scholarly journals Sensitivity analysis using anchored ANOVA expansion and high-order moments computation

2015 ◽  
Vol 102 (9) ◽  
pp. 1554-1584 ◽  
Author(s):  
Kunkun Tang ◽  
Pietro M. Congedo ◽  
Rémi Abgrall
Keyword(s):  
Sensitivity Analysis ◽  
High Order

scholarly journals Development of the high-order decoupled direct method in three dimensions for particulate matter: enabling advanced sensitivity analysis in air quality models

2012 ◽  
Vol 5 (2) ◽  
pp. 355-368 ◽  
Author(s):  
W. Zhang ◽  
S. L. Capps ◽  
Y. Hu ◽  
A. Nenes ◽  
S. L. Napelenok ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Particulate Matter ◽  
Air Quality ◽  
Direct Method ◽  
Statistical Significance ◽  
Second Order ◽  
High Order ◽  
Three Dimensions ◽  
So2 Emissions ◽  
Aerosol Module

Abstract. The high-order decoupled direct method in three dimensions for particulate matter (HDDM-3D/PM) has been implemented in the Community Multiscale Air Quality (CMAQ) model to enable advanced sensitivity analysis. The major effort of this work is to develop high-order DDM sensitivity analysis of ISORROPIA, the inorganic aerosol module of CMAQ. A case-specific approach has been applied, and the sensitivities of activity coefficients and water content are explicitly computed. Stand-alone tests are performed for ISORROPIA by comparing the sensitivities (first- and second-order) computed by HDDM and the brute force (BF) approximations. Similar comparison has also been carried out for CMAQ sensitivities simulated using a week-long winter episode for a continental US domain. Second-order sensitivities of aerosol species (e.g., sulfate, nitrate, and ammonium) with respect to domain-wide SO2, NOx, and NH3 emissions show agreement with BF results, yet exhibit less noise in locations where BF results are demonstrably inaccurate. Second-order sensitivity analysis elucidates poorly understood nonlinear responses of secondary inorganic aerosols to their precursors and competing species. Adding second-order sensitivity terms to the Taylor series projection of the nitrate concentrations with a 50% reduction in domain-wide NOx or SO2 emissions rates improves the prediction with statistical significance.

scholarly journals On the Need to Determine Accurately the Impact of Higher-Order Sensitivities on Model Sensitivity Analysis, Uncertainty Quantification and Best-Estimate Predictions

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6318
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Confidence Intervals ◽  
Large Scale ◽  
Neutron Transport ◽  
Higher Order ◽  
High Order ◽  
Tolerance Limits ◽  
Scale Models ◽  
Accurate Quantification

This work aims at underscoring the need for the accurate quantification of the sensitivities (i.e., functional derivatives) of the results (a.k.a. “responses”) produced by large-scale computational models with respect to the models’ parameters, which are seldom known perfectly in practice. The large impact that can arise from sensitivities of order higher than first has been highlighted by the results of a third-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark, which will be briefly reviewed in this work to underscore that neglecting the higher-order sensitivities causes substantial errors in predicting the expectation and variance of model responses. The importance of accurately computing the higher-order sensitivities is further highlighted in this work by presenting a text-book analytical example from the field of neutron transport, which impresses the need for the accurate quantification of higher-order response sensitivities by demonstrating that their neglect would lead to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis) of the model response’s distribution in the phase space of model parameters. The incorporation of response sensitivities in methodologies for uncertainty quantification, data adjustment and predictive modeling currently available for nuclear engineering systems is also reviewed. The fundamental conclusion highlighted by this work is that confidence intervals and tolerance limits on results predicted by models that only employ first-order sensitivities are likely to provide a false sense of confidence, unless such models also demonstrate quantitatively that the second- and higher-order sensitivities provide negligibly small contributions to the respective tolerance limits and confidence intervals. The high-order response sensitivities to parameters underlying large-scale models can be computed most accurately and most efficiently by employing the high-order comprehensive adjoint sensitivity analysis methodology, which overcomes the curse of dimensionality that hampers other methods when applied to large-scale models involving many parameters.

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