivity analysis were found to be effective ways of identifying appropriate parameter values and their importance. The prediction of unmeasured states such as the autotroph population enabled the effects of alternative control actions to be better understood and the most suitable measures found.

scholarly journals Global Sensitivity Analysis and Adaptive Stochastic Sampling of a Subsurface-Flow Model Using Active Subspaces

2019 ◽  
Author(s):  
Daniel Erdal ◽  
Olaf A. Cirpka
Keyword(s):  
Sensitivity Analysis ◽  
Flow Model ◽  
Global Sensitivity Analysis ◽  
Subsurface Flow ◽  
Full Model ◽  
Stochastic Sampling ◽  
Global Sensitivity ◽  
Parameter Combination ◽  
Active Subspaces ◽  
Active Subspace

Abstract. Integrated hydrological modelling 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 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 parameter, 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 meaningful be done with second-order polynomials.

scholarly journals Sampling behavioral model parameters for ensemble-based sensitivity analysis using Gaussian process emulation and active subspaces

2020 ◽  
Vol 34 (11) ◽  
pp. 1813-1830
Author(s):  
Daniel Erdal ◽  
Sinan Xiao ◽  
Wolfgang Nowak ◽  
Olaf A. Cirpka
Keyword(s):  
Sensitivity Analysis ◽  
Gaussian Process ◽  
Parameter Space ◽  
Global Sensitivity Analysis ◽  
Model Parameters ◽  
Large Sample Size ◽  
Global Sensitivity ◽  
Environmental Models ◽  
Additional Costs ◽  
Active Subspace

Abstract Ensemble-based uncertainty quantification and global sensitivity analysis of environmental models requires generating large ensembles of parameter-sets. This can already be difficult when analyzing moderately complex models based on partial differential equations because many parameter combinations cause an implausible model behavior even though the individual parameters are within plausible ranges. In this work, we apply Gaussian Process Emulators (GPE) as surrogate models in a sampling scheme. In an active-training phase of the surrogate model, we target the behavioral boundary of the parameter space before sampling this behavioral part of the parameter space more evenly by passive sampling. Active learning increases the subsequent sampling efficiency, but its additional costs pay off only for a sufficiently large sample size. We exemplify our idea with a catchment-scale subsurface flow model with uncertain material properties, boundary conditions, and geometric descriptors of the geological structure. We then perform a global-sensitivity analysis of the resulting behavioral dataset using the active-subspace method, which requires approximating the local sensitivities of the target quantity with respect to all parameters at all sampled locations in parameter space. The Gaussian Process Emulator implicitly provides an analytical expression for this gradient, thus improving the accuracy of the active-subspace construction. When applying the GPE-based preselection, 70–90% of the samples were confirmed to be behavioral by running the full model, whereas only 0.5% of the samples were behavioral in standard Monte-Carlo sampling without preselection. The GPE method also provided local sensitivities at minimal additional costs.

A unified approach for global sensitivity analysis based on active subspace and Kriging

2022 ◽  
Vol 217 ◽  
pp. 108080
Author(s):  
Changcong Zhou ◽  
Zhuangke Shi ◽  
Sergei Kucherenko ◽  
Haodong Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Unified Approach ◽  
Global Sensitivity ◽  
Active Subspace

scholarly journals Active Subspace Methods in Theory and Practice: Applications to Kriging Surfaces

2014 ◽  
Vol 36 (4) ◽  
pp. A1500-A1524 ◽  
Author(s):  
Paul G. Constantine ◽  
Eric Dow ◽  
Qiqi Wang
Keyword(s):  
Theory And Practice ◽  
Subspace Methods ◽  
Active Subspace

Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis

2013 ◽  
Vol 52 ◽  
pp. 28-46 ◽  
Author(s):  
Hany S. Abdel-Khalik ◽  
Youngsuk Bang ◽  
Congjian Wang
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Subspace Methods
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